Multi-configuration time-dependent

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

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

Schrödinger equation The Schrödinger equation is a linear partial differential equation that governs the wave function of a quantum-mechanical system. It is a key result in quantum mechanics, and its discovery was a significant landmark in the development of the ...

for multidimensional dynamical systems consisting of distinguishable

particles In the physical sciences, a particle (or corpuscule 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 su ...

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

potential energy surface A potential energy surface (PES) describes the energy of a system, especially a collection of atoms, in terms of certain parameters, normally the positions of the atoms. The surface might define the energy as a function of one or more coordinates ...

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 (often abbreviated df or DOF) refers to the number of independent variables or parameters of a thermodynamic system. In various scientific fields, the word "freedom" is used to describe the limits to which physical movement or ...

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 that describes the quantum state of a physical system. It allows for the calculation of the probabilities of the outcomes of any measurement performed upon this system, using ...

References

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External links

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