Molecular dynamics algorithms for quantum Monte Carlo methods (original) (raw)
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Application of a new reverse Monte Carlo algorithm to polyatomic molecular systems. I. Liquid water
Chemical Physics, 2001
Using a new reverse Monte Carlo algorithm, we present simulations that reproduce very well several structural and thermodynamic properties of liquid water. Both Monte Carlo, molecular dynamics simulations and experimental radial distribution functions used as input are accurately reproduced using a small number of molecules and no external constraints. Ad hoc energy and hydrogen bond analysis show the physical consistency and limitations of the generated RMC configurations.
A dynamic Monte Carlo method suitable for molecular simulations
The Journal of Chemical Physics, 1992
A dynamic Monte Carlo (MC) method for simulations has been presented which is similar to the well-known Brownian dynamics method, but is suitable for many systems and can readily be adopted to isobaric simulations. This dynamic MC has been applied to several systems and shows similar accuracy and improved efficiency compared with routine methods. It samples configuration space approximately according to the equilibrium probability density and is applicable to NPT simulations of rather complex systems, also with rigid constraints.
Hydrogen molecule ion: Path-integral Monte Carlo approach
Physical Review A, 2007
Path integral Monte Carlo approach is used to study the coupled quantum dynamics of the electron and nuclei in hydrogen molecule ion. The coupling effects are demonstrated by comparing differences in adiabatic Born-Oppenheimer and non-adiabatic simulations, and inspecting projections of the full three-body dynamics onto adiabatic Born-Oppenheimer approximation.
Physical Review B, 2018
We discuss electronic properties and their evolution for the linear chain of H2 molecules in the presence of a uniform external force f acting along the chain. The system is described by an extended Hubbard model within a fully microscopic approach. Explicitly, the microscopic parameters describing the intra-and inter-site Coulomb interactions are determined together with the hopping integrals by optimizing the system ground state energy and the single-particle wave functions in the correlated state. The many-body wave function is taken in the Jastrow form and the Variational Monte-Carlo (VMC) method is used in combination with an ab initio approach to determine the energy. Both the effective Bohr radii of the renormalized single-particle wave functions and the many-body wave function parameters are determined for each f. Hence, the evolution of the system can be analyzed in detail as a function of the equilibrium intermolecular distance, which in turn is determined for each f value. The transition to the atomic state, including the Peierls distortion stability, can thus be studied in a systematic manner, particularly near the threshold of the dissociation of the molecular into atomic chain. The computational reliability of VMC approach is also estimated.
The Journal of Chemical Physics, 2012
Configurational-bias Monte Carlo has been incorporated into the Wang-Landau method. Although the Wang-Landau algorithm enables the calculation of the complete density of states, its applicability to continuous molecular systems has been limited to simple models. With the inclusion of more advanced sampling techniques, such as configurational-bias, the Wang-Landau method can be used to simulate complex chemical systems. The accuracy and efficiency of the method is assessed using as a test case systems of linear alkanes represented by a united-atom model. With strict convergence criteria, the density of states derived from the Wang-Landau algorithm yields the correct heat capacity when compared to conventional Boltzmann sampling simulations.
An exact quantum Monte Carlo calculation of the helium–helium intermolecular potential. II
The Journal of Chemical Physics, 2001
We report "exact" ab initio calculations of potential energies for the interaction of two helium atoms. The quantum Monte Carlo method used is exact in that it requires no mathematical or physical approximations beyond those of the Schriidinger equation. As in most Monte Carlo methods there is a statistical or sampling error which is readily estimated. For the equilibrium internuclear distance of 5.6 bohr, the calculated electronic energy is -5.807 483 6 f 0.000 000 3 hartrees and the corresponding well depth (e/k) is 11.01 f 0.10 K. The calculated total energies are approximately 0.004 hartrees or 1200 K below the most recent variational calculations of Liu and McLean [J. Chem. Phys. 92, 2348 (1989)]. The calculated interaction energies are in excellent agreement with the interaction energies of Liu and McLean and with a recent experimental/theoretical compromise potential energy curve of Aziz and Slaman [J. Chem. Phys. 94, 8047 ( 199 1 )] which successfully predicts a variety of experimental measurements. The error bars of the "exact" quantum Monte Carlo interaction energies straddle the Liu-McLean and Aziz-Slaman results. The Monte Carlo results support the existence of a bound dimer state.
Variational quantum monte carlo calculation of the ground state energy of hydrogen molecule
Bayero Journal of Pure and Applied Sciences, 2010
The ground state energy of the hydrogen molecule was numerically analysed using the quantum Monte Carlo (QMC) method. The type of QMC method used in this work is the Variational Quantum Monte Carlo [VQMC]. This analysis was done under the context of the accuracy of Born-Oppenheimer approximation [fixed nuclei restriction]. The ground state energies of Hydrogen molecule for different interproton separation ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − 0 0. 1 4. 0 A are computed and compared with previous numerical and empirical results that are essentially exact. It has been found that the ground state energy of the hydrogen molecule obtained in this work approaches the precise value of-31.94eV.
Dissecting the Hydrogen Bond: A Quantum Monte Carlo Approach
Journal of Chemical Theory and Computation, 2008
We present a Quantum Monte Carlo study of the dissociation energy and the dispersion curve of the water dimer, a prototype of hydrogen bonded system. Our calculations are based on a wave function which is a modern and fully correlated implementation of the Pauling's valence bond idea: the Jastrow Antisymmetrised Geminal Power (JAGP) [Casula et al. J. Chem. Phys. 2003, 119, 6500-6511]. With this variational wave function we obtain a binding energy of -4.5(0.1) kcal/ mol that is only slightly increased to -4.9(0.1) kcal/mol by using the Lattice Regularized Diffusion Monte Carlo (LRDMC). This projection technique allows for the substantial improvement in the correlation energy of a given variational guess and indeed, when applied to the JAGP, yields a binding energy in fair agreement with the value of -5.0 kcal/mol reported by experiments and other theoretical works. The minimum position, the curvature, and the asymptotic behavior of the dispersion curve are well reproduced both at the variational and the LRDMC level. Moreover, thanks to the simplicity and the accuracy of our variational approach, we are able to dissect the various contributions to the binding energy of the water dimer in a systematic and controlled way. This is achieved by appropriately switching off determinantal and Jastrow variational terms in the JAGP. Within this scheme, we estimate that the dispersive van der Waals contribution to the electron correlation is substantial and amounts to 1.5(0.2) kcal/mol, this value being comparable with the intermolecular covalent energy that we find to be 1.1(0.2) kcal/mol. The present Quantum Monte Carlo approach based on the JAGP wave function is revealed as a promising tool for the interpretation and the quantitative description of weakly interacting systems, where both dispersive and covalent energy contributions play an important role.
Ab initio molecular dynamics simulation of liquid water by quantum Monte Carlo
The Journal of chemical physics, 2015
Although liquid water is ubiquitous in chemical reactions at roots of life and climate on the earth, the prediction of its properties by high-level ab initio molecular dynamics simulations still represents a formidable task for quantum chemistry. In this article, we present a room temperature simulation of liquid water based on the potential energy surface obtained by a many-body wave function through quantum Monte Carlo (QMC) methods. The simulated properties are in good agreement with recent neutron scattering and X-ray experiments, particularly concerning the position of the oxygen-oxygen peak in the radial distribution function, at variance of previous density functional theory attempts. Given the excellent performances of QMC on large scale supercomputers, this work opens new perspectives for predictive and reliable ab initio simulations of complex chemical systems.