Molecular dynamics nuclear Schrodinger equation

In Section II, molecular dynamics within the BO approximation was introduced. As shown in Appendix A, the full nuclear Schrodinger equation is, however. 

Bound-state photoabsorption, direct molecular dynamics, nuclear motion Schrodinger equation, 365-373... 

Discrete Fourier transform (DFT), non-adiabatic coupling, Longuet-Higgins phase-based treatment, two-dimensional two-surface system, scattering calculation, 153-155 Discrete variable representation (DVR) direct molecular dynamics, nuclear motion Schrodinger equation, 364-373 non-adiabatic coupling, quantum dressed classical mechanics, 177-183 formulation, 181-183... 

In this section, the basic theory of molecular dynamics is presented. Starting from the BO approximation to the nuclear Schrodinger equation, the picture of nuclear dynamics is that of an evolving wavepacket. As this picture may be unusual to readers used to thinking about nuclei as classical particles, a few prototypical examples are shown. 

Rather than solve a Schrodinger equation with the Nuclear Hamiltonian (above), a common approximation is to assume that atoms are heavy enough so that classical mechanics is a good enough approximation. Motion of the particles on the potential surface, according to the laws of classical mechanics, is then the subject of classical trajectory analysis or molecular dynamics. These come about by replacing Equation (7) on page 164 with its classical equivalent ... 

The development of an ab initio quantum molecular dynamics method is guided by the need to overcome two main obstacles. First, one needs to develop an efficient, yet accurate, method for solving the electronic Schrodinger equation for both ground and excited electronic states. Second, the quantum mechanical character of the nuclear dynamics must be addressed. (This is necessary for the description of photochemical and tunneling processes.) This section provides a detailed discussion of the approaches we have taken to solve these two problems. 

Nuclear motion Schrodinger equation direct molecular dynamics, 363-373 vibronic coupling, adiabatic effects, 382-384 electronic states ... 

Schiff approximation, electron nuclear dynamics (END), molecular systems, 339—342 Schrodinger equation ... 

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