Static and Dynamical Correlation in Diradical Molecules by Quantum Monte Carlo Using the Jastrow Antisymmetrized Geminal Power Ansatz

Abstract

Diradical molecules are essential species involved in many organic and inorganic chemical reactions. The computational study of their electronic structure is often challenging, because a reliable description of the correlation, and in particular of the static one, requires multireference techniques. The Jastrow correlated antisymmetrized geminal power (JAGP) is a compact and efficient wave function ansatz, based on the valence-bond representation, which can be used within quantum Monte Carlo (QMC) approaches. The AGP part can be rewritten in terms of molecular orbitals, obtaining a multideterminant expansion with zero-seniority number. In the present work we demonstrate the capability of the JAGP ansatz to correctly describe the electronic structure of two diradical prototypes: the orthogonally twisted ethylene, C2H4, and the methylene, CH2, representing respectively a homosymmetric and heterosymmetric system. In the orthogonally twisted ethylene, we find a degeneracy of π and π* molecular orbitals, as correctly predicted by multireference procedures, and our best estimates of the twisting barrier, using respectively the variational Monte Carlo (VMC) and the lattice regularized diffusion Monte Carlo (LRDMC) methods, are 71.9(1) and 70.2(2) kcal/mol, in very good agreement with the high-level MR-CISD+Q value, 69.2 kcal/mol. In the methylene we estimate an adiabatic triplet-singlet (X̃(3)B1-ã(1)A1) energy gap of 8.32(7) and 8.64(6) kcal/mol, using respectively VMC and LRDMC, consistently with the experimental-derived finding for Te, 9.363 kcal/mol. On the other hand, we show that the simple ansatz of a Jastrow correlated single determinant (JSD) wave function is unable to provide an accurate description of the electronic structure in these diradical molecules, both at variational level (VMC torsional barrier of C2H4 of 99.3(2) kcal/mol, triplet-singlet energy gap of CH2 of 13.45(10) kcal/mol) and, more remarkably, in the fixed-nodes projection schemes (LRDMC torsional barrier of 97.5(2) kcal/mol, triplet-singlet energy gap of 13.36(8) kcal/mol) showing that a poor description of the static correlation yields an inaccurate nodal surface. The suitability of JAGP to correctly describe diradicals with a computational cost comparable with that of a JSD calculation, in combination with a favorable scalability of QMC algorithms with the system size, opens new perspectives in the ab initio study of large diradical systems, like the transition states in cycloaddition reactions and the thermal isomerization of biological chromophores.

π-Conjugation in trans-1,3-Butadiene: Static and Dynamical Electronic Correlations Described through Quantum Monte Carlo

“…13,25,30,32,34,35 Furthermore, given a previously optimized trial wave function Ψ T (x ̅ ;{α ̅ }), it is possible to recover all of the electronic correlation depending only on its nodal surface, through the Diffusion Monte Carlo (DMC) algorithms, like the Lattice Regularized Diffusion Monte Carlo 36 (LRDMC) used in this work.…”

“…25 In the following sections, we will briefly illustrate the three representations of AGP used in our investigation, and the Jastrow factor.…”

“…The AGP is based on the Resonating Valence Bond (RVB) representation introduced by Pauling for the description of the chemical bonds 24 and can be compared to a multideterminantal approach that considers a constraint set of molecular excitations. 23, 25 In the case of closed shell molecular systems of N e electrons in a spin singlet state, i.e. N e /2 = N e ↑ = N e ↓ , like 1,3-butadiene, the determinantal AGP part is written as the antisymmetrized product:…”

“…24 In quantum chemical methods like Configuration Interaction (CI), Complete Active Space (CAS), or CC, based on the multideterminantal expansion of the ground state wave function, the role of each single determinant in recovering the static or the dynamical electronic correlation is well distinguished by looking at its weight in the expansion. Usually when two or more leading determinants have nearly the same weight, they are said to recover static correlation, which is the case of diradical species 25 and multicenter metallo-organic complexes. Oppositely, in cases where many determinants are present with a rather small weight compared to the leading ones, these determinants are responsible for the recovering of the dynamical electronic correlation.…”

Quantum Monte Carlo Treatment of the Charge Transfer and Diradical Electronic Character in a Retinal Chromophore Minimal Model

“…Although we have not performed, for computational reasons, the continuous extrapolation of the lattice mesh size a → 0, we know from previous works 32,56 and preliminary calculations that the bias given by the finite mesh size a = 0.3 au is almost negligible in the evaluations of the considered energy differences.…”