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Mihálka ZÉ, Szabados Á, Surján PR. Improving half-projected spin-contaminated wave functions by multi-configuration perturbation theory. J Chem Phys 2021; 154:234110. [PMID: 34241248 DOI: 10.1063/5.0053727] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Allowing triplet components of individual geminals, spin-contaminated strongly orthogonal geminal wave functions may emerge, which can be ameliorated by spin-projection techniques. Of the latter, half-projection was previously shown to be useful, offering a compromise between the amount of remaining spin-contamination and the violation of size consistency generated by projection. This paper investigates how a half-projected spin-contaminated geminal wave function can be improved by multi-configuration perturbation theory to incorporate dynamical correlation effects.
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Affiliation(s)
- Zsuzsanna É Mihálka
- Laboratory of Theoretical Chemistry, Institute of Chemistry, Faculty of Science, and George Hevesy Doctoral School of Chemistry, ELTE Eötvös Loránd University, H-1518 Budapest 112, P.O. Box 32, Budapest, Hungary
| | - Ágnes Szabados
- Laboratory of Theoretical Chemistry, Institute of Chemistry, Faculty of Science, ELTE Eötvös Loránd University, H-1518 Budapest 112, P.O. Box 32, Budapest, Hungary
| | - Péter R Surján
- Laboratory of Theoretical Chemistry, Institute of Chemistry, Faculty of Science, ELTE Eötvös Loránd University, H-1518 Budapest 112, P.O. Box 32, Budapest, Hungary
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Manna S, Ray SS, Chattopadhyay S, Chaudhuri RK. A simplified account of the correlation effects to bond breaking processes: The Brillouin-Wigner perturbation theory using a multireference formulation. J Chem Phys 2019. [DOI: 10.1063/1.5097657] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Shovan Manna
- Department of Chemistry, Indian Institute of Engineering Science and Technology, Shibpur, Howrah 711103, India
| | - Suvonil Sinha Ray
- Department of Chemistry, University of Calcutta, Kolkata 700009, India
| | - Sudip Chattopadhyay
- Department of Chemistry, Indian Institute of Engineering Science and Technology, Shibpur, Howrah 711103, India
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Banerjee D, Ghosh A, Chattopadhyay S, Ghosh P, Chaudhuri RK. Revisiting the ‘cis-effect’ in 1,2-difluoro derivatives of ethylene and diazene usingab initiomultireference methods. Mol Phys 2014. [DOI: 10.1080/00268976.2014.938710] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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4
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Search of truncation of ( N−1) electron basis containing full connected triple excitations in computing main and satellite ionization potentials via Fock-space coupled cluster approach. J Comput Chem 2013; 34:1291-310. [DOI: 10.1002/jcc.23255] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/27/2012] [Revised: 12/17/2012] [Accepted: 01/21/2013] [Indexed: 01/23/2023]
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Zoboki T, Szabados Á, Surján PR. Linearized Coupled Cluster Corrections to Antisymmetrized Product of Strongly Orthogonal Geminals: Role of Dispersive Interactions. J Chem Theory Comput 2013; 9:2602-8. [DOI: 10.1021/ct400138m] [Citation(s) in RCA: 36] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Affiliation(s)
- Tamás Zoboki
- Institute of Chemistry,
Laboratory of Theoretical Chemistry,
P.O.B. 32, H-1518 Budapest 112, Hungary
| | - Ágnes Szabados
- Institute of Chemistry,
Laboratory of Theoretical Chemistry,
P.O.B. 32, H-1518 Budapest 112, Hungary
| | - Péter R. Surján
- Institute of Chemistry,
Laboratory of Theoretical Chemistry,
P.O.B. 32, H-1518 Budapest 112, Hungary
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Jeszenszki P, Surján PR, Szabados Á. Spin-adaptation and redundancy in state-specific multireference perturbation theory. J Chem Phys 2013; 138:124110. [DOI: 10.1063/1.4795436] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Chen Z, Hoffmann MR. Orbitally invariant internally contracted multireference unitary coupled cluster theory and its perturbative approximation: Theory and test calculations of second order approximation. J Chem Phys 2012; 137:014108. [DOI: 10.1063/1.4731634] [Citation(s) in RCA: 39] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Mahapatra US, Chattopadhyay S. Diagnosis of the performance of the state-specific multireference coupled-cluster method with different truncation schemes. J Comput Chem 2012; 33:1285-303. [PMID: 22419455 DOI: 10.1002/jcc.22960] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/13/2011] [Revised: 02/06/2012] [Accepted: 02/07/2012] [Indexed: 11/06/2022]
Abstract
We have tested the linked version of a iterative (partial) triples correction for the Jeziorski-Monkhorst ansatz based state-specific multireference coupled cluster (SS-MRCC) approach with singles and doubles (SD) excitations [abbreviated as SS-MRCCSDT-1a and SS-MRCCSDT-1a+d]. The assessments of SS-MRCCSDT-1a and SS-MRCCSDT-1a+d schemes have been performed on the ground potential energy surface (PES) of P4, Li(2),Be(2) systems which demand the MR description, and on study of the excitation energy between the ground and first excited state for P4 system. Illustrations in the isomerization of cyclobutadiene also show the power of the schemes. One of the designed features of the SS-MRCCSDT-n methods introduced here is that they do not require storage of the triples amplitudes. In the entire range of geometries, we found a definite improvement provided by SS-MRCC with SDT-1a and SDT-1a+d schemes over the standard SD one. In the nondegenerate regions of PES, the closeness of the performance of the single-reference CC to the SS-MRCC methods increases after inclusion of even partial triple excitations. Generally, the performance of the SS-MRCCSDT-1a+d approach is closer to the corresponding full configuration interaction (FCI) one than to the SS-MRCCSDT-1a specially in the degenerate geometries (as is evident from nonparallelism error). The deviation from FCI for the first excited state of the P4 model using various SS-MRCC theories with different truncation schemes obtained by converging on the second root of the effective Hamiltonian has also been reported. We also compare our results with the current generation state-of-the-art single and multireference CC calculations to envisage the usefulness of the present approach. Initial implementation indicates that the SS-MRCCSDT-n formalism can provide not only reliable excitation energies and barrier height even when used in a relatively small model space, but also offers a considerable promise in generating the entire energy surface with low nonparallelity error.
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Affiliation(s)
- Uttam Sinha Mahapatra
- Department of Physics, Maulana Azad College, 8 Rafi Ahmed KidwaiRoad, Kolkata 700013, India.
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Das S, Pathak S, Datta D, Mukherjee D. Inactive excitations in Mukherjee's state-specific multireference coupled cluster theory treated with internal contraction: Development and applications. J Chem Phys 2012; 136:164104. [DOI: 10.1063/1.3703312] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Mao S, Cheng L, Liu W, Mukherjee D. A spin-adapted size-extensive state-specific multi-reference perturbation theory. I. Formal developments. J Chem Phys 2012; 136:024105. [DOI: 10.1063/1.3672083] [Citation(s) in RCA: 43] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Lyakh DI, Musiał M, Lotrich VF, Bartlett RJ. Multireference Nature of Chemistry: The Coupled-Cluster View. Chem Rev 2011; 112:182-243. [DOI: 10.1021/cr2001417] [Citation(s) in RCA: 363] [Impact Index Per Article: 27.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Dmitry I. Lyakh
- Quantum Theory Project, University of Florida, Gainesville, Florida 32611, United States
| | - Monika Musiał
- Quantum Theory Project, University of Florida, Gainesville, Florida 32611, United States
| | - Victor F. Lotrich
- Quantum Theory Project, University of Florida, Gainesville, Florida 32611, United States
| | - Rodney J. Bartlett
- Quantum Theory Project, University of Florida, Gainesville, Florida 32611, United States
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Evangelista FA, Gauss J. An orbital-invariant internally contracted multireference coupled cluster approach. J Chem Phys 2011; 134:114102. [DOI: 10.1063/1.3559149] [Citation(s) in RCA: 129] [Impact Index Per Article: 9.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Das S, Mukherjee D, Kállay M. Full implementation and benchmark studies of Mukherjee’s state-specific multireference coupled-cluster ansatz. J Chem Phys 2010; 132:074103. [DOI: 10.1063/1.3310288] [Citation(s) in RCA: 106] [Impact Index Per Article: 7.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Hoffmann MR, Datta D, Das S, Mukherjee D, Szabados Á, Rolik Z, Surján PR. Comparative study of multireference perturbative theories for ground and excited states. J Chem Phys 2009; 131:204104. [DOI: 10.1063/1.3265769] [Citation(s) in RCA: 49] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022] Open
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Kong L, Shamasundar KR, Demel O, Nooijen M. State specific equation of motion coupled cluster method in general active space. J Chem Phys 2009; 130:114101. [DOI: 10.1063/1.3089302] [Citation(s) in RCA: 56] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/14/2023] Open
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Use of a convenient size-extensive normalization in multi-reference coupled cluster (MRCC) theory with incomplete model space: A novel valence universal MRCC formulation. Chem Phys 2009. [DOI: 10.1016/j.chemphys.2008.12.008] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Prochnow E, Evangelista FA, Schaefer HF, Allen WD, Gauss J. Analytic gradients for the state-specific multireference coupled cluster singles and doubles model. J Chem Phys 2009; 131:064109. [DOI: 10.1063/1.3204017] [Citation(s) in RCA: 68] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/23/2023] Open
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Evangelista FA, Allen WD, Schaefer HF. Coupling term derivation and general implementation of state-specific multireference coupled cluster theories. J Chem Phys 2007; 127:024102. [PMID: 17640114 DOI: 10.1063/1.2743014] [Citation(s) in RCA: 242] [Impact Index Per Article: 14.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Simple closed-form expressions are derived for the "same vacuum" renormalization terms that arise in state-specific multireference coupled cluster (MRCC) theories. Explicit equations are provided for these coupling terms through the triple excitation level of MRCC theory, and a general expression is included for arbitrary-order excitations. The first production-level code (PSIMRCC) for state-specific and rigorously size-extensive Mukherjee multireference coupled cluster singles and doubles (MkCCSD) computations has been written. This code is also capable of evaluating analogous Brillouin-Wigner multireference energies (BWCCSD), including a posteriori size-extensivity corrections. Using correlation-consistent basis sets (cc-pVXZ, X=D,T,Q), MkCCSD and BWCCSD were tested and compared on two classic multireference problems: (1) the dissociation potential curve of molecular fluorine (F(2)) and (2) the structure and vibrational frequencies of ozone. Comparison with experimental data shows that the Mukherjee method is generally superior to the Brillouin-Wigner theory in predicting energies, structures, and vibrational frequencies. Particularly accurate results for F(2) are obtained by applying the MkCCSD method with localized molecular orbitals. Although the MkCCSD theory greatly improves upon single-reference CCSD for the geometric parameters and a(1) vibrational frequencies of ozone, the antisymmetric stretching frequency omega(3)(b(2)) remains pathological and cannot be properly treated without the inclusion of connected triple excitations. Finally, preliminary multireference MkCCSD results are reported for the singlet-triplet splittings in ortho-, meta-, and para-benzyne, coming within 1.5 kcal mol(-1) of experiment in all cases.
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Chattopadhyay S, Mitra A, Sinha D. Explicitly intruder-free valence-universal multireference coupled cluster theory as applied to ionization spectroscopy. J Chem Phys 2007; 125:244111. [PMID: 17199344 DOI: 10.1063/1.2403858] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Although it is quite promising to compute the spectroscopic energies [say, ionization potential (IP)] via the traditional valence-universal multireference coupled cluster (VUMRCC) method based on the description of the complete model space being seriously plagued by the perennial intruder state problem, the eigenvalue independent partitioning (EIP) based VUMRCC (coined as EIP-MRCC) method is quite effective to predict the spectroscopic energies in an intruder-free manner. Hence, the EIP-MRCC method is suitable for generating both the principal IPs and the satellite IPs of the inner-valence region. An EIP strategy converts the nonlinear VUMRCC equations for M(m,n) dimensional model space of m hole and n particle to a non-Hermitian eigenproblem of larger dimension whose M(m,n) roots are only physically meaningful. To increase the quality of the computed energy differences in the sense of chemical accuracy and to locate the correct position of it in the spectrum, the inclusion of higher-body cluster operators on top of all the standard singles-doubles is not the only pivotal issue, the effect of the size of the basis set is also equally important. This paper illustrates these issues by calculating the principal and satellite IPs of HF and HCl molecules using various basis sets (viz., Dunning's cc-pVDZ, cc-pVTZ, and cc-pVQZ) via EIP-MRCC method with full inclusion of triples (abbreviated as EIP-MRCCSDT). The results seem quite encouraging in comparison with the experimental values. The controversial 2Pi satellite at 28.67 eV of HCl of Svensson et al. [J. Chem. Phys. 89, 7193 (1988)] is also reported.
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Affiliation(s)
- Sudip Chattopadhyay
- Department of Chemistry, Bengal Engineering and Science University, Shibpur, Howrah 711103, India.
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An externally-corrected size-extensive single-root MRCC formalism: Its kinship with the rigorously size-extensive state-specific MRCC theory. ACTA ACUST UNITED AC 2006. [DOI: 10.1016/j.theochem.2006.03.017] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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22
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Towards the Development and Applications of Manifestly Spin-free Multi-reference Coupled Electron-pair Approximation-like Methods: A State Specific Approach. Theor Chem Acc 2006. [DOI: 10.1007/s00214-006-0108-2] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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Nooijen * M, Shamasundar KR, Mukherjee D. Reflections on size-extensivity, size-consistency and generalized extensivity in many-body theory. Mol Phys 2005. [DOI: 10.1080/00268970500083952] [Citation(s) in RCA: 80] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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Szabados A, Rolik Z, Tóth G, Surján PR. Multiconfiguration perturbation theory: Size consistency at second order. J Chem Phys 2005; 122:114104. [PMID: 15836198 DOI: 10.1063/1.1862235] [Citation(s) in RCA: 51] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A modified version of a previously elaborated multiconfiguration perturbation theory (MCPT) [Rolik et al. J. Chem. Phys. 119, 1922 (2003)] is presented. In the modified formulation size consistency is ensured at second order in energy, by omitting projectors from the zero order Hamiltonian operator. This MCPT formulation is abbreviated as SC2-MCPT (size consistent at second order). To ensure proper separability, we also require that energy denominators are constructed as differences of some one-particle energies. A similar choice for energy denominators also renders the well-known multireference Moller-Plesset (MRMP) energy size consistent at second order. The same thing applies to the related multireference perturbation theory by Witek, Nakano, and Hirao.
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Affiliation(s)
- Agnes Szabados
- Department of Theoretical Chemistry, Loránd Eötvös University, Budapest, Hungary
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Chattopadhyay S, Mahapatra US. Molecular Applications of a State-Specific Multireference Coupled Electron-Pair Approximation (SS-MRCEPA)-like Method. J Phys Chem A 2004. [DOI: 10.1021/jp048638a] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Sudip Chattopadhyay
- Department of Physical Chemistry, Indian Association for the Cultivation of Science, Calcutta 700032, India, and Department of Chemistry, Bengal Engineering and Science University, Howrah-711103, India
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