scholarly journals A new scheme for fixed node diffusion quantum Monte Carlo with pseudopotentials: Improving reproducibility and reducing the trial-wave-function bias

2019 ◽  
Vol 151 (13) ◽  
pp. 134105 ◽  
Author(s):  
Andrea Zen ◽  
Jan Gerit Brandenburg ◽  
Angelos Michaelides ◽  
Dario Alfè
Keyword(s):  
Monte Carlo ◽  
Wave Function ◽  
Quantum Monte Carlo ◽  
Trial Wave Function ◽  
Fixed Node

THE DIFFUSION QUANTUM MONTE CARLO METHOD: DESIGNING TRIAL WAVE FUNCTIONS FOR NiO

2003 ◽  
Vol 17 (28) ◽  
pp. 5425-5434 ◽  
Author(s):  
R. J. NEEDS ◽  
M. D. TOWLER
Keyword(s):  
Monte Carlo ◽  
Wave Function ◽  
Monte Carlo Method ◽  
Transition Metal ◽  
Quantum Monte Carlo ◽  
Monte Carlo Study ◽  
Trial Wave Function ◽  
Wave Functions ◽  
Quantum Monte Carlo Method

A brief overview of the diffusion quantum Monte Carlo method is given. The importance of the trial wave function is emphasised and we discuss how to design satisfactory forms for transition metal monoxides. Some results of a diffusion quantum Monte Carlo study of NiO are reported.

scholarly journals Phase separation in the two-dimensional Hubbard model: A fixed-node quantum Monte Carlo study

1998 ◽  
Vol 58 (22) ◽  
pp. R14685-R14688 ◽  
Author(s):  
A. C. Cosentini ◽  
M. Capone ◽  
L. Guidoni ◽  
G. B. Bachelet
Keyword(s):  
Monte Carlo ◽  
Phase Separation ◽  
Hubbard Model ◽  
Quantum Monte Carlo ◽  
Monte Carlo Study ◽  
Two Dimensional ◽  
Fixed Node

scholarly journals OPTIMIZATION OF QUANTUM MONTE CARLO WAVE FUNCTION: STEEPEST DESCENT METHOD

2010 ◽  
Vol 21 (04) ◽  
pp. 523-533 ◽  
Author(s):  
M. EBRAHIM FOULAADVAND ◽  
MOHAMMAD ZARENIA
Keyword(s):  
Monte Carlo ◽  
Wave Function ◽  
Quantum Monte Carlo ◽  
Descent Method ◽  
Steepest Descent ◽  
Steepest Descent Method ◽  
Direct Energy Minimization ◽  
Direct Energy ◽  
Spatial Coordinates ◽  
Quantum Monte Carlo Method

We have employed the steepest descent method to optimize the variational groundstate quantum Monte Carlo wave function for He , Li , Be , B and C atoms. We have used both the direct energy minimization and the variance minimization approaches. Our calculations show that in spite of receiving insufficient attention, the steepest descent method can successfully minimize the wave function. All the derivatives of the trial wave function respect to spatial coordinates and variational parameters have been computed analytically. Our groundstate energies are in a very good agreement with those obtained with diffusion quantum Monte Carlo method (DMC) and the exact results.

QUANTUM MONTE CARLO SIMULATIONS OF FERMIONS: A MATHEMATICAL ANALYSIS OF THE FIXED-NODE APPROXIMATION

2006 ◽  
Vol 16 (09) ◽  
pp. 1403-1440 ◽  
Author(s):  
ERIC CANCÈS ◽  
BENJAMIN JOURDAIN ◽  
TONY LELIÈVRE
Keyword(s):  
Monte Carlo ◽  
Importance Sampling ◽  
Mathematical Analysis ◽  
Ground State ◽  
Quantum Monte Carlo ◽  
Stochastic Methods ◽  
Sampling Function ◽  
Long Time ◽  
Nodal Surfaces ◽  
Fixed Node

The Diffusion Monte Carlo (DMC) method is a powerful strategy to estimate the ground state energy E0 of an N-body Schrödinger Hamiltonian H = -½Δ + V with high accuracy. It consists of writing E0 as the long-time limit of an expectation value of a drift-diffusion process with a source term, and numerically simulating this process by means of a collection of random walkers. As for a number of stochastic methods, a DMC calculation makes use of an importance sampling function ψI which hopefully approximates some ground state ψ0 of H. In the fermionic case, it has been observed that the DMC method is biased, except in the special case when the nodal surfaces of ψI coincide with those of a ground state of H. The approximation due to the fact that, in practice, the nodal surfaces of ψI differ from those of the ground states of H, is referred to as the Fixed Node Approximation (FNA). Our purpose in this paper is to provide a mathematical analysis of the FNA. We prove that, under convenient hypotheses, a DMC calculation performed with the importance sampling function ψI, provides an estimation of the infimum of the energy 〈ψ, Hψ〉 on the set of the fermionic test functions ψ that exactly vanish on the nodal surfaces of ψI.

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