Multi-configuration time-dependent Hartree
quantum chemistry algorithm

Multi-configuration time-dependent Hartree (MCTDH) is an approach to quantum molecular dynamics, an algorithm to solve the time-dependent Schrödinger equation for multidimensional dynamical systems consisting of distinguishable particles. The nuclei of molecules is one example of such particles and their vibrational motion is a form of time-dependence. The method uses an overall wavefunction composed of products of single-particle wavefunctions as first proposed by Douglas Hartree in 1927. The "multiconfiguration" part of the method refers to combining multiple such products.
MCTDH can predict the motion of the nuclei of a molecular system evolving on one or several coupled electronic potential energy surfaces. It is an approximate method whose numerical efficiency decreases with growing accuracy.
MCTDH is suited for multi-dimensional problems, in particular for problems that are difficult or even impossible to solve in conventional ways.
Methods
Basic algorithm
Wavefunction expansion
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