Quantum Monte Carlo - Maple Application Center
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Quantum Monte Carlo

: Jong Ho Choi
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Quantum Monte Carlo (QMC) method is a numerical method to calculate energy of quantum system. Monte Carlo method is commonly used method to calculated an average of a variables in large dimensional space (e.g. a physical variable in a classical phase space). Metropolis-Hasting algorithm make sampling of a variable to follow specific probability distribution possible. In quantum mechanics, Monte Carlo process can be used, but the variable (energy) and the probability distribution depends on wavefunctions. Variational Monte Carlo (VMC) method is simpler method that a approximated trial wavefunctions are used for the Monte Carlo sampling. This method has a systematic error due to the wavefunctions. The more accurate method is Diffusion Monte Carlo (DMC) method where we sample energies from the exact ground state wave functions. QMC method can be used for complex system like transition metals. As an example, the transition energy of Cu atom and Cu+ ion result of Caffarel et. al. is presented and compared with other method: Hartree-Fock, Coupled-cluster, and Density functional theory. Application uses the Maple Quantum Chemistry Toolbox. 

Application Details

Publish Date: March 06, 2023
Created In: Maple 2022
Language: English

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