Quantum and Semiclassical Molecular Dynamics

  • Stavros C. Farantos
Part of the SpringerBriefs in Molecular Science book series (BRIEFSMOLECULAR)


The two formulations of classical mechanics, Lagrangian and Hamiltonian, lead to two expressions of quantum mechanics, the path integral and canonical, respectively. After an introduction to the principles of these two theories, subjects related to calculations of molecular dynamics are discussed. Converting Schrödinger equation into quantum Hamilton’s complex equations, the complexification of the classical Hamilton’s equations, and the quantum and classical autocorrelation functions are described. Semiclassical theories based on periodic orbits, tori and the more general approach of initial value representation method are topics of this chapter. Finally, an introduction of how to numerically solve the Schrödinger equation in a Cartesian coordinate system, which results in a simple form molecular Hamiltonian, is provided.


Periodic Orbit Trace Formula Hamiltonian Operator Polyatomic Molecule Monodromy Matrix 
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Copyright information

© The Author(s) 2014

Authors and Affiliations

  1. 1.Department of ChemistryUniversity of CreteIraklionGreece
  2. 2.Institute of Electronic Structure and LaserFoundation for Research and Technology-HellasIraklionGreece

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