General Correlated Geminal Ansatz for Electronic Structure Calculations: Exploiting Pfaffians in Place of Determinants

Abstract

We propose here a single Pfaffian correlated variational ansatz that dramatically improves the accuracy with respect to the single determinant one, while remaining at a similar computational cost. A much larger correlation energy is indeed determined by the most general two electron pairing function, including both singlet and triplet channels, combined with a many-body Jastrow factor, including all possible spin−spin, spin−density, and density−density terms. The main technical ingredient to exploit this accuracy is the use of the Pfaffian for antisymmetrizing a highly correlated pairing function, thus recovering the Fermi statistics for electrons with an affordable computational cost. Moreover, the application of the diffusion Monte Carlo, within the fixed node approximation, allows us to obtain very accurate binding energies for the first preliminary calculations reported in this study: C 2 , N 2 , and O 2 and the benzene molecule. This is promising and remarkable, considering that they represent extremely difficult molecules even for computationally demanding multideterminant approaches, and opens therefore the way for realistic and accurate electronic simulations with an algorithm scaling at most as the fourth power of the number of electrons.

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

“…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].…”

Highly accurate ab-initio thermochemistry via real-space quantum Monte Carlo: Benzene

“…For the reference wave-function |Φ , we will discuss three forms. The first will be the restricted Hartree-Fock (RHF) wave-function [21], the second will be the Ŝz projected generalized Hartree-Fock ( Ŝz GHF) wavefunction [22][23][24][25], and the last will be the anti-symmetrized geminal power (AGP) wave-function [25][26][27][28]. All parameters in the wave-functions, including those in the Jastrow factors and reference, are optimized within VMC.…”

“…We present these energies in Table II. Comparing the two wave ENBO LRDMC-JRHF [28] 2.2083( 7) LRDMC-JAGP [28] 2.1741 (7) TABLE II. ENBO from all-electron LR-DMC calculations using the guiding wave-functions on the left.…”

Parent Hamiltonians of Jastrow wavefunctions

“…In this spirit, so-called Slater-Jastrow wave functions can be constructed as products of Jastrow functions and Slater determinants of single-particle wavefunctions, e.g., to describe electronic systems. An alternative approach to construct fermionic wave-functions starts from pair orbitals and use Pfaffian wave-functions [11,12]. In addition, generalizations of the Jastrow form to include higher-order correlations have also been proposed.…”