Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2211.05447 · Journal of Chemical Theory and Computation

Toward Chemical Accuracy Using the Jastrow Correlated Antisymmetrized Geminal Power Ansatz

Abhishek Raghav, Ryo Maezono, Kenta Hongo, Sandro Sorella, Kousuke Nakano

Published Apr 4, 2023• 12 citations
arXivHTMLPDF

Abstract

High Resolution Image Download MS PowerPoint Slide Herein, we report accurate atomization energy calculations for 55 molecules in the Gaussian-2 (G2) set using lattice regularized diffusion Monte Carlo (LRDMC). We compare the Jastrow–Slater determinant ansatz with a more flexible JsAGPs (Jastrow correlated antisymmetrized geminal power with singlet correlation) ansatz . AGPs is built from pairing functions, which explicitly include pairwise correlations among electrons, and hence, this ansatz is expected to be more efficient in recovering the correlation energy. The AGPs wave functions are first optimized at the variational Monte Carlo (VMC) level, which includes both the Jastrow factor and the nodal surface optimization. This is followed by the LRDMC projection of the ansatz . Remarkably, for many molecules, the LRDMC atomization energies obtained using the JsAGPs ansatz reach chemical accuracy (∼1 kcal/mol), and for most other molecules, the atomization energies are accurate within ∼5 kcal/mol. We obtained a mean absolute deviation of 1.6 kcal/mol with JsAGPs and 3.2 kcal/mol with JDFT ( J astrow factor + Slater determinant with DFT orbitals) ansatzes . This work shows the effectiveness of the flexible AGPs ansatz for atomization energy calculations and electronic structure simulations in general.

DOI
10.1021/acs.jctc.2c01141

Related papers

General Correlated Geminal Ansatz for Electronic Structure Calculations: Exploiting Pfaffians in Place of Determinants

Claudio Genovese, Tomonori Shirakawa, Kousuke Nakano +1 more

High Resolution Image Download MS PowerPoint Slide We propose here a single Pfaffian correlated variational ansatz that dramatically improves the accuracy with respect to the single determinant one, while remaining at a similar computational cost. A much larger correlation energy is indeed determined by the most general two electron pairing function, including both singlet and triplet channels, combined with a many-body Jastrow factor, including all possible spin–spin, spin–density, and density–density terms. The main technical ingredient to exploit this accuracy is the use of the Pfaffian for antisymmetrizing a highly correlated pairing function, thus recovering the Fermi statistics for electrons with an affordable computational cost. Moreover, the application of the diffusion Monte Carlo, within the fixed node approximation, allows us to obtain very accurate binding energies for the first preliminary calculations reported in this study: C 2, N 2, and O 2 and the benzene molecule. This is promising and remarkable, considering that they represent extremely difficult molecules even for computationally demanding multideterminant approaches, and opens therefore the way for realistic and accurate electronic simulations with an algorithm scaling at most as the fourth power of the number of electrons.

arXiv:2002.03347•Journal of Chemical Theory and Computation•Aug 17, 2020•21 citations

Basis-free neural-network geminal and Jastrow factors for variational Monte Carlo

Jan Kessler, Thomas D. Kühne

Neural-network quantum states offer a flexible route to compact many-electron wave functions, but their practical accuracy depends strongly on how fermionic antisymmetry, electron correlation, and optimization noise are treated. Here we combine an antisymmetrized geminal power (AGP) determinant with feed-forward neural networks that replace conventional basis-set expansions in the geminal and in two Jastrow-factor constructions. The resulting basis-free Jastrow--AGP ansatz is optimized by variational Monte Carlo and is designed to separate two tasks: the AGP part defines the nodal surface, while the neural-network Jastrow factor recovers dynamical correlation at fixed nodes. This separation makes it possible to distinguish errors associated with dynamical correlation from those caused by static, multireference correlation. Applications to the hydrogen molecule and the rectangular hydrogen tetramer show sub-millihartree accuracy when the AGP nodes are adequate, and expose the residual nodal limitation near the large-radius square geometry of the hydrogen tetramer. These results clarify where neural-network building blocks can improve a compact geminal ansatz and where additional nodal flexibility is required.

arXiv:2605.17083•May 16, 2026•0 citations

Benchmark all-electron ab initio quantum Monte Carlo calculations for small molecules

Norbert Nemec, Michael D. Towler, Richard J. Needs

We study the efficiency, precision and accuracy of all-electron variational and diffusion quantum Monte Carlo calculations using Slater basis sets. Starting from wave functions generated by Hartree-Fock and density functional theory, we describe an algorithm to enforce the electron-nucleus cusp condition by linear projection. For the 55 molecules in the G2 set, the diffusion quantum Monte Carlo calculations recovers an average of 95% of the correlation energy and reproduces bond energies to a mean absolute deviation of 3.2 kcal/mol. Comparing the individual total energies with essentially exact values, we investigate the error cancellation in atomization and chemical reaction path energies, giving additional insight into the sizes of nodal surface errors.

arXiv:0908.2041•The Journal of Chemical Physics•Jan 21, 2010•81 citations

Performance of the Diffusion Quantum Monte Carlo Method with a Single-Slater-Jastrow Trial Wavefunction Using Natural Orbitals and Density Functional Theory Orbitals on Atomization Energies of the Gaussian-2 Set

Ting Wang, Xiaojun Zhou, Fan Wang

Performance of the fixed-node diffusion quantum Monte Carlo method (FN-DMC) with a single Slater-Jastrow trial wavefunction using natural orbitals (NOs) from MP2, CCSD, CCSD(T), and CASSCF as well as density functional theory orbitals on atomization energies of the molecules in the Gaussian-2 set is investigated in this work. The effects of spin contamination and pseudopotentials (PPs) are also studied. Our results show that the DMC energy with NOs from MP2 or CCSD(T) is the lowest on average, whereas that from CASSCF is only lower than the DMC energy using Hartree-Fock orbitals. Atomization energies are generally underestimated with DMC, and mean absolute deviations of DMC atomization energies are about 2.8 kcal/mol with NOs from MP2 or CCSD(T) and about 2.7 kcal/mol with NOs from CASSCF or B3LYP orbitals. The better performance of the latter two orbitals is due to a more effective error cancellation. The accuracy of the present FN-DMC is similar to CCSD(T)/aug-cc-pVQZ on atomization energies. In addition, the error of DMC atomization energies tends to be larger for molecules with multiple bonds. DMC energies of the open-shell systems with spin-restricted orbitals are generally higher than those with spin-unrestricted orbitals if spin contamination is not serious and the atomization energies are improved to some extent. Furthermore, our results indicate that the error of the PPs is rather small at the CCSD(T) level, but could be more pronounced in DMC calculations and DMC atomization energies are improved with some newly developed PPs.

The Journal of Physical Chemistry A•Apr 5, 2019•18 citations

Efficient calculation of unbiased atomic forces in ab initio variational Monte Carlo

Kousuke Nakano, Michele Casula, Giacomo Tenti

quantum Monte Carlo (QMC) is a state-of-the-art numerical approach for evaluating accurate expectation values of many-body wave functions. However, one of the major drawbacks that still hinders widespread QMC applications is the lack of an affordable scheme to compute unbiased atomic forces. In this study, we propose an efficient method to obtain unbiased atomic forces and pressures in the variational Monte Carlo (VMC) framework with the Jastrow-correlated Slater determinant ansatz or the Jastrow antisymmetrized geminal power ansatz, exploiting the gauge-invariant and locality properties of their geminal representation. We demonstrate the effectiveness of our method for H 2 and Cl 2 molecules and for the cubic boron nitride crystal. Our framework has a better algorithmic scaling with the system size than the traditional finite-difference method and, in practical applications, is as efficient as single-point VMC calculations. Thus, it paves the way to study dynamical properties of materials, such as phonons, and is beneficial for pursuing more reliable machine-learning interatomic potentials based on unbiased VMC forces. Published by the American Physical Society 2024

arXiv:2312.17608•Physical review. B./Physical review. B•May 28, 2024•9 citations

Geminal embedding scheme for optimal atomic basis set construction in correlated calculations

Sandro Sorella, Nicolas Devaux, Mario Dagrada +2 more

We introduce an efficient method to construct optimal and system adaptive basis sets for use in electronic structure and quantum Monte Carlo calculations. The method is based on an embedding scheme in which a reference atom is singled out from its environment, while the entire system (atom and environment) is described by a Slater determinant or its antisymmetrized geminal power (AGP) extension. The embedding procedure described here allows for the systematic and consistent contraction of the primitive basis set into geminal embedded orbitals (GEOs), with a dramatic reduction of the number of variational parameters necessary to represent the many-body wave function, for a chosen target accuracy. Within the variational Monte Carlo method, the Slater or AGP part is determined by a variational minimization of the energy of the whole system in presence of a flexible and accurate Jastrow factor, representing most of the dynamical electronic correlation. The resulting GEO basis set opens the way for a fully controlled optimization of many-body wave functions in electronic structure calculation of bulk materials, namely, containing a large number of electrons and atoms. We present applications on the water molecule, the volume collapse transition in cerium, and the high-pressure liquid hydrogen.

arXiv:1602.00035•The Journal of Chemical Physics•Dec 28, 2015•23 citations
High Resolution Image Download MS PowerPoint Slide Herein, we report accurate atomization energy calculations for 55 molecules in the Gaussian-2 (G2) set using lattice regularized diffusion Monte Carlo (LRDMC). We compare the Jastrow–Slater determinant ansatz with a more flexible JsAGPs (Jastrow correlated antisymmetrized geminal power with singlet correlation) ansatz . AGPs is built from pairing functions, which explicitly include pairwise correlations among electrons, and hence, this ansatz is expected to be more efficient in recovering the correlation energy. The AGPs wave functions are first optimized at the variational Monte Carlo (VMC) level, which includes both the Jastrow factor and the nodal surface optimization. This is followed by the LRDMC projection of the ansatz . Remarkably, for many molecules, the LRDMC atomization energies obtained using the JsAGPs ansatz reach chemical accuracy (∼1 kcal/mol), and for most other molecules, the atomization energies are accurate within ∼5 kcal/mol. We obtained a mean absolute deviation of 1.6 kcal/mol with JsAGPs and 3.2 kcal/mol with JDFT ( J astrow factor + Slater determinant with DFT orbitals) ansatzes . This work shows the effectiveness of the flexible AGPs ansatz for atomization energy calculations and electronic structure simulations in general.
High Resolution Image Download MS PowerPoint Slide We propose here a single Pfaffian correlated variational ansatz that dramatically improves the accuracy with respect to the single determinant one, while remaining at a similar computational cost. A much larger correlation energy is indeed determined by the most general two electron pairing function, including both singlet and triplet channels, combined with a many-body Jastrow factor, including all possible spin–spin, spin–density, and density–density terms. The main technical ingredient to exploit this accuracy is the use of the Pfaffian for antisymmetrizing a highly correlated pairing function, thus recovering the Fermi statistics for electrons with an affordable computational cost. Moreover, the application of the diffusion Monte Carlo, within the fixed node approximation, allows us to obtain very accurate binding energies for the first preliminary calculations reported in this study: C 2, N 2, and O 2 and the benzene molecule. This is promising and remarkable, considering that they represent extremely difficult molecules even for computationally demanding multideterminant approaches, and opens therefore the way for realistic and accurate electronic simulations with an algorithm scaling at most as the fourth power of the number of electrons.
Neural-network quantum states offer a flexible route to compact many-electron wave functions, but their practical accuracy depends strongly on how fermionic antisymmetry, electron correlation, and optimization noise are treated. Here we combine an antisymmetrized geminal power (AGP) determinant with feed-forward neural networks that replace conventional basis-set expansions in the geminal and in two Jastrow-factor constructions. The resulting basis-free Jastrow--AGP ansatz is optimized by variational Monte Carlo and is designed to separate two tasks: the AGP part defines the nodal surface, while the neural-network Jastrow factor recovers dynamical correlation at fixed nodes. This separation makes it possible to distinguish errors associated with dynamical correlation from those caused by static, multireference correlation. Applications to the hydrogen molecule and the rectangular hydrogen tetramer show sub-millihartree accuracy when the AGP nodes are adequate, and expose the residual nodal limitation near the large-radius square geometry of the hydrogen tetramer. These results clarify where neural-network building blocks can improve a compact geminal ansatz and where additional nodal flexibility is required.
We study the efficiency, precision and accuracy of all-electron variational and diffusion quantum Monte Carlo calculations using Slater basis sets. Starting from wave functions generated by Hartree-Fock and density functional theory, we describe an algorithm to enforce the electron-nucleus cusp condition by linear projection. For the 55 molecules in the G2 set, the diffusion quantum Monte Carlo calculations recovers an average of 95% of the correlation energy and reproduces bond energies to a mean absolute deviation of 3.2 kcal/mol. Comparing the individual total energies with essentially exact values, we investigate the error cancellation in atomization and chemical reaction path energies, giving additional insight into the sizes of nodal surface errors.
Performance of the fixed-node diffusion quantum Monte Carlo method (FN-DMC) with a single Slater-Jastrow trial wavefunction using natural orbitals (NOs) from MP2, CCSD, CCSD(T), and CASSCF as well as density functional theory orbitals on atomization energies of the molecules in the Gaussian-2 set is investigated in this work. The effects of spin contamination and pseudopotentials (PPs) are also studied. Our results show that the DMC energy with NOs from MP2 or CCSD(T) is the lowest on average, whereas that from CASSCF is only lower than the DMC energy using Hartree-Fock orbitals. Atomization energies are generally underestimated with DMC, and mean absolute deviations of DMC atomization energies are about 2.8 kcal/mol with NOs from MP2 or CCSD(T) and about 2.7 kcal/mol with NOs from CASSCF or B3LYP orbitals. The better performance of the latter two orbitals is due to a more effective error cancellation. The accuracy of the present FN-DMC is similar to CCSD(T)/aug-cc-pVQZ on atomization energies. In addition, the error of DMC atomization energies tends to be larger for molecules with multiple bonds. DMC energies of the open-shell systems with spin-restricted orbitals are generally higher than those with spin-unrestricted orbitals if spin contamination is not serious and the atomization energies are improved to some extent. Furthermore, our results indicate that the error of the PPs is rather small at the CCSD(T) level, but could be more pronounced in DMC calculations and DMC atomization energies are improved with some newly developed PPs.
quantum Monte Carlo (QMC) is a state-of-the-art numerical approach for evaluating accurate expectation values of many-body wave functions. However, one of the major drawbacks that still hinders widespread QMC applications is the lack of an affordable scheme to compute unbiased atomic forces. In this study, we propose an efficient method to obtain unbiased atomic forces and pressures in the variational Monte Carlo (VMC) framework with the Jastrow-correlated Slater determinant ansatz or the Jastrow antisymmetrized geminal power ansatz, exploiting the gauge-invariant and locality properties of their geminal representation. We demonstrate the effectiveness of our method for H 2 and Cl 2 molecules and for the cubic boron nitride crystal. Our framework has a better algorithmic scaling with the system size than the traditional finite-difference method and, in practical applications, is as efficient as single-point VMC calculations. Thus, it paves the way to study dynamical properties of materials, such as phonons, and is beneficial for pursuing more reliable machine-learning interatomic potentials based on unbiased VMC forces. Published by the American Physical Society 2024
We introduce an efficient method to construct optimal and system adaptive basis sets for use in electronic structure and quantum Monte Carlo calculations. The method is based on an embedding scheme in which a reference atom is singled out from its environment, while the entire system (atom and environment) is described by a Slater determinant or its antisymmetrized geminal power (AGP) extension. The embedding procedure described here allows for the systematic and consistent contraction of the primitive basis set into geminal embedded orbitals (GEOs), with a dramatic reduction of the number of variational parameters necessary to represent the many-body wave function, for a chosen target accuracy. Within the variational Monte Carlo method, the Slater or AGP part is determined by a variational minimization of the energy of the whole system in presence of a flexible and accurate Jastrow factor, representing most of the dynamical electronic correlation. The resulting GEO basis set opens the way for a fully controlled optimization of many-body wave functions in electronic structure calculation of bulk materials, namely, containing a large number of electrons and atoms. We present applications on the water molecule, the volume collapse transition in cerium, and the high-pressure liquid hydrogen.