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Faulstich FM, Kristiansen HE, Csirik MA, Kvaal S, Pedersen TB, Laestadius A. S-Diagnostic─An a Posteriori Error Assessment for Single-Reference Coupled-Cluster Methods. J Phys Chem A 2023; 127:9106-9120. [PMID: 37874274 DOI: 10.1021/acs.jpca.3c01575] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2023]
Abstract
We propose a novel a posteriori error assessment for the single-reference coupled-cluster (SRCC) method called the S-diagnostic. We provide a derivation of the S-diagnostic that is rooted in the mathematical analysis of different SRCC variants. We numerically scrutinized the S-diagnostic, testing its performance for (1) geometry optimizations, (2) electronic correlation simulations of systems with varying numerical difficulty, and (3) the square-planar copper complexes [CuCl4]2-, [Cu(NH3)4]2+, and [Cu(H2O)4]2+. Throughout the numerical investigations, the S-diagnostic is compared to other SRCC diagnostic procedures, that is, the T1, D1, max T2, and D2 diagnostics as well as different indices of multideterminantal and multireference character in coupled-cluster theory. Our numerical investigations show that the S-diagnostic outperforms the T1, D1, max T2 and D2 diagnostics and is comparable to the indices of multideterminantal and multireference character in coupled-cluster theory in their individual fields of applicability. The experiments investigating the performance of the S-diagnostic for geometry optimizations using SRCC reveal that the S-diagnostic correlates well with different error measures at a high level of statistical relevance. The experiments investigating the performance of the S-diagnostic for electronic correlation simulations show that the S-diagnostic correctly predicts strong multireference regimes. The S-diagnostic, moreover, correctly detects the successful SRCC computations for [CuCl4]2-, [Cu(NH3)4]2+, and [Cu(H2O)4]2+, which have been known to be misdiagnosed by T1 and D1 diagnostics in the past. This shows that the S-diagnostic is a promising candidate for an a posteriori diagnostic for SRCC calculations.
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Affiliation(s)
- Fabian M Faulstich
- Department of Mathematics, Rensselaer Polytechnic Institute, Troy, New York 12180, United States
| | - Håkon E Kristiansen
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, Oslo 0315, Norway
| | - Mihaly A Csirik
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, Oslo 0315, Norway
- Department of Computer Science, Oslo Metropolitan University, Oslo 0130, Norway
| | - Simen Kvaal
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, Oslo 0315, Norway
| | - Thomas Bondo Pedersen
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, Oslo 0315, Norway
| | - Andre Laestadius
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, Oslo 0315, Norway
- Department of Computer Science, Oslo Metropolitan University, Oslo 0130, Norway
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Deeth RJ. Ligand Field Theory for Linear ML
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Complexes. Eur J Inorg Chem 2021. [DOI: 10.1002/ejic.202100936] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Affiliation(s)
- Robert J. Deeth
- Department of Chemistry University of Warwick CV4 7AL Coventry UK
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3
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Giner E, Tew DP, Garniron Y, Alavi A. Interplay between Electronic Correlation and Metal–Ligand Delocalization in the Spectroscopy of Transition Metal Compounds: Case Study on a Series of Planar Cu2+ Complexes. J Chem Theory Comput 2018; 14:6240-6252. [DOI: 10.1021/acs.jctc.8b00591] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Emmanuel Giner
- Laboratoire de Chimie théorique, Sorbonne Universit, UMR 7616, 4 place Jussieu, 75252 Paris, France
| | - David P. Tew
- Max Planck Institute for Solid State Research, Heisenbergstraβe 1, 70569 Stuttgart, Germany
| | - Yann Garniron
- Laboratoire de Chimie et Physique Quantique, UMR 5626, Universit Paul Sabatier, 118 route de Narbonne 31062 Toulouse, France
| | - Ali Alavi
- Max Planck Institute for Solid State Research, Heisenbergstraβe 1, 70569 Stuttgart, Germany
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4
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Lyle J, Chandramoulee SR, Hamilton JR, Traylor BA, Guasco TL, Jagau TC, Mabbs R. Characterization of the vibrational properties of copper difluoride anion and neutral ground states via direct and indirect photodetachment spectroscopy. J Chem Phys 2018; 149:084302. [DOI: 10.1063/1.5040122] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022] Open
Affiliation(s)
- Justin Lyle
- Chemistry Department, Washington University in St. Louis, St. Louis, Missouri 63130, USA
| | | | - Jacob R. Hamilton
- Chemistry Department, Millikin University, Decatur, Illinois 62522, USA
| | - Blaine A. Traylor
- Chemistry Department, Millikin University, Decatur, Illinois 62522, USA
| | - Timothy L. Guasco
- Chemistry Department, Millikin University, Decatur, Illinois 62522, USA
| | - Thomas-C. Jagau
- Department Chemie, University of Munich (LMU), D-81377 Munich, Germany
| | - Richard Mabbs
- Chemistry Department, Washington University in St. Louis, St. Louis, Missouri 63130, USA
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Giner E, Angeli C. Spin density and orbital optimization in open shell systems: A rational and computationally efficient proposal. J Chem Phys 2016; 144:104104. [DOI: 10.1063/1.4943187] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022] Open
Affiliation(s)
- Emmanuel Giner
- Dipartimento di Scienze Chimiche e Famaceutiche, Universita di Ferrara, Via Fossato di Mortara 17, I-44121 Ferrara, Italy
| | - Celestino Angeli
- Dipartimento di Scienze Chimiche e Famaceutiche, Universita di Ferrara, Via Fossato di Mortara 17, I-44121 Ferrara, Italy
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Giner E, Angeli C. Metal-ligand delocalization and spin density in the CuCl2 and [CuCl4]2− molecules: Some insights from wave function theory. J Chem Phys 2015; 143:124305. [DOI: 10.1063/1.4931639] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Emmanuel Giner
- Dipartimento di Scienze Chimiche e Famaceutiche, Universita di Ferrara, Via Fossato di Mortara 17, I-44121 Ferrara, Italy
| | - Celestino Angeli
- Dipartimento di Scienze Chimiche e Famaceutiche, Universita di Ferrara, Via Fossato di Mortara 17, I-44121 Ferrara, Italy
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Caffarel M, Giner E, Scemama A, Ramírez-Solís A. Spin Density Distribution in Open-Shell Transition Metal Systems: A Comparative Post-Hartree–Fock, Density Functional Theory, and Quantum Monte Carlo Study of the CuCl2 Molecule. J Chem Theory Comput 2014; 10:5286-96. [DOI: 10.1021/ct5004252] [Citation(s) in RCA: 37] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Michel Caffarel
- CNRS-Laboratoire de Chimie
et Physique Quantiques, IRSAMC, Université Paul Sabatier, 118 Route
de Narbonne, 31062 Toulouse Cedex, France
| | - Emmanuel Giner
- CNRS-Laboratoire de Chimie
et Physique Quantiques, IRSAMC, Université Paul Sabatier, 118 Route
de Narbonne, 31062 Toulouse Cedex, France
| | - Anthony Scemama
- CNRS-Laboratoire de Chimie
et Physique Quantiques, IRSAMC, Université Paul Sabatier, 118 Route
de Narbonne, 31062 Toulouse Cedex, France
| | - Alejandro Ramírez-Solís
- CNRS-Laboratoire de Chimie
et Physique Quantiques, IRSAMC, Université Paul Sabatier, 118 Route
de Narbonne, 31062 Toulouse Cedex, France
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8
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Atsumi M, Lindh R, González L, Gourlaouen C, Daniel C. Ab initio and DFT analysis of the low-lying electronic states of metal dihalides: quantum chemical calculations on the neutral BrMCl (M = Cu, Ag, Au). Phys Chem Chem Phys 2013; 15:10151-7. [DOI: 10.1039/c3cp51150b] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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9
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Zou W, Boggs JE. Theoretical study of the electronic states of CuCl2. J Chem Phys 2009; 130:154313. [DOI: 10.1063/1.3103252] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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11
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Zou W, Bersuker IB, Boggs JE. Do non-centro-symmetric linear X-Y-X molecules exist? The case for the (I)Π2u state of CuCl2. J Chem Phys 2008; 129:114107. [DOI: 10.1063/1.2977739] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/13/2023] Open
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12
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DFT tests for group 8 transition metal carbonyl complexes. J Mol Model 2008; 14:171-81. [DOI: 10.1007/s00894-007-0259-7] [Citation(s) in RCA: 42] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/04/2007] [Accepted: 11/29/2007] [Indexed: 10/22/2022]
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Ramírez-Solís A. On the performance of local, semilocal, and nonlocal exchange-correlation functionals on transition metal molecules. J Chem Phys 2007; 126:224105. [PMID: 17581042 DOI: 10.1063/1.2739539] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The lowest singlet-triplet transition (X (1)Sigma+-(3)Sigma+) of AgI has been used to study systematically the performance of local [local density approximation (LDA)], semilocal [generalized gradient approximation (GGA)], and nonlocal (semiempiric hybrid and meta)-type exchange-correlation functionals on a transition metal molecule where dynamic electronic correlation effects are essential. Previous benchmark ab initio calculations showed that the triplet ground state possesses a shallow well in the Franck-Condon region before becoming repulsive at longer internuclear distance [A. Ramirez-Solis, J. Chem. Phys. 118, 104 (2003)]. Several density functional theory (DFT) descriptions are compared with the benchmark complete active space self-consistent-field+averaged coupled pair functional results, using the same relativistic effective core potentials and optimized Gaussian basis sets. A rather unreliable performance of exchange-correlation functionals was found when ascending the various rungs in DFT Jacob's ladder for this complex molecule. While some of the simpler (LDA and GGA) functionals correctly predict the presence of a short-distance maximum for the (3)Sigma+ state, more sophisticated hybrid and meta-functionals lead to totally repulsive or oscillating curves for the ground triplet state. A thorough discussion addressing the local versus nonlocal character of the exchange and correlation effects on the triplet potential curve is presented. The author concludes that any new efforts directed at producing more accurate exchange-correlation functionals must take into account the more complex electronic structure arising in transition metal molecules, whether these efforts follow the dominant pragmatic semiempiric trend or the more philosophically correct nonempiric pathway to develop better exchange-correlation functionals; only then will the Kohn-Sham version of DFT make the necessary improvements to correctly describe the electronic structure of complex transition metal systems.
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Affiliation(s)
- A Ramírez-Solís
- Department of Chemistry and Biochemistry, University of California at Santa Barbara, Santa Barbara, California 93106-9510, USA.
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14
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The Spectroscopy of Copper and Silver Monohalides: What Modern Quantum Chemistry Can and Cannot do. Theor Chem Acc 2006. [DOI: 10.1007/s00214-006-0110-8] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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15
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Ramírez-Solís A, Poteau R, Daudey JP. The electronic spectrum of AgCl2: Ab initio benchmark versus density-functional theory calculations on the lowest ligand-field states including spin-orbit effects. J Chem Phys 2006; 124:034307. [PMID: 16438583 DOI: 10.1063/1.2145879] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The X 2pi(g), 2sigma(g)+, and 2delta(g) states of AgCl2 have been studied through benchmark ab initio complete active space self-consistent field plus second-order complete active space multireference Moller-Plesset algorithm (CASSCF+CASPT2) and complete active space self-consistent field plus averaged coupled pair functional (CASSCF+ACPF) and density-functional theory (DFT) calculations using especially developed basis sets to study the transition energies, geometries, vibrational frequencies, Mulliken charges, and spin densities. The spin-orbit (SO) effects were included through the effective Hamiltonian formalism using the LambdaSSigma ACPF energies as diagonal elements. At the ACPF level, the ground state is 2pi(g) in contradiction with ligand-field theory, SCF, and large CASSCF; the adiabatic excitation energies for the 2sigma(g)+ and 2delta(g) states are 1640 and 18,230 cm(-1), respectively. The inclusion of the SO effects leads to a pure omega = 32(2pi(g)) ground state, a omega = 12 (66%2pi(g) and 34%2sigma(g)+) A state, a omega = 12 (34%2pi(g) and 66%2sigma(g)+) B state, a omega = 52(2delta(g))C state, and a omega = 32(99%2delta(g))D state. The X-A, X-B, X-C, and X-D transition energies are 485, 3715, 17 246, and 20 110 cm(-1), respectively. The B97-2, B3LYP, and PBE0 functionals overestimate by approximately 100% the X 2pi(g)-2sigma(g)+T(e) but provide a qualitative energetic ordering in good agreement with ACPF results. B3LYP with variable exchange leads to a 42% optimal Hartree-Fock exchange for transition energies but all equilibrium geometries get worsened. Asymptotic corrections to B3LYP do not provide improved values. The nature of the bonding in the X 2pi(g) state is very different from that of CuCl2 since the Mulliken charge on the metal is 1.1 while the spin density is only 0.35. DFT strongly delocalizes the spin density providing even smaller values of around 0.18 on Ag not only for the ground state, but also for the 2sigma(g)+ state.
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Affiliation(s)
- A Ramírez-Solís
- Laboratoire de Physique Quantique IRSAMC, UMR 5626 du CNRS, Université Paul Sabatier, 118, Route de Narbonne, 31062 Toulouse Cedex, France.
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Moreira IDPR, Illas F. A unified view of the theoretical description of magnetic coupling in molecular chemistry and solid state physics. Phys Chem Chem Phys 2006; 8:1645-59. [PMID: 16633648 DOI: 10.1039/b515732c] [Citation(s) in RCA: 152] [Impact Index Per Article: 8.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Abstract
The magnetic interactions in organic diradicals, dinuclear inorganic complexes and ionic solids are presented from a unified point of view. Effective Hamiltonian theory is revised to show that, for a given system, it permits the definition of a general, unbiased, spin model Hamiltonian. Mapping procedures are described which in most cases permit one to extract the relevant magnetic coupling constants from ab initio calculations of the energies of the pertinent electronic states. Density functional theory calculations within the broken symmetry approach are critically revised showing the contradictions of this procedure when applied to molecules and solids without the guidelines of the appropriate mapping. These concepts are illustrated by describing the application of state-of-the-art methods of electronic structure calculations to a series of representative molecular and solid state systems.
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Affiliation(s)
- Ibério de P R Moreira
- Departament de Química Física & Centre Especial de Recerca en Química Teòrica, Universitat de Barcelona i Parc Científic de Barcelona, C/ Martí i Franquès 1, E-08028, Barcelona, Spain
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Caffarel M, Daudey JP, Heully JL, Ramírez-Solís A. Towards accurate all-electron quantum Monte Carlo calculations of transition-metal systems: Spectroscopy of the copper atom. J Chem Phys 2005; 123:94102. [PMID: 16164336 DOI: 10.1063/1.2011393] [Citation(s) in RCA: 31] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In this work we present all-electron fixed-node diffusion Monte Carlo (FN-DMC) calculations of the low-lying electronic states of the copper atom and its cation. The states considered are those which are the most relevant for the organometallic chemistry of copper-containing systems, namely, the (2)S, (2)D, and (2)P electronic states of Cu and the (1)S ground state of Cu(+). We systematically compare our FN-DMC results to CCSD(T) calculations using very large atomic-natural-orbital-type all-electron basis sets. The FN-DMC results presented in this work provide, to the best of our knowledge, the most accurate nonrelativistic all-electron correlation energies for the lowest-lying states of copper and its cation. To compare our results to experimental data we include the relativistic contributions for all states through numerical Dirac-Fock calculations, which for copper (Z=29) provide almost the entire relativistic effects. It is found that the fixed-node errors using Hartree-Fock nodes for the lowest transition energies of copper and the first ionization potential of the atom cancel out within statistical fluctuations. The overall accuracy achieved with quantum Monte Carlo for the nonrelativistic correlation energy (statistical fluctuations of about 1600 cm(-1) and near cancelation of fixed-node errors) is good enough to reproduce the experimental spectrum when relativistic effects are included. These results illustrate that, despite the presence of the large statistical fluctuations associated with core electrons, accurate all-electron FN-DMC calculations for transition metals are nowadays feasible using extensive but accessible computer resources.
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Affiliation(s)
- Michel Caffarel
- Laboratoire de Physique Quantique, IRSAMC Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex, France.
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