ArticleJournal of chemical theory and computation2020
Variational Principles in Quantum Monte Carlo: The Troubled Story of Variance Minimization.
Article in Journal of chemical theory and computation, 2020. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 12 papers.
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12 citing papers in PubMed, 39 citations in OpenAlex.
- Valence and core ionization energies of atoms and small molecules using variational Monte Carlo with explicit correlation and Slater-type basis sets.Journal of molecular modeling · 2026Article
- Freeze-and-Release Direct Optimization Method for Variational Calculations of Excited Electronic States.Journal of chemical theory and computation · 2026Article
- Computing Excited States of Molecules Using Normalizing Flows.Journal of chemical theory and computation · 2025Article
- Energy Landscapes for the Unitary Coupled Cluster Ansatz.Journal of chemical theory and computation · 2025Article
- An Improved Penalty-Based Excited-State Variational Monte Carlo Approach with Deep-Learning Ansatzes.Journal of chemical theory and computation · 2024Article
- Fighting Noise with Noise: A Stochastic Projective Quantum Eigensolver.Journal of chemical theory and computation · 2024Article
- Ab initio quantum chemistry with neural-network wavefunctions.Nature reviews. Chemistry · 2023Review
- State-Specific Configuration Interaction for Excited States.Journal of chemical theory and computation · 2023Article
- Double Excitation Energies from Quantum Monte Carlo Using State-Specific Energy Optimization.Journal of chemical theory and computation · 2022Article
- Energy Landscape of State-Specific Electronic Structure Theory.Journal of chemical theory and computation · 2022Article
- Reference Excitation Energies of Increasingly Large Molecules: A QMC Study of Cyanine Dyes.Journal of chemical theory and computation · 2022Article
- Tailoring CIPSI Expansions for QMC Calculations of Electronic Excitations: The Case Study of Thiophene.Journal of chemical theory and computation · 2021Article
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Authors and funding
5 authors at 3 institutions in 3 countries.
Funding
No grant is acknowledged in the PubMed record.
Abstract
We investigate the use of different variational principles in quantum Monte Carlo, namely, energy and variance minimization, prompted by the interest in the robust and accurate estimation of electronic excited states. For two prototypical, challenging molecules, we readily reach the accuracy of the best available reference excitation energies using energy minimization in a state-specific or state-average fashion for states of different or equal symmetry, respectively. On the other hand, in variance minimization, where the use of suitable functionals is expected to target specific states regardless of the symmetry, we encounter severe problems for a variety of wave functions: as the variance converges, the energy drifts away from that of the selected state. This unexpected behavior is sometimes observed even when the target is the ground state and generally prevents the robust estimation of total and excitation energies. We analyze this problem using a very simple wave function and infer that the optimization finds little or no barrier to escape from a local minimum or local plateau, eventually converging to a lower-variance state instead of the target state. For the increasingly complex systems becoming in reach of quantum Monte Carlo simulations, variance minimization with current functionals appears to be an impractical route.
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