Multi-configuration time-dependent

Hartree The hartree (symbol: ''E''h), also known as the Hartree energy, is the measurement unit, unit of energy in the atomic units system, named after the British physicist Douglas Hartree. Its CODATA recommended value is = The hartree is approximat ...

(MCTDH) is a general algorithm to solve the time-dependent

Schrödinger equation The Schrödinger equation is a partial differential equation that governs the wave function of a non-relativistic quantum-mechanical system. Its discovery was a significant landmark in the development of quantum mechanics. It is named after E ...

for multidimensional dynamical systems consisting of distinguishable

particles In the physical sciences, a particle (or corpuscle in older texts) is a small localized object which can be described by several physical or chemical properties, such as volume, density, or mass. They vary greatly in size or quantity, from s ...

. MCTDH can thus determine the quantal motion of the nuclei of a molecular system evolving on one or several

coupled ''Coupled'' is an American dating game show that aired on Fox from May 17 to August 2, 2016. It was hosted by television personality, Terrence J and created by Mark Burnett, of '' Survivor'', '' The Apprentice'', '' Are You Smarter than a 5th ...

electronic

potential energy surface A potential energy surface (PES) or energy landscape describes the energy of a Physical system, system, especially a collection of atoms, in terms of certain Parameter, parameters, normally the positions of the atoms. The Surface (mathematics), ...

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 In many scientific fields, the degrees of freedom of a system is the number of parameters of the system that may vary independently. For example, a point in the plane has two degrees of freedom for translation: its two coordinates; a non-infinite ...

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 operator In quantum mechanics, a density matrix (or density operator) is a matrix used in calculating the probabilities of the outcomes of measurements performed on physical systems. It is a generalization of the state vectors or wavefunctions: while thos ...

References

* * *

External links

The Heidelberg MCTDH Homepage
Quantum chemistry Scattering {{scattering-stub