Geminal-based configuration interaction

We propose and implement an algorithm to calculate the norm and reduced density matrices of the antisymmetrized geminal power (AGP) of any rank with polynomial cost. Our method scales quadratically per element of the reduced density matrices. Numerical tests indicate that our method is very fast and capable of treating systems with a few thousand orbitals and hundreds of electrons reliably in double-precision. In addition, we present reconstruction formulae that allows one to decompose higher order reduced density matrices in terms of linear combinations of lower order ones and geminal coefficients, thereby reducing the computational cost significantly.

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“…the attractive pairing Hamiltonian in Ref. 21 ) we have not observed these potential numerical issues.…”

Section: A Direct Decompositionmentioning

confidence: 59%

“…Here, we report the runtime measurements of two calculations: (1) the energy of the pairing Hamiltonian (reduced BCS); (2) AGP-CI calculations as reported in Ref. 21 . See Appendix C for the computer environments used in these benchmarks.…”

Section: Runtime Of Energy and Agp-cimentioning

confidence: 99%

Efficient evaluation of AGP reduced density matrices

Khamoshi

Henderson

Scuseria

2019

The Journal of Chemical Physics

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“…The respective eigenfunctions of the reduced two-particle density matrix are often called natural geminals. We note that natural geminals in electronic systems have long been explored; see, e.g., [29][30][31][32][33][34][35][36][37][38][39][40].…”

Section: Introductionmentioning

confidence: 99%

Fragmentation of Identical and Distinguishable Bosons’ Pairs and Natural Geminals of a Trapped Bosonic Mixture

Alon

2021

Atoms

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In a mixture of two kinds of identical bosons, there are two types of pairs: identical bosons’ pairs, of either species, and pairs of distinguishable bosons. In the present work, the fragmentation of pairs in a trapped mixture of Bose–Einstein condensates is investigated using a solvable model, the symmetric harmonic-interaction model for mixtures. The natural geminals for pairs made of identical or distinguishable bosons are explicitly contracted by diagonalizing the intra-species and inter-species reduced two-particle density matrices, respectively. Properties of pairs’ fragmentation in the mixture are discussed, the role of the mixture’s center-of-mass and relative center-of-mass coordinates is elucidated, and a generalization to higher-order reduced density matrices is made. As a complementary result, the exact Schmidt decomposition of the wave function of the bosonic mixture is constructed. The entanglement between the two species is governed by the coupling of their individual center-of-mass coordinates, and it does not vanish at the limit of an infinite number of particles where any finite-order intra-species and inter-species reduced density matrix per particle is 100% condensed. Implications are briefly discussed.

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“…Moreover, according to Lestrange et al, these inconveniences originating from the use of the grid points can be mitigated by using an efficient algorithm and Lebedev integration grids. On the other hand, unfortunately, the PHF method is not size consistent, but Scuseria and co‐workers have attempted to reduce the size consistency errors while exploring the origin of the errors …”

Section: Introductionmentioning

confidence: 99%

“…Although the spin‐rotation operator is employed in the PHF method, we note that rotations of the spin quantization axis should be treated not classically but quantum mechanically . Indeed, the so‐called Pederson–Khanna (PK) method, which calculates zero‐field splitting (ZFS) tensors at the density functional theory level, was formulated on the basis of the classical rotations of the spin quantization axis, but later it has been pointed out that especially for triplet molecules the PK method systematically underestimates ZFS values by a factor of two .…”

Section: Introductionmentioning

confidence: 99%

A mathematical discussion of Pons Viver's implementation of Löwdin's spin projection operator

Yoshizawa

2020

Int J of Quantum Chemistry

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Recently, the molecular electronic structure theories for efficiently treating static (or strong) correlation in a black-box manner have attracted much attention. In these theories, a spin projection operator is used to recover the spin symmetry of a broken-symmetry Slater determinant. Very recently, Pons Viver proposed the practical and exact implementation of Löwdin's spin projection operator (Int. J. Quantum Chem. 2019, 119, e25770). In the present study, we attempt to supply mathematical proofs to Pons Viver's proposals and show a condition for establishing Pons Viver's implementation. Moreover, we explicitly derive the (spin projected) extended Hartree-Fock (EHF) equations on the basis of the model of common orbitals (ie, closed-shell orbitals used in the restricted open-shell Hartree-Fock (ROHF) method), which was combined by Pons Viver with the EHF method. K E Y W O R D S extended Hartree-Fock method, extended pairing theorem, spin projection operator, static correlation 1 | INTRODUCTIONRecently, in the field of molecular electronic structure theory, Scuseria and co-workers have developed the projected Hartree-Fock (PHF) method in order to efficiently treat static (or strong) correlation in a black-box manner. [1][2][3][4] In the PHF method, to deliberatively break spin symmetry of a single Slater determinant and then variationally restore it, a spin projection operator such as Löwdin's spin projection operator [5] is employed. [1] Concretely, the projection operator is expressed as an integration of the spin-rotation operator (ie, Percus-Rotenberg integration [6] ) and it can be numerically evaluated with grid points. [3,7] As a result, one must determine the appropriate number of grid points, and then one must calculate the rotated Fock matrix at each grid point. [7] These results may give a negative image to the PHF method, but it has been reported that the PHF method has modest mean-field computational cost. [1][2][3] Moreover, according to Lestrange et al, [7] these inconveniences originating from the use of the grid points can be mitigated by using an efficient algorithm and Lebedev integration grids. On the other hand, unfortunately, the PHF method is not size consistent, [1] but Scuseria and co-workers have attempted to reduce the size consistency errors while exploring the origin of the errors. [8,9] On the other hand, to obtain a wave function of the desired spin multiplicity from an unrestricted Hartree-Fock (UHF) wave function, Mayer et al [10][11][12] already derived the (spin projected) extended Hartree-Fock (EHF) equations by using both Löwdin's spin projection operator and generalized Brillouin theorem [13][14][15] in the 1970s. It has been known that for small molecules, the EHF method yields good results, [12] but its computational cost is high due to its quite complicated equations. [16] Moreover, the EHF method is also not size consistent [16][17][18] and another serious shortcoming of the EHF method is that for large systems the EHF energy per particle reduces to

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Geminal-based configuration interaction

Cited by 54 publications

References 33 publications

Efficient evaluation of AGP reduced density matrices

Efficient evaluation of AGP reduced density matrices

Fragmentation of Identical and Distinguishable Bosons’ Pairs and Natural Geminals of a Trapped Bosonic Mixture

A mathematical discussion of Pons Viver's implementation of Löwdin's spin projection operator

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