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Scemama A, Savin A. Long-Range Configuration Interaction with an Ab Initio Short-Range Correction and an Asymptotic Lower Bound†. J Phys Chem A 2024; 128:6316-6323. [PMID: 39020462 DOI: 10.1021/acs.jpca.4c02837] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/19/2024]
Abstract
Short-range corrections to long-range selected configuration interaction calculations are derived from perturbation theory considerations and applied to harmonium (with two to six electrons for some low-lying states). No fitting to reference data is used, and the method is applicable to ground and excited states. The formulas derived are rigorous when the physical interaction is approached. In this regime, the second-order expression provides a lower bound to the long-range full configuration interaction energy. A long-range/short-range separation of the interaction between electrons at a distance of the order of one atomic unit provides total energies within chemical accuracy, and, for the systems studied, provide better results than short-range density functional approximations.
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Affiliation(s)
- Anthony Scemama
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, 31062 Toulouse, France
| | - Andreas Savin
- Laboratoire de Chimie Théorique, CNRS and Sorbonne University, 4 place Jussieu, 75252 Paris, France
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Scemama A, Savin A. Modified Expression for the Hamiltonian Expectation Value Exploiting the Short-Range Behavior of the Wave Function. J Phys Chem A 2024; 128:4923-4935. [PMID: 38848465 DOI: 10.1021/acs.jpca.4c01888] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/09/2024]
Abstract
The expectation value of the Hamiltonian using a model wave function is widely used to estimate the eigenvalues of electronic Hamiltonians. We explore here a modified formula for models based on a long-range interaction. It scales differently the singlet and triplet components of the repulsion between electrons not present in the model (its short-range part). The scaling factors depend uniquely on the parameter used in defining the model interaction and are constructed using only exact properties. We show results for the ground states and low-lying excited states of Harmonium with two to six electrons. We obtain important improvements for the estimation of the exact energy, not only over the model energy but also over the expectation value of the Hamiltonian.
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Affiliation(s)
- Anthony Scemama
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, 31062, Toulouse, France
| | - Andreas Savin
- Laboratoire de Chimie Théorique, CNRS and Sorbonne University 4 place Jussieu, 75252 Paris, France
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Hou L, Irons TJP, Wang Y, Furness JW, Wibowo-Teale AM, Sun J. Capturing the electron-electron cusp with the coupling-constant averaged exchange-correlation hole: A case study for Hooke's atoms. J Chem Phys 2024; 160:014103. [PMID: 38180252 DOI: 10.1063/5.0173370] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/21/2023] [Accepted: 11/15/2023] [Indexed: 01/06/2024] Open
Abstract
In density-functional theory, the exchange-correlation (XC) energy can be defined exactly through the coupling-constant (λ) averaged XC hole n̄xc(r,r'), representing the probability depletion of finding an electron at r' due to an electron at r. Accurate knowledge of n̄xc(r,r') has been crucial for developing XC energy density-functional approximations and understanding their performance for molecules and materials. However, there are very few systems for which accurate XC holes have been calculated since this requires evaluating the one- and two-particle reduced density matrices for a reference wave function over a range of λ while the electron density remains fixed at the physical (λ = 1) density. Although the coupled-cluster singles and doubles (CCSD) method can yield exact results for a two-electron system in the complete basis set limit, it cannot capture the electron-electron cusp using finite basis sets. Focusing on Hooke's atom as a two-electron model system for which certain analytic solutions are known, we examine the effect of this cusp error on the XC hole calculated using CCSD. The Lieb functional is calculated at a range of coupling constants to determine the λ-integrated XC hole. Our results indicate that, for Hooke's atoms, the error introduced by the description of the electron-electron cusp using Gaussian basis sets at the CCSD level is negligible compared to the basis set incompleteness error. The system-, angle-, and coupling-constant-averaged XC holes are also calculated and provide a benchmark against which the Perdew-Burke-Ernzerhof and local density approximation XC hole models are assessed.
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Affiliation(s)
- Lin Hou
- Department of Physics and Engineering Physics, Tulane University, New Orleans, Louisiana 70118, USA
| | - Tom J P Irons
- School of Chemistry, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
| | - Yanyong Wang
- Department of Physics and Engineering Physics, Tulane University, New Orleans, Louisiana 70118, USA
| | - James W Furness
- Department of Physics and Engineering Physics, Tulane University, New Orleans, Louisiana 70118, USA
| | - Andrew M Wibowo-Teale
- School of Chemistry, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033, N-0315 Oslo, Norway
| | - Jianwei Sun
- Department of Physics and Engineering Physics, Tulane University, New Orleans, Louisiana 70118, USA
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Pašteka LF, Helgaker T, Saue T, Sundholm D, Werner HJ, Hasanbulli M, Major J, Schwerdtfeger P. Atoms and molecules in soft confinement potentials. Mol Phys 2020. [DOI: 10.1080/00268976.2020.1730989] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Affiliation(s)
- L. F. Pašteka
- Centre for Advanced Study (CAS) at the Norwegian Academy of Science and Letters, Oslo, Norway
- Department of Physical and Theoretical Chemistry & Laboratory for Advanced Materials, Faculty of Natural Sciences, Comenius University, Bratislava, Slovakia
| | - T. Helgaker
- Centre for Advanced Study (CAS) at the Norwegian Academy of Science and Letters, Oslo, Norway
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, Oslo, Norway
| | - T. Saue
- Centre for Advanced Study (CAS) at the Norwegian Academy of Science and Letters, Oslo, Norway
- Laboratoire de Chimie et Physique Quantiques, UMR 5626 CNRS – Universitè Toulouse III (Paul Sabatier), Toulouse Cedex 09, France
| | - D. Sundholm
- Centre for Advanced Study (CAS) at the Norwegian Academy of Science and Letters, Oslo, Norway
- Department of Chemistry, University of Helsinki, Helsinki, Finland
| | - H.-J. Werner
- Centre for Advanced Study (CAS) at the Norwegian Academy of Science and Letters, Oslo, Norway
- Institute for Theoretical Chemistry, University of Stuttgart, Stuttgart, Germany
| | - M. Hasanbulli
- Centre for Theoretical Chemistry and Physics, The New Zealand Institute for Advanced Study, Massey University Auckland, Auckland, New Zealand
| | - J. Major
- Centre for Theoretical Chemistry and Physics, The New Zealand Institute for Advanced Study, Massey University Auckland, Auckland, New Zealand
| | - P. Schwerdtfeger
- Centre for Advanced Study (CAS) at the Norwegian Academy of Science and Letters, Oslo, Norway
- Centre for Theoretical Chemistry and Physics, The New Zealand Institute for Advanced Study, Massey University Auckland, Auckland, New Zealand
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Cioslowski J. One-Electron Reduced Density Matrix Functional Theory of Spin-Polarized Systems. J Chem Theory Comput 2020; 16:1578-1585. [DOI: 10.1021/acs.jctc.9b01155] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Jerzy Cioslowski
- Institute of Physics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland
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Cioslowski J, Mihálka ZÉ, Szabados Á. Bilinear Constraints upon the Correlation Contribution to the Electron-Electron Repulsion Energy as a Functional of the One-Electron Reduced Density Matrix. J Chem Theory Comput 2019; 15:4862-4872. [PMID: 31294976 DOI: 10.1021/acs.jctc.9b00443] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Perturbative analysis of the functional U[n, ψ] that yields the correlation component U of the electron-electron repulsion energy in terms of the vectors ψ(1) and n of the natural spinorbitals and their occupation numbers (the 1-matrix functional) facilitates examination of the flaws inherent to the present implementations of the density matrix functional theory. Recognizing that the practical usefulness of any approximate 1-matrix functional hinges upon its capability of exactly reproducing the leading contribution to U at the limit of vanishing electron-electron interactions gives rise to asymptotic bilinear constraints for the (exact or model) 2-cumulant G2 that enters the expression for U. The asymptotic behavior of certain blocks of G2 is found to be equally important. These identities, which are obtained for both the single-determinantal and a model multideterminantal cases, take precedence over the linear constraints commonly enforced in the course of approximate construction of such functionals. This observation reveals the futility of designing sophisticated approximations tailored for the second-order contribution to G2 while neglecting proper formulation of the respective first-order contribution that in the case of the so-called JKL-only functionals requires abandoning the JK-dependence altogether. It has its repercussions not only for the functionals of the PNOF family but also for the expressions involving only the L-type two-electron repulsion integrals (in the guise of their exchange counterparts) that account only for the correlation effects due to electrons with antiparallel spins and are well-defined only for spin-unpolarized and high-spin systems (yielding vanishing U for the latter).
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Affiliation(s)
- Jerzy Cioslowski
- Institute of Physics , University of Szczecin , Wielkopolska 15 , 70-451 Szczecin , Poland
| | - Zsuzsanna É Mihálka
- Laboratory of Theoretical Chemistry, Institute of Chemistry, Faculty of Science , ELTE Eötvös Loránd University , POB 32, H-1518 Budapest , Hungary.,Hevesy György Ph.D. School of Chemistry, Faculty of Science , ELTE Eötvös Loránd University , POB 32, H-1518 Budapest , Hungary
| | - Ágnes Szabados
- Laboratory of Theoretical Chemistry, Institute of Chemistry, Faculty of Science , ELTE Eötvös Loránd University , POB 32, H-1518 Budapest , Hungary
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