Introduction to the Variational Monte Carlo Method in Quantum Chemistry and Physics

Part of the Molecular Modeling and Simulation book series (MMAS)


Variational Monte Carlo (VMC) methods are a powerful set of quantum Monte Carlo (QMC) methods that may not only be used to determine the variational energy of a fully parameterized wave function, but to optimize wave functions as well. Because they can provide highly accurate trial wave functions for more advanced quantum Monte Carlo methods at a comparatively low cost, they may be viewed as the foundation upon which modern quantum Monte Carlo methods are built. In this chapter, I provide a basic introduction to VMC methods intended for beginning graduate students and workers in the fields of quantum physics and chemistry unfamiliar with the topic. I begin with a general introduction to quantum Monte Carlo methods and then describe how VMC methods fit into this larger context. I then describe how VMC may be used to determine the variational energy of a given wave function and subsequently detail how this algorithm can be modified to optimize wave functions. After illustrating how a number of basic VMC algorithms work, I elucidate how two of the most important modern VMC methods—the Linear and Stochastic Reconfiguration methods—work. To provide context, I present a few recent, novel applications of VMC methods to important problems in chemistry and physics, including the Hubbard model, excited state chemistry, and the calculation of accurate atomization energies. I end with a discussion of possible future directions for VMC algorithms.


Wave Function Hubbard Model Mean Absolute Deviation Ground State Wave Function Quantum Monte Carlo 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The author would like to acknowledge Drs. James Gubernatis and Miguel Morales-Silva for their continuous support and encouragement of my quantum Monte Carlo efforts over the many years. BMR would also like to thank the Lawrence Fellowship Program for funding and Mr. Raymond Clay and Dr. Cyrus Umrigar for their help editing this manuscript. Portions of this work were performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.


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© Springer Science+Business Media Singapore 2017

Authors and Affiliations

  1. 1.Lawrence Livermore National LaboratoryQuantum Simulations GroupLivermoreUSA
  2. 2.Department of ChemistryBrown UniversityProvidenceUSA

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