Diffusion Quantum Monte Carlo Method Research Articles

Correlation energy of the paramagnetic electron gas at the thermodynamic limit

The variational and diffusion quantum Monte Carlo methods are used to calculate the correlation energy of the paramagnetic three-dimensional homogeneous electron gas at intermediate to high density. Ground-state energies in finite cells are determined using Slater-Jastrow-backflow trial wave functions, and finite-size errors are removed using twist-averaged boundary conditions and extrapolation of the energy per particle to the thermodynamic limit of infinite system size. Our correlation energies in the thermodynamic limit are more accurate than previous results. The present diffusion quantum Monte Carlo energies together with our recently reported [Phys. Rev. B 105, 245135 (2022)] results at low density, are used to parametrize the correlation energy of the electron gas using a functional form that satisfies the exact asymptotic behavior at high density.

Barrier heights, reaction energies and bond dissociation energies for RH + HO2 reactions with coupled-cluster theory, density functional theory and diffusion quantum Monte Carlo methods.

Hydrogen abstraction reactions by the HO2 radical from hydrocarbon molecules are an important class of reactions in the autoignition of hydrocarbon fuels. Performance of DLPNO-CC and DFT methods using three hybrids and four double hybrids as well as FN-DMC with the single-Slater-Jastrow trial wavefunction on barrier heights and reaction energies of RH + HO2 reactions as well as bond dissociation energies of the involved X-H molecules is evaluated by comparison with the highly accurate CCSD(T)-F12b/CBS results in this study. Our results show that the DLPNO-CCSD(T)-F12 method can achieve highly accurate barrier heights, reaction energies and X-H bond energies for RH + HO2 reactions at a relatively low computational cost, and it is applicable to the H-abstraction reactions of larger molecules. Among all DFAs, MN15 and the employed double hybrids can achieve accurate barrier heights and reaction energies with MADs of less than or around 2 kJ mol-1, but their error on X-H bond energies is more pronounced. Only DSD-BLYP and DSD-PBEB95 can provide X-H bond energies with MADs less than 4 kJ mol-1. Considering dispersion correction in DFT calculations does not improve these barrier heights and reaction energies. The error of FN-DMC on barrier heights and reaction energies is slightly larger than that of MN15 and those of double hybrids, but it can achieve results within chemical accuracy for these reactions and the X-H bond energies.

Low-density phase diagram of the three-dimensional electron gas

Variational and diffusion quantum Monte Carlo methods are employed to investigate the zero-temperature phase diagram of the three-dimensional homogeneous electron gas at very low density. Fermi fluid and body-centered cubic Wigner crystal ground state energies are determined using Slater-Jastrow-backflow and Slater-Jastrow many-body wave functions at different densities and spin polarizations in finite simulation cells. Finite-size errors are removed using twist-averaged boundary conditions and extrapolation of the energy per particle to the thermodynamic limit of infinite system size. Unlike previous studies, our results show that the electron gas undergoes a first-order quantum phase transition directly from a paramagnetic fluid to a body-centered cubic crystal at density parameter $r_\text{s} = 86.6(7)$, with no region of stability for an itinerant ferromagnetic fluid. However there is a possible magnetic phase transition from an antiferromagnetic crystal to a ferromagnetic crystal at $r_\text{s}=93(3)$.

Diffusion quantum Monte Carlo method on diradicals using single- and multi-determinant-Jastrow trial wavefunctions and different orbitals.

In this work, the diffusion quantum Monte Carlo (DMC) method is employed to calculate the energies of singlet and triplet states for a series of organic diradicals and diatomic diradicals with π2 configuration. Single-determinant-Jastrow (SDJ) trial wavefunctions for triplet states, two-determinant-Jastrow (2DJ) trial wavefunctions for the singlet states, and multi-determinant-Jastrow (MDJ) trial wavefunctions are employed in DMC calculations using restricted open-shell B3LYP (ROB3LYP) orbitals, complete-active-space self-consistent field (CASSCF) orbitals, state-average CASSCF orbitals, or frozen-CASSCF orbitals. Our results show that DMC energies using either SDJ/2DJ or MDJ with ROB3LYP orbitals are close to or lower than those with the other orbitals for organic diradicals, while they are not very sensitive to the employed orbitals for diatomic diradicals. Furthermore, using MDJ can reduce DMC energies to some extent for most of the investigated organic diradicals and some diatomic diradicals. The importance of MDJ on DMC energies can be estimated based on the percentage of main determinants in the CASCI wavefunction. On the other hand, singlet-triplet gaps can be calculated reasonably with DMC using MDJ with a mean absolute error of less than 2 kcal/mol with all these orbitals. CASCI wavefunctions using density functional theory orbitals are preferred in constructing MDJ trial wavefunctions in practical DMC calculations since it is easier to obtain such wavefunctions than CASSCF methods.

Reliable radical stabilization energies from diffusion Monte Carlo calculations.

We assess the performance of variational (VMC) and diffusion (DMC) quantum Monte Carlo methods for calculating the radical stabilization energies of a set of 43 carbon-centered radical species. Even using simple single-determinant trial wavefunctions, both methods perform exceptionally well, with mean absolute deviations from reference values well under the chemical accuracy standard of 1 kcal/mol. In addition, the use of DMC results in a highly concentrated spread of errors, with all 43 results within chemical accuracy at the 95% confidence level. These results indicate that DMC is an extremely reliable method for calculating radical stabilization energies and could be used as a benchmark method for larger systems in future.

Electronic Structure of Nanoclusters by Quantum Monte Carlo Methods

The valence electron binding energies of the atomic clusters $$\hbox {XAl}_3^-$$ (X = Si, Ge, and Sn) and $$\hbox {YAl}_4^-$$ (Y = Li, Na, and Cu) are investigated using a combination of the fixed-node diffusion quantum Monte Carlo method (FN-DMC), the density functional theory, and the Hartree–Fock approximation. A brief review of the used theoretical approaches is presented with emphasis on the variational and diffusion Monte Carlo techniques and their applications to study the electronic structures of atomic clusters. The obtained results for the vertical detachment energies (VDE) from the FN-DMC are in excellent agreement with available experimental photoelectron spectroscopy data. A comparison between the FN-DMC results and HF ones allows to quantify the electron correlation effects and their impact on the stability of the clusters. The analysis reveals that the electron correlation enhances the VDE of the atomic clusters significantly and plays an essential role in their stability.

Variational and diffusion quantum Monte Carlo calculations with the CASINO code.

We present an overview of the variational and diffusion quantum Monte Carlo methods as implemented in the casino program. We particularly focus on developments made in the last decade, describing state-of-the-art quantum Monte Carlo algorithms and software and discussing their strengths and weaknesses. We review a range of recent applications of casino.

Electronic structure of metal-doped aluminum clusters by quantum Monte Carlo method

Using the fixed-node diffusion quantum Monte Carlo method (FN-DMC), the density functional theory (DFT), and the Hartree-Fock (HF) approximation, we investigate the valence electron binding energies of atomic clusters. Calculations are applied to the metal-doped anionic aluminum clusters (X = K, Rb, Ag, and Au) and their vertical detachment energies (VDE) are obtained. A comparison between the FN-DMC results and the HF ones allows us to quantify the electron correlation effects and their impact on the stability of the clusters. The analysis reveals that the electron correlation enhances the vertical detachment energies of the atomic clusters significantly.

Electron Confinement and Magnetism of (LaTiO3)1/(SrTiO3)5 Heterostructure: A Diffusion Quantum Monte Carlo Study.

We have applied the diffusion quantum Monte Carlo (DMC) method to study the electron confinement and magnetic structure in the (LaTiO3)1/(SrTiO3)5 heterostructure. The DMC results were compared with various density functional theory (DFT) methods, including local density approximation (LDA), generalized gradient approximation (GGA), LDA+U, and GGA+U, as well as the recently proposed strongly constrained appropriately normed (SCAN) and van der Waals-Bayesian error estimation functional (vdW-BEEF). We found that many-body correlations are crucial to accurately describe the localization of the two-dimensional (2D) electron gas around the lanthanum planes. DMC predicts 20% more electron density within the first interfacial titanium layer in (LaTiO3)1/(SrTiO3)5 than LDA+U, suggesting that the degree of confinement of the 2D electron gas in the interfacial region is underestimated with semilocal DFT approximations. DMC yields the ferromagnetic (FM) state as the ground state of (LaTiO3)1/(SrTiO3)5 and the antiferromagnetic (AFM) and nonmagnetic (NM) states that are higher in energy by 37(15) and 238(15) meV per lanthanum atom at the interface, respectively. Most DFT methods yield the FM and NM states within less than 25 meV in energy and could not find the AFM state.

Quantum Monte Carlo Study of the Water Dimer Binding Energy and Halogen-π Interactions.

Halogen-π systems are involved with competition between halogen bonding and π-interaction. Using the diffusion quantum Monte Carlo (DMC) method, we compare the interaction of benzene with diatomic halogens (X2: Cl2/Br2) with the typical hydrogen bonding in the water dimer, taking into account explicit correlations of up to three bodies. The benzene-Cl2/Br2 binding energies (13.07 ± 0.42/16.62 ± 0.02 kJ/mol) attributed to both halogen bonding and dispersion are smaller than but comparable to the typical hydrogen bonding in the water dimer binding energy (20.88 ± 0.27 kJ/mol). All of the above values are in good agreement with those from the coupled-cluster with single, double, and noniterative triple excitations (CCSD(T)) results at the complete basis set limit (benzene-Cl2/Br2: 12.78/16.17 kJ/mol; water dimer: 21.0 kJ/mol).

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.

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.

Binding energies of excitonic complexes in type-II quantum rings from diffusion quantum Monte Carlo calculations

Excitonic complexes in type-II quantum-ring heterostructures may be considered as artificial atoms due to the confinement of only one charge-carrier type in an artificial nucleus. Binding energies of excitons, trions, and biexcitons in these nanostructures are then effectively ionization energies of these artificial atoms. The binding energies reported here are calculated within the effective-mass approximation using the diffusion quantum Monte Carlo method and realistic geometries for gallium antimonide rings in gallium arsenide. The electrons form a halo outside the ring, with very little charge density inside the central cavity of the ring. The de-excitonization and binding energies of the complexes are relatively independent of the precise shape of the ring.

Singlet-triplet gaps in diradicals obtained with diffusion quantum Monte Carlo using a Slater-Jastrow trial wavefunction with a minimum number of determinants.

Diradicals are essential species in a wide range of chemical processes, whereas the computational study of their electronic structure often remains a challenge due to near-degeneracy of the frontier molecular orbitals. The fixed-node diffusion quantum Monte Carlo (FN-DMC) method is employed to calculate adiabatic energy gaps of some typical diradicals with the Slater-Jastrow trial wavefunction. The antisymmetrized part of the trial wavefunction is taken to be a linear combination of a minimum number of determinants using RB3LYP orbitals from the closed-shell singlet state or ROB3LYP orbitals from the triplet state. Our results show that using the two-determinant-Jastrow trial wavefunction is necessary to achieve reliable energy differences between closed-shell singlet states. The energy of the triplet state with MS = 1 is calculated to be lower than that with MS = 0 with FN-DMC even using trial wavefunctions with spin-pure states as their antisymmetrized parts and this difference is reduced with better orbitals. This indicates that the fixed-node error is smaller for the triplet state with MS = 1. Adiabatic energy gaps obtained from the present FN-DMC calculations are in reasonable agreement with available experimental values. Compared with results of the high level EOM-SF-CC method, energy gaps of FN-DMC with RB3LYP orbitals are slightly better than those using ROB3LYP orbitals and results of EOM-SF-CCSD. The present FN-DMC calculations using the simplest ansatz for the trial wavefunction can achieve reasonable results for these diradicals and they can readily be applied to large diradicals.

Quantum Monte Carlo study of the electron binding energies and aromaticity of small neutral and charged boron clusters.

The valence electron binding energies and the aromaticity of neutral and charged small boron clusters with three and four atoms are investigated using a combination of the fixed-node diffusion quantum Monte Carlo (FN-DMC) method, the density functional theory, and the Hartree-Fock approximation. The obtained electron binding energies such as the adiabatic detachment energy, vertical detachment energy, adiabatic ionization potential, and the vertical ionization potential are in excellent agreement with available experimental measurements. Their decomposition into three physical components such as the electrostatic potential and exchange interaction, the relaxation energy, and the electronic correlation effects has allowed us to determine that the neutral boron clusters are stabilized by the electrostatic and exchange interactions, while the anionic ones are stabilized by the relaxation and correlation effects. The aromaticity is studied based on electronic structure principles descriptor and on the resonance energy. The FN-DMC results from the electronic structure principles of the energy, hardness, and eletrophilicity have supported the aromaticity of , , and B4 and partially supported the aromaticity of the clusters B3, , and . The obtained values for the resonance energy of the clusters , B3, , B4, , and are 55.1(7), 54.2(8), 33.9(7), 84(1), 67(1), and 58(1) kcal/mol, respectively. Therefore, the order of decreasing stability of the trimer is , while for the tetramer it is , which is in agreement with the results from the molecular orbital analysis.

Fixed-Node Diffusion Quantum Monte Carlo Method on Dissociation Energies and Their Trends for R-X Bonds (R = Me, Et, i-Pr, t-Bu).

Achieving both bond dissociation energies (BDEs) and their trends for the R-X bonds with R = Me, Et, i-Pr, and t-Bu reliably is nontrivial. Density functional theory (DFT) methods with traditional exchange-correlation functionals usually have large error on both the BDEs and their trends. The M06-2X functional gives rise to reliable BDEs, but the relative BDEs are determined not as accurately. More demanding approaches such as some double-hybrid functionals, for example, G4 and CCSD(T), are generally required to achieve the BDEs and their trends reliably. The fixed-node diffusion quantum Monte Carlo method (FN-DMC) is employed to calculated BDEs of these R-X bonds with X = H, CH3, OCH3, OH, and F in this work. The single Slater-Jastrow wave function is adopted as trial wave function, and pseudopotentials (PPs) developed for quantum Monte Carlo calculations are chosen. Error of these PPs is modest in wave function methods, while it is more pronounced in DFT calculations. Our results show that accuracy of BDEs with FN-DMC is similar to that of M06-2X and G4, and trends in BDEs are calculated more reliably than M06-2X. Both BDEs and trends in BDEs of these bonds are reproduced reasonably with FN-DMC. FN-DMC using PPs can thus be applied to BDEs and their trends of similar chemical bonds in larger molecules reliably and provide valuable information on properties of these molecules.

Nuclear quantum effects induce metallization of dense solid molecular hydrogen.

We present an accurate computational study of the electronic structure and lattice dynamics of solid molecular hydrogen at high pressure. The band-gap energies of the C2/c, Pc, and P63/m structures at pressures of 250, 300, and 350 GPa are calculated using the diffusion quantum Monte Carlo (DMC) method. The atomic configurations are obtained from ab initio path-integral molecular dynamics (PIMD) simulations at 300 K and 300 GPa to investigate the impact of zero-point energy and temperature-induced motion of the protons including anharmonic effects. We find that finite temperature and nuclear quantum effects reduce the band-gaps substantially, leading to metallization of the C2/c and Pc phases via band overlap; the effect on the band-gap of the P63/m structure is less pronounced. Our combined DMC-PIMD simulations predict that there are no excitonic or quasiparticle energy gaps for the C2/c and Pc phases at 300 GPa and 300 K. Our results also indicate a strong correlation between the band-gap energy and vibron modes. This strong coupling induces a band-gap reduction of more than 2.46 eV in high-pressure solid molecular hydrogen. Comparing our DMC-PIMD with experimental results available, we conclude that none of the structures proposed is a good candidate for phases III and IV of solid hydrogen. © 2017 Wiley Periodicals, Inc.

Diffusion quantum Monte Carlo calculations of SrFeO3 and LaFeO3.

The equations of state, formation energy, and migration energy barrier of the oxygen vacancy in SrFeO3 and LaFeO3 were calculated with the diffusion quantum Monte Carlo (DMC) method. Calculations were also performed with various Density Functional Theory (DFT) approximations for comparison. DMC reproduces the measured cohesive energies of these materials with errors below 0.23(5) eV and the structural properties within 1% of the experimental values. The DMC formation energies of the oxygen vacancy in SrFeO3 and LaFeO3 under oxygen-rich conditions are 1.3(1) and 6.24(7) eV, respectively. Similar calculations with semi-local DFT approximations for LaFeO3 yielded vacancy formation energies 1.5 eV lower. Comparison of charge density evaluated with DMC and DFT approximations shows that DFT tends to overdelocalize the electrons in defected SrFeO3 and LaFeO3. Calculations with DMC and local density approximation yield similar vacancy migration energy barriers, indicating that steric/electrostatic effects mainly determine migration barriers in these materials.

A benchmark study of Li2+, Li2−, LiH+ and LiH−: Quantum Monte-Carlo and coupled-cluster computations

For the first time, very accurate potential energy curves (PEC) have been computed by the all electron Diffusion Quantum Monte-Carlo (DMC) and CCSD(T) methods for the ground-state of the Li2+, Li2−, LiH+ and LiH− ions. In addition to the molecular moieties, Li+, Li−, H− ions have also been studied by the aforementioned methods. The employed trial wave functions for the DMC calculations are a multiplication of multi-configuration expansions which are prepared by the Complete Active Space Self-Consistent Field method (CASSCF) with the aug-cc-pVTZ and the aug-cc-pCVTZ basis sets and the Jastrow factor. The CCSD(T) computations with all electrons correlated, have been performed by the cc-pV5Z, aug-cc-pCVQZ and aug-cc-pV6Z basis sets. In addition, the correlation energies for all of the studied atomic and molecular species have been calculated. For the studied molecular species, the Hartree-Fock energies in the complete basis set limit (ECBS) have not been reported. In this work for each of the molecular systems, the most negative energy which has been computed by the cc-pV5Z or aug-cc-pCVQZ basis sets has been used. The obtained PECs by the DMC and CCSD(T) methods are used to calculate the vibration-rotation energy levels and spectroscopic constants.

A quantum Monte Carlo study of the structural and electronic properties of small cationic and neutral lithium clusters.

Using the fixed-node diffusion quantum Monte Carlo method, we calculate the total energy of small cationic and neutral lithium clusters. We estimate the ionization potential, atomic binding energy, dissociation energy, and the second difference in energy. We present a critical analysis of the structural and electronic properties of the clusters. The bond lengths and binding and dissociation energies obtained from the calculations are in excellent agreement with the available experimental results. A comparative analysis of the dissociation energy and the second difference in energy indicates that the cationic clusters Li3+, Li5+, and Li7+ are the most stable ones. We have also studied the electron correlation effects in the lithium clusters. The cationic clusters of odd-number size are relatively more favored in terms of correlation energy than their neighbors of even-number size. In the range of cluster sizes under investigation, we find that the contribution of electron correlation to ionization potential is not larger than 28% of its total values, whereas it enhances significantly the dissociation energy of the clusters reaching up to 70% of its total values for the most stable ones.

Quantum Monte Carlo study of the energetics of the rutile, anatase, brookite, and columbiteTiO2polymorphs

The relative energies of the low-pressure rutile, anatase, and brookite polymorphs and the high-pressure columbite polymorph of TiO$_2$ have been calculated as a function of temperature using the diffusion quantum Monte Carlo (DMC) method and density functional theory (DFT). The vibrational energies are found to be important on the scale of interest and significant quartic anharmonicity is found in the rutile phase. Static-lattice DFT calculations predict that anatase is lower in energy than rutile, in disagreement with experiment. The accurate description of electronic correlations afforded by DMC calculations and the inclusion of anharmonic vibrational effects contribute to stabilizing rutile with respect to anatase. Our calculations predict a phase transition from anatase to rutile TiO$_2$ at $630 \pm 210$ K.