Multiple-Resonance Local Wave Functions for Accurate Excited States in Quantum Monte Carlo

Abstract

We introduce a novel class of local multideterminant Jastrow-Slater wave functions for the efficient and accurate treatment of excited states in quantum Monte Carlo. The wave function is expanded as a linear combination of excitations built from multiple sets of localized orbitals that correspond to the bonding patterns of the different Lewis resonance structures of the molecule. We capitalize on the concept of orbital domains of local coupled-cluster methods, which is here applied to the active space to select the orbitals to correlate and construct the important transitions. The excitations are further grouped into classes, which are ordered in importance and can be systematically included in the Jastrow-Slater wave function to ensure a balanced description of all states of interest. We assess the performance of the proposed wave function in the calculation of vertical excitation energies and excited-state geometry optimization of retinal models whose π → π* state has a strong intramolecular charge-transfer character. We find that our multiresonance wave functions recover the reference values of the total energies of the ground and excited states with only a small number of excitations and that the same expansion can be flexibly used at very different geometries. Furthermore, significant computational saving can also be gained in the orbital optimization step by selectively mixing occupied and virtual orbitals based on spatial considerations without loss of accuracy on the excitation energy. Our multiresonance wave functions are therefore compact, accurate, and very promising for the calculation of multiple excited states of different character in large molecules.

Excited States with Selected Configuration Interaction-Quantum Monte Carlo: Chemically Accurate Excitation Energies and Geometries

“…These developments also open very interesting prospects for the application of QMC to geometry relaxation in the excited state, where most electronic structure methods either lack the required accuracy or are computationally quite expensive due to their scaling with system size. To date, there are very few studies to assess the ability of QMC to predict excited-state geometries [22][23][24][25], while most of the relatively limited literature on excited-state QMC calculations is primarily concerned with vertical excitation energies [26][27][28][29][30][31][32][33][34][35][36][37][38][39][40]. Importantly, all these studies are characterized by the use of very different wave functions ranging from the simple ansatz of a CI singles wave function to complete active space (CAS) expansions, sometimes truncated or only partially optimized in the presence of the Jastrow factor due to the limitations previously faced in sampling and optimizing large numbers of determinants.…”

Construction of explicitly correlated geminal-projected particle-hole creation operators for many-electron systems using the diagrammatic factorization approach

“…[40,41] The Jastrow function can also be augmented by a linear combination of determinants. [51][52][53][54][55][56][57][58][59][60][61][62][63][64][65] In the transcorrelated method, a similarity transformation is performed on the Hamiltonian using an explicitly correlated function. [50,66,67] Explicit dependence on r 12 term in the wave function has been implemented in other methods such as MP2-R12, [68][69][70][71] and coupled cluster, [72][73][74][75][76][77] and geminal augmented MCSCF.…”

Excited-state calculations with quantum Monte Carlo

“…Furthermore, thanks to the presence of the Jastrow factor, QMC results are generally less dependent on the basis set. For instance, excitations and excited-state gradients show a faster convergence with basis set than multiconfigurational approaches, and an augmented double basis set with polarization functions is often sufficient in both VMC and DMC for the description of excited-state properties [24,63,64].…”

“…In particular, the VMC and DMC excitations are well converged already when very few determinants of a CAS expansion are kept in the determinantal component of the wave function [9,84]. Furthermore, the demands on the size of the basis set are also less severe and one can obtain converged excitation energies with rather small basis sets [24,63,64]. We note that most of the recent QMC calculations for excited states have attempted to achieve a balanced static description of the states of interest either by employing a CAS in the determinantal component or a truncated multi-reference ansatz where one keeps the union of the configuration state functions resulting from an appropriate truncation scheme (e.g.…”

“…Researchers have also been actively investigating more complex functional forms [18][19][20][21][22] to recover missing correlation and allow a more compact wave function than the one obtained with a multi-determinant component. A local correlation description has also been shown to be a promising route to achieve smaller expansions and reduced computational costs for ground and excited states [23,24]. In parallel, algorithms have been explored for a more automatic selection of the determinantal component, avoiding the possible pitfalls of a manual choice based on chemical intuition [15,[25][26][27][28][29][30].…”