The Born–Huang approximation
(named after
Max Born and
Huang Kun
Huang Kun (; September 2, 1919 – July 6, 2005) was a Chinese physicist and an academician of the Chinese Academy of Sciences. He was awarded the State Preeminent Science and Technology Award (the highest science award in China) by President Jia ...
) is an approximation closely related to the
Born–Oppenheimer approximation. It takes into account diagonal nonadiabatic effects in the electronic
Hamiltonian
Hamiltonian may refer to:
* Hamiltonian mechanics, a function that represents the total energy of a system
* Hamiltonian (quantum mechanics), an operator corresponding to the total energy of that system
** Dyall Hamiltonian, a modified Hamiltonian ...
better than the Born–Oppenheimer approximation. Despite the addition of correction terms, the
electronic state
A quantum mechanical system or particle that is bound—that is, confined spatially—can only take on certain discrete values of energy, called energy levels. This contrasts with classical particles, which can have any amount of energy. The t ...
s remain uncoupled under the Born–Huang approximation, making it an adiabatic approximation.
Shape
The Born–Huang approximation asserts that the representation matrix of nuclear kinetic energy operator in the basis of Born–Oppenheimer electronic wavefunctions is diagonal:
:
Consequences
The Born–Huang approximation loosens the Born–Oppenheimer approximation by including some electronic matrix elements, while at the same time maintains its diagonal structure in the nuclear equations of motion. As a result, the nuclei still move on isolated surfaces, obtained by the addition of a small correction to the Born–Oppenheimer
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 coordinat ...
.
Under the Born–Huang approximation, the Schrödinger equation of the molecular system simplifies to
:
The quantity