Titlebook: Nonlinear Hamiltonian Mechanics Applied to Molecular Dynamics; Theory and Computati Stavros C. Farantos Book 2014 The Author(s) 2014 Chemic

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2191-5407 material: .This brief presents numerical methods for describing and calculating invariant phase space structures, as well as solving the classical and quantum equations of motion for polyatomic molecules. Examples covered include simple model systems to realistic cases of molecules spectroscopicall

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2191-5407 te molecular dynamics by investigating invariant structures in phase space. Intramolecular energy transfer, and the breaking and forming of a chemical bond have now found a rigorous explanation by studying phase space structures..978-3-319-09987-3978-3-319-09988-0Series ISSN 2191-5407 Series E-ISSN 2191-5415

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Book 2014quations of motion for polyatomic molecules. Examples covered include simple model systems to realistic cases of molecules spectroscopically studied..Vibrationally excited and reacting molecules are nonlinear dynamical systems, and thus, nonlinear mechanics is the proper theory to elucidate molecula

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Dynamical Systems,eriodic orbits by varying a parameter in the potential function or the energy of the system are investigated. Methods of analysing non-periodic orbits, regular and chaotic, such as Poincaré surfaces of section, maximal Lyapunov exponent and autocorrelation functions are introduced and explained.

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Quantum and Semiclassical Molecular Dynamics,value representation method are topics of this chapter. Finally, an introduction of how to numerically solve the Schr?dinger equation in a Cartesian coordinate system, which results in a simple form molecular Hamiltonian, is provided.

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Numerical Methods,amined and comparisons with the more popular pseudospectral methods is made. For the location of periodic orbits the multiple shooting method is developed as it has been thoroughly tested. Finally, computer codes for studying classical nonlinear molecular dynamics and solving the Schr?dinger equation are described.