The Static–Dynamic–Static Family of Methods for Strongly Correlated Electrons: Methodology and Benchmarking

Song, Yiying; Guo, Yang; Lei, Yibo; Zhang, Ning; Liu, Wenjian

doi:10.1007/s41061-021-00351-9

Cited by 23 publications

(19 citation statements)

References 172 publications

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“…The improved virtual orbital scheme ,, was used in this work. More advanced virtual space decomposition approaches , will be evaluated in a future work.…”

Section: Discussionmentioning

confidence: 99%

Exact-Two-Component Relativistic Multireference Second-Order Perturbation Theory

Jenkins

et al. 2022

J. Chem. Theory Comput.

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As the relativistic corrections become stronger for laterow elements, the fully perturbative treatment of spin−orbit coupling and dynamic correlation may become inadequate for accurate descriptions of chemical properties. In this work, we introduce a determinant-based Kramers-unrestricted exact-two-component multireference second-order perturbation (X2C-MRPT2) method which variationally includes relativistic corrections with a perturbative dynamic correlation. The restricted active space partitioning scheme is employed to provide an adjustable correlation space for the secondorder perturbation treatment. The multistate perturbation theory is also developed to improve the descriptions of ground and excited states. Benchmark studies of atomic fine-structure splittings and spectroscopic constants of molecular monohydrides using X2C-MRPT2 are compared to the other perturbative and variational approaches. The results suggest that X2C-MRPT2 is a highly accurate alternative to the fully variational multireference configuration interaction method at only a small fraction of the computational cost.

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“…The improved virtual orbital scheme ,, was used in this work. More advanced virtual space decomposition approaches , will be evaluated in a future work.…”

Section: Discussionmentioning

confidence: 99%

Exact-Two-Component Relativistic Multireference Second-Order Perturbation Theory

Jenkins

et al. 2022

J. Chem. Theory Comput.

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“…Several remarks can be made here. Up to now, both the external

{({}|, | Ξ_{k}^{(1)} > |)}_{k = 1}^{N_{Q}}

and secondary

{({}|, | Θ_{k} > |)}_{k = 1}^{N_{S}}

states are state‐specific to the primary

{({}|, | Ψ_{k}^{(0)} >)}_{k = 1}^{N_{P}}

states (i.e., N Q = N S = N P ), such that the dimension of Equation () is just three times the number ( N P ) of wanted states, irrespective of the numbers of correlated electrons and orbitals. This Ansatz is best characterized as “internally and externally contracted minimal MRCI with singles and doubles and augmented with secondary states” (ixc‐MRCISD + s), denoted as SDSCI for short 156 . The diagonalization of large matrices only for a smaller number ( N P ) of states in unrestricted SDS methods (e.g., internally contracted multireference configuration interaction with singles and doubles (ic‐MRCISD) 157,158 ) is completely avoided here.…”

Section: Electron Correlationmentioning

confidence: 99%

Perspective: Simultaneous treatment of relativity, correlation, and QED

Liu

2022

WIREs Comput Mol Sci

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Electronic structure calculations of many-electron systems should in principle treat relativistic, correlation, and quantum electrodynamics (QED) effects simultaneously to a high precision, so as to match experimental measurements as close as possible. While both relativistic and QED effects can readily be built into the many-electron Hamiltonian, electron correlation is more difficult to describe due to the exponential growth of the number of parameters in the wave function. Compared with the spin-free case, spin-orbit interaction results in the loss of spin symmetry and concomitant complex algebra, thereby rendering the treatment of electron correlation even more difficult. Possible solutions to these issues are highlighted here.

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“…Because of difficulties in treating molecular dissociations, chemical reactions, and the quasi-degenerate excited states with the single-reference perturbation theories, multireference approaches are needed. Multireference perturbation theory (MRPT) − has been proven to be a powerful method. Among them, to list a few, there are Hylleraas variational perturbation theory of Davidson et al., CASPT2 and CASPT3, multireference Møller–Plesset perturbation theory of Hirao, , the MRPT of Davidson et al, , the state-specific MRPT, ,,,, the n -electron valence perturbation theory (NVPT2 and NVPT3), MRPT of Chen, Davidson, and Iwata, , the multiconfiguration perturbation theories of Surján et al., ,, the generalized Van Vleck perturbation theory of Hoffmann et al, , the size extensive and orbital invariant MRPT of Chen et al, valence bond perturbation theory of Wu et al, , the block correlated second-order perturbation theory of Li et al, , the multireference Rayleigh–Schrödinger perturbation theory of Chen et al, and the iCIPT2 for strongly correlated electrons by Liu et al , More studies on the MRPT can also be found from refs and .…”

Section: Introductionmentioning

confidence: 99%

Block Effective Hamiltonian Theory and Its Application

Hou

Chen

2022

J. Chem. Theory Comput.

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Block effective Hamiltonian theory (BEHT) is presented in this work. Configuration interaction functions are divided into P, Q, and R spaces. Effective Hamiltonian is constructed with the partitioning technique within the P space. The eigenvalue problem of the effective Hamiltonian is then solved iteratively. It is demonstrated that the ground-state energies of N 2 , HF, and F 2 calculated with BEHT converge to the multireference configuration interaction energies from below and the iteration number becomes smaller as BEHT energy becomes closer to the exact energy. The accuracy of BEHT is better than that of the second-order multireference perturbation theory, although the matrix elements in both methods are the same. The ionization potentials of the singlet state of HF, the doublet state of F, and the triplet state of NH and the potential energy curves of CH 4 , C 2 , and N 2 are calculated with BEHT and compared with experiments and results of CASSCF, CCSD, and CCSD(T) and the results of the full configuration interaction if available. The iteration numbers are all less than 10 in this study. These calculations show the good performances of BEHT in comparison with other theoretical approximation methods.

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The Static–Dynamic–Static Family of Methods for Strongly Correlated Electrons: Methodology and Benchmarking

Cited by 23 publications

References 172 publications

Exact-Two-Component Relativistic Multireference Second-Order Perturbation Theory

Exact-Two-Component Relativistic Multireference Second-Order Perturbation Theory

Perspective: Simultaneous treatment of relativity, correlation, and QED

Block Effective Hamiltonian Theory and Its Application

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