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* Introduction




This web site is the QMC tutorial of the LTTC winter school


This web site contains the QMC tutorial of the 2021 LTTC winter school


[[https://www.irsamc.upstlse.fr/lttc/Luchon][Tutorials in Theoretical Chemistry]].




We propose different exercises to understand quantum Monte Carlo (QMC)


methods. In the first section, we propose to compute the energy of a


methods. In the first section, we start with the computation of the energy of a


hydrogen atom using numerical integration. The goal of this section is


to introduce the /local energy/.


Then we introduce the variational Monte Carlo (VMC) method which


to familarize yourself with the concept of /local energy/.


Then, we introduce the variational Monte Carlo (VMC) method which


computes a statistical estimate of the expectation value of the energy


associated with a given wave function.


Finally, we introduce the diffusion Monte Carlo (DMC) method which


gives the exact energy of the hydrogen atom and of the H_2 molecule.


associated with a given wave function, and apply this approach to the


hydrogen atom.


Finally, we present the diffusion Monte Carlo (DMC) method which


we use here to estimate the exact energy of the hydrogen atom and of the H_2 molecule.




Code examples will be given in Python and Fortran. You can use


whatever language you prefer to write the program.


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the wave functions considered here are real: for an $N$ electron


system where the electrons move in the 3dimensional space,


$\Psi : \mathbb{R}^{3N} \rightarrow \mathbb{R}$. In addition, $\Psi$


is defined everywhere, continuous and infinitely differentiable.


is defined everywhere, continuous, and infinitely differentiable.




All the quantities are expressed in /atomic units/ (energies,


coordinates, etc).



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