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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] [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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2
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Valeev EF, Harrison RJ, Holmes AA, Peterson CC, Penchoff DA. Direct Determination of Optimal Real-Space Orbitals for Correlated Electronic Structure of Molecules. J Chem Theory Comput 2023; 19:7230-7241. [PMID: 37791808 DOI: 10.1021/acs.jctc.3c00732] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/05/2023]
Abstract
We demonstrate how to determine numerically nearly exact orthonormal orbitals that are optimal for the evaluation of the energy of arbitrary (correlated) states of atoms and molecules by minimization of the energy Lagrangian. Orbitals are expressed in real space using a multiresolution spectral element basis that is refined adaptively to achieve the user-specified target precision while avoiding the ill-conditioning issues that plague AO basis set expansions traditionally used for correlated models of molecular electronic structure. For light atoms, the orbital solver, in conjunction with a variational electronic structure model [selected Configuration Interaction (CI)] provides energies of comparable precision to a state-of-the-art atomic CI solver. The computed electronic energies of atoms and molecules are significantly more accurate than the counterparts obtained with the orbital sets of the same rank expanded in Gaussian AO bases, and can be determined even when linear dependence issues preclude the use of the AO bases. It is feasible to optimize more than 100 fully correlated numerical orbitals on a single computer node, and significant room exists for additional improvement. These findings suggest that real-space orbital representations might be the preferred alternative to AO representations for high-end models of correlated electronic states of molecules and materials.
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Affiliation(s)
- Edward F Valeev
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Robert J Harrison
- Department of Applied Mathematics & Statistics, Stony Brook University, Stony Brook, New York 11794, United States
| | - Adam A Holmes
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Charles C Peterson
- Office of Advanced Research Computing, University of California, Los Angeles, Los Angeles, California 90095, United States
| | - Deborah A Penchoff
- UT Innovative Computing Laboratory, University of Tennessee, Knoxville, Tennessee 37996, United States
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3
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Kottmann JS, Schleich P, Tamayo-Mendoza T, Aspuru-Guzik A. Reducing Qubit Requirements while Maintaining Numerical Precision for the Variational Quantum Eigensolver: A Basis-Set-Free Approach. J Phys Chem Lett 2021; 12:663-673. [PMID: 33393305 DOI: 10.1021/acs.jpclett.0c03410] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
We present a basis-set-free approach to the variational quantum eigensolver using an adaptive representation of the spatial part of molecular wave functions. Our approach directly determines system-specific representations of qubit Hamiltonians while fully omitting globally defined basis sets. In this work, we use directly determined pair-natural orbitals on the level of second-order perturbation theory. This results in compact qubit Hamiltonians with high numerical accuracy. We demonstrate initial applications with compact Hamiltonians on up to 22 qubits where conventional representation would for the same systems require 40-100 or more qubits. We further demonstrate reductions in the quantum circuits through the structure of the pair-natural orbitals.
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Affiliation(s)
- Jakob S Kottmann
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Canada
- Department of Computer Science, University of Toronto, Toronto, Canada
| | - Philipp Schleich
- Center for Computational Engineering Science, RWTH Aachen University, Aachen, Germany
| | - Teresa Tamayo-Mendoza
- Department of Computer Science, University of Toronto, Toronto, Canada
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts, United States
| | - Alán Aspuru-Guzik
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Canada
- Department of Computer Science, University of Toronto, Toronto, Canada
- Vector Institute for Artificial Intelligence, Toronto, Canada
- Canadian Institute for Advanced Research (CIFAR) Lebovic Fellow, Toronto, Canada
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4
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Calvin JA, Peng C, Rishi V, Kumar A, Valeev EF. Many-Body Quantum Chemistry on Massively Parallel Computers. Chem Rev 2020; 121:1203-1231. [DOI: 10.1021/acs.chemrev.0c00006] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Affiliation(s)
- Justus A. Calvin
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Chong Peng
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Varun Rishi
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Ashutosh Kumar
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Edward F. Valeev
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
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5
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Kottmann JS, Bischoff FA, Valeev EF. Direct determination of optimal pair-natural orbitals in a real-space representation: The second-order Moller–Plesset energy. J Chem Phys 2020; 152:074105. [DOI: 10.1063/1.5141880] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Jakob S. Kottmann
- Institut für Chemie, Humboldt-Universität zu Berlin, Brook-Taylor-Str. 2, 12489 Berlin-Adlershof, Germany
| | - Florian A. Bischoff
- Institut für Chemie, Humboldt-Universität zu Berlin, Brook-Taylor-Str. 2, 12489 Berlin-Adlershof, Germany
| | - Edward F. Valeev
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, USA
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6
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Kunitsa AA, Hirata S. Grid-based diffusion Monte Carlo for fermions without the fixed-node approximation. Phys Rev E 2020; 101:013311. [PMID: 32069646 DOI: 10.1103/physreve.101.013311] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/04/2019] [Indexed: 06/10/2023]
Abstract
A diffusion Monte Carlo algorithm is introduced that can determine the correct nodal structure of the wave function of a few-fermion system and its ground-state energy without an uncontrolled bias. This is achieved by confining signed random walkers to the points of a uniform infinite spatial grid, allowing them to meet and annihilate one another to establish the nodal structure without the fixed-node approximation. An imaginary-time propagator is derived rigorously from a discretized Hamiltonian, governing a non-Gaussian, sign-flipping, branching, and mutually annihilating random walk of particles. The accuracy of the resulting stochastic representations of a fermion wave function is limited only by the grid and imaginary-time resolutions and can be improved in a controlled manner. The method is tested for a series of model problems including fermions in a harmonic trap as well as the He atom in its singlet or triplet ground state. For the latter case, the energies approach from above with increasing grid resolution and converge within 0.015E_{h} of the exact basis-set-limit value for the grid spacing of 0.08 a.u. with a statistical uncertainty of 10^{-5}E_{h} without an importance sampling or Jastrow factor.
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Affiliation(s)
- Alexander A Kunitsa
- Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - So Hirata
- Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
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7
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Ratcliff LE, Thornton WS, Mayagoitia ÁV, Romero NA. Combining Pseudopotential and All Electron Density Functional Theory for the Efficient Calculation of Core Spectra Using a Multiresolution Approach. J Phys Chem A 2019; 123:4465-4474. [PMID: 31063395 DOI: 10.1021/acs.jpca.8b11310] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Broadly speaking, the calculation of core spectra such as electron energy loss spectra (EELS) at the level of density functional theory (DFT) usually relies on one of two approaches: conceptually more complex but computationally efficient projector augmented wave based approaches or more straightforward but computationally more intensive all electron (AE) based approaches. In this work we present an alternative method, which aims to find a middle ground between the two. Specifically, we have implemented an approach in the multiwavelet madness molecular DFT code that permits a combination of atoms treated at the AE and pseudopotential (PSP) level. Atoms for which one wishes to calculate the core edges are thus treated at an AE level, while the remainder can be treated at the PSP level. This is made possible thanks to the multiresolution approach of madness, which permits accurate and efficient calculations at both the AE and PSP level. Through examples of a small molecule and a carbon nanotube, we demonstrate the potential applications of our approach.
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Affiliation(s)
- Laura E Ratcliff
- Department of Materials , Imperial College London , London SW7 2AZ , U.K.,Argonne Leadership Computing Facility , Argonne National Laboratory , Illinois 60439 , United States
| | - W Scott Thornton
- Stony Brook University , Stony Brook , New York 11794 , United States
| | - Álvaro Vázquez Mayagoitia
- Argonne Leadership Computing Facility , Argonne National Laboratory , Illinois 60439 , United States.,Computational Science Division , Argonne National Laboratory , Illinois 60439 , United States
| | - Nichols A Romero
- Argonne Leadership Computing Facility , Argonne National Laboratory , Illinois 60439 , United States.,Computational Science Division , Argonne National Laboratory , Illinois 60439 , United States
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8
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Bischoff FA. Computing accurate molecular properties in real space using multiresolution analysis. ADVANCES IN QUANTUM CHEMISTRY 2019. [DOI: 10.1016/bs.aiq.2019.04.003] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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9
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Clement MC, Zhang J, Lewis CA, Yang C, Valeev EF. Optimized Pair Natural Orbitals for the Coupled Cluster Methods. J Chem Theory Comput 2018; 14:4581-4589. [PMID: 30068085 DOI: 10.1021/acs.jctc.8b00294] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We present the coupled-cluster singles and doubles method formulated in terms of truncated pair natural orbitals (PNO) that are optimized to minimize the effect of truncation. Compared to the standard ground-state PNO coupled-cluster approaches, in which truncated PNOs derived from first-order Møller-Plesset (MP1) amplitudes are used to compress the CC wave operator, the iteratively optimized PNOs ("iPNOs") offer moderate improvement for small PNO ranks but rapidly increase their effectiveness for large PNO ranks. The error introduced by PNO truncation in the CCSD energy is reduced by orders of magnitude in the asymptotic regime, with an insignificant increase in PNO ranks. The effect of PNO optimization is particularly effective when combined with Neese's perturbative correction for the PNO incompleteness of the CCSD energy. The use of the perturbative correction in combination with the PNO optimization procedure seems to produce the most precise approximation to the canonical CCSD energies for small and large PNO ranks. For the standard benchmark set of noncovalent binding energies, remarkable improvements with respect to the standard PNO approach range from a factor of 3 with PNO truncation threshold τPNO = 10-6 (with the maximum PNO truncation error in the binding energy of only 0.1 kcal/mol) to more than 2 orders of magnitude with τPNO = 10-9.
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Affiliation(s)
- Marjory C Clement
- Department of Chemistry , Virginia Tech , Blacksburg , Virginia 24061 , United States
| | - Jinmei Zhang
- Computational Research Division , Lawrence Berkeley National Laboratory , Berkeley , California 94720 , United States
| | - Cannada A Lewis
- Department of Chemistry , Virginia Tech , Blacksburg , Virginia 24061 , United States
| | - Chao Yang
- Computational Research Division , Lawrence Berkeley National Laboratory , Berkeley , California 94720 , United States
| | - Edward F Valeev
- Department of Chemistry , Virginia Tech , Blacksburg , Virginia 24061 , United States
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10
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Herbst MF, Dreuw A, Avery JE. Toward quantum-chemical method development for arbitrary basis functions. J Chem Phys 2018; 149:084106. [DOI: 10.1063/1.5044765] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022] Open
Affiliation(s)
- Michael F. Herbst
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
| | - Andreas Dreuw
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
| | - James Emil Avery
- Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, 2100 København, Denmark
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11
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Mardirossian N, McClain JD, Chan GKL. Lowering of the complexity of quantum chemistry methods by choice of representation. J Chem Phys 2018; 148:044106. [PMID: 29390857 DOI: 10.1063/1.5007779] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The complexity of the standard hierarchy of quantum chemistry methods is not invariant to the choice of representation. This work explores how the scaling of common quantum chemistry methods can be reduced using real-space, momentum-space, and time-dependent intermediate representations without introducing approximations. We find the scalings of exact Gaussian basis Hartree-Fock theory, second-order Møller-Plesset perturbation theory, and coupled cluster theory (specifically, linearized coupled cluster doubles and the distinguishable cluster approximation with doubles) to be O(N3), O(N3), and O(N5), respectively, where N denotes the system size. These scalings are not asymptotic and hold over all ranges of N.
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Affiliation(s)
- Narbe Mardirossian
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - James D McClain
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Garnet Kin-Lic Chan
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
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12
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Jensen SR, Flå T, Jonsson D, Monstad RS, Ruud K, Frediani L. Magnetic properties with multiwavelets and DFT: the complete basis set limit achieved. Phys Chem Chem Phys 2018; 18:21145-61. [PMID: 27087397 DOI: 10.1039/c6cp01294a] [Citation(s) in RCA: 31] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022]
Abstract
Multiwavelets are emerging as an attractive alternative to traditional basis sets such as Gaussian-type orbitals and plane waves. One of their distinctive properties is the ability to reach the basis set limit (often a chimera for traditional approaches) reliably and consistently by fixing the desired precision ε. We present our multiwavelet implementation of the linear response formalism, applied to static magnetic properties, at the self-consistent field level of theory (both for Hartree-Fock and density functional theories). We demonstrate that the multiwavelets consistently improve the accuracy of the results when increasing the desired precision, yielding results that have four to five digits precision, thus providing a very useful benchmark which could otherwise only be estimated by extrapolation methods. Our results show that magnetizabilities obtained with the augmented quadruple-ζ basis (aug-cc-pCVQZ) are practically at the basis set limit, whereas absolute nuclear magnetic resonance shielding tensors are more challenging: even by making use of a standard extrapolation method, the accuracy is not substantially improved. In contrast, our results provide a benchmark that: (1) confirms the validity of the extrapolation ansatz; (2) can be used as a reference to achieve a property-specific extrapolation scheme, thus providing a means to obtain much better extrapolated results; (3) allows us to separate functional-specific errors from basis-set ones and thus to assess the level of cancellation between basis set and functional errors often exploited in density functional theory.
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Affiliation(s)
- Stig Rune Jensen
- Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Tromsø - The Arctic University of Norway, N-9037 Tromsø, Norway.
| | - Tor Flå
- Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Tromsø - The Arctic University of Norway, N-9037 Tromsø, Norway. and Department of Mathematics and Statistics, University of Tromsø - The Arctic University of Norway, N-9037 Tromsø, Norway
| | - Dan Jonsson
- High-Performance Computing Group, University of Tromsø - The Arctic University of Norway, N-9037 Tromsø, Norway
| | - Rune Sørland Monstad
- Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Tromsø - The Arctic University of Norway, N-9037 Tromsø, Norway.
| | - Kenneth Ruud
- Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Tromsø - The Arctic University of Norway, N-9037 Tromsø, Norway.
| | - Luca Frediani
- Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Tromsø - The Arctic University of Norway, N-9037 Tromsø, Norway.
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13
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Madsen NK, Godtliebsen IH, Losilla SA, Christiansen O. Tensor-decomposed vibrational coupled-cluster theory: Enabling large-scale, highly accurate vibrational-structure calculations. J Chem Phys 2018; 148:024103. [DOI: 10.1063/1.5001569] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
| | | | | | - Ove Christiansen
- Department of Chemistry, Aarhus University, 8000 Aarhus C, Denmark
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14
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Kottmann JS, Bischoff FA. Coupled-Cluster in Real Space. 1. CC2 Ground State Energies Using Multiresolution Analysis. J Chem Theory Comput 2017; 13:5945-5955. [PMID: 28902997 DOI: 10.1021/acs.jctc.7b00694] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
A framework to calculate CC2 approximated coupled-cluster ground state correlation energies in a multiresolution basis is derived and implemented into the MADNESS library. The CC2 working equations are formulated in first quantization which makes them suitable for real-space methods. The first quantized equations can be interpreted diagrammatically using the usual diagrams from second quantization with adjusted interpretation rules. Singularities arising from the nuclear and electronic potentials are regularized by explicitly taking the nuclear and electronic cusps into account. The regularized three- and six-dimensional cluster functions are represented directly on an adaptive grid. The resulting equations are free of singularities and virtual orbitals, which results in a low intrinsic scaling. Correlation energies close to the basis set limit are computed for small molecules. This work is the first step toward CC2 excitation energies in a multiresolution basis.
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Affiliation(s)
- Jakob S Kottmann
- Institut für Chemie, Humboldt-Universität zu Berlin , Unter den Linden 6, D-10099 Berlin, Germany
| | - Florian A Bischoff
- Institut für Chemie, Humboldt-Universität zu Berlin , Unter den Linden 6, D-10099 Berlin, Germany
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15
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Kottmann JS, Bischoff FA. Coupled-Cluster in Real Space. 2. CC2 Excited States Using Multiresolution Analysis. J Chem Theory Comput 2017; 13:5956-5965. [DOI: 10.1021/acs.jctc.7b00695] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Jakob S. Kottmann
- Institut für Chemie, Humboldt-Universität zu Berlin, Unter den Linden 6, D-10099 Berlin, Germany
| | - Florian A. Bischoff
- Institut für Chemie, Humboldt-Universität zu Berlin, Unter den Linden 6, D-10099 Berlin, Germany
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16
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Madsen NK, Godtliebsen IH, Christiansen O. Efficient algorithms for solving the non-linear vibrational coupled-cluster equations using full and decomposed tensors. J Chem Phys 2017; 146:134110. [DOI: 10.1063/1.4979498] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Niels K. Madsen
- Department of Chemistry, Aarhus University, 8000 Aarhus C, Denmark
| | | | - Ove Christiansen
- Department of Chemistry, Aarhus University, 8000 Aarhus C, Denmark
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17
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Bischoff FA. Analytic second nuclear derivatives of Hartree-Fock and DFT using multi-resolution analysis. J Chem Phys 2017; 146:124126. [PMID: 28388127 DOI: 10.1063/1.4978957] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022] Open
Abstract
We present the formalism, implementation, and numerical results for the computation of second derivatives with respect to nuclear displacements of molecules in the formalism of multi-resolution analysis. The highly singular nuclear potentials are partially regularized to improve the numerical stability. Vibrational frequencies are well reproduced to within an RMS of a few cm-1 compared to large basis set LCAO (linear combination of atomic orbitals) calculations. Intermolecular modes, hindered rotations, and heavy atoms may lead to loss of precision. Tight precision thresholds are therefore necessary to converge to numerically stable results.
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Affiliation(s)
- Florian A Bischoff
- Institut für Chemie, Humboldt-Universität zu Berlin, Unter den Linden 6, D-10099 Berlin, Germany
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18
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Johnson CM, Doran AE, Zhang J, Valeev EF, Hirata S. Monte Carlo explicitly correlated second-order many-body perturbation theory. J Chem Phys 2016; 145:154115. [DOI: 10.1063/1.4964854] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Cole M. Johnson
- Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - Alexander E. Doran
- Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - Jinmei Zhang
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, USA
| | - Edward F. Valeev
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, USA
| | - So Hirata
- Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
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19
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Hirata S, Shiozaki T, Johnson CM, Talman JD. Numerical solution of the Sinanoǧlu equation using a multicentre radial-angular grid. Mol Phys 2016. [DOI: 10.1080/00268976.2016.1199822] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
Affiliation(s)
- So Hirata
- Department of Chemistry, University of Illinois at Urbana-Champaign , Urbana, IL, USA
| | - Toru Shiozaki
- Department of Chemistry, Northwestern University , Evanston, IL, USA
| | - Cole M. Johnson
- Department of Chemistry, University of Illinois at Urbana-Champaign , Urbana, IL, USA
| | - James D. Talman
- Department of Applied Mathematics, University of Western Ontario , London, Canada
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20
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Khoromskaia V, Khoromskij BN. Tensor numerical methods in quantum chemistry: from Hartree–Fock to excitation energies. Phys Chem Chem Phys 2015; 17:31491-509. [DOI: 10.1039/c5cp01215e] [Citation(s) in RCA: 41] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
Abstract
We resume the recent successes of the grid-based tensor numerical methods and discuss their prospects in real-space electronic structure calculations.
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Affiliation(s)
- Venera Khoromskaia
- Max-Planck-Institute for Dynamics of Complex Systems
- Magdeburg
- Germany
- Max-Planck Institute for Mathematics in the Sciences
- Leipzig
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21
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Yanai T, Fann GI, Beylkin G, Harrison RJ. Multiresolution quantum chemistry in multiwavelet bases: excited states from time-dependent Hartree–Fock and density functional theory via linear response. Phys Chem Chem Phys 2015; 17:31405-16. [DOI: 10.1039/c4cp05821f] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
A fully numerical method for the time-dependent Hartree–Fock and density functional theory (TD-HF/DFT) with the Tamm–Dancoff (TD) approximation is presented in a multiresolution analysis (MRA) approach.
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Affiliation(s)
- Takeshi Yanai
- Department of Theoretical and Computational Molecular Science
- Institute for Molecular Science
- Okazaki
- Japan
| | - George I. Fann
- Computer Science and Mathematics Division
- Oak Ridge National Laboratory
- Oak Ridge
- USA
| | - Gregory Beylkin
- Department of Applied Mathematics
- University of Colorado at Boulder
- Boulder
- USA
| | - Robert J. Harrison
- Institute for Advanced Computational Science
- Stony Brook University
- Stony Brook
- USA
- Computational Science Center
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22
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Toivanen EA, Losilla SA, Sundholm D. The grid-based fast multipole method – a massively parallel numerical scheme for calculating two-electron interaction energies. Phys Chem Chem Phys 2015; 17:31480-90. [DOI: 10.1039/c5cp01173f] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
A grid-based fast multipole method has been developed for calculating two-electron interaction energies for non-overlapping charge densities.
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Affiliation(s)
| | | | - Dage Sundholm
- Department of Chemistry
- University of Helsinki
- Finland
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23
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Frediani L, Sundholm D. Real-space numerical grid methods in quantum chemistry. Phys Chem Chem Phys 2015; 17:31357-9. [DOI: 10.1039/c5cp90198g] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Abstract
This themed issue reports on recent progress in the fast developing field of real-space numerical grid methods in quantum chemistry.
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Affiliation(s)
- Luca Frediani
- Centre for Theoretical and Computational Chemistry
- Department of Chemistry
- UiT The Arctic University of Norway
- N-9037 Tromsø
- Norway
| | - Dage Sundholm
- Department of Chemistry
- University of Helsinki
- Finland
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24
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Bischoff FA. Regularizing the molecular potential in electronic structure calculations. I. SCF methods. J Chem Phys 2014; 141:184105. [DOI: 10.1063/1.4901021] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022] Open
Affiliation(s)
- Florian A. Bischoff
- Institut für Chemie, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany
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25
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Bischoff FA. Regularizing the molecular potential in electronic structure calculations. II. Many-body methods. J Chem Phys 2014; 141:184106. [DOI: 10.1063/1.4901022] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022] Open
Affiliation(s)
- Florian A. Bischoff
- Institut für Chemie, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany
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26
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Abstract
A method is suggested to build simple multiconfigurational wave functions specified uniquely by an energy cutoff Λ. These are constructed from a model space containing determinants with energy relative to that of the most stable determinant no greater than Λ. The resulting Λ-CI wave function is adaptive, being able to represent both single-reference and multireference electronic states. We also consider a more compact wave function parameterization (Λ+SD-CI), which is based on a small Λ-CI reference and adds a selection of all the singly and doubly excited determinants generated from it. We report two heuristic algorithms to build Λ-CI wave functions. The first is based on an approximate prescreening of the full configuration interaction space, while the second performs a breadth-first search coupled with pruning. The Λ-CI and Λ+SD-CI approaches are used to compute the dissociation curve of N2 and the potential energy curves for the first three singlet states of C2. Special attention is paid to the issue of energy discontinuities caused by changes in the size of the Λ-CI wave function along the potential energy curve. This problem is shown to be solvable by smoothing the matrix elements of the Hamiltonian. Our last example, involving the Cu2O2(2+) core, illustrates an alternative use of the Λ-CI method: as a tool to both estimate the multireference character of a wave function and to create a compact model space to be used in subsequent high-level multireference coupled cluster computations.
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Affiliation(s)
- Francesco A Evangelista
- Department of Chemistry and Cherry L. Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, USA
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27
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Leclerc A, Carrington T. Calculating vibrational spectra with sum of product basis functions without storing full-dimensional vectors or matrices. J Chem Phys 2014; 140:174111. [DOI: 10.1063/1.4871981] [Citation(s) in RCA: 65] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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28
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Quantum Chemistry Methods with Multiwavelet Bases on Massive Parallel Computers. ACTA ACUST UNITED AC 2014. [DOI: 10.1016/b978-0-444-63378-1.00001-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register]
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29
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Bischoff FA, Valeev EF. Computing molecular correlation energies with guaranteed precision. J Chem Phys 2013; 139:114106. [DOI: 10.1063/1.4820404] [Citation(s) in RCA: 28] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
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