Multi-configuration time-dependent Hartree
Encyclopedia
Multi-configuration time-dependent Hartree
(MCTDH) is a general algorithm to solve the time-dependent Schrödinger equation
for multidimensional dynamical systems consisting of distinguishable particles
. MCTDH can thus determine the quantal motion of the nuclei of a molecular system
evolving on one or several coupled
electronic potential energy surface
s. MCTDH by its very nature is an approximate method. However, it can be made as accurate as any competing method, but its numerical efficiency deteriorates with growing accuracy.
MCTDH is designed for multi-dimensional problems, in particular for problems that are difficult or even impossible to attack in a conventional way. There is no or only little gain when treating systems with less than three degrees of freedom
by MCTDH. MCTDH will in general be best suited for systems with 4 to 12 degrees of freedom. Because of hardware limitations it may in general not be possible to treat much larger systems. For a certain class of problems, however, one can go much further. The MCTDH program package has recently been generalised to enable the propagation of density operators.
Douglas Hartree
Douglas Rayner Hartree PhD, FRS was an English mathematician and physicist most famous for the development of numerical analysis and its application to the Hartree-Fock equations of atomic physics and the construction of the meccano differential analyser.-Early life:Douglas Hartree was born in...
(MCTDH) is a general algorithm to solve the time-dependent Schrödinger equation
Schrödinger equation
The Schrödinger equation was formulated in 1926 by Austrian physicist Erwin Schrödinger. Used in physics , it is an equation that describes how the quantum state of a physical system changes in time....
for multidimensional dynamical systems consisting of distinguishable particles
Elementary particle
In particle physics, an elementary particle or fundamental particle is a particle not known to have substructure; that is, it is not known to be made up of smaller particles. If an elementary particle truly has no substructure, then it is one of the basic building blocks of the universe from which...
. MCTDH can thus determine the quantal motion of the nuclei of a molecular system
Molecule
A molecule is an electrically neutral group of at least two atoms held together by covalent chemical bonds. Molecules are distinguished from ions by their electrical charge...
evolving on one or several coupled
Vibronic coupling
In theoretical chemistry, the vibronic coupling terms, , are proportional to the interaction between electronic and nuclear motions of molecules. The term "vibronic" originates from the concatenation of the terms "vibrational" and "electronic"...
electronic potential energy surface
Potential energy surface
A potential energy surface is generally used within the adiabatic or Born–Oppenheimer approximation in quantum mechanics and statistical mechanics to model chemical reactions and interactions in simple chemical and physical systems...
s. MCTDH by its very nature is an approximate method. However, it can be made as accurate as any competing method, but its numerical efficiency deteriorates with growing accuracy.
MCTDH is designed for multi-dimensional problems, in particular for problems that are difficult or even impossible to attack in a conventional way. There is no or only little gain when treating systems with less than three degrees of freedom
Degrees of freedom (physics and chemistry)
A degree of freedom is an independent physical parameter, often called a dimension, in the formal description of the state of a physical system...
by MCTDH. MCTDH will in general be best suited for systems with 4 to 12 degrees of freedom. Because of hardware limitations it may in general not be possible to treat much larger systems. For a certain class of problems, however, one can go much further. The MCTDH program package has recently been generalised to enable the propagation of density operators.