A hybrid approach to excited-state-specific variational Monte Carlo and doubly excited states

Abstract

We extend our hybrid linear-method/accelerated-descent variational Monte Carlo optimization approach to excited states and investigate its efficacy in double excitations. In addition to showing a superior statistical efficiency when compared to the linear method, our tests on small molecules show good energetic agreement with benchmark methods. We also demonstrate the ability to treat double excitations in systems that are too large for a full treatment by using selected configuration interaction methods via an application to 4-aminobenzonitrile. Finally, we investigate the stability of state-specific variance optimization against collapse to other states’ variance minima and find that symmetry, Ansatz quality, and sample size all have roles to play in achieving stability.

Supporting Notebook for "Energy Landscape of State-Specific Electronic Structure Theory"

“…The index-1 variance saddle points connecting states adjacent in energy may then explain why the optimisation drifts through eigenstates sequentially in energy 83 and why this issue is more prevalent in systems with small energy gaps. 23 Alternatively, the VMC wave function may simply not extend far enough into the exact variance basin of attraction of the target state to create an approximate local minimum. However, the use of highly-sophisticated wave functions in Ref.…”

“…17 Furthermore, linear response methods are generally applied under the adiabatic approximation and are limited to single excitations. 17,21 In principle, statespecific approaches can approximate both single and double excitations, 1,22,23 although the open-shell character of single excitations requires a multi-configurational approach. 4,[24][25][26][27] Underpinning excited state-specific methods is the fundamental idea that ground-state wave functions can also be used to describe an electronic excited state.…”

“…89 These approaches are particularly easy to combine with stochastic methods such as variational Monte-Carlo 83,87,90 (VMC) and have been proposed as an excited-state extension of variational quantum eigensolvers. 91,92 However, variance optimisation is prone to convergence issues that include drifting away from the intended target state, 23,83 and very little is known about the properties of the variance optimisation landscape, or its stationary points.…”

Using projection operators with maximum overlap methods to simplify challenging self‐consistent field optimization

“…In the last few decades, computational chemistry has experienced extraordinary advances in ground state and excited state methodologies. [1][2][3][4][5][6][7] In particular, ground state Kohn-Sham (KS) Density Functional Theory (DFT) and linear response time dependent Density Functional Theory (TD-DFT) have become the workhorses of modern computational chemistry. Despite these advancements, practitioners often experience significant challenges with both ground and excited state calculations.…”

Applying generalized variational principles to excited-state-specific complete active space self-consistent field theory

“…Looking at the wider world of excited state theory, there has been remarkable progress in formulating fully state-specific methods in recent years, which augurs well for progress in this direction in CASSCF theory. Examples of this progress include work in variational Monte Carlo, [24][25][26] variance-based self-consistent field (SCF) theory, 27,28 more robust level shifting approaches in SCF methods, 29 core spectroscopy, [30][31][32][33] and perturbation theory. 34 Especially relevant to the current study is the "WΓ" approach to state-specific CASSCF (SS-CASSCF), 35 in which an approximate variational principle and density matrix information are used to carefully follow a particular CI root during a two-step optimization that goes back and forth between orbital relaxation steps and CI diagonalization steps.…”