Optimization of quantum Monte Carlo wavefunctions using analytical derivatives

1992 ◽  
Vol 70 (2) ◽  
pp. 366-371 ◽  
Author(s):  
Hartmut Bueckert ◽  
Stuart M. Rothstein ◽  
Jan Vrbik
Keyword(s):  
Monte Carlo ◽  
Electron Correlation ◽  
Ground State ◽  
Quantum Monte Carlo ◽  
Numerical Evaluation ◽  
Monte Carlo Optimization ◽  
Technical Issues ◽  
Numerical Performance ◽  
Analytical Derivatives ◽  
State Wavefunctions

We show how to optimize many-parameter wavefunctions for use in quantum Monte Carlo by deriving and utilizing formulas for analytical rather than numerical evaluation of the required derivatives. We present these in a form which is easily vectorizable for use on a supercomputer. We also discuss several technical issues of variational Monte Carlo to ensure both an unbiased and efficient optimization. Finally, we illustrate our optimization scheme's numerical performance by optimizing ground-state wavefunctions for LiH and H2O, each with more than 100 variational parameters. Keywords: quantum Monte Carlo, optimization, electron correlation, LiH, H2O.

A quantum Monte Carlo study on electron correlation effects in small aluminum hydride clusters

2015 ◽  
Vol 39 (3) ◽  
pp. 2195-2201 ◽  
Author(s):  
J. Higino Damasceno ◽  
J. N. Teixeira Rabelo ◽  
Ladir Cândido
Keyword(s):  
Monte Carlo ◽  
Electron Correlation ◽  
Quantum Monte Carlo ◽  
Aluminum Hydride ◽  
Monte Carlo Study ◽  
Binding Energies ◽  
Electron Interaction ◽  
Correlation Effects ◽  
Ionic Clusters ◽  
Electron Correlation Effects

Using accurate methods we calculate binding energies to discuss the electron–electron interaction in the formation of AlnHm ionic clusters.

A survey on pure sampling in quantum Monte Carlo methods

2013 ◽  
Vol 91 (7) ◽  
pp. 505-510 ◽  
Author(s):  
Stuart M. Rothstein
Keyword(s):  
Monte Carlo ◽  
Ground State ◽  
Quantum Monte Carlo ◽  
Sampling Methods ◽  
Electrical Response ◽  
Distribution Functions ◽  
Monte Carlo Algorithm ◽  
Position Operator ◽  
Trial Solution ◽  
Mixed Distribution

The most commonly employed diffusion Monte Carlo algorithm and some of its variants afford a way to sample configuration space from a so-called “mixed distribution”, the product of an input trial solution to the Schrödinger equation for the ground state and its unknown exact solution. This mixed distribution is sufficient to compute the ground state energy and other properties represented by operators that commute with the Hamiltonian. These energy-related properties are exact, save for a small bias introduced by the input trial function’s incorrect exchange nodes, the so-called “fixed-node error”. However, properties represented by operators that commute with the position operator are also of interest. When calculated by sampling from the mixed distribution, these properties are much more strongly biased by the input trial function. Our objective is to review methods that allow sampling from the desired “pure” distribution, one that is unbiased except for the exchange node error. Thereby, one accurately calculates physical properties such as the dipole and other electrical moments, electrical response properties of molecules, and particle distribution functions for clusters. We survey the results of calculations that employ pure-sampling methods through what has been published in year 2012. Our review also touches on truly exact sampling methods.

scholarly journals Unconventional phase transitions in strongly anisotropic 2D (pseudo)spin systems

2018 ◽  
Vol 185 ◽  
pp. 08006
Author(s):  
Vitaly Konev ◽  
Evgeny Vasinovich ◽  
Vasily Ulitko ◽  
Yury Panov ◽  
Alexander Moskvin
Keyword(s):  
Magnetic Field ◽  
Monte Carlo ◽  
Phase Transitions ◽  
Ground State ◽  
Quantum Monte Carlo ◽  
Mean Field ◽  
Spin Systems ◽  
Field Approach ◽  
Generalized Mean

We have applied a generalized mean-field approach and quantum Monte-Carlo technique for the model 2D S = 1 (pseudo)spin system to find the ground state phase with its evolution under application of the (pseudo)magnetic field. The comparison of the two methods allows us to clearly demonstrate the role of quantum effects. Special attention is given to the role played by an effective single-ion anisotropy ("on-site correlation").

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