Antisymmetrized geminal powers with larger chemical basis sets

Uemura, Wataru; Nakajima, Takahito

doi:10.1103/physreva.99.012519

Cited by 9 publications

(12 citation statements)

References 40 publications

(53 reference statements)

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“…As a result, the energy obtained for the system of the water molecule with STO-3G basis set that we used in ref. [36] came closer to the exact value. Table I shows the result with complex parameters.…”

Section: Resultsmentioning

confidence: 54%

“…Here, the result with real parameters and the full-CI result was taken from ref. [36]. We observed that after changing the parameters to be complex, the resulting energy is closer to the exact energy.…”

Section: Methodsmentioning

confidence: 68%

“…[28][29][30][31][32][33][34] We have recently shown the formula for the density matrices for geminal states and variational calculations with the superpositions of geminal states. [35,36] The result were, in some cases, highly accurate when compared with the exact diagonalization. An algorithm was included to avoid the divergent-like behavior of the AGP energy.…”

Section: Introductionmentioning

confidence: 86%

“…The tensor product with the cross term is defined similar to that in ref. [36]. For example, the first line…”

Section: Formalismmentioning

confidence: 99%

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Required number of states increases only moderately with the problem size for antisymmetrized geminal powers

Uemura,

Nakajima

2019

Preprint

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We propose an algorithm to obtain the ground-state energy of a many-electron system using the variational wave function of a linear combination of antisymmetrized geminal powers. We optimized this algorithm to obtain the energy and the other parameters of a many-electron system. Also we clarified the bottleneck of the total calculation in the tensor contraction and successfully reduced the computational time. As a result, we can use an extended number of geminal states to obtain the ground state of the water molecule and Hubbard models. The result for the water molecule with the Dunning double-zeta basis is of the sub-milihartree order above the energy of exact diagonalization. Further, we observe that the result for the one-dimensional Hubbard model with 14 sites shows good tendency to capture the right ground state and that for the two-dimensional Hubbard model still lacks some part of the energy reflecting the large size of the Hilbert space. We conclude that the required number of terms for geminal states for sufficiently accurate energy is only moderately affected by the problem size. We further show other technical details for the numerical algorithms of geminal states in the variation process. It is expected that with the use of more extended computing resources and larger sizes of electronic systems, our algorithm can provide improved results.

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Section: Resultsmentioning

confidence: 54%

Section: Methodsmentioning

confidence: 68%

Section: Introductionmentioning

confidence: 86%

“…The tensor product with the cross term is defined similar to that in ref. [36]. For example, the first line…”

Section: Formalismmentioning

confidence: 99%

See 2 more Smart Citations

Required number of states increases only moderately with the problem size for antisymmetrized geminal powers

Uemura,

Nakajima

2019

Preprint

Self Cite

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“…In this paper, we explore an alternative perspective. Rather than writing the wave function in terms of AGP and operators that replace geminals, we write the wave function as a linear combination of AGPs (LC-AGP), 4,11,12 which has the advantage that matrix elements between two different AGP states are simple. LC-AGP is related to the symmetric tensor decomposition of the exact wave function, 4,11 and non-orthogonal construction of AGP bases is natural due to the close connection between AGPs and elementary symmetric polynomials (ESPs).…”

Section: Introductionmentioning

confidence: 99%

Construction of linearly independent non-orthogonal AGP states

Dutta,

Chen,

Henderson

et al. 2021

Preprint

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We show how to construct a linearly independent set of antisymmetrized geminal power (AGP) states, which allows us to rewrite our recently introduced geminal replacement (GR) models as linear combinations of non-orthogonal AGPs. This greatly simplifies the evaluation of matrix elements and permits us to introduce an AGP-based selective configuration interaction (SCI) method, which can reach arbitrary excitation levels relative to a reference AGP, balancing accuracy and cost as we see fit.

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Transformation to a geminal basis and stationary conditions for the exact wave function therein

Sørensen

2024

Theor Chem Acc

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We show the transformation from a one-particle basis to a geminal basis, transformations between different geminal bases demonstrate the Lie algebra of a geminal basis. From the basis transformations, we express both the wave function and Hamiltonian in the geminal basis. The necessary and sufficient conditions of the exact wave function expanded in a geminal basis are shown to be a Brillouin theorem of geminals. The variational optimization of the geminals in the antisymmetrized geminal power (AGP), antisymmetrized product of geminals (APG) and the full geminal product (FGP) wave function ansätze are discussed. We show that using a geminal replacement operator to describe geminal rotations introduce both primary and secondary rotations. The secondary rotations rotate two geminals in the reference at the same time due to the composite boson nature of geminals. Due to the completeness of the FGP, where all possible geminal combinations are present, the FGP is exact. The number of parameters in the FGP scale exponentially with the number of particles, like the full configuration interaction (FCI). Truncation in the FGP expansion can give compact representations of the wave function since the reference function in the FGP can be either the AGP or APG wave function.

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Antisymmetrized geminal powers with larger chemical basis sets

Cited by 9 publications

References 40 publications

Required number of states increases only moderately with the problem size for antisymmetrized geminal powers

Required number of states increases only moderately with the problem size for antisymmetrized geminal powers

Construction of linearly independent non-orthogonal AGP states

Transformation to a geminal basis and stationary conditions for the exact wave function therein

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