XI. Quantum Dynamics

Nuclei move according to the time-dependent Schrödinger equation:

Exact solution of time-dependent Schrödinger equation only possible for degrees of freedom
A. TDSCF (time-dependent self-consistent-field)
-N-particle wavefunction is a single product of N 1-particle wavefunctions
-each particle moving in an average field due to the other particles
Advantage
-computationally simple and fast
N coupled 1-dimensional equations that can be solved self-consistently
Disadvantage
-missing important correlation (i.e. inadequate for describing charge transfer reactions)
B. MC-TDSCF (multiconfigurational time-dependent self-consistent-field)
N-particle wavefunction is a linear combination of products of N 1-particle wavefunctions
Advantage
-incorporates significant correlation
Disadvantage
-computationally much more complicated and slower than TDSCF
C. Semiclassical methods
1. Gaussian wavepackets
-approximate the total wavefunction as a product of 1-particle wavefunctions that are each a generalized complex Gaussian with parameters for the position (of the center), the momentum, the width, and the phase
-algebraic manipulation leads to simple equations of motion for these Gaussian parameters
2. Path integral methods
-represent each atom as a string of beads
-algebraic manipulation leads to slightly altered classical molecular dynamics simulations on these beads