In non-relativistic quantum chemistry, one of the most common methods of taking account of electron correlation effects is through second-order MBPT. Its use is common because it is relatively inexpensive as compared to the other available electron correlation methods. When no restrictions are placed upon the spin orbitals which are used to construct the DF wavefunction and the related excited determinants, the application of MBPT generally follows the method suggested by Møller and Plesset[13] (MP), which is based upon the more general Rayleigh-Schrödinger perturbation theory (RSPT). A good overview of MBPT as applied to the solution of the non-relativistic Hamiltonian may be found in one of several elementary texts and reviews[14,15]. These methods begin with the assumption that the problem of finding eigenfunctions of the Hamiltonian may be divided into a part that is relatively easy to solve, and a part which is more difficult:
is known as the unperturbed or zeroth-order
Hamiltonian, while 
is the perturbation.
In relativistic
Møller-Plesset perturbation theory, 
is simply the Dirac-Fock
operator. Higher order corrections to the zeroth-order, DF wavefunction,
may be constructed via combinations of the other solutions to the zeroth
order Hamiltonian, the aforementioned excited determinants. With this
partitioning of the Hamiltonian, the zeroth order energy is simply the sum
of orbital eigenvalues for the occupied spinors of the DF wavefunction. The
first-order correction to the energy only depends upon the zeroth-order
wavefunction and simply reproduces the DF energy:
In order to obtain the second order correction to the energy, however, the first order corrections to the wavefunction are required:
The first order correction to 
is given by the expansion
Where the expansion coefficients, 
, are determined via the relation
Because of the form of 
, only the 
are non-zero.
This determines the second order correction to the energy (and the first
order correction to the Dirac-Fock energy)
The DHF MP2 method is much more reasonable computationally than most of the other relativistic, correlated techniques. Evaluation of the DHF MP2 energy requires only a limited transformation of the atomic two-electron integrals. Because only electronic solutions are desired, transformations involving unoccupied, positronic single particle solutions need not be performed. This sort of limitation is enforced for integral transformations preceding any correlated calculation, but in the case of the DHF MP2 energy, the transformation of the first two indexes may be performed over the unoccupied spinors, while transformation of the final pair of indexes is performed over the occupied spinors. Dyall presents an implementation of the DHF MP2 which further restricts the integrals which require transformation via the implementation of Kramer's' restriction on the spinors and the use of double group symmetry. The low computational cost of the MP2 method is its greatest virtue. Unfortunately, the non-relativistic implementation of this technique is known to be unreliable for a wide variety of systems, and the application of the MP2 method is usually performed only in cases where higher level techniques such as coupled-cluster methods are too costly to perform.