dorsal/arxiv
View SchemaOptimization of quantum Monte Carlo wave functions by energy minimization
| Authors | Julien Toulouse, C. J. Umrigar |
|---|---|
| Categories | |
| ArXiv ID | physics/0701039 |
| URL | https://arxiv.org/abs/physics/0701039 |
| DOI | 10.1063/1.2437215 |
| Journal | Journal of Chemical Physics 126, 084102 (2007) |
Abstract
We study three wave function optimization methods based on energy minimization in a variational Monte Carlo framework: the Newton, linear and perturbative methods. In the Newton method, the parameter variations are calculated from the energy gradient and Hessian, using a reduced variance statistical estimator for the latter. In the linear method, the parameter variations are found by diagonalizing a non-symmetric estimator of the Hamiltonian matrix in the space spanned by the wave function and its derivatives with respect to the parameters, making use of a strong zero-variance principle. In the less computationally expensive perturbative method, the parameter variations are calculated by approximately solving the generalized eigenvalue equation of the linear method by a nonorthogonal perturbation theory. These general methods are illustrated here by the optimization of wave functions consisting of a Jastrow factor multiplied by an expansion in configuration state functions (CSFs) for the C$_2$ molecule, including both valence and core electrons in the calculation. The Newton and linear methods are very efficient for the optimization of the Jastrow, CSF and orbital parameters. The perturbative method is a good alternative for the optimization of just the CSF and orbital parameters. Although the optimization is performed at the variational Monte Carlo level, we observe for the C$_2$ molecule studied here, and for other systems we have studied, that as more parameters in the trial wave functions are optimized, the diffusion Monte Carlo total energy improves monotonically, implying that the nodal hypersurface also improves monotonically.
{
"annotation_id": "67763b7f-234f-44e2-af16-f6eddff3b71a",
"date_created": "2026-03-02T18:01:14.470000Z",
"date_modified": "2026-03-02T18:01:14.470000Z",
"file_hash": "087f86141153b9350affba0e5947ad0f00b87c152144f189d6ad03186c9444fc",
"private": false,
"record": {
"abstract": "We study three wave function optimization methods based on energy\nminimization in a variational Monte Carlo framework: the Newton, linear and\nperturbative methods. In the Newton method, the parameter variations are\ncalculated from the energy gradient and Hessian, using a reduced variance\nstatistical estimator for the latter. In the linear method, the parameter\nvariations are found by diagonalizing a non-symmetric estimator of the\nHamiltonian matrix in the space spanned by the wave function and its\nderivatives with respect to the parameters, making use of a strong\nzero-variance principle. In the less computationally expensive perturbative\nmethod, the parameter variations are calculated by approximately solving the\ngeneralized eigenvalue equation of the linear method by a nonorthogonal\nperturbation theory. These general methods are illustrated here by the\noptimization of wave functions consisting of a Jastrow factor multiplied by an\nexpansion in configuration state functions (CSFs) for the C$_2$ molecule,\nincluding both valence and core electrons in the calculation. The Newton and\nlinear methods are very efficient for the optimization of the Jastrow, CSF and\norbital parameters. The perturbative method is a good alternative for the\noptimization of just the CSF and orbital parameters. Although the optimization\nis performed at the variational Monte Carlo level, we observe for the C$_2$\nmolecule studied here, and for other systems we have studied, that as more\nparameters in the trial wave functions are optimized, the diffusion Monte Carlo\ntotal energy improves monotonically, implying that the nodal hypersurface also\nimproves monotonically.",
"arxiv_id": "physics/0701039",
"authors": [
"Julien Toulouse",
"C. J. Umrigar"
],
"categories": [
"physics.chem-ph",
"cond-mat.mtrl-sci",
"cond-mat.other",
"physics.comp-ph"
],
"doi": "10.1063/1.2437215",
"journal_ref": "Journal of Chemical Physics 126, 084102 (2007)",
"title": "Optimization of quantum Monte Carlo wave functions by energy minimization",
"url": "https://arxiv.org/abs/physics/0701039"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "1643c395-0e2f-447f-8ca1-d4717b780ec9",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}