Abstract
We aim to improve upon the variational Monte Carlo (VMC) approach for excitations replacing the Jastrow factor by an auxiliary bosonic (AB) ground state and multiplying it by a fermionic component factor. The instantaneous change in imaginary time of an arbitrary excitation in the original interacting fermionic system is obtained by measuring observables via the ground-state distribution of walkers of an AB system that is subject to an auxiliary effective potential. The effective potential is used to (i) drive the AB system’s ground-state configuration space toward the configuration space of the excitations of the original fermionic system and (ii) subtract from a diffusion Monte Carlo (DMC) calculation contributions that can be included in conventional approximations, such as mean-field and configuration interaction (CI) methods. In this novel approach, the AB ground state is treated statistically in DMC, whereas the fermionic component of the original system is expanded in a basis. The excitation energies of the fermionic eigenstates are obtained by sampling a fermion-boson coupling term on the AB ground state. We show that this approach can take advantage of and correct for approximate eigenstates obtained via mean-field calculations or truncated interactions. We demonstrate that the AB ground-state factor incorporates the correlations missed by standard Jastrow factors, further reducing basis truncation errors. Relevant parts of the theory have been tested in soluble model systems and exhibit excellent agreement with exact analytical data and CI and VMC approaches. In particular, for limited basis set expansions and sufficient statistics, AB approaches outperform CI and VMC in terms of basis size for the same systems. The implementation of this method in current codes, despite being demanding, will be facilitated by reusing procedures already developed for calculating ground-state properties with DMC and excitations with VMC.
| Original language | English |
|---|---|
| Article number | 114118 |
| Journal | Journal of Chemical Physics |
| Volume | 159 |
| Issue number | 11 |
| DOIs | |
| State | Published - Sep 21 2023 |
Funding
This manuscript has been authored by UT-Battelle, LLC, under contract Grant No. DE-AC05-00OR22725 with the US Department of Energy (DOE). The U.S. government retains and the publisher, by accepting the article for publication, acknowledges that the U.S. government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for U.S. government purposes. DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan ( http://energy.gov/downloads/doe-public-access-plan ). The work by FAR (method development, tests, and manuscript writing) and J.T.K. (method development and manuscript contributions) was supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences program, Materials Sciences and Engineering Division. The work by PRCK (general background guidance, critical context, and manuscript contributions) was supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences program, Materials Sciences and Engineering Division, as part of the Computational Materials Sciences program and the Center for Predictive Simulation of Functional Materials. The authors would like to thank Erica Heinrich for technical editing and related corrections.
| Funders | Funder number |
|---|---|
| Basic Energy Sciences Program | |
| U.S. Department of Energy | |
| Foundation for Agronomic Research | |
| Office of Science | |
| Division of Materials Sciences and Engineering |