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It seems that QMC has all the requisites to become the method of choice in the future, as, we believe, it can fulfill all three of these requirements. Clearly, QMC’s ability to scale up and treat the many-body effects directly is invaluable. But QMC also has many other attributes. For example, it is straightforward to include thermal, zero-point, or classical nuclear effects in PIMC. Certainly, until the fermion sign problem is solved, there is always a question mark hanging over the field: Is the method a fundamental advance, or is it merely a candidate for the most accurate approximate scheme currently known?

Alder, Phys. Rev. Lett. 45, 566 (1980). J. B. Anderson, J . Chem. Phys. 63, 1499 (1975). D. M. Ceperley, Physica B 108, 875 (1981). D. M. Ceperley and B. J. Alder, J . Chem. Phys. 81, 5833 (1984). B. L. Hammond, W. A . , and P. J. Reynolds, Monte Carlo Methods in A b Initio Quantum Chemistry, World Scientific, Singapore, 1994. D. M. Ceperley and M. H. Kalos, in Monte Carlo Methods in Statistical Physics, K. , Springer-Verlag, Berlin, 1979. K. E. Schmidt and M. H. Kalos, in Monte Carlo Methods in Statistical Physics II, K.

H. MAK Department of Chemistry, University of Southern California, Los Angeles, California REINHOLD EGGER Fakultat f u r Physik, Universitat Freiburg, Freiburg, Germany CONTENTS I. Introduction 11. General Strategy 111. Real-Time QMC for Spin-Boson Dynamics A. Spin-Boson Models B. Discretization of the Path Integral C. Elimination of Quasiclassical Degrees of Freedom D. Monte Carlo Sampling IV. Applications A. Dynamical Test of the Centroid Quantum Transition-State Theory for Electron Transfer Reactions B.

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