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Hu Y, Wang Z, Wang F, Meissner L. Triple Electron Attachments with a New Intermediate-Hamiltonian Fock-Space Coupled-Cluster Method. J Phys Chem A 2024; 128:8279-8291. [PMID: 39270002 PMCID: PMC11440602 DOI: 10.1021/acs.jpca.4c03772] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/05/2024] [Revised: 08/12/2024] [Accepted: 09/05/2024] [Indexed: 09/15/2024]
Abstract
The implementation of a new intermediate-Hamiltonian Fock-space coupled-cluster (IHFSCC) scheme for the (3,0) sector of the Fock space is reported. In this IHFSCC approach, the three-body contributions in the cluster operator S(3,0) corresponding to the (3,0) sector of the Fock space are considered, while S(1,0) and S(2,0) at the (1,0) and (2,0) level only include one- and two-body operators. By introducing a suitable partition of the wave operator, the intermediate Hamiltonian, which only depends on the two-body operator of S(1,0), is obtained. S(2,0) and S(3,0) are not required within this new IHFSCC scheme, and a large reference space can be possibly employed. The performance of this (3,0) IHFSCC method in calculating triple ionization potentials and excitation energies for atoms and cations with a ground p3 configuration as well as adiabatic excitation energies for some molecules is investigated. The effect of the number of active virtual orbitals and three different types of orbitals, i.e., reference orbitals, restricted open-shell Hartree-Fock orbitals (ROHF) of the target systems, and canonicalized ROHF orbitals, on IHFSCC results, is also studied. Our calculations indicate that reasonable results can be achieved with this (3,0) IHFSCC method when a minimal reference space is employed. Further increasing the number of active orbitals does not necessarily improve the results. In addition, the IHFSCC results using canonicalized ROHF orbitals generally agree well with reference values, and they are not very sensitive to the number of active orbitals compared with results using the reference orbitals. The new (3,0) IHFSCC method can be applied to open-shell systems with three unpaired electrons with reasonable accuracy at a relatively low computational cost.
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Affiliation(s)
- Yanmei Hu
- Institute
of Atomic and Molecular Physics, Key Laboratory of High Energy Density
Physics and Technology, Ministry of Education, Sichuan University, Chengdu 610065, People’s
Republic of China
| | - Zhifan Wang
- College
of Chemistry and Life Science, Chengdu Normal
University, Chengdu 611130, People’s Republic
of China
| | - Fan Wang
- Institute
of Atomic and Molecular Physics, Key Laboratory of High Energy Density
Physics and Technology, Ministry of Education, Sichuan University, Chengdu 610065, People’s
Republic of China
| | - Leszek Meissner
- Institute
of Physics, Nicholaus Copernicus University, Grudziadzka 5/7, Toruń 87-100, Poland
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2
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Lu Y, Wang Z, Wang F. Intermediate Hamiltonian Fock-space coupled-cluster theory for excitation energies, double ionization potentials, and double electron attachments with spin–orbit coupling. J Chem Phys 2022; 156:114111. [DOI: 10.1063/5.0076462] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The intermediate Hamiltonian Fock-space coupled-cluster methods at the singles and doubles level (IHFSCCSD) for excitation energies in the (1p, 1h) sector, double ionization potentials in the (0p, 2h) sector, and double electron attachments in the (2p, 0h) sector of the Fock space are implemented based on the CCSD method with spin–orbit coupling (SOC) included in the post-Hartree–Fock treatment using a closed-shell reference in this work. The active space is chosen to contain those orbitals that have the largest contribution to principal ionized or electron-attached states obtained from the equation-of-motion coupled-cluster calculations. Both time-reversal symmetry and spatial symmetry are exploited in the implementation. Our results show that the accuracy of IHFSCCSD results is closely related to the active space, and the sufficiency of the active space can be assessed from the percentage of transitions within the active space. In addition, unreasonable results may be encountered when the ionized or electron-attached states with a somewhat larger contribution from double excitations are included to determine the active space and cluster operators in the (0p, 1h) or (1p, 0h) sector of the Fock space. A larger active space may be required to describe SO splitting reliably than that in the scalar-relativistic calculations in some cases. The IHFSCCSD method with SOC developed in this work can provide reliable results for heavy-element systems when a sufficient active space built upon the principal ionization potential/electron affinity states is adopted.
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Affiliation(s)
- Yanzhao Lu
- Institute of Atomic and Molecular Physics, Key Laboratory of High Energy Density Physics and Technology, Ministry of Education, Sichuan University, Chengdu 610065, People’s Republic of China
| | - Zhifan Wang
- College of Chemistry and Life Science, Chengdu Normal University, Chengdu 611130, People’s Republic of China
| | - Fan Wang
- Institute of Atomic and Molecular Physics, Key Laboratory of High Energy Density Physics and Technology, Ministry of Education, Sichuan University, Chengdu 610065, People’s Republic of China
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Bouammali MA, Suaud N, Maurice R, Guihéry N. Extraction of giant Dzyaloshinskii-Moriya interaction from ab initio calculations: First-order spin-orbit coupling model and methodological study. J Chem Phys 2021; 155:164305. [PMID: 34717350 DOI: 10.1063/5.0065213] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The Dzyaloshinskii-Moriya interaction is expected to be at the origin of interesting magnetic properties, such as multiferroicity, skyrmionic states, and exotic spin orders. Despite this, its theoretical determination is far from being established, neither from the point of view of ab initio methodologies nor from that of the extraction technique to be used afterward. Recently, a very efficient way to increase its amplitude has been demonstrated near the first-order spin-orbit coupling regime. Within the first-order regime, the anisotropic spin Hamiltonian involving the Dzyaloshinskii-Moriya operator becomes inappropriate. Nevertheless, in order to approach this regime and identify the spin Hamiltonian limitations, it is necessary to characterize the underlying physics. To this end, we have developed a simple electronic and spin-orbit model describing the first-order regime and used ab initio calculations to conduct a thorough methodological study.
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Affiliation(s)
- Mohammed-Amine Bouammali
- Laboratoire de Chimie et Physique Quantiques, UMR5626, University of Toulouse 3, Paul Sabatier, 18 route de Narbonne, 31062 Toulouse, France
| | - Nicolas Suaud
- Laboratoire de Chimie et Physique Quantiques, UMR5626, University of Toulouse 3, Paul Sabatier, 18 route de Narbonne, 31062 Toulouse, France
| | - Rémi Maurice
- Subatech, UMR CNRS 6457, IN2P3/IMT Atlantique/University of Nantes, 4 rue A. Kastler, 44307 Nantes Cedex 3, France
| | - Nathalie Guihéry
- Laboratoire de Chimie et Physique Quantiques, UMR5626, University of Toulouse 3, Paul Sabatier, 18 route de Narbonne, 31062 Toulouse, France
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Chakravarti D, Hazra K, Kayal R, Sasmal S, Mukherjee D. Exploration of interlacing and avoided crossings in a manifold of potential energy curves by a unitary group adapted state specific multi-reference perturbation theory (UGA-SSMRPT). J Chem Phys 2021; 155:014101. [PMID: 34241385 DOI: 10.1063/5.0054731] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The Unitary Group Adapted State-Specific Multi-Reference Perturbation Theory (UGA-SSMRPT2) developed by Mukherjee et al. [J. Comput. Chem. 36, 670 (2015)] has successfully realized the goal of studying bond dissociation in a numerically stable, spin-preserving, and size-consistent manner. We explore and analyze here the efficacy of the UGA-SSMRPT2 theory in the description of the avoided crossings and interlacings between a manifold of potential energy curves for states belonging to the same space-spin symmetry. Three different aspects of UGA-SSMRPT2 have been studied: (a) We introduce and develop the most rigorous version of UGA-SSMRPT2 that emerges from the rigorous version of UGA-SSMRCC utilizing a linearly independent virtual manifold; we call this the "projection" version of UGA-SSMRPT2 (UGA-SSMRPT2 scheme P). We compare and contrast this approach with our earlier formulation that used extra sufficiency conditions via amplitude equations (UGA-SSMRPT2 scheme A). (b) We present the results for a variety of electronic states of a set of molecules, which display the striking accuracy of both the two versions of UGA-SSMRPT2 with respect to three different situations involving weakly avoided crossings, moderate/strongly avoided crossings, and interlacing in a manifold of potential energy curves (PECs) of the same symmetry. Accuracy of our results has been benchmarked against IC-MRCISD + Q.
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Affiliation(s)
- Dibyajyoti Chakravarti
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Kolkata, India
| | - Koustav Hazra
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Kolkata, India
| | - Riya Kayal
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Kolkata, India
| | - Sudip Sasmal
- Physikalisch-Chemisches Institut, Universität Heidelberg, Heidelberg, Germany
| | - Debashis Mukherjee
- Centre for Quantum Engineering, Research, and Education (CQuERE), TCG-CREST, Kolkata, India
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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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Garniron Y, Giner E, Malrieu JP, Scemama A. Alternative definition of excitation amplitudes in multi-reference state-specific coupled cluster. J Chem Phys 2017; 146:154107. [DOI: 10.1063/1.4980034] [Citation(s) in RCA: 8] [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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7
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Giner E, David G, Scemama A, Malrieu JP. A simple approach to the state-specific MR-CC using the intermediate Hamiltonian formalism. J Chem Phys 2016; 144:064101. [DOI: 10.1063/1.4940781] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022] Open
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8
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Affiliation(s)
- Wenjian Liu
- Beijing
National Laboratory for Molecular Sciences, Institute of Theoretical
and Computational Chemistry, State Key Laboratory of Rare Earth Materials
Chemistry and Applications, College of Chemistry and Molecular Engineering,
and Center for Computational Science and Engineering, Peking University, Beijing 100871, People’s Republic of China
| | - Mark R. Hoffmann
- Chemistry
Department, University of North Dakota, Grand Forks, North Dakota 58202-9024, United States
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Sen A, Sen S, Mukherjee D. Aspects of Size-Consistency of Orbitally Noninvariant Size-Extensive Multireference Perturbation Theories: A Case Study Using UGA-SSMRPT2 as a Prototype. J Chem Theory Comput 2015; 11:4129-45. [PMID: 26575908 DOI: 10.1021/acs.jctc.5b00457] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Profiling a potential energy surface (PES), all the way to dissociate a molecular state into particular fragments and to display real or avoided crossings, requires a multireference description and the maintenance of size-consistency. The many body methods, which suit this purpose, should thus be size-extensive. Size-extensive theories, which are invariant with respect to transformation among active orbitals are, in principle, size-consistent. Relatively cheaper size-extensive theories, which do not possess this invariance, can still be size-consistent if the active orbitals are localized on the asymptotic fragments. Such methods, if perturbative in nature, require the use of an unperturbed Hamiltonian, which has orbital invariance with respect to the transformation within active, core, and virtual orbitals. The principal focus of this paper is to numerically realize size-consistency with localized active orbitals using our recently developed orbitally noninvariant Unitary Group Adapted State Specific Multireference second order Perturbation Theory (UGA-SSMRPT2) as a prototype method. Our findings expose certain generic potential pitfalls of size-extensive but orbitally noninvariant MRPT theories, which are mostly related to the inability of reaching proper localized active orbitals in the fragments due to the artifacts of the orbital generation procedure. Despite the invariance of the zeroth order CAS function, lack of invariance of the MRPT itself then leads to size-inconsistency. In particular, reaching symmetry broken fragment active orbitals is an issue of concern where suitable state-averaging might ameliorate the problem, but then one has to abandon full orbital optimization. Additionally, there can be situations where the orbitals of the fragment reached as an asymptote of the supermolecule are not the same as those obtained from the optimization of the fragments individually and will require additional transformation. Moreover, for a certain PES, one may either abandon the use of optimized orbitals for that state to preserve proper symmetry and degeneracy in the fragment orbitals or be satisfied with the use of optimized orbitals, which generate broken symmetric orbitals in the fragmentation limit. All these pathologies are illustrated using the PES of various electronic states of multiply bonded systems like N2, C2H2, HCN, C2, and O2. Subject to such proviso, the UGA-SSMRPT2 turns out to be an excellent theory for studying the PES leading to fragmentation of strongly correlated systems satisfying the requirements of size-consistency with localized active orbitals. An unexpected spin-off of our studies is the realization that the size-inextensive MRMP2, which bears a close structural similarity with our theory, might under certain situations display size-consistency. We analyze this feature concretely in our paper. Our studies may serve as a benchmark for monitoring numerically the size-consistency of any state specific multireference theory which is size-extensive but not invariant with respect to transformation of active orbitals.
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Affiliation(s)
- Avijit Sen
- Raman Center for Atomic, Molecular and Optical Sciences, Indian Association for the Cultivation of Science , Kolkata 700 032, India
| | - Sangita Sen
- Raman Center for Atomic, Molecular and Optical Sciences, Indian Association for the Cultivation of Science , Kolkata 700 032, India
| | - Debashis Mukherjee
- Raman Center for Atomic, Molecular and Optical Sciences, Indian Association for the Cultivation of Science , Kolkata 700 032, India
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Sen A, Sen S, Samanta PK, Mukherjee D. Unitary group adapted state specific multireference perturbation theory: Formulation and pilot applications. J Comput Chem 2015; 36:670-88. [DOI: 10.1002/jcc.23851] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/02/2014] [Revised: 01/01/2015] [Accepted: 01/05/2015] [Indexed: 11/11/2022]
Affiliation(s)
- Avijit Sen
- Raman Centre for Atomic, Molecular and Optical Sciences; Indian Association for the Cultivation of Sciences; Jadavpur Kolkata India
| | - Sangita Sen
- Raman Centre for Atomic, Molecular and Optical Sciences; Indian Association for the Cultivation of Sciences; Jadavpur Kolkata India
| | - Pradipta Kumar Samanta
- Raman Centre for Atomic, Molecular and Optical Sciences; Indian Association for the Cultivation of Sciences; Jadavpur Kolkata India
| | - Debashis Mukherjee
- Raman Centre for Atomic, Molecular and Optical Sciences; Indian Association for the Cultivation of Sciences; Jadavpur Kolkata India
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11
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Pradines B, Suaud N, Malrieu JP. In Search of a Rational Dressing of Intermediate Effective Hamiltonians. J Phys Chem A 2014; 119:5207-17. [DOI: 10.1021/jp509893r] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Barthélémy Pradines
- Laboratoire de Chimie et
Physique Quantiques, IRSAMC, Université de Toulouse 3 Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex, France
- Laboratoire de Chimie et Physique Quantiques
UMR 5626, CNRS, 118 route de Narbonne, 31062 Toulouse Cedex, France
| | - Nicolas Suaud
- Laboratoire de Chimie et
Physique Quantiques, IRSAMC, Université de Toulouse 3 Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex, France
- Laboratoire de Chimie et Physique Quantiques
UMR 5626, CNRS, 118 route de Narbonne, 31062 Toulouse Cedex, France
| | - Jean-Paul Malrieu
- Laboratoire de Chimie et
Physique Quantiques, IRSAMC, Université de Toulouse 3 Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex, France
- Laboratoire de Chimie et Physique Quantiques
UMR 5626, CNRS, 118 route de Narbonne, 31062 Toulouse Cedex, France
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