Analytic Gradients for Selected Configuration Interaction

Alternative CNDOL Fockians for fast and accurate description of molecular exciton properties

CNDOL is an a priori, approximate Fockian for molecular wave functions. In this study, we employ several modes of singly excited configuration interaction (CIS) to model molecular excitation properties by using four combinations of the one electron operator terms. Those options are compared to the experimental and theoretical data for a carefully selected set of molecules. The resulting excitons are represented by CIS wave functions that encompass all valence electrons in the system for each excited state energy. The Coulomb-exchange term associated to the calculated excitation energies is rationalized to evaluate theoretical exciton binding energies. This property is shown to be useful for discriminating the charge donation ability of molecular and supermolecular systems. Multielectronic 3D maps of exciton formal charges are showcased, demonstrating the applicability of these approximate wave functions for modeling properties of large molecules and clusters at nanoscales. This modeling proves useful in designing molecular photovoltaic devices. Our methodology holds potential applications in systematic evaluations of such systems and the development of fundamental artificial intelligence databases for predicting related properties.

Scalable Quantum Monte Carlo with Direct-Product Trial Wave Functions

The computational demand posed by applying multi-Slater determinant trials in phaseless auxiliary-field quantum Monte Carlo methods (MSD-AFQMC) is particularly significant for molecules exhibiting strong correlations. Here, we propose using direct-product wave functions as trials for MSD-AFQMC, aiming to reduce computational overhead by leveraging the compactness of multi-Slater determinant trials in direct-product form (DP-MSD). This efficiency arises when the active space can be divided into noncoupling subspaces, a condition we term "decomposable active space". By employing localized-active space self-consistent field wave functions as an example of such trials, we demonstrate our proposed approach across a range of molecular systems, each exhibiting varying degrees of complexity in their electronic structures. Our findings indicate that the compact DP-MSD trials can reduce computational costs substantially, by up to 36 times for the C2H6N4 molecule where the two double bonds between nitrogen N=N are clearly separated by a C-C single bond, while maintaining accuracy when active spaces are decomposable. In the case of larger systems such as the benzene dimer, characterized by weak coupling between the two monomers, we observed a decrease in computational cost compared to using a complete active space trial, yet we retained the same level of accuracy. However, for systems where these active subspaces strongly couple, a scenario we refer to as "strong subspace coupling", the method's accuracy decreases compared to that achieved with a complete active space approach. We anticipate that our method will be beneficial for systems with noncoupling to weakly coupling subspaces that require local multireference treatments.

Modular Approach to Selected Configuration Interaction in an Arbitrary Spin Basis: Implementation and Comparison of Approaches

A modular selected configuration interaction (SCI) code has been developed that is based on the existing Monte-Carlo configuration interaction code (MCCI). The modularity allows various selection protocols to be implemented with ease and allows for fair comparison between wave functions built via different criteria. We have initially implemented adaptations of existing SCI theories, which are based on either energy- or coefficient-driven selection schemes. These codes have been implemented not only in the basis of Slater determinants (SDs) but also in the basis of configuration state functions (CSFs) and extended to state-averaged regimes. This allows one to take advantage of the reduced dimensionality of the wave function in the CSF basis and also the guarantee of pure spin states. All SCI methods were found to be able to predict potential energy surfaces to high accuracy, producing compact wave functions, when compared to full configuration interaction (FCI) for a variety of bond-breaking potential energy surfaces. The compactness of the error-controlled adaptive configuration interaction approach, particularly in the CSF basis, was apparent with nonparallelity errors within chemical accuracy while containing as little as 0.02% of the FCI CSF space. The size-to-accuracy was also extended to FCI spaces approaching one billion configurations.

Analytic Non-adiabatic Couplings for Selected Configuration Interaction via Approximate Degenerate Coupled Perturbed Hartree-Fock

We use degenerate perturbation theory and assume that for degenerate pairs of orbitals, the coupled perturbed Hartree-Fock coefficients are symmetric in the degenerate basis to show [Formula: see text] is the only modification needed in the original molecular orbital basis. This enables us to develop efficient and accurate analytic nonadiabatic couplings between electronic states for selected configuration interactions (CIs). Even when the states belong to different irreducible representations, degenerate orbital pairs cannot be excluded by symmetry. For various excited states of carbon monoxide and trigonal planar ammonia, we benchmark the method against the full CI and find it to be accurate. We create a semi-numerical approach and use it to show that the analytic approach is correct even when a high-symmetry structure is distorted to break symmetry so that near degeneracies in orbitals occur. For a range of geometries of trigonal planar ammonia, we find that the analytic non-adiabatic couplings for selected CI can achieve sufficient accuracy using a small fraction of the full CI space.

Approximate Excited-State Geometry Optimization with the State-Averaged Adaptive Sampling Configuration Interaction Algorithm with Large Active Spaces

The selected configuration interaction (SCI) wave function is a useful approximation to the full configuration interaction (FCI) one. The adaptive sampling CI (ASCI) method is a deterministic SCI method. By combining ASCI and orbital optimization, the ASCI self-consistent field (ASCI-SCF) method, which is an approximation of the complete active space self-consistent field (CASSCF) method, can be formulated as well. However, their applicability has been tested mainly on the systems in their electronically ground states. In this work, we implement the state-average (SA) ansatz in ASCI-SCF calculations to calculate excited states. We also derive expressions for the approximate analytical gradient and implement them as a computer program. We demonstrate the applicability of the current method for calculating vertical and adiabatic excitation energies and optimizing the molecular geometries of thermally activated delayed fluorescence (TADF) molecules.