Configuration interaction with antisymmetrized geminal powers

Abstract

To avoid the combinatorial computational cost of configuration interaction (CI), we have previously introduced the symmetric tensor decomposition CI (STD-CI) method, where we take advantage of the antisymmetric nature of the electronic wave function and express the CI coefficients compactly as a series of Kronecker product states (STD series) [W. Uemura and O. Sugino, Phys.Rev. Lett. 109, 253001 (2012)]. Here we extend the variational degrees of freedom by using different molecular orbitals for different terms in the STD series. This scheme is equivalent to the linear combination of the Hartree-Fock-Bogoliubov state or the antisymmetrized geminal powers (AGP). The total energy converges very rapidly within 0.72 µHartree taking only 10 terms for the water molecule, and the convergence is likewise fast for Hubbard tetramers. The computational cost scales as the fifth power of the number of electrons and the square of the number of terms in the STD series, indicating the promise of this AGP-based scheme for highly accurate and efficient computation of quantum systems.

Four-body correlation embedded in antisymmetrized geminal power wave function

“…Note in addition that Ref. [4] reported that information loss easily occurs although that is not so important in the present case. Whereas, we need only 1 trial run for AGP4.…”

Antisymmetrized geminal powers with larger chemical basis sets

“…With this modification, we successfully reproduced the total energy of STO-3G water converged case. In this case, the energy was obtained with quadruple precision arrays in previous research [26], but we were able to reproduce almost the same energy with the same input geminal matrices using double precision arrays. From this we have concluded that the stabilization of the total energy with double precision variables is achieved by use of this eigenvalue technique.…”

“…Total For comparison, the full-CI calculation with our own code and the CASSCF calculation using the Gaussian09 package was taken from ref. [26]. The Hartree-Fock calculation was done with our own code.…”

“…First, we present the basic expressions in our AGPbased formalism. Some parts of these expressions have appeared in ref [26]. We give the expression of the wave function as…”

“…For the water molecule, we have tested the STO-3G basis set and the Dunning zeta For the STO-3G case, we have used the same system as that of ref. [26]. For the DZ basis case, we have used the system in ref.…”