1
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Gasevic T, Bursch M, Ma Q, Grimme S, Werner HJ, Hansen A. The p-block challenge: assessing quantum chemistry methods for inorganic heterocycle dimerizations. Phys Chem Chem Phys 2024. [PMID: 38661329 DOI: 10.1039/d3cp06217a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/26/2024]
Abstract
The elements of the p-block of the periodic table are of high interest in various chemical and technical applications like frustrated Lewis-pairs (FLP) or opto-electronics. However, high-quality benchmark data to assess approximate density functional theory (DFT) for their theoretical description are sparse. In this work, we present a benchmark set of 604 dimerization energies of 302 "inorganic benzenes" composed of all non-carbon p-block elements of main groups III to VI up to polonium. This so-called IHD302 test set comprises two classes of structures formed by covalent bonding and by weaker donor-acceptor (WDA) interactions, respectively. Generating reliable reference data with ab initio methods is challenging due to large electron correlation contributions, core-valence correlation effects, and especially the slow basis set convergence. To compute reference values for these dimerization reactions, after thorough testing, we applied a computational protocol using state-of-the-art explicitly correlated local coupled cluster theory termed PNO-LCCSD(T)-F12/cc-VTZ-PP-F12(corr.). It includes a basis set correction at the PNO-LMP2-F12/aug-cc-pwCVTZ level. Based on these reference data, we assess 26 DFT methods in combination with three different dispersion corrections and the def2-QZVPP basis set, five composite DFT approaches, and five semi-empirical quantum mechanical methods. For the covalent dimerizations, the r2SCAN-D4 meta-GGA, the r2SCAN0-D4 and ωB97M-V hybrids, and the revDSD-PBEP86-D4 double-hybrid functional are found to be the best-performing methods among the evaluated functionals of the respective class. However, since def2 basis sets for the 4th period are not associated to relativistic pseudo-potentials, we obtained significant errors in the covalent dimerization energies (up to 6 kcal mol-1) for molecules containing p-block elements of the 4th period. Significant improvements were achieved for systems containing 4th row elements by using ECP10MDF pseudopotentials along with re-contracted aug-cc-pVQZ-PP-KS basis sets introduced in this work with the contraction coefficients taken from atomic DFT (PBE0) calculations. Overall, the IHD302 set represents a challenge to contemporary quantum chemical methods. This is due to a large number of spatially close p-element bonds which are underrepresented in other benchmark sets, and the partial covalent bonding character for the WDA interactions. The IHD302 set may be helpful to develop more robust and transferable approximate quantum chemical methods in the future.
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Affiliation(s)
- Thomas Gasevic
- Mulliken Center for Theoretical Chemistry, Rheinische Friedrich-Wilhelms-Universität Bonn, Beringstr. 4, 53115 Bonn, Germany.
| | - Markus Bursch
- Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, 45470 Mülheim an der Ruhr, Germany.
- FACCTs GmbH, 50677, Koeln, Germany
| | - Qianli Ma
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, D-70569 Stuttgart, Germany.
| | - Stefan Grimme
- Mulliken Center for Theoretical Chemistry, Rheinische Friedrich-Wilhelms-Universität Bonn, Beringstr. 4, 53115 Bonn, Germany.
| | - Hans-Joachim Werner
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, D-70569 Stuttgart, Germany.
| | - Andreas Hansen
- Mulliken Center for Theoretical Chemistry, Rheinische Friedrich-Wilhelms-Universität Bonn, Beringstr. 4, 53115 Bonn, Germany.
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2
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Zhang T, Banerjee S, Koulias LN, Valeev EF, DePrince AE, Li X. Dirac-Coulomb-Breit Molecular Mean-Field Exact-Two-Component Relativistic Equation-of-Motion Coupled-Cluster Theory. J Phys Chem A 2024. [PMID: 38651293 DOI: 10.1021/acs.jpca.3c08167] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/25/2024]
Abstract
We present a relativistic equation-of-motion coupled-cluster with single and double excitation formalism within the exact two-component framework (X2C-EOM-CCSD), where both scalar relativistic effects and spin-orbit coupling are variationally included at the reference level. Three different molecular mean-field treatments of relativistic corrections, including the one-electron, Dirac-Coulomb, and Dirac-Coulomb-Breit Hamiltonian, are considered in this work. Benchmark calculations include atomic excitations and fine-structure splittings arising from spin-orbit coupling. Comparison with experimental values and relativistic time-dependent density functional theory is also carried out. The computation of the oscillator strength using the relativistic X2C-EOM-CCSD approach allows for studies of spin-orbit-driven processes, such as the spontaneous phosphorescence lifetime.
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Affiliation(s)
- Tianyuan Zhang
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Samragni Banerjee
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Lauren N Koulias
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Edward F Valeev
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - A Eugene DePrince
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, United States
| | - Xiaosong Li
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
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3
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Shumilov KD, Jenkins AJ, La Pierre HS, Vlaisavljevich B, Li X. Overdestabilization vs Overstabilization in the Theoretical Analysis of f-Orbital Covalency. J Am Chem Soc 2024. [PMID: 38648269 DOI: 10.1021/jacs.4c01665] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/25/2024]
Abstract
The complex nature of the f-orbital electronic structures and their interaction with the chemical environment pose significant computational challenges. Advanced computational techniques that variationally include scalar relativities and spin-orbit coupling directly at the molecular orbital level have been developed to address this complexity. Among these, variational relativistic multiconfigurational multireference methods stand out for their high accuracy and systematic improvement in studies of f-block complexes. Additionally, these advanced methods offer the potential for calibrating low-scaling electronic structure methods such as density functional theory. However, studies on the Cl K-edge X-ray absorption spectra of the [Ce(III)Cl6]3- and [Ce(IV)Cl6]2- complexes show that time-dependent density functional theory with approximate exchange-correlation kernels can lead to inaccuracies, resulting in an overstabilization of 4f orbitals and incorrect assessments of covalency. In contrast, approaches utilizing small active space wave function methods may understate the stability of these orbitals. The results herein demonstrate the need for large active space, multireference, and variational relativistic methods in studying f-block complexes.
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Affiliation(s)
- Kirill D Shumilov
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Andrew J Jenkins
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Henry S La Pierre
- School of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, Georgia 30332, United States
- Nuclear and Radiological Engineering and Medical Physics Program, School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, United States
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99352, United States
| | - Bess Vlaisavljevich
- Department of Chemistry, University of South Dakota, Vermillion, South Dakota 57069, United States
| | - Xiaosong Li
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
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4
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Fitzpatrick A, Nykänen A, Talarico NW, Lunghi A, Maniscalco S, García-Pérez G, Knecht S. Self-Consistent Field Approach for the Variational Quantum Eigensolver: Orbital Optimization Goes Adaptive. J Phys Chem A 2024; 128:2843-2856. [PMID: 38547028 DOI: 10.1021/acs.jpca.3c05882] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/12/2024]
Abstract
We present a self-consistent field (SCF) approach within the adaptive derivative-assembled problem-tailored ansatz variational quantum eigensolver (ADAPT-VQE) framework for efficient quantum simulations of chemical systems on near-term quantum computers. To this end, our ADAPT-VQE-SCF approach combines the idea of generating an ansatz with a small number of parameters, resulting in shallow-depth quantum circuits with a direct minimization of an energy expression that is correct to second order with respect to changes in the molecular orbital basis. Our numerical analysis, including calculations for the transition-metal complex ferrocene [Fe (C5H5)2], indicates that convergence in the self-consistent orbital optimization loop can be reached without a considerable increase in the number of two-qubit gates in the quantum circuit by comparison to a VQE optimization in the initial molecular orbital basis. Moreover, the orbital optimization can be carried out simultaneously within each iteration of the ADAPT-VQE cycle. ADAPT-VQE-SCF thus allows us to implement a routine analogous to the complete active space SCF, a cornerstone of state-of-the-art computational chemistry, in a hardware-efficient manner on near-term quantum computers. Hence, ADAPT-VQE-SCF paves the way toward a paradigm shift for quantitative quantum-chemistry simulations on quantum computers by requiring fewer qubits and opening up for the use of large and flexible atomic orbital basis sets in contrast to earlier methods that are predominantly based on the idea of full active spaces with minimal basis sets.
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Affiliation(s)
- Aaron Fitzpatrick
- Algorithmiq Ltd, Kanavakatu 3C, Helsinki FI-00160, Finland
- Trinity Quantum Alliance, Unit 16, Trinity Technology and Enterprise Centre, Pearse Street, Dublin 2 D02 YN67, Ireland
| | - Anton Nykänen
- Algorithmiq Ltd, Kanavakatu 3C, Helsinki FI-00160, Finland
| | | | - Alessandro Lunghi
- School of Physics, AMBER and CRANN Institute, Trinity College, Dublin 2, Ireland
| | | | | | - Stefan Knecht
- Algorithmiq Ltd, Kanavakatu 3C, Helsinki FI-00160, Finland
- ETH Zürich, Department of Chemistry and Applied Life Sciences Vladimir-Prelog-Weg 1-5/10, Zürich 8093, Switzerland
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5
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Inoue N, Watanabe Y, Nakano H. Generalized Foldy-Wouthuysen transformation for relativistic two-component methods: Systematic analysis of two-component Hamiltonians. J Comput Chem 2024; 45:523-535. [PMID: 37997192 DOI: 10.1002/jcc.27251] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/31/2023] [Revised: 10/24/2023] [Accepted: 10/26/2023] [Indexed: 11/25/2023]
Abstract
The generalized Foldy-Wouthuysen (GFW) transformation was proposed as a generic form that unifies four types of transformations in relativistic two-component methods: unnormalized GFW(UN), and normalized form 1, form 2, and form 3 (GFW(N1), GFW(N2), and GFW(N3)). The GFW transformation covers a wide range of transformations beyond the simple unitary transformation of the Dirac Hamiltonian, allowing for the systematic classification of all existing two-component methods. New two-component methods were also systematically derived based on the GFW transformation. These various two-component methods were applied to hydrogen-like and helium-like ions. Numerical errors in energy were evaluated and classified into four types: the one-electron Hamiltonian approximation, the two-electron operator approximation, the newly defined "picture difference error (PDE)," and the error in determining the transformation, and errors in multi-electron systems were discussed based on this classification.
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Affiliation(s)
- Nobuki Inoue
- Department of Chemistry, Graduate School of Science, Kyushu University, Fukuoka, Japan
| | - Yoshihiro Watanabe
- Department of Chemistry, Graduate School of Science, Kyushu University, Fukuoka, Japan
| | - Haruyuki Nakano
- Department of Chemistry, Graduate School of Science, Kyushu University, Fukuoka, Japan
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6
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Ehrman J, Shumilov K, Jenkins AJ, Kasper JM, Vitova T, Batista ER, Yang P, Li X. Unveiling Hidden Shake-Up Features in the Uranyl M 4-Edge Spectrum. JACS Au 2024; 4:1134-1141. [PMID: 38559711 PMCID: PMC10976573 DOI: 10.1021/jacsau.3c00838] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/28/2023] [Revised: 02/14/2024] [Accepted: 02/15/2024] [Indexed: 04/04/2024]
Abstract
The M4,5-edge high energy resolution X-ray absorption near-edge structure (HR-XANES) spectra of actinyls offer valuable insights into the electronic structure and bonding properties of heavy-element complexes. To conduct a comprehensive spectral analysis, it is essential to employ computational methods that accurately account for relativistic effects and electron correlation. In this work, we utilize variational relativistic multireference configurational interaction methods to compute and analyze the X-ray M4-edge absorption spectrum of uranyl. By employing these advanced computational techniques, we achieve excellent agreement between the calculated spectral features and experimental observations. Moreover, the calculations unveil significant shake-up features, which arise from the intricate interplay between strongly correlated 3d core-electron and ligand excitations. This research provides important theoretical insights into the spectral characteristics of heavy-element complexes. Furthermore, it establishes the foundation for utilizing M4,5-edge spectroscopy as a means to investigate the chemical activities of such complexes. By leveraging this technique, we can gain a deeper understanding of the bonding behavior and reactivity of heavy-element compounds.
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Affiliation(s)
- Jordan
N. Ehrman
- Department
of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Kirill Shumilov
- Department
of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Andrew J. Jenkins
- Department
of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Joseph M. Kasper
- Theoretical
Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Tonya Vitova
- Institute
for Nuclear Waste Disposal (INE), Karlsruhe
Institute of Technology, P.O. Box 3640, Karlsruhe D-76021, Germany
| | - Enrique R. Batista
- Theoretical
Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Ping Yang
- Theoretical
Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Xiaosong Li
- Department
of Chemistry, University of Washington, Seattle, Washington 98195, United States
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7
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Gasevic T, Kleine Büning JB, Grimme S, Bursch M. Benchmark Study on the Calculation of 207Pb NMR Chemical Shifts. Inorg Chem 2024; 63:5052-5064. [PMID: 38446045 PMCID: PMC10951955 DOI: 10.1021/acs.inorgchem.3c04539] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/21/2023] [Revised: 02/08/2024] [Accepted: 02/14/2024] [Indexed: 03/07/2024]
Abstract
A benchmark set for the computation of 207Pb nuclear magnetic resonance (NMR) chemical shifts is presented. The PbS50 set includes conformer ensembles of 50 lead-containing molecular compounds and their experimentally measured 207Pb NMR chemical shifts. Various bonding motifs at the Pb center with up to seven bonding partners are included. Six different solvents were used in the measurements. The respective shifts lie in the range between +10745 and -5030 ppm. Several calculation settings are assessed by evaluating computed 207Pb NMR shifts for the use with different density functional approximations (DFAs), relativistic approaches, treatment of the conformational space, and levels for geometry optimization. Relativistic effects were included explicitly with the zeroth order regular approximation (ZORA), for which only the spin-orbit variant was able to yield reliable results. In total, seven GGAs and three hybrid DFAs were tested. Hybrid DFAs significantly outperform GGAs. The most accurate DFAs are mPW1PW with a mean absolute deviation (MAD) of 429 ppm and PBE0 with an MAD of 446 ppm. Conformational influences are small as most compounds are rigid, but more flexible structures still benefit from Boltzmann averaging. Including explicit relativistic treatments such as SO-ZORA in the geometry optimization does not show any significant improvement over the use of effective core potentials (ECPs).
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Affiliation(s)
- Thomas Gasevic
- Mulliken
Center for Theoretical Chemistry, Clausius Institute for Physical
and Theoretical Chemistry, University of
Bonn, Beringstr. 4, 53115 Bonn, Germany
| | - Julius B. Kleine Büning
- Mulliken
Center for Theoretical Chemistry, Clausius Institute for Physical
and Theoretical Chemistry, University of
Bonn, Beringstr. 4, 53115 Bonn, Germany
| | - Stefan Grimme
- Mulliken
Center for Theoretical Chemistry, Clausius Institute for Physical
and Theoretical Chemistry, University of
Bonn, Beringstr. 4, 53115 Bonn, Germany
| | - Markus Bursch
- Max-Planck-Institut
für Kohlenforschung, Kaiser-Wilhelm-Platz 1, 45470 Mülheim an der Ruhr, Germany
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8
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Liao C, Hoyer CE, Banerjee Ghosh R, Jenkins AJ, Knecht S, Frisch MJ, Li X. Comparison of Variational and Perturbative Spin-Orbit Coupling within Two-Component CASSCF. J Phys Chem A 2024. [PMID: 38489510 DOI: 10.1021/acs.jpca.3c08031] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/17/2024]
Abstract
The modeling of spin-orbit coupling (SOC) remains a challenge in computational chemistry due to the high computational cost. With the rising popularity of spin-driven processes and f-block metals in chemistry and materials science, it is incumbent on the community to develop accurate multiconfigurational SOC methods that scale to large systems and understand the limits of different treatments of SOC. Herein, we introduce an implementation of perturbative SOC in scalar-relativistic two-component CASSCF (srX2C-CASSCF-SO). Perspectives on the limitations and accuracy of srX2C-CASSCF-SO are presented via benchmark calculations.
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Affiliation(s)
- Can Liao
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Chad E Hoyer
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Rahoul Banerjee Ghosh
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Andrew J Jenkins
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Stefan Knecht
- Algorithmiq Ltd, Kanavakatu 3C, FI-00160 Helsinki, Finland
- ETH Zürich, Department of Chemistry and Applied Life Sciences, Vladimir-Prelog-Weg 1-5/10, CH-8093 Zürich, Switzerland
| | - Michael J Frisch
- Gaussian Inc., 340 Quinnipiac Street, Bldg 40, Wallingford, Connecticut 06492, United States
| | - Xiaosong Li
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
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9
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Liu W. Unified construction of relativistic Hamiltonians. J Chem Phys 2024; 160:084111. [PMID: 38415836 DOI: 10.1063/5.0188794] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/23/2023] [Accepted: 02/09/2024] [Indexed: 02/29/2024] Open
Abstract
It is shown that the four-component (4C), quasi-four-component (Q4C), and exact two-component (X2C) relativistic Hartree-Fock equations can be implemented in a unified manner by making use of the atomic nature of the small components of molecular 4-spinors. A model density matrix approximation can first be invoked for the small-component charge/current density functions, which gives rise to a static, pre-molecular mean field to be combined with the one-electron term. As a result, only the nonrelativistic-like two-electron term of the 4C/Q4C/X2C Fock matrix needs to be updated during the iterations. A "one-center small-component" approximation can then be invoked in the evaluation of relativistic integrals, that is, all atom-centered small-component basis functions are regarded as extremely localized near the position of the atom to which they belong such that they have vanishing overlaps with all small- or large-component functions centered at other nuclei. Under these approximations, the 4C, Q4C, and X2C mean-field and many-electron Hamiltonians share precisely the same structure and accuracy. Beyond these is the effective quantum electrodynamics Hamiltonian that can be constructed in the same way. Such approximations lead to errors that are orders of magnitude smaller than other sources of errors (e.g., truncation errors in the one- and many-particle bases as well as uncertainties of experimental measurements) and are, hence, safe to use for whatever purposes. The quaternion forms of the 4C, Q4C, and X2C equations are also presented in the most general way, based on which the corresponding Kramers-restricted open-shell variants are formulated for "high-spin" open-shell systems.
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Affiliation(s)
- Wenjian Liu
- Qingdao Institute for Theoretical and Computational Sciences, School of Chemistry and Chemical Engineering, Shandong University, Qingdao, Shandong 266237, People's Republic of China
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10
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Kleine Büning JB, Grimme S, Bursch M. Machine learning-based correction for spin-orbit coupling effects in NMR chemical shift calculations. Phys Chem Chem Phys 2024; 26:4870-4884. [PMID: 38230684 DOI: 10.1039/d3cp05556f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2024]
Abstract
As one of the most powerful analytical methods for molecular and solid-state structure elucidation, NMR spectroscopy is an integral part of chemical laboratories associated with a great research interest in its computational simulation. Particularly when heavy atoms are present, a relativistic treatment is essential in the calculations as these influence also the nearby light atoms. In this work, we present a Δ-machine learning method that approximates the contribution to 13C and 1H NMR chemical shifts that stems from spin-orbit (SO) coupling effects. It is built on computed reference data at the spin-orbit zeroth-order regular approximation (ZORA) DFT level for a set of 6388 structures with 38 740 13C and 64 436 1H NMR chemical shifts. The scope of the methods covers the 17 most important heavy p-block elements that exhibit heavy atom on the light atom (HALA) effects to covalently bound carbon or hydrogen atoms. Evaluated on the test data set, the approach is able to recover roughly 85% of the SO contribution for 13C and 70% for 1H from a scalar-relativistic PBE0/ZORA-def2-TZVP calculation at virtually no extra computational costs. Moreover, the method is transferable to other baseline DFT methods even without retraining the model and performs well for realistic organotin and -lead compounds. Finally, we show that using a combination of the new approach with our previous Δ-ML method for correlation contributions to NMR chemical shifts, the mean absolute NMR shift deviations from non-relativistic DFT calculations to experimental values can be halved.
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Affiliation(s)
- Julius B Kleine Büning
- Mulliken Center for Theoretical Chemistry, Clausius Institute for Physical and Theoretical Chemistry, University of Bonn, Beringstr. 4, 53115 Bonn, Germany.
| | - Stefan Grimme
- Mulliken Center for Theoretical Chemistry, Clausius Institute for Physical and Theoretical Chemistry, University of Bonn, Beringstr. 4, 53115 Bonn, Germany.
| | - Markus Bursch
- Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, 45470 Mülheim an der Ruhr, Germany.
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11
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Franzke YJ, Bruder F, Gillhuber S, Holzer C, Weigend F. Paramagnetic Nuclear Magnetic Resonance Shifts for Triplet Systems and Beyond with Modern Relativistic Density Functional Methods. J Phys Chem A 2024; 128:670-686. [PMID: 38195394 DOI: 10.1021/acs.jpca.3c07093] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2024]
Abstract
An efficient framework for the calculation of paramagnetic NMR (pNMR) shifts within exact two-component (X2C) theory and (current-dependent) density functional theory (DFT) up to the class of local hybrid functionals (LHFs) is presented. Generally, pNMR shifts for systems with more than one unpaired electron depend on the orbital shielding contribution and a temperature-dependent term. The latter includes zero-field splitting (ZFS), hyperfine coupling (HFC), and the g-tensor. For consistency, we calculate these three tensors at the same level of theory, i.e., using scalar-relativistic X2C augmented with spin-orbit perturbation theory. Results for pNMR chemical shifts of transition-metal complexes reveal that this X2C-DFT framework can yield good results for both the shifts and the individual tensor contributions of metallocenes and related systems, especially if the HFC constant is large. For small HFC constants, the relative error is often large, and sometimes the sign may be off. 4d and 5d complexes with more complicated structures demonstrate the limitations of a fully DFT-based approach. Additionally, a Co-based complex with a very large ZFS and pronounced multireference character is not well described. Here, a hybrid DFT-multireference framework is necessary for accurate results. Our results show that X2C is sufficient to describe relativistic effects and computationally cheaper than a fully relativistic approach. Thus, it allows use of large basis sets for converged HFCs. Overall, current-dependent meta-generalized gradient approximations and LHFs show some potential; however, the currently available functionals leave a lot to be desired, and the predictive power is limited.
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Affiliation(s)
- Yannick J Franzke
- Fachbereich Chemie, Philipps-Universität Marburg, Hans-Meerwein-Straße 4, 35032 Marburg, Germany
| | - Florian Bruder
- Fachbereich Chemie, Philipps-Universität Marburg, Hans-Meerwein-Straße 4, 35032 Marburg, Germany
| | - Sebastian Gillhuber
- Institute of Inorganic Chemistry, Karlsruhe Institute of Technology (KIT), Engesserstraße 15, 76131 Karlsruhe, Germany
| | - Christof Holzer
- Institute of Theoretical Solid State Physics, Karlsruhe Institute of Technology (KIT), Wolfgang-Gaede-Straße 1, 76131 Karlsruhe, Germany
| | - Florian Weigend
- Fachbereich Chemie, Philipps-Universität Marburg, Hans-Meerwein-Straße 4, 35032 Marburg, Germany
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12
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Brakestad A, Jensen SR, Tantardini C, Pitteloud Q, Wind P, Užulis J, Gulans A, Hopmann KH, Frediani L. Scalar Relativistic Effects with Multiwavelets: Implementation and Benchmark. J Chem Theory Comput 2024; 20:728-737. [PMID: 38181377 PMCID: PMC10809714 DOI: 10.1021/acs.jctc.3c01095] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/03/2023] [Revised: 12/18/2023] [Accepted: 12/19/2023] [Indexed: 01/07/2024]
Abstract
The importance of relativistic effects in quantum chemistry is widely recognized, not only for heavier elements but throughout the periodic table. At the same time, relativistic effects are strongest in the nuclear region, where the description of electrons through a linear combination of atomic orbitals becomes more challenging. Furthermore, the choice of basis sets for heavier elements is limited compared with lighter elements where precise basis sets are available. Thanks to the framework of multiresolution analysis, multiwavelets provide an appealing alternative to overcoming this challenge: they lead to robust error control and adaptive algorithms that automatically refine the basis set description until the desired precision is reached. This allows one to achieve a proper description of the nuclear region. In this work, we extended the multiwavelet-based code MRChem to the scalar zero-order regular approximation framework. We validated our implementation by comparing the total energies for a small set of elements and molecules. To confirm the validity of our implementation, we compared both against a radial numerical code for atoms and the plane-wave-based code EXCITING.
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Affiliation(s)
- Anders Brakestad
- Hylleraas
Centre for Quantum Molecular Sciences, UiT
The Arctic University of Norway, Tromsø 9037, Norway
- Department
of Chemistry, UiT The Arctic University
of Norway, Tromsø 9037, Norway
| | - Stig Rune Jensen
- Hylleraas
Centre for Quantum Molecular Sciences, UiT
The Arctic University of Norway, Tromsø 9037, Norway
- Department
of Chemistry, UiT The Arctic University
of Norway, Tromsø 9037, Norway
| | - Christian Tantardini
- Hylleraas
Centre for Quantum Molecular Sciences, UiT
The Arctic University of Norway, Tromsø 9037, Norway
- Department
of Chemistry, UiT The Arctic University
of Norway, Tromsø 9037, Norway
- Department
of Materials Science and NanoEngineering, Rice University, Houston, Texas 77005, United States
| | - Quentin Pitteloud
- Hylleraas
Centre for Quantum Molecular Sciences, UiT
The Arctic University of Norway, Tromsø 9037, Norway
- Department
of Chemistry, UiT The Arctic University
of Norway, Tromsø 9037, Norway
| | - Peter Wind
- Hylleraas
Centre for Quantum Molecular Sciences, UiT
The Arctic University of Norway, Tromsø 9037, Norway
- Department
of Chemistry, UiT The Arctic University
of Norway, Tromsø 9037, Norway
| | - Jānis Užulis
- Department
of Physics, University of Latvia, Jelgavas iela 3, Riga, Latvia 1004, Latvia
| | - Andris Gulans
- Department
of Physics, University of Latvia, Jelgavas iela 3, Riga, Latvia 1004, Latvia
| | | | - Luca Frediani
- Hylleraas
Centre for Quantum Molecular Sciences, UiT
The Arctic University of Norway, Tromsø 9037, Norway
- Department
of Chemistry, UiT The Arctic University
of Norway, Tromsø 9037, Norway
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13
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Yuan X, Halbert L, Pototschnig JV, Papadopoulos A, Coriani S, Visscher L, Pereira Gomes AS. Formulation and Implementation of Frequency-Dependent Linear Response Properties with Relativistic Coupled Cluster Theory for GPU-Accelerated Computer Architectures. J Chem Theory Comput 2024; 20:677-694. [PMID: 38193434 DOI: 10.1021/acs.jctc.3c00812] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2024]
Abstract
We present the development and implementation of relativistic coupled cluster linear response theory (CC-LR), which allows the determination of molecular properties arising from time-dependent or time-independent electric, magnetic, or mixed electric-magnetic perturbations (within a common gauge origin for the magnetic properties) as well as taking into account the finite lifetime of excited states in the framework of damped response theory. We showcase our implementation, which is capable to offload the computationally intensive tensor contractions characteristic of coupled cluster theory onto graphical processing units, in the calculation of (a) frequency-(in)dependent dipole-dipole polarizabilities of IIB atoms and selected diatomic molecules, with a particular emphasis on the calculation of valence absorption cross sections for the I2 molecule; (b) indirect spin-spin coupling constants for benchmark systems such as the hydrogen halides (HX, X = F-I) as well the H2Se-H2O dimer as a prototypical system containing hydrogen bonds; and (c) optical rotations at the sodium D line for hydrogen peroxide analogues (H2Y2, Y = O, S, Se, Te). Thanks to this implementation, we are able to show the similarities in performance, but often the significant discrepancies, between CC-LR and approximate methods such as density functional theory. Comparing standard CC response theory with the flavor based upon the equation of motion formalism, we find that for valence properties such as polarizabilities, the two frameworks yield very similar results across the periodic table as found elsewhere in the literature; for properties that probe the core region, such as spin-spin couplings, on the other hand, we show a progressive differentiation between the two as relativistic effects become more important. Our results also suggest that as one goes down the periodic table, it may become increasingly difficult to measure pure optical rotation at the sodium D line due to the appearance of absorbing states.
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Affiliation(s)
- Xiang Yuan
- Univ. Lille, CNRS, UMR 8523─PhLAM─Physique des Lasers Atomes et Molécules, F-59000 Lille, France
- Department of Chemistry and Pharmaceutical Sciences, Faculty of Science, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, The Netherlands
| | - Loïc Halbert
- Univ. Lille, CNRS, UMR 8523─PhLAM─Physique des Lasers Atomes et Molécules, F-59000 Lille, France
| | - Johann Valentin Pototschnig
- Department of Chemistry and Pharmaceutical Sciences, Faculty of Science, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, The Netherlands
| | - Anastasios Papadopoulos
- Department of Chemistry and Pharmaceutical Sciences, Faculty of Science, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, The Netherlands
| | - Sonia Coriani
- DTU Chemistry─Department of Chemistry, Technical University of Denmark, DK-2800 Kongens Lyngby, Denmark
| | - Lucas Visscher
- Department of Chemistry and Pharmaceutical Sciences, Faculty of Science, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, The Netherlands
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14
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Zhang C, Lipparini F, Stopkowicz S, Gauss J, Cheng L. Cholesky Decomposition-Based Implementation of Relativistic Two-Component Coupled-Cluster Methods for Medium-Sized Molecules. J Chem Theory Comput 2024; 20:787-798. [PMID: 38198515 DOI: 10.1021/acs.jctc.3c01236] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2024]
Abstract
A Cholesky decomposition (CD)-based implementation of relativistic two-component coupled-cluster (CC) and equation-of-motion CC (EOM-CC) methods using an exact two-component Hamiltonian augmented with atomic-mean-field spin-orbit integrals (the X2CAMF scheme) is reported. The present CD-based implementation of X2CAMF-CC and EOM-CC methods employs atomic-orbital-based algorithms to avoid the construction of two-electron integrals and intermediates involving three and four virtual indices. Our CD-based implementation extends the applicability of X2CAMF-CC and EOM-CC methods to medium-sized molecules with the possibility to correlate around 1000 spinors. Benchmark calculations for uranium-containing small molecules were performed to assess the dependence of the CC results on the Cholesky threshold. A Cholesky threshold of 10-4 is shown to be sufficient to maintain chemical accuracy. Example calculations to illustrate the capability of the CD-based relativistic CC methods are reported for the bond-dissociation energy of the uranium hexafluoride molecule, UF6, with up to quadruple-ζ basis sets, and the lowest excitation energy in the solvated uranyl ion [UO22+(H2O)12].
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Affiliation(s)
- Chaoqun Zhang
- Department of Chemistry, the Johns Hopkins University, Baltimore, Maryland 21218, United States
| | - Filippo Lipparini
- Dipartimento di Chimica e Chimica Industriale, Università di Pisa, Via G. Moruzzi 13, Pisa I-56124, Italy
| | - Stella Stopkowicz
- Fachrichtung Chemie, Universität des Saarlandes, Saarbrücken D-66123, Germany
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033, Blindern, Oslo N-0315, Norway
| | - Jürgen Gauss
- Department Chemie, Johannes Gutenberg-Universität Mainz, Duesbergweg 10-14, Mainz D-55128, Germany
| | - Lan Cheng
- Department of Chemistry, the Johns Hopkins University, Baltimore, Maryland 21218, United States
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15
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Takashima C, Nakai H. Range Separation Method for Density Functional Theory Based on Two-Electron Infinite-Order Two-Component Hamiltonian. J Chem Theory Comput 2024; 20:738-751. [PMID: 38193820 DOI: 10.1021/acs.jctc.3c01102] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2024]
Abstract
The range separation method for density functional theory (DFT) was extended to a two-component relativistic theory based on the unitary transformation of one- and two-electron operators and a density operator. In the framework of the spin-free infinite-order two-component Hamiltonian, we implemented several types of two-electron integrals of range-separated two-electron interactions arising from the unitary transformation. Numerical assessments were performed using long-range-corrected (LC)-DFT, which utilizes the range separation of an exchange functional. The present method successfully reproduced the reference values obtained by the four-component LC-DFT calculations when the whole unitary transformations of one-electron, full-range, and range-separated two-electron operators and a density operator were considered. An efficient scheme for the unitary transformation, which is termed the local unitary transformation (LUT), was also applied to the range-separated two-electron term and other operators. The LUT method reduced the computational costs of the LC-DFT calculations significantly without any loss of accuracy.
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Affiliation(s)
- Chinami Takashima
- Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
| | - Hiromi Nakai
- Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
- Waseda Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
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16
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Zhang C, Zheng X, Liu J, Asthana A, Cheng L. Analytic gradients for relativistic exact-two-component equation-of-motion coupled-cluster singles and doubles method. J Chem Phys 2023; 159:244113. [PMID: 38153147 DOI: 10.1063/5.0175041] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/04/2023] [Accepted: 11/20/2023] [Indexed: 12/29/2023] Open
Abstract
A first implementation of analytic gradients for spinor-based relativistic equation-of-motion coupled-cluster singles and doubles method using an exact two-component Hamiltonian augmented with atomic mean-field spin-orbit integrals is reported. To demonstrate its applicability, we present calculations of equilibrium structures and harmonic vibrational frequencies for the electronic ground and excited states of the radium mono-amide molecule (RaNH2) and the radium mono-methoxide molecule (RaOCH3). Spin-orbit coupling is shown to quench Jahn-Teller effects in the first excited state of RaOCH3, resulting in a C3v equilibrium structure. The calculations also show that the radium atoms in these molecules serve as efficient optical cycling centers.
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Affiliation(s)
- Chaoqun Zhang
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Xuechen Zheng
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Junzi Liu
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Ayush Asthana
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Lan Cheng
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, USA
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17
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Yuan X, Halbert L, Visscher L, Pereira Gomes AS. Frequency-Dependent Quadratic Response Properties and Two-Photon Absorption from Relativistic Equation-of-Motion Coupled Cluster Theory. J Chem Theory Comput 2023; 19:9248-9259. [PMID: 38079602 DOI: 10.1021/acs.jctc.3c01011] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2023]
Abstract
We present the implementation of quadratic response theory based upon the relativistic equation-of-motion coupled cluster method. We showcase our implementation, whose generality allows us to consider both time-dependent and time-independent electric and magnetic perturbations, by considering the static and frequency-dependent hyperpolarizability of hydrogen halides (HX, X = F-At), providing comprehensive insights into their electronic response characteristics. Additionally, we evaluated the Verdet constant for noble gases Xe and Rn and discussed the relative importance of relativistic and electron correlation effects for these magneto-optical properties. Finally, we calculate the two-photon absorption cross sections of transition [ns1S0 → (n + 1)s1S0] of Ga+ and In+, which are suggested as candidates for new ion clocks. As our implementation allows for the use of nonrelativistic Hamiltonians as well, we have compared our EOM-QRCC results to the QR-CC implementation in the DALTON code and show that the differences between CC and EOMCC response are in general smaller than 5% for the properties considered. Collectively, the results underscore the versatility of our implementation and its potential as a benchmark tool for other approximated models, such as density functional theory for higher-order properties.
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Affiliation(s)
- Xiang Yuan
- Physique des Lasers Atomes et Molecules, Universite de Lille, F-59000 Lille, France
- Department of Chemistry and Pharmaceutical Sciences, Faculty of Science, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, The Netherlands
| | - Loïc Halbert
- Physique des Lasers Atomes et Molecules, Universite de Lille, F-59000 Lille, France
| | - Lucas Visscher
- Department of Chemistry and Pharmaceutical Sciences, Faculty of Science, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, The Netherlands
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18
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Zhang C, Yu P, Conn CJ, Hutzler NR, Cheng L. Relativistic coupled-cluster calculations of RaOH pertinent to spectroscopic detection and laser cooling. Phys Chem Chem Phys 2023; 25:32613-32621. [PMID: 38009218 DOI: 10.1039/d3cp04040b] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2023]
Abstract
A relativistic coupled-cluster study of the low-lying electronic states in the radium monohydroxide molecule (RaOH), a radioactive polyatomic molecule of interest to laser cooling and to the search of new physics beyond the Standard Model, is reported. The level positions of the A2Π1/2 and C2Σ states have been computed with an accuracy of around 200 cm-1 to facilitate spectroscopic observation of RaOH using laser induced fluorescence spectroscopy, thereby exploiting the systematic convergence of electron-correlation and basis-set effects in relativistic coupled-cluster calculations. The energy level for the B2Δ3/2 state has also been calculated accurately to conclude that the B2Δ3/2 state lies above the A2Π1/2 state. This confirms X2Σ ↔ A2Π1/2 as a promising optical cycling transition for laser cooling RaOH.
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Affiliation(s)
- Chaoqun Zhang
- Department of Chemistry, The Johns Hopkins University, Baltimore, MD 21218, USA.
| | - Phelan Yu
- Division of Physics, Mathematics, and Astronomy, California Institute of Technology, Pasadena, CA 91125, USA.
| | - Chandler J Conn
- Division of Physics, Mathematics, and Astronomy, California Institute of Technology, Pasadena, CA 91125, USA.
| | - Nicholas R Hutzler
- Division of Physics, Mathematics, and Astronomy, California Institute of Technology, Pasadena, CA 91125, USA.
| | - Lan Cheng
- Department of Chemistry, The Johns Hopkins University, Baltimore, MD 21218, USA.
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19
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Rueda Espinosa KJ, Kananenka AA, Rusakov AA. Novel Computational Chemistry Infrastructure for Simulating Astatide in Water: From Basis Sets to Force Fields Using Particle Swarm Optimization. J Chem Theory Comput 2023; 19:7998-8012. [PMID: 38014419 DOI: 10.1021/acs.jctc.3c00826] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2023]
Abstract
Using the example of astatine, the heaviest naturally occurring halogen whose isotope At-211 has promising medical applications, we propose a new infrastructure for large-scale computational models of heavy elements with strong relativistic effects. In particular, we focus on developing an accurate force field for At- in water based on reliable relativistic density functional theory (DFT) calculations. To ensure the reliability of such calculations, we design novel basis sets for relativistic DFT, via the particle swarm optimization algorithm to optimize the coefficients of the new basis sets and the polarization-consistent basis set idea's extension to heavy elements to eliminate the basis set error from DFT calculations. The resulting basis sets enable the well-grounded evaluation of relativistic DFT against "gold-standard" CCSD(T) results. Accounting for strong relativistic effects, including spin-orbit interaction, via our redesigned infrastructure, we elucidate a noticeable dissimilarity between At- and I- in halide-water force field parameters, radial distribution functions, diffusion coefficients, and hydration energies. This work establishes the framework for the systematic development of polarization-consistent basis sets for relativistic DFT and accurate force fields for molecular dynamics simulations to be used in large-scale models of complex molecular systems with elements from the bottom of the periodic table, including actinides and even superheavy elements.
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Affiliation(s)
- Kennet J Rueda Espinosa
- Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716, United States
| | - Alexei A Kananenka
- Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716, United States
| | - Alexander A Rusakov
- Department of Chemistry, Oakland University, Rochester, Michigan 48309, United States
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20
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Bruder F, Franzke YJ, Holzer C, Weigend F. Zero-field splitting parameters within exact two-component theory and modern density functional theory using seminumerical integration. J Chem Phys 2023; 159:194117. [PMID: 37987521 DOI: 10.1063/5.0175758] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/08/2023] [Accepted: 10/26/2023] [Indexed: 11/22/2023] Open
Abstract
An efficient implementation of zero-field splitting parameters based on the work of Schmitt et al. [J. Chem. Phys. 134, 194113 (2011)] is presented. Seminumerical integration techniques are used for the two-electron spin-dipole contribution and the response equations of the spin-orbit perturbation. The original formulation is further generalized. First, it is extended to meta-generalized gradient approximations and local hybrid functionals. For these functional classes, the response of the paramagnetic current density is considered in the coupled-perturbed Kohn-Sham equations for the spin-orbit perturbation term. Second, the spin-orbit perturbation is formulated within relativistic exact two-component theory and the screened nuclear spin-orbit (SNSO) approximation. The accuracy of the implementation is demonstrated for transition-metal and diatomic main-group compounds. The efficiency is assessed for Mn and Mo complexes. Here, it is found that coarse integration grids for the seminumerical schemes lead to drastic speedups while introducing clearly negligible errors. In addition, the SNSO approximation substantially reduces the computational demands and leads to very similar results as the spin-orbit mean field Ansatz.
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Affiliation(s)
- Florian Bruder
- Fachbereich Chemie, Philipps-Universität Marburg, Hans-Meerwein-Straße 4, 35032 Marburg, Germany
| | - Yannick J Franzke
- Fachbereich Chemie, Philipps-Universität Marburg, Hans-Meerwein-Straße 4, 35032 Marburg, Germany
| | - Christof Holzer
- Institute of Theoretical Solid State Physics, Karlsruhe Institute of Technology (KIT), Wolfgang-Gaede-Straße 1, 76131 Karlsruhe, Germany
| | - Florian Weigend
- Fachbereich Chemie, Philipps-Universität Marburg, Hans-Meerwein-Straße 4, 35032 Marburg, Germany
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21
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Franzke YJ, Holzer C. Exact two-component theory becoming an efficient tool for NMR shieldings and shifts with spin-orbit coupling. J Chem Phys 2023; 159:184102. [PMID: 37937936 DOI: 10.1063/5.0171509] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/09/2023] [Accepted: 09/04/2023] [Indexed: 11/09/2023] Open
Abstract
We present a gauge-origin invariant exact two-component (X2C) approach within a modern density functional framework, supporting meta-generalized gradient approximations such as TPSS and range-separated hybrid functionals such as CAM-B3LYP. The complete exchange-correlation kernel is applied, including the direct contribution of the field-dependent basis functions and the reorthonormalization contribution from the perturbed overlap matrix. Additionally, the finite nucleus model is available for the electron-nucleus potential and the vector potential throughout. Efficiency is ensured by the diagonal local approximation to the unitary decoupling transformation in X2C as well as the (multipole-accelerated) resolution of the identity approximation for the Coulomb term (MARI-J, RI-J) and the seminumerical exchange approximation. Errors introduced by these approximations are assessed and found to be clearly negligible. The applicability of our implementation to large-scale calculations is demonstrated for a tin pincer-type system as well as low-valent tin and lead complexes. Here, the calculation of the Sn nuclear magnetic resonance shifts for the pincer-type ligand with about 2400 basis functions requires less than 1 h for hybrid density functionals. Further, the impact of spin-orbit coupling on the nucleus-independent chemical shifts and the corresponding ring currents of all-metal aromatic systems is studied.
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Affiliation(s)
- Yannick J Franzke
- Fachbereich Chemie, Philipps-Universität Marburg, Hans-Meerwein-Straße 4, 35032 Marburg, Germany
| | - Christof Holzer
- Institute of Theoretical Solid State Physics, Karlsruhe Institute of Technology (KIT), Wolfgang-Gaede-Straße 1, 76131 Karlsruhe, Germany
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22
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Vindel-Zandbergen P, Kȩdziera D, Żółtowski M, Kłos J, Żuchowski P, Felker PM, Lique F, Bačić Z. H2O-HCN complex: A new potential energy surface and intermolecular rovibrational states from rigorous quantum calculations. J Chem Phys 2023; 159:174302. [PMID: 37909452 DOI: 10.1063/5.0173751] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/24/2023] [Accepted: 10/13/2023] [Indexed: 11/03/2023] Open
Abstract
In this work the H2O-HCN complex is quantitatively characterized in two ways. First, we report a new rigid-monomer 5D intermolecular potential energy surface (PES) for this complex, calculated using the symmetry-adapted perturbation theory based on density functional theory method. The PES is based on 2833 ab initio points computed employing the aug-cc-pVQZ basis set, utilizing the autoPES code, which provides a site-site analytical fit with the long-range region given by perturbation theory. Next, we present the results of the quantum 5D calculations of the fully coupled intermolecular rovibrational states of the H2O-HCN complex for the total angular momentum J values of 0, 1, and 2, performed on the new PES. These calculations rely on the quantum bound-state methodology developed by us recently and applied to a variety of noncovalently bound binary molecular complexes. The vibrationally averaged ground-state geometry of H2O-HCN determined from the quantum 5D calculations agrees very well with that from the microwave spectroscopic measurements. In addition, the computed ground-state rotational transition frequencies, as well as the B and C rotational constants calculated for the ground state of the complex, are in excellent agreement with the experimental values. The assignment of the calculated intermolecular vibrational states of the H2O-HCN complex is surprisingly challenging. It turns out that only the excitations of the intermolecular stretch mode can be assigned with confidence. The coupling among the angular degrees of freedom (DOFs) of the complex is unusually strong, and as a result most of the excited intermolecular states are unassigned. On the other hand, the coupling of the radial, intermolecular stretch mode and the angular DOFs is weak, allowing straightforward assignment of the excitation of the former.
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Affiliation(s)
| | - Dariusz Kȩdziera
- Faculty of Chemistry, Nicolaus Copernicus University in Toruń, ul. Gagarina 7, 87-100 Toruń, Poland
| | - Michał Żółtowski
- University of Rennes, CNRS, IPR (Institut de Physique de Rennes) - UMR 6251, F-35000 Rennes, France
- LOMC - UMR 6294, CNRS-Université du Havre, 25 rue Philippe Lebon, BP1123, 76 063 Le Havre cedex, France
| | - Jacek Kłos
- Joint Quantum Institute, University of Maryland, College Park, Maryland 20742, USA
| | - Piotr Żuchowski
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, ul. Grudziądzka 5, 87-100 Toruń, Poland
| | - Peter M Felker
- Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095-1569, USA
| | - François Lique
- University of Rennes, CNRS, IPR (Institut de Physique de Rennes) - UMR 6251, F-35000 Rennes, France
| | - Zlatko Bačić
- Department of Chemistry, New York University, New York, New York 10003, USA
- Simons Center for Computational Physical Chemistry at New York University, New York, New York 10003, USA
- NYU-ECNU Center for Computational Chemistry at NYU Shanghai, 3663 Zhongshan Road North, Shanghai 200062, China
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23
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Mejia-Rodriguez D, Aprà E, Autschbach J, Bauman NP, Bylaska EJ, Govind N, Hammond JR, Kowalski K, Kunitsa A, Panyala A, Peng B, Rehr JJ, Song H, Tretiak S, Valiev M, Vila FD. NWChem: Recent and Ongoing Developments. J Chem Theory Comput 2023; 19:7077-7096. [PMID: 37458314 DOI: 10.1021/acs.jctc.3c00421] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2023]
Abstract
This paper summarizes developments in the NWChem computational chemistry suite since the last major release (NWChem 7.0.0). Specifically, we focus on functionality, along with input blocks, that is accessible in the current stable release (NWChem 7.2.0) and in the "master" development branch, interfaces to quantum computing simulators, interfaces to external libraries, the NWChem github repository, and containerization of NWChem executable images. Some ongoing developments that will be available in the near future are also discussed.
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Affiliation(s)
- Daniel Mejia-Rodriguez
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99352, United States
| | - Edoardo Aprà
- Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory, Richland, Washington 99352, United States
| | - Jochen Autschbach
- Department of Chemistry, University at Buffalo, State University of New York, Buffalo, New York 14260-3000, United States
| | - Nicholas P Bauman
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99352, United States
| | - Eric J Bylaska
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99352, United States
| | - Niranjan Govind
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99352, United States
| | - Jeff R Hammond
- Accelerated Computing, NVIDIA Helsinki Oy, Porkkalankatu 1, 00180 Helsinki, Finland
| | - Karol Kowalski
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99352, United States
| | - Alexander Kunitsa
- Zapata Computing, Inc., 100 Federal Street, Boston, Massachusetts 02110, United States
| | - Ajay Panyala
- Advanced Computing, Mathematics, and Data Division, Pacific Northwest National Laboratory, Richland, Washington 99352, United States
| | - Bo Peng
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99352, United States
| | - John J Rehr
- Department of Physics, University of Washington, Seattle, Washington 98195, United States
| | - Huajing Song
- Physics and Chemistry of Materials, Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Sergei Tretiak
- Physics and Chemistry of Materials, Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
- Center for Integrated Nanotechnologies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Marat Valiev
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99352, United States
| | - Fernando D Vila
- Department of Physics, University of Washington, Seattle, Washington 98195, United States
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24
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Hellmann R. Cross Second Virial Coefficients of the H 2O-H 2 and H 2S-H 2 Systems from First-Principles. J Chem Eng Data 2023; 68:2212-2222. [PMID: 37736252 PMCID: PMC10510380 DOI: 10.1021/acs.jced.3c00300] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 05/23/2023] [Accepted: 07/14/2023] [Indexed: 09/23/2023]
Abstract
The cross second virial coefficients B12 for the interactions of water (H2O) with molecular hydrogen (H2) and of hydrogen sulfide (H2S) with H2 were obtained at temperatures in the range from 150 to 2000 K from new intermolecular potential energy surfaces (PESs) for the respective molecule pairs. The PESs are based on interaction energies determined for about 12 000 configurations of each molecule pair employing different high-level quantum-chemical ab initio methods up to coupled cluster with single, double, triple, and perturbative quadruple excitations [CCSDT(Q)]. Furthermore, the interaction energies were corrected for scalar relativistic effects. Both classical and semiclassical values for B12 were extracted from the PESs using the Mayer-sampling Monte Carlo approach. While our results for the H2O-H2 system validate the older first-principles results of Hodges et al. [J. Chem. Phys. 2004, 120, 710-720], B12 for the H2S-H2 system was, to the best of our knowledge, hitherto neither measured experimentally nor predicted from first principles.
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Affiliation(s)
- Robert Hellmann
- Institut für Thermodynamik, Helmut-Schmidt-Universität/Universität
der Bundeswehr Hamburg, Holstenhofweg 85, 22043 Hamburg, Germany
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25
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Ehrman J, Martinez-Baez E, Jenkins AJ, Li X. Improving One-Electron Exact-Two-Component Relativistic Methods with the Dirac-Coulomb-Breit-Parameterized Effective Spin-Orbit Coupling. J Chem Theory Comput 2023; 19:5785-5790. [PMID: 37589436 DOI: 10.1021/acs.jctc.3c00479] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/18/2023]
Abstract
In photochemical processes, spin-orbit coupling plays a crucial role in determining the outcome of the reaction. However, the exact treatment of the Dirac-Coulomb-Breit two-electron operator required for rigorous inclusion of spin-orbit coupling is computationally prohibitive. To address this challenge, we present a Dirac-Coulomb-Breit-parameterized screened-nuclear spin-orbit factor to approximate two-electron spin-orbit couplings in the effective one-electron spin-orbit Hamiltonian. We propose two schemes, the universal and row-dependent parameterizations, to further improve the accuracy of the method. Benchmark calculations on both atomic and molecular systems are performed and compared to results from the computationally expensive four-component Dirac-Coulomb-Breit method. The Dirac-Coulomb-Breit-parameterized approach offers a more computationally feasible method for accurate spin-orbit coupling calculations.
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Affiliation(s)
- Jordan Ehrman
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Ernesto Martinez-Baez
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Andrew J Jenkins
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Xiaosong Li
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
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26
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Motta LC, Autschbach J. Actinide inverse trans influence versus cooperative pushing from below and multi-center bonding. Nat Commun 2023; 14:4307. [PMID: 37463900 DOI: 10.1038/s41467-023-39626-8] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/19/2023] [Accepted: 06/22/2023] [Indexed: 07/20/2023] Open
Abstract
Actinide-ligand bonds with high multiplicities remain poorly understood. Decades ago, an effect known as 6p pushing from below (PFB) was proposed to enhance actinide covalency. A related effect-also poorly understood-is inverse trans influence (ITI). The present computational study of actinide-ligand covalent interactions with high bond multiplicities quantifies the energetic contributions from PFB and identifies a hitherto overlooked fourth bonding interaction for 2nd-row ligands in the studied organometallic systems. The latter are best described by a terminal O/N ligand exhibiting quadruple bonding interactions with the actinide. The 4th interaction may be characterized as a multi-center or charge-shift bond involving the trans ligand. It is shown in this work that the 4th bonding interaction is a manifestation of ITI, assisted by PFB, and provides a long-sought missing piece in the understanding of actinide chemistry.
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Affiliation(s)
- Laura C Motta
- Department of Chemistry, University at Buffalo, State University of New York, Buffalo, NY, 14260-3000, USA
- Department of Marine Chemistry & Geochemistry, Woods Hole Oceanographic Institution, Woods Hole, MA, 02543-1050, USA
| | - Jochen Autschbach
- Department of Chemistry, University at Buffalo, State University of New York, Buffalo, NY, 14260-3000, USA.
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27
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Troß J, Carter-Fenk K, Cole-Filipiak NC, Schrader P, Word M, McCaslin LM, Head-Gordon M, Ramasesha K. Excited-State Dynamics during Primary C-I Homolysis in Acetyl Iodide Revealed by Ultrafast Core-Level Spectroscopy. J Phys Chem A 2023; 127:4103-4114. [PMID: 37103479 DOI: 10.1021/acs.jpca.3c01414] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/28/2023]
Abstract
In typical carbonyl-containing molecules, bond dissociation events follow initial excitation to nπC═O* states. However, in acetyl iodide, the iodine atom gives rise to electronic states with mixed nπC═O* and nσC-I* character, leading to complex excited-state dynamics, ultimately resulting in dissociation. Using ultrafast extreme ultraviolet (XUV) transient absorption spectroscopy and quantum chemical calculations, we present an investigation of the primary photodissociation dynamics of acetyl iodide via time-resolved spectroscopy of core-to-valence transitions of the I atom after 266 nm excitation. The probed I 4d-to-valence transitions show features that evolve on sub-100-fs time scales, reporting on excited-state wavepacket evolution during dissociation. These features subsequently evolve to yield spectral signatures corresponding to free iodine atoms in their spin-orbit ground and excited states with a branching ratio of 1.1:1 following dissociation of the C-I bond. Calculations of the valence excitation spectrum via equation-of-motion coupled cluster with single and double substitutions (EOM-CCSD) show that initial excited states are of spin-mixed character. From the initially pumped spin-mixed state, we use a combination of time-dependent density functional theory (TDDFT)-driven nonadiabatic ab initio molecular dynamics and EOM-CCSD calculations of the N4,5 edge to reveal a sharp inflection point in the transient XUV signal that corresponds to rapid C-I homolysis. By examining the molecular orbitals involved in the core-level excitations at and around this inflection point, we are able to piece together a detailed picture of C-I bond photolysis in which d → σ* transitions give way to d → p excitations as the bond dissociates. We also report theoretical predictions of short-lived, weak 4d → 5d transitions in acetyl iodide, validated by weak bleaching in the experimental transient XUV spectra. This joint experimental-theoretical effort has thus unraveled the detailed electronic structure and dynamics of a strongly spin-orbit coupled system.
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Affiliation(s)
- Jan Troß
- Combustion Research Facility, Sandia National Laboratories, Livermore, California 94550, United States
| | - Kevin Carter-Fenk
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, United States
| | - Neil C Cole-Filipiak
- Combustion Research Facility, Sandia National Laboratories, Livermore, California 94550, United States
| | - Paul Schrader
- Combustion Research Facility, Sandia National Laboratories, Livermore, California 94550, United States
| | - Mi'Kayla Word
- Combustion Research Facility, Sandia National Laboratories, Livermore, California 94550, United States
| | - Laura M McCaslin
- Combustion Research Facility, Sandia National Laboratories, Livermore, California 94550, United States
| | - Martin Head-Gordon
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, United States
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Krupa Ramasesha
- Combustion Research Facility, Sandia National Laboratories, Livermore, California 94550, United States
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28
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Abstract
The self-consistent and complex spin-orbit exact two-component (X2C) formalism for NMR spin-spin coupling constants [ J. Chem. Theory Comput. 17, 2021, 3874-3994] is reduced to a scalar one-component ansatz. This way, the first-order response term can be partitioned into the Fermi-contact (FC) and spin-dipole (SD) interactions as well as the paramagnetic spin-orbit (PSO) contribution. The FC+SD terms are real and symmetric, while the PSO term is purely imaginary and antisymmetric. The relativistic one-component approach is combined with a modern density functional treatment up to local hybrid functionals including the response of the current density. Computational demands are reduced by factors of 8-24 as shown for a large tin compound consisting of 137 atoms. Limitations of the current ansatz are critically assessed for Sn, Pb, Pd, and Pt compounds, i.e. the one-component treatment is not sufficient for tin compounds featuring a few heavy halogen atoms.
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Affiliation(s)
- Yannick J Franzke
- Fachbereich Chemie, Philipps-Universität Marburg, Hans-Meerwein-Str. 4, 35032 Marburg, Germany
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29
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Kotov AA, Kozhedub YS, Glazov DA, Iliaš M, Pershina V, Shabaev VM. Relativistic Coupled-Cluster Calculations of Spectroscopic Properties of Copernicium and Flerovium Monoxides. Chemphyschem 2023; 24:e202200680. [PMID: 36383485 DOI: 10.1002/cphc.202200680] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/08/2022] [Revised: 11/11/2022] [Accepted: 11/13/2022] [Indexed: 11/17/2022]
Abstract
Calculations of spectroscopic properties of the CnO and FlO molecules are performed using ab initio all-electron 4c- and 2c-relativistic coupled-cluster approaches with single, double, and perturbative triple excitations. The corresponding calculation for HgO is also accomplished for comparison with the published data. The dependence of the results on the parameters of the basis set and approximations used is investigated in detail. The overall relative uncertainties of the recommended values on the level of 1-2 % are reached. The calculated spectroscopic constants are indicative of the following trend in the reactivity of the oxides HgO>FlO>CnO. This is confirmed by the trend in the adsorption energies, Eads , of these molecules on the surfaces of gold, quartz, and Teflon. The predicted rather low Eads values for the latter case should guarantee their delivery from the recoil chamber to the chemistry set up in gas-phase experiments.
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Affiliation(s)
- Artem A Kotov
- Department of Physics, St. Petersburg State University, 199034, St. Petersburg, Russia
| | - Yury S Kozhedub
- Department of Physics, St. Petersburg State University, 199034, St. Petersburg, Russia
| | - Dmitry A Glazov
- Department of Physics, St. Petersburg State University, 199034, St. Petersburg, Russia
| | - Miroslav Iliaš
- Department of Chemistry, Faculty of Natural Sciences, Matej Bel University, Tajovského 40, 97401, Banská Bystrica, Slovakia.,Helmholtz-Institut Mainz, Johannes Gutenberg-Universität, 55099, Mainz, Germany.,GSI Helmholtzzentrum für Schwerionenforschung GmbH, Planckstr. 1, 64291, Darmstadt, Germany
| | - Valeria Pershina
- GSI Helmholtzzentrum für Schwerionenforschung GmbH, Planckstr. 1, 64291, Darmstadt, Germany
| | - Vladimir M Shabaev
- Department of Physics, St. Petersburg State University, 199034, St. Petersburg, Russia
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30
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Liao C, Kasper JM, Jenkins AJ, Yang P, Batista ER, Frisch MJ, Li X. State Interaction Linear Response Time-Dependent Density Functional Theory with Perturbative Spin-Orbit Coupling: Benchmark and Perspectives. JACS Au 2023; 3:358-367. [PMID: 36873704 PMCID: PMC9975852 DOI: 10.1021/jacsau.2c00659] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/04/2022] [Revised: 01/17/2023] [Accepted: 01/18/2023] [Indexed: 06/18/2023]
Abstract
Spin-orbit coupling (SOC) is an important driving force in photochemistry. In this work, we develop a perturbative spin-orbit coupling method within the linear response time-dependent density function theory framework (TDDFT-SO). A full state interaction scheme, including singlet-triplet and triplet-triplet coupling, is introduced to describe not only the coupling between the ground and excited states, but also between excited states with all couplings between spin microstates. In addition, expressions to compute spectral oscillator strengths are presented. Scalar relativity is included variationally using the second-order Douglas-Kroll-Hess Hamiltonian, and the TDDFT-SO method is validated against variational SOC relativistic methods for atomic, diatomic, and transition metal complexes to determine the range of applicability and potential limitations. To demonstrate the robustness of TDDFT-SO for large-scale chemical systems, the UV-Vis spectrum of Au25(SR)18 - is computed and compared to experiment. Perspectives on the limitation, accuracy, and capability of perturbative TDDFT-SO are presented via analyses of benchmark calculations. Additionally, an open-source Python software package (PyTDDFT-SO) is developed and released to interface with the Gaussian 16 quantum chemistry software package to perform this calculation.
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Affiliation(s)
- Can Liao
- Department
of Chemistry, University of Washington, Seattle, Washington98195, United States
| | - Joseph M. Kasper
- Theoretical
Division, Los Alamos National Laboratory, Los Alamos, New Mexico87545, United States
| | - Andrew J. Jenkins
- Department
of Chemistry, University of Washington, Seattle, Washington98195, United States
| | - Ping Yang
- Theoretical
Division, Los Alamos National Laboratory, Los Alamos, New Mexico87545, United States
| | - Enrique R. Batista
- Theoretical
Division, Los Alamos National Laboratory, Los Alamos, New Mexico87545, United States
| | - Michael J. Frisch
- Gaussian
Inc., 340 Quinnipiac Street, Bldg 40, Wallingford, Connecticut06492, United States
| | - Xiaosong Li
- Department
of Chemistry, University of Washington, Seattle, Washington98195, United States
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31
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Moitra T, Konecny L, Kadek M, Rubio A, Repisky M. Accurate Relativistic Real-Time Time-Dependent Density Functional Theory for Valence and Core Attosecond Transient Absorption Spectroscopy. J Phys Chem Lett 2023; 14:1714-1724. [PMID: 36757216 PMCID: PMC9940299 DOI: 10.1021/acs.jpclett.2c03599] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/25/2022] [Accepted: 02/03/2023] [Indexed: 06/18/2023]
Abstract
First principles theoretical modeling of out-of-equilibrium processes observed in attosecond pump-probe transient absorption spectroscopy (TAS) triggering pure electron dynamics remains a challenging task, especially for heavy elements and/or core excitations containing fingerprints of scalar and spin-orbit relativistic effects. To address this, we formulate a methodology for simulating TAS within the relativistic real-time, time-dependent density functional theory (RT-TDDFT) framework, for both the valence and core energy regimes. Especially for TAS, full four-component (4c) RT simulations are feasible but computationally demanding. Therefore, in addition to the 4c approach, we also introduce the atomic mean-field exact two-component (amfX2C) Hamiltonian accounting for one- and two-electron picture-change corrections within RT-TDDFT. amfX2C preserves the accuracy of the parent 4c method at a fraction of its computational cost. Finally, we apply the methodology to study valence and near-L2,3-edge TAS processes of experimentally relevant systems and provide additional physical insights using relativistic nonequilibrium response theory.
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Affiliation(s)
- Torsha Moitra
- Hylleraas
Centre for Quantum Molecular Sciences, Department of Chemistry, UiT The Arctic University of Norway, 9037 Tromsø, Norway
| | - Lukas Konecny
- Hylleraas
Centre for Quantum Molecular Sciences, Department of Chemistry, UiT The Arctic University of Norway, 9037 Tromsø, Norway
- Max
Planck Institute for the Structure and Dynamics of Matter, Center for Free Electron Laser Science, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Marius Kadek
- Hylleraas
Centre for Quantum Molecular Sciences, Department of Chemistry, UiT The Arctic University of Norway, 9037 Tromsø, Norway
- Department
of Physics, Northeastern University, Boston, Massachusetts 02115, United States
- Algorithmiq
Ltd., Kanavakatu 3C, FI-00160 Helsinki, Finland
| | - Angel Rubio
- Max
Planck Institute for the Structure and Dynamics of Matter, Center for Free Electron Laser Science, Luruper Chaussee 149, 22761 Hamburg, Germany
- Center
for Computational Quantum Physics (CCQ), The Flatiron Institute, 162 Fifth Avenue, New York New York 10010, United States
- Nano-Bio
Spectroscopy Group, Departamento de Física de Materiales, Universidad del País Vasco, 20018 San Sebastian, Spain
| | - Michal Repisky
- Hylleraas
Centre for Quantum Molecular Sciences, Department of Chemistry, UiT The Arctic University of Norway, 9037 Tromsø, Norway
- Department
of Physical and Theoretical Chemistry, Faculty of Natural Sciences, Comenius University, 84104 Bratislava, Slovakia
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32
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Elliott SN, Keçeli M, Ghosh MK, Somers KP, Curran HJ, Klippenstein SJ. High-Accuracy Heats of Formation for Alkane Oxidation: From Small to Large via the Automated CBH-ANL Method. J Phys Chem A 2023; 127:1512-1531. [PMID: 36695527 DOI: 10.1021/acs.jpca.2c07248] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023]
Abstract
It is generally challenging to obtain high-accuracy predictions for the heat of formation for species with more than a handful of heavy atoms, such as those of importance in standard combustion mechanisms. To this end, we construct the CBH-ANL approach and illustrate that, for a set of 194 alkane oxidation species, it can be used to produce ΔHf(0 K) values with 2σ uncertainties of 0.2-0.5 kcal mol-1. This set includes the alkanes, hydroperoxides, and alkyl, peroxy, and hydroperoxyalkyl radicals for 17 representative hydrocarbon fuels containing up to 10 heavy atoms with various degrees of branching in the alkane backbone. The CBH-ANL approach, automated in the QTC and AutoMech software suites, builds balanced chemical equations for the calculation of ΔHf(0 K), in which the reference species may be up to five heavy atoms. The high-level ANL0 and ANL1 reference ΔHf(0 K) values are further refined for even the largest of these reference species with a novel laddering approach. We perform a comprehensive quantification of the uncertainties for both the individual reference species (the largest of which is 0.15 kcal mol-1) and the propagation of those uncertainties when used in the calculation of ΔHf(0 K) for the 194 target species. We examine the sensitivity of the predicted ΔHf(0 K) values to (i) electronic energies from various methods, including ωB97X-D/cc-pVTZ, B2PLYP-D3/cc-pVTZ, CCSD(T)-F12b/cc-pVDZ-F12//B2PLYP-D3/cc-pVTZ, and CCSD(T)-F12b/cc-pVTZ-F12//B2PLYP-D3/cc-pVTZ; (ii) the zero-point vibrational energies (ZPVEs), where we consider harmonic ZPVEs as well as two scaling-based estimates of the anharmonic ZPVEs, all implemented for both ωB97X-D/cc-pVTZ and B2PLYP-D3/cc-pVTZ calculations; (iii) the particular CBH-ANL scheme employed; and (iv) the procedure for choosing the reference conformer for the analyses. The discussion concludes with a summary of the estimated overall uncertainty in the predictions and a validation of the predictions for the alkane subset.
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Affiliation(s)
- Sarah N Elliott
- Chemical Sciences and Engineering Division, Argonne National Laboratory, Lemont, Illinois60439, United States
| | - Murat Keçeli
- Computational Science Division, Argonne National Laboratory, Lemont, Illinois60439, United States
| | - Manik K Ghosh
- Combustion Chemistry Centre, School of Chemistry, Ryan Institute, MaREI, National University of Ireland, GalwayH91 TK33, Ireland
| | - Kieran P Somers
- Combustion Chemistry Centre, School of Chemistry, Ryan Institute, MaREI, National University of Ireland, GalwayH91 TK33, Ireland
| | - Henry J Curran
- Combustion Chemistry Centre, School of Chemistry, Ryan Institute, MaREI, National University of Ireland, GalwayH91 TK33, Ireland
| | - Stephen J Klippenstein
- Chemical Sciences and Engineering Division, Argonne National Laboratory, Lemont, Illinois60439, United States
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33
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Wang X, Sharma S. Relativistic Semistochastic Heat-Bath Configuration Interaction. J Chem Theory Comput 2023; 19:848-855. [PMID: 36700783 DOI: 10.1021/acs.jctc.2c01025] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/27/2023]
Abstract
In this work we present the extension of semistochastic heat-bath configuration interaction (SHCI) to work with any two-component and four-component Hamiltonian. The vertical detachment energy (VDE) of AuH2- and zero-field splitting (ZFS) of NpO22+ is calculated by correlating more than 100 spinors in both cases. This work demonstrates the capability of SHCI to treat problems where both relativistic effect and electron correlation are important.
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Affiliation(s)
- Xubo Wang
- Department of Chemistry, University of Colorado Boulder, Boulder, Colorado80309, United States
| | - Sandeep Sharma
- Department of Chemistry, University of Colorado Boulder, Boulder, Colorado80309, United States
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34
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Konecny L, Komorovsky S, Vicha J, Ruud K, Repisky M. Exact Two-Component TDDFT with Simple Two-Electron Picture-Change Corrections: X-ray Absorption Spectra Near L- and M-Edges of Four-Component Quality at Two-Component Cost. J Phys Chem A 2023; 127:1360-1376. [PMID: 36722848 PMCID: PMC9923756 DOI: 10.1021/acs.jpca.2c08307] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/02/2023]
Abstract
X-ray absorption spectroscopy (XAS) has gained popularity in recent years as it probes matter with high spatial and elemental sensitivities. However, the theoretical modeling of XAS is a challenging task since XAS spectra feature a fine structure due to scalar (SC) and spin-orbit (SO) relativistic effects, in particular near L and M absorption edges. While full four-component (4c) calculations of XAS are nowadays feasible, there is still interest in developing approximate relativistic methods that enable XAS calculations at the two-component (2c) level while maintaining the accuracy of the parent 4c approach. In this article we present theoretical and numerical insights into two simple yet accurate 2c approaches based on an (extended) atomic mean-field exact two-component Hamiltonian framework, (e)amfX2C, for the calculation of XAS using linear eigenvalue and damped response time-dependent density functional theory (TDDFT). In contrast to the commonly used one-electron X2C (1eX2C) Hamiltonian, both amfX2C and eamfX2C account for the SC and SO two-electron and exchange-correlation picture-change (PC) effects that arise from the X2C transformation. As we demonstrate on L- and M-edge XAS spectra of transition metal and actinide compounds, the absence of PC corrections in the 1eX2C approximation results in a substantial overestimation of SO splittings, whereas (e)amfX2C Hamiltonians reproduce all essential spectral features such as shape, position, and SO splitting of the 4c references in excellent agreement, while offering significant computational savings. Therefore, the (e)amfX2C PC correction models presented here constitute reliable relativistic 2c quantum-chemical approaches for modeling XAS.
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Affiliation(s)
- Lukas Konecny
- Hylleraas
Centre for Quantum Molecular Sciences, Department of Chemistry, UiT The Arctic University of Norway, N-9037Tromsø, Norway,Center
for Free Electron Laser Science, Max Planck
Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, 22761Hamburg, Germany,
| | - Stanislav Komorovsky
- Institute
of Inorganic Chemistry, Slovak Academy of Sciences, Dúbravská cesta 9, SK-84536Bratislava, Slovakia
| | - Jan Vicha
- Centre
of Polymer Systems, University Institute,
Tomas Bata University in Zlín, CZ-76001Zlín, Czech Republic
| | - Kenneth Ruud
- Hylleraas
Centre for Quantum Molecular Sciences, Department of Chemistry, UiT The Arctic University of Norway, N-9037Tromsø, Norway,Norwegian
Defence Research Establishment, P.O.
Box 25, 2027Kjeller, Norway
| | - Michal Repisky
- Hylleraas
Centre for Quantum Molecular Sciences, Department of Chemistry, UiT The Arctic University of Norway, N-9037Tromsø, Norway,Department
of Physical and Theoretical Chemistry, Faculty of Natural Sciences, Comenius University, Ilkovicova 6, SK-84215Bratislava, Slovakia,
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35
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Talukdar K, Buragohain H, Nayak MK, Vaval N, Pal S. Relativistic coupled-cluster study of SrF for low-energy precision tests of fundamental physics. Theor Chem Acc 2023; 142:15. [DOI: 10.1007/s00214-023-02953-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/15/2023]
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36
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Inoue N, Nakajima T. Douglas-Kroll and infinite order two-component transformations of Dirac-Fock operator. J Chem Phys 2023; 158:044103. [PMID: 36725498 DOI: 10.1063/5.0131926] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2023] Open
Abstract
We extended the conventional Douglas-Kroll (DK) and infinite order two-component (IOTC) methods to a technique applicable to Fock matrices, called extended DK (EDK) and extended IOTC (EIOTC), respectively. First, we defined a strategy to divide the Dirac-Fock operator into zero- and first-order terms. We then demonstrated that the first-order extended DK transformation, which is the Foldy-Wouthuysen transformation for the zero-order term, as well as the second- and third-order EDK and EIOTC, could be well defined. The EDK- and EIOTC-transformed Fock matrix, kinetic energy operator, nuclear attraction operator, and density matrix were derived. These equations were numerically evaluated, and it was found that these methods were accurate. In particular, EIOTC was consistent with the four-component approach. Four-component and extended two-component calculations are more expensive than non-relativistic calculations due to small-component-type two-electron integrals. We developed a new approximation formula, RIS-V, for small-component-type two-electron integrals, including the spin-orbit interaction between electrons. These results suggest that the RIS-V formula effectively accelerates the four-component and extended two-component methods.
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Affiliation(s)
- Nobuki Inoue
- RIKEN Center for Computational Science, 7-1-26 Minatojima-minami, Cyuo-ku, Kobe, Hyogo 650-0047, Japan
| | - Takahito Nakajima
- RIKEN Center for Computational Science, 7-1-26 Minatojima-minami, Cyuo-ku, Kobe, Hyogo 650-0047, Japan
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37
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Graubner T, Karttunen AJ, Kraus F. A Computational Study on Closed-Shell Molecular Hexafluorides MF 6 (M=S, Se, Te, Po, Xe, Rn, Cr, Mo, W, U) - Molecular Structure, Anharmonic Frequency Calculations, and Prediction of the NdF 6 Molecule. Chemphyschem 2023; 24:e202200903. [PMID: 36688413 DOI: 10.1002/cphc.202200903] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/09/2022] [Revised: 01/23/2023] [Accepted: 01/23/2023] [Indexed: 01/24/2023]
Abstract
Quantum chemical methods were used to study the molecular structure and anharmonic IR spectra of the experimentally known closed-shell molecular hexafluorides MF6 (M=S, Se, Te, Xe, Mo, W, U). First, the molecular structures and harmonic frequencies were investigated using Density Functional Theory (DFT) with all-electron basis sets and explicitly considering the influence of spin-orbit coupling. Second, anharmonic frequencies and IR intensities were calculated with the CCSD(T) coupled cluster method and compared, where available, with IR spectra recorded by us. These comparisons showed satisfactory results. The anharmonic IR spectra provide means for identifying experimentally too little studied or unknown MF6 molecules with M=Cr, Po, Rn. To the best of our knowledge, we predict the NdF6 molecule for the first time and show it to be a true local minimum on the potential energy surface. We used intrinsic bond orbital (IBO) analyses to characterize the bonding situation in comparison with the UF6 molecule.
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Affiliation(s)
- Tim Graubner
- Fluorchemie, Fachbereich Chemie, Philipps-Universität Marburg, Hans-Meerwein-Straße 4, 35032, Marburg, Germany
| | - Antti J Karttunen
- Department of Chemistry and Materials Science, Aalto University, 00076, Espoo, Finland
| | - Florian Kraus
- Fluorchemie, Fachbereich Chemie, Philipps-Universität Marburg, Hans-Meerwein-Straße 4, 35032, Marburg, Germany
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38
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Begley JM, Aroeira GJR, Turney JM, Douberly GE, Schaefer HF. Enthalpies of formation for Criegee intermediates: A correlation energy convergence study. J Chem Phys 2023; 158:034302. [PMID: 36681629 DOI: 10.1063/5.0127588] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022] Open
Abstract
Criegee intermediates, formed from the ozonolysis of alkenes, are known to have a role in atmospheric chemistry, including the modulation of the oxidizing capacity of the troposphere. Although studies have been conducted since their discovery, the synthesis of these species in the laboratory has ushered in a new wave of investigations of these structures, both theoretically and experimentally. In some of these theoretical studies, high-order corrections for correlation energy are included to account for the mid multi-reference character found in these systems. Many of these studies include a focus on kinetics; therefore, the calculated energies should be accurate (<1 kcal/mol in error). In this research, we compute the enthalpies of formation for a small set of Criegee intermediates, including higher-order coupled cluster corrections for correlation energy up to coupled cluster with perturbative quintuple excitations. The enthalpies of formation for formaldehyde oxide, anti-acetaldehyde oxide, syn-acetaldehyde oxide, and acetone oxide are presented at 0 K as 26.5, 15.6, 12.2, and 0.1 kcal mol-1, respectively. Additionally, we do not recommend the coupled cluster with perturbative quadruple excitations [CCSDT(Q)] energy correction, as it is approximately twice as large as that of the coupled cluster with full quadruple excitations (CCSDTQ). Half of the CCSDT(Q) energy correction may be included as a reliable, cost-effective estimation of CCSDTQ energies for Criegee intermediates.
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Affiliation(s)
- James M Begley
- Department of Chemistry, Center for Computational Quantum Chemistry, University of Georgia, Athens, Georgia 30602, USA
| | - Gustavo J R Aroeira
- Department of Chemistry, Center for Computational Quantum Chemistry, University of Georgia, Athens, Georgia 30602, USA
| | - Justin M Turney
- Department of Chemistry, Center for Computational Quantum Chemistry, University of Georgia, Athens, Georgia 30602, USA
| | - Gary E Douberly
- Department of Chemistry, Center for Computational Quantum Chemistry, University of Georgia, Athens, Georgia 30602, USA
| | - Henry F Schaefer
- Department of Chemistry, Center for Computational Quantum Chemistry, University of Georgia, Athens, Georgia 30602, USA
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39
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Abstract
We present the first implementation of spin-orbit coupling effects in fully internally contracted second-order quasidegenerate N-electron valence perturbation theory (SO-QDNEVPT2). The SO-QDNEVPT2 approach enables the computations of ground- and excited-state energies and oscillator strengths combining the description of static electron correlation with an efficient treatment of dynamic correlation and spin-orbit coupling. In addition to SO-QDNEVPT2 with the full description of one- and two-body spin-orbit interactions at the level of two-component Breit-Pauli Hamiltonian, our implementation also features a simplified approach that takes advantage of spin-orbit mean-field approximation (SOMF-QDNEVPT2). The accuracy of these methods is tested for the group 14 and 16 hydrides, 3d and 4d transition metal ions, and two actinide dioxides (neptunyl and plutonyl dications). The zero-field splittings of group 14 and 16 molecules computed using SO-QDNEVPT2 and SOMF-QDNEVPT2 are in good agreement with the available experimental data. For the 3d transition metal ions, the SO-QDNEVPT2 method is significantly more accurate than SOMF-QDNEVPT2, while no substantial difference in the performance of two methods is observed for the 4d ions. Finally, we demonstrate that for the actinide dioxides the results of SO-QDNEVPT2 and SOMF-QDNEVPT2 are in good agreement with the data from previous theoretical studies of these systems. Overall, our results demonstrate that SO-QDNEVPT2 and SOMF-QDNEVPT2 are promising multireference methods for treating spin-orbit coupling with a relatively low computational cost.
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Affiliation(s)
- Rajat Majumder
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio43210, United States
| | - Alexander Yu Sokolov
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio43210, United States
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40
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Barysz M. Relativistic perturbative and infinite-order two-component methods for heavy elements: Radium atom. Advances in Quantum Chemistry 2023. [DOI: 10.1016/bs.aiq.2023.02.001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/18/2023]
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41
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Liu W. Perspective: Simultaneous treatment of relativity, correlation, and
QED. WIREs Comput Mol Sci 2022. [DOI: 10.1002/wcms.1652] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Affiliation(s)
- Wenjian Liu
- Qingdao Institute for Theoretical and Computational Sciences, Institute of Frontier and Interdisciplinary Science Shandong University Qingdao Shandong China
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42
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Yalouz S, Sekaran S, Fromager E, Saubanère M. Quantum embedding of multi-orbital fragments using the block-Householder transformation. J Chem Phys 2022; 157:214112. [DOI: 10.1063/5.0125683] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/09/2022] Open
Abstract
Recently, some of the authors introduced the use of the Householder transformation as a simple and intuitive method for embedding local molecular fragments [see Sekaran et al., Phys. Rev. B 104, 035121 (2021) and Sekaran et al., Computation 10, 45 (2022)]. In this work, we present an extension of this approach to the more general case of multi-orbital fragments using the block version of the Householder transformation applied to the one-body reduced density matrix, unlocking the applicability to general quantum chemistry/condensed matter physics Hamiltonians. A step-by-step construction of the block Householder transformation is presented. Both physical and numerical areas of interest of the approach are highlighted. The specific mean-field (noninteracting) case is thoroughly detailed as it is shown that the embedding of a given N spin–orbital fragment leads to the generation of two separated sub-systems: (1) a 2 N spin–orbitals “fragment+bath” cluster that exactly contains N electrons and (2) a remaining cluster’s “environment” described by so-called core electrons. We illustrate the use of this transformation in different cases of embedding scheme for practical applications. We particularly focus on the extension of the previously introduced Local Potential Functional Embedding Theory and Householder-transformed Density Matrix Functional Embedding Theory to the case of multi-orbital fragments. These calculations are realized on different types of systems, such as model Hamiltonians (Hubbard rings) and ab initio molecular systems (hydrogen rings).
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Affiliation(s)
- Saad Yalouz
- Laboratoire de Chimie Quantique, Institut de Chimie, CNRS/Université de Strasbourg, 4 Rue Blaise Pascal, 67000 Strasbourg, France
| | - Sajanthan Sekaran
- Laboratoire de Chimie Quantique, Institut de Chimie, CNRS/Université de Strasbourg, 4 Rue Blaise Pascal, 67000 Strasbourg, France
| | - Emmanuel Fromager
- Laboratoire de Chimie Quantique, Institut de Chimie, CNRS/Université de Strasbourg, 4 Rue Blaise Pascal, 67000 Strasbourg, France
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43
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Carter-Fenk K, Cunha LA, Arias-Martinez JE, Head-Gordon M. Electron-Affinity Time-Dependent Density Functional Theory: Formalism and Applications to Core-Excited States. J Phys Chem Lett 2022; 13:9664-9672. [PMID: 36215404 DOI: 10.1021/acs.jpclett.2c02564] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/16/2023]
Abstract
The lack of particle-hole attraction and orbital relaxation within time-dependent density functional theory (TDDFT) lead to extreme errors in the prediction of K-edge X-ray absorption spectra (XAS). We derive a linear-response formalism that uses optimized orbitals of the n - 1-electron system as the reference, building orbital relaxation and a proper hole into the initial density. Our approach is an exact generalization of the static-exchange approximation that ameliorates the particle-hole interaction error associated with the adiabatic approximation and reduces errors in TDDFT XAS by orders of magnitude. With a statistical performance of just 0.5 eV root-mean-square error and the same computational scaling as TDDFT under the core-valence separation approximation, we anticipate that this approach will be of great utility in XAS calculations of large systems.
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Affiliation(s)
- Kevin Carter-Fenk
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California94720, United States
| | - Leonardo A Cunha
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California94720, United States
| | - Juan E Arias-Martinez
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California94720, United States
| | - Martin Head-Gordon
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California94720, United States
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California94720, United States
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44
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Abstract
Benchmark spinor-based relativistic coupled-cluster calculations for the ionization energies of the uranium atom, the uranium monoxide molecule (UO), and the uranium dioxide molecule (UO2) and for the bond dissociation energies of UO and UO2 are reported. The accuracy of these calculations in the treatments of relativistic, electron-correlation, and basis-set effects is analyzed. The intrinsic convergence of the computed results and the favorable comparison with the experimental values demonstrate the unique applicability of the spinor representation of quantum-chemical methods to open-shell uranium-containing atomic and molecular species with uranium oxidation states ranging from U(0) to U(V).
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Affiliation(s)
- Chaoqun Zhang
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, United States
| | - Lan Cheng
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, United States
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45
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Knecht S, Repisky M, Jensen HJA, Saue T. Exact two-component Hamiltonians for relativistic quantum chemistry: Two-electron picture-change corrections made simple. J Chem Phys 2022; 157:114106. [PMID: 36137811 DOI: 10.1063/5.0095112] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Based on self-consistent field (SCF) atomic mean-field (amf) quantities, we present two simple yet computationally efficient and numerically accurate matrix-algebraic approaches to correct both scalar-relativistic and spin-orbit two-electron picture-change effects (PCEs) arising within an exact two-component (X2C) Hamiltonian framework. Both approaches, dubbed amfX2C and e(xtended)amfX2C, allow us to uniquely tailor PCE corrections to mean-field models, viz. Hartree-Fock or Kohn-Sham DFT, in the latter case also avoiding the need for a point-wise calculation of exchange-correlation PCE corrections. We assess the numerical performance of these PCE correction models on spinor energies of group 18 (closed-shell) and group 16 (open-shell) diatomic molecules, achieving a consistent ≈10-5 Hartree accuracy compared to reference four-component data. Additional tests include SCF calculations of molecular properties such as absolute contact density and contact density shifts in copernicium fluoride compounds (CnFn, n = 2,4,6), as well as equation-of-motion coupled-cluster calculations of x-ray core-ionization energies of 5d- and 6d-containing molecules, where we observe an excellent agreement with reference data. To conclude, we are confident that our (e)amfX2C PCE correction models constitute a fundamental milestone toward a universal and reliable relativistic two-component quantum-chemical approach, maintaining the accuracy of the parent four-component one at a fraction of its computational cost.
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Affiliation(s)
- Stefan Knecht
- Algorithmiq Ltd, Kanavakatu 3C, FI-00160 Helsinki, Finland
| | - Michal Repisky
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, UiT-The Arctic University of Norway, N-9037 Tromsø, Norway
| | - Hans Jørgen Aagaard Jensen
- Department of Physics, Chemistry and Pharmacy, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark
| | - Trond Saue
- Laboratoire de Chimie et Physique Quantiques (CNRS UMR 5626), Université Toulouse III - Paul Sabatier, 118 Route de Narbonne, F-31062 Toulouse Cedex, France
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46
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Gusmão EF, Haiduke RLA. Relativistic adapted Gaussian basis sets free of variational prolapse of small and medium size for hydrogen through xenon. J Comput Chem 2022; 43:1901-1910. [PMID: 36056621 DOI: 10.1002/jcc.26990] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/25/2022] [Revised: 06/20/2022] [Accepted: 08/03/2022] [Indexed: 11/09/2022]
Abstract
Two new relativistic adapted Gaussian basis sets of small and medium size are presented for all elements from Hydrogen through Xenon. These sets are free of variational prolapse and were developed with the polynomial generator coordinate Dirac-Fock method to be used with two finite nuclear models, uniform sphere and Gaussian. The largest basis set errors for electronic configurations from the Aufbau principle are around 10.0 and 4.7 mHartree for the small- and medium-size sets, respectively, which is in accordance with the accuracy level expected in each case. Hence, to our knowledge, these are the smallest prolapse free basis sets developed for these elements.
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Affiliation(s)
- Eriosvaldo Florentino Gusmão
- Departamento de Química e Física Molecular, Instituto de Química de São Carlos, Universidade de São Paulo, Av. Trabalhador São-Carlense, 400, São Carlos, São Paulo, Brazil
| | - Roberto Luiz Andrade Haiduke
- Departamento de Química e Física Molecular, Instituto de Química de São Carlos, Universidade de São Paulo, Av. Trabalhador São-Carlense, 400, São Carlos, São Paulo, Brazil
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47
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Cheng L. Relativistic exact two-component coupled-cluster calculations of electronic g-factors for heavy-atom-containing molecules pertinent to search of new physics. Mol Phys 2022. [DOI: 10.1080/00268976.2022.2113567] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/15/2022]
Affiliation(s)
- Lan Cheng
- Department of Chemistry, The Johns Hopkins University, Baltimore, MD, USA
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48
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Motta LC, Autschbach J. Theoretical Evaluation of Metal-Ligand Bonding in Neptunium Compounds in Relation to 237Np Mössbauer Spectroscopy. Inorg Chem 2022; 61:13399-13412. [PMID: 35960509 DOI: 10.1021/acs.inorgchem.2c01516] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The 237Np Mössbauer isomer shift and quadrupole splitting (QS) are powerful probes for the metal-ligand bonding of neptunium, a 5f-element of vital importance in the nuclear fuel cycle. A large set of Np compounds with different oxidation states (III) to (VII) is studied to investigate, by first-principles calculations, isomer shifts and the QS trends in relation to the Np oxidation state. Natural Bond Orbital analysis reveals that in addition to donation bonding to the 5f shell, participation of the 6d and 7s neptunium shells in covalent (donation) bonding substantially impacts the isomer shifts. The isomer shift cannot be interpreted solely by the 5f shell electron count. The isomer shift for Np(II) compounds is estimated to be in the range of 31-34 mm/s, less positive than for Np(III) compounds. For the QS, density functional calculations fail to reproduce the quadrupole splitting for some Np(VI) ionic solids. A multiconfigurational wave function approach reproduces the observed QS trends. The calculations give a semiquantitative interpretation of the trends for Np oxidation states (V) to (VII). The contrasting QS for standard and "reverse" neptunyl(VI), at the opposite extremes of the observed QS scale, arises predominantly from the different crystal environments.
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Affiliation(s)
- Laura C Motta
- Department of Chemistry, University at Buffalo, State University of New York, Buffalo, New York 14260-3000, United States
| | - Jochen Autschbach
- Department of Chemistry, University at Buffalo, State University of New York, Buffalo, New York 14260-3000, United States
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49
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Abstract
In this work we develop a variational relativistic density matrix renormalization group (DMRG) approach within the exact-two-component (X2C) framework (X2C-DMRG), using spinor orbitals optimized with the two-component relativistic complete active space self-consistent field. We investigate fine-structure splittings of p- (Ga, In, Tl) and d-block (Sc, Y, La) atoms and excitation energies of monohydride molecules (GeH, SnH, and TlH) with X2C-DMRG calculations using an all-electron relativistic Hamiltonian in a Kramers-unrestricted basis. We find that X2C-DMRG yields accurate 2P and 2D splittings compared to multireference configuration interaction with singles and doubles (MRCISD). We also investigated the degree of symmetry breaking in the atomic multiplets and convergence of electron correlation in the total energies. Symmetry breaking can be large in some cases (∼30 meV); however, increasing the number of renormalized block states m for the DMRG optimization recovers the symmetry breaking by several orders of magnitude. Encouragingly, we find the convergence of electron correlation to be close to MRCISDTQ5 quality. Relativistic X2C-DMRG approaches are important for cases where spin-orbit coupling is significant and the underlying reference wave function requires a large determinantal space. We are able to obtain quantitatively correct fine-structure splittings for systems up to 1019 number of determinants with traditional CI approaches, which are currently unfeasible to converge for the field.
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Affiliation(s)
- Chad E Hoyer
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Hang Hu
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Lixin Lu
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Stefan Knecht
- Algorithmiq Ltd., Kanavakatu 3C, FI-00160 Helsinki, Finland.,Abteilung SHE Chemie, GSI Helmholtzzentrum für Schwerionenforschung, DE-64291 Darmstadt, Germany.,Department Chemie, Johannes-Gutenberg Universität Mainz, DE-55128 Mainz, Germany
| | - Xiaosong Li
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
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50
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Bruder F, Franzke YJ, Weigend F. Paramagnetic NMR Shielding Tensors Based on Scalar Exact Two-Component and Spin-Orbit Perturbation Theory. J Phys Chem A 2022; 126:5050-5069. [PMID: 35857421 DOI: 10.1021/acs.jpca.2c03579] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
The temperature-dependent Fermi-contact and pseudocontact terms are important contributions to the paramagnetic NMR shielding tensor. Herein, we augment the scalar-relativistic (local) exact two-component (X2C) framework with spin-orbit perturbation theory including the screened nuclear spin-orbit correction for the EPR hyperfine coupling and g tensor to compute these temperature-dependent terms. The accuracy of this perturbative ansatz is assessed with the self-consistent spin-orbit two-component and four-component treatments serving as reference. This shows that the Fermi-contact and pseudocontact interaction is sufficiently described for paramagnetic NMR shifts; however, larger deviations are found for the EPR spectra and the principle components of the EPR properties of heavy elements. The impact of the perturbative treatment is further compared to that of the density functional approximation and the basis set. Large-scale calculations are routinely possible with the multipole-accelerated resolution of the identity approximation and the seminumerical exchange approximation, as shown for [CeTi6O3(OiPr)9(salicylate)6].
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Affiliation(s)
- Florian Bruder
- Fachbereich Chemie, Philipps-Universität Marburg, 35032 Marburg, Germany
| | - Yannick J Franzke
- Fachbereich Chemie, Philipps-Universität Marburg, 35032 Marburg, Germany
| | - Florian Weigend
- Fachbereich Chemie, Philipps-Universität Marburg, 35032 Marburg, Germany
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