Size-consistency corrections for configuration interaction calculations

We propose a size-consistent generalization of the recently developed spin-extended configuration interaction with singles and doubles (ECISD), where a CI wave function is explicitly spin-projected. The size-consistent effect is effectively incorporated by treating quadruples within the formulation of coupled electron pair approximation. As in coupled-cluster theory, quadruple excitations are approximated by a disconnected product of double excitations. Despite its conceptual similarity to the standard single-and multireference analogues, such a generalization requires careful derivation, as the spin-projected CI space is non-orthogonal and overcomplete. Although our methods generally yield better results than ECISD, size-consistency is only approximately retained because the action of a symmetry-projection operator is size-inconsistent. In this work, we focus on simple models where exclusion-principle-violating terms, which eliminate undesired contributions to the correlation effects, are either completely neglected or averaged. These models possess an orbital-invariant energy functional that is to be minimized by diagonalizing an energy-shifted effective Hamiltonian within the singles and doubles manifold. This allows for a straightforward generalization of the ECISD analytical gradients needed to determine molecular properties and geometric optimization. Given the multireference nature of the spin-projected Hartree-Fock method, the proposed approaches are expected to handle static correlation, unlike single-reference analogues. We critically assess the performance of our methods using dissociation curves of molecules, singlet-triplet splitting gaps, hyperfine coupling constants, and the chromium dimer. The size-consistency and size-extensivity of the methods are also discussed.

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“…54 Meissner suggested a different averaging by considering the actual number of pairs, ne 2 . 24 The averaged pair-energy in this case becomes…”

Section: B Pair-energy and Several Approximationsmentioning

confidence: 99%

Bridging Single- and Multireference Domains for Electron Correlation: Spin-Extended Coupled Electron Pair Approximation

Tsuchimochi

Ten‐no

2017

J. Chem. Theory Comput.

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“…Due to the rapidly growing sizes of the corre-Ž sponding Hamiltonian matrices the largest ones having dimensions 17,384,100 and 6,620,909 corresponding, respectively, to the FCI and SDTQ-CI 4y . calculations on Fluoranthene and the C system , 28 the direct CI method as first proposed and develw x oped by Roos 18 , combined with the SGA w x methodology 12 , has been implemented in PP-PACK for setting up H, and the diagonalization is w x performed by a modified iterative procedure 19 w x as originally proposed by Davidson 20 . A separate graphical compact representation of the orw Ä 4 Ä 4 bital and spin spaces i.e., and in diagram Ž .…”

Section: Resultsmentioning

confidence: 99%

“…fullerene the smallest closed-shell fullerene , and 4y Ž the C fullerene anion of T symmetry the for- 28 d mal fullerene moiety present in the smallest experw x. imentally observed fullerene, U@C 9 . For these 28 latter systems we present also charge density and nearest-neighbor bond order results in order to investigate the usefulness of the SD-CI wave functions in reproducing at least qualitatively the correlation effects present in these systems.…”

Section: Introductionmentioning

confidence: 99%

IPM approach to Hubbard model. Applications and limitations of restricted CI calculations to ground states of some ? networks containing fused 5- and 6-membered rings

Flocke

Schmalz

2000

Int. J. Quant. Chem.

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ABSTRACT:The validity of the independent particle model IPM approach in treating the Hubbard model with uniform hopping parameter t and uniform on-site < < repulsion term U is investigated for several Urt ratios on the ground states of some networks containing fused 5-and 6-membered rings with up to N s 32 electrons. It is Ž . shown that single and double excitation configuration interaction SD-CI based on a closed-shell Huckel-type reference determinant plus a correction added for the sizë consistency error using appropriate known correction terms leads to sensible estimates of < < the ground-state energy for up to Urt F 4. The IPM approach is hence well suited for < < treating the chemically relevant region of Urt f 1.5 y 2 for systems. The systems studied in this work involve several fullerene-type fragments with up to N s 16, for Ž . which a full configuration interaction FCI calculation is possible, and three larger Ž . Ž . . triple, and quadruple excitations SDTQ-CI could be performed as a guide. SD-CI calculations on these latter systems further reproduced qualitatively correct charge densities and nearest-neighbor bond orders. Wherever possible, the obtained results were compared with those obtained by different methods present in the literature, based on Monte Carlo approaches. Further we indicated a strategy as to how to perform optimum Ž . FCI HubbardrPariser᎐Parr᎐Pople PPP calculations as far as computation time is concerned.

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“…The overall accuracy of the wave function increases as the multireference set accounts for a larger portion of the wave function. In fact, if the MR space represents the portion p of the total wave function and E − E MR the amount by which the SD excitations have lowered the energy then an estimate of the error in the energy is (E − E MR )(1 − p)/p [185,186].…”

Section: Capturing Higher-order Correlation Effectsmentioning

confidence: 99%

Advanced multiconfiguration methods for complex atoms: I. Energies and wave functions

Fischer

Godefroid

Brage

et al. 2016

J. Phys. B: At. Mol. Opt. Phys.

260

231

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Abstract. Multiconfiguration wave function expansions combined with configuration interaction methods are a method of choice for complex atoms where atomic state functions are expanded in a basis of configuration state functions. Combined with a variational method such as the multiconfiguration Hartree-Fock (MCHF) or multiconfiguration Dirac-Hartree-Fock (MCDHF), the associated set of radial functions can be optimized for the levels of interest. The present review updates the variational MCHF theory to include MCDHF, describes the multireference single and double (MRSD) process for generating expansions and the systematic procedure of a computational scheme for monitoring convergence. It focuses on the calculations of energies and wave functions from which other atomic properties can be predicted such as transition rates, hyperfine structures and isotope shifts, for example.PACS numbers: 31. 31.15ag, 32.70.Cs

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Size-consistency corrections for configuration interaction calculations

Cited by 104 publications

References 13 publications

Bridging Single- and Multireference Domains for Electron Correlation: Spin-Extended Coupled Electron Pair Approximation

Bridging Single- and Multireference Domains for Electron Correlation: Spin-Extended Coupled Electron Pair Approximation

IPM approach to Hubbard model. Applications and limitations of restricted CI calculations to ground states of some ? networks containing fused 5- and 6-membered rings

Advanced multiconfiguration methods for complex atoms: I. Energies and wave functions

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