What is it about?
The fixed-node variant of the diffusion quantum Monte Carlo method (FN-DMC) is capable of obtaining the exact eigenvalues (albeit numerically with statistical error) of a many-electron Hamilton operator, provided that the nodal hypersurface of the exact wave function is given. The use of nodes of a trial wave function leads to the node location error. The authors have developed local criteria to assess the accuracy of the nodes based on the distances of the nodal hypersurfaces of PsiT, TPsiT, and HPsiT which coincide for the exact wave function. These criteria are used to develop direct optimization methods for the nodal hypersurface. The optimization of the nodes is demonstrated for simple wave functions of the Be atom and the C2 molecule and verified with FN-DMC calculations.
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Why is it important?
Diffusion Monte-Carlo calculations converge to the exact energies if one knows exactly the nodal lines of any given quantum system. This paper shows realistic benchmark calculations, namely the Be atom and the C2 molecule.
Perspectives
This paper has been rather influential in quantum chemistry based on its citations.
Dr Tony Cyril Scott
RWTH-Aachen University
Read the Original
This page is a summary of: Direct optimization of nodal hypersurfaces in approximate wave functions, The Journal of Chemical Physics, April 2007, American Institute of Physics,
DOI: 10.1063/1.2716640.
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