Variational Principles in Quantum Monte Carlo: The Troubled Story of Variance Minimization

Cuzzocrea, Alice; Scemama, Anthony; Briels, Willem J.; Moroni, Saverio; Filippi, Claudia

doi:10.1021/acs.jctc.0c00147

Cited by 34 publications

(132 citation statements)

References 44 publications

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“…As the CIPSI wave function approaches the FCI limit, the CI variance goes to zero. For various small molecules [17][18][19], we have found that matching the PT2 energy contributions leads to expansions with also very similar variances. In general, this is not always the case and one of the two criteria might be more suitable than the other for the computation of the CI excitation energies of a particular system.…”

Section: Methodsmentioning

confidence: 78%

“…The use of the aug-cc-pVTZ basis set further reduces the excitation energy by about 0.02 eV. We note that, for the longer cyanine chains, the smaller maug-cc-pVDZ basis set is found to be sufficient for the computation of this excitation energy [18].…”

Section: Capturing Orbital Correlationmentioning

confidence: 82%

“…In the DMC calculations, we treat the pseudopotentials beyond the locality approximation using the T-move algorithm [33] and employ an imaginary time-step of 0.05 a.u. which we have already tested for one of the cyanine chains and shown to yield excitation energies converged to better than 0.01 eV [18] We compute all energies on the ground-state geometries of CN3-CN11 determined with all-electron PBE0/cc-pVQZ in Ref. [7] and obtain the geometries for CN13 to CN19 at the same level of theory with the Gaussian 09 program [34].…”

Section: Computational Detailsmentioning

confidence: 99%

“…In particular, we generate the ground-and excited-state expansions at the CIPSI level to have either matched PT2 energy corrections or CI variances, which we use as measures of the "distance" of the wave functions from the FCI limit. Imposing that the determinantal components satisfy either the iso-PT2 or iso-variance criterion was previously found to lead to QMC excitation energies which were converged to the best reference values with a handful of determinants [17,18], even when the error on the starting CI excitation energy was relatively large [19].…”

Section: A Building the Expansionsmentioning

confidence: 99%

“…Here, we employ quantum Monte Carlo (QMC) to revisit the vertical excitation energies of cyanine dyes of the simple form C n H n (NH 2 ) + 2 with n an odd number ranging from 1 to 17, combining the use of sophisticated multi-determinant wave functions with recent developments for their efficient optimization in variational Monte Carlo (VMC) [13][14][15][16]. In particular, we build on our successful treatment at chemical accuracy of the excitation energies and optimal excited-state structures of small, prototypical molecules [17][18][19], where the determinantal components of the multiple states are generated in an automatic and balanced manner with the configuration interaction using a perturbative selection made iteratively (CIPSI) approach [20]. Studying the bright excitation of cyanine dyes enables us to demonstrate the accuracy of our protocol for the shorter chains, where high-level coupled cluster (CC) offers a good compromise in terms of accuracy versus computational cost.…”

Section: Introductionmentioning

confidence: 99%

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Reference excitation energies of increasingly large molecules: a QMC study of cyanine dyes

Cuzzocrea¹,

Moroni²,

Scemama³

et al. 2021

Preprint

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We revisit here the lowest vertical excitations of cyanine dyes using quantum Monte Carlo and leverage on recent developments to systematically improve on previous results. In particular, we employ a protocol for the construction of compact and accurate multi-determinant Jastrow-Slater wave functions for multiple states, which we have recently validated on the excited-state properties of several small prototypical molecules. Here, we obtain quantum Monte Carlo excitation energies in excellent agreement with high-level coupled cluster for all the cyanines where the coupled cluster method is applicable. Furthermore, we push our protocol to longer chains, demonstrating that quantum Monte Carlo is a viable methodology to establish reference data at system sizes which are hard to reach with other high-end approaches of similar accuracy. Finally, we determine which ingredients are key to an accurate treatment of these challenging systems and rationalize why a description of the excitation based on only active π orbitals lacks the desired accuracy for the shorter chains.

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Section: Methodsmentioning

confidence: 78%

Section: Capturing Orbital Correlationmentioning

confidence: 82%

Section: Computational Detailsmentioning

confidence: 99%

Section: A Building the Expansionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Reference excitation energies of increasingly large molecules: a QMC study of cyanine dyes

Cuzzocrea¹,

Moroni²,

Scemama³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

In Silico Chemical Experiments in the Age of AI: From Quantum Chemistry to Machine Learning and Back

Aldossary,

Campos‐Gonzalez‐Angulo,

Pablo‐García

et al. 2024

Advanced Materials

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Computational chemistry is an indispensable tool for understanding molecules and predicting chemical properties. However, traditional computational methods face significant challenges due to the difficulty of solving the Schrödinger equations and the increasing computational cost with the size of the molecular system. In response, there has been a surge of interest in leveraging artificial intelligence (AI) and machine learning (ML) techniques to in silico experiments. Integrating AI and ML into computational chemistry increases the scalability and speed of the exploration of chemical space. However, challenges remain, particularly regarding the reproducibility and transferability of ML models. This review highlights the evolution of ML in learning from, complementing, or replacing traditional computational chemistry for energy and property predictions. Starting from models trained entirely on numerical data, a journey set forth toward the ideal model incorporating or learning the physical laws of quantum mechanics. This paper also reviews existing computational methods and ML models and their intertwining, outlines a roadmap for future research, and identifies areas for improvement and innovation. Ultimately, the goal is to develop AI architectures capable of predicting accurate and transferable solutions to the Schrödinger equation, thereby revolutionizing in silico experiments within chemistry and materials science.

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A promising intersection of excited‐state‐specific methods from quantum chemistry and quantum Monte Carlo

Otis

Neuscamman

2023

WIREs Comput Mol Sci

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We present a discussion of recent progress in excited‐state‐specific quantum chemistry and quantum Monte Carlo alongside a demonstration of how a combination of methods from these two fields can offer reliably accurate excited state predictions across singly excited, doubly excited, and charge transfer states. Both of these fields have seen important advances supporting excited state simulation in recent years, including the introduction of more effective excited‐state‐specific optimization methods, improved handling of complicated wave function forms, and ways of explicitly balancing the quality of wave functions for ground and excited states. To emphasize the promise that exists at this intersection, we provide demonstrations using a combination of excited‐state‐specific complete active space self‐consistent field theory, selected configuration interaction, and state‐specific variance minimization. These demonstrations show that combining excited‐state‐specific quantum chemistry and variational Monte Carlo can be more reliably accurate than either equation of motion coupled cluster theory or multi‐reference perturbation theory, and that it can offer new clarity in cases where existing high‐level methods do not agree.This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods Software > Quantum Chemistry

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Variational Principles in Quantum Monte Carlo: The Troubled Story of Variance Minimization

Cited by 34 publications

References 44 publications

Reference excitation energies of increasingly large molecules: a QMC study of cyanine dyes

Reference excitation energies of increasingly large molecules: a QMC study of cyanine dyes

In Silico Chemical Experiments in the Age of AI: From Quantum Chemistry to Machine Learning and Back

A promising intersection of excited‐state‐specific methods from quantum chemistry and quantum Monte Carlo

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