Correlation energy functional in the density-matrix functional theory

Publisher Website
Google Scholar
Abstract
A new systematic method is presented to construct a correlation energy functional in the density-matrix functional theory. A new exact relation, particle-hole symmetry, is presented, which states that the exact functional gives the same correlation energy for the first-order reduced density matrix (1-RDM) and the corresponding hole 1-RDM. Nakatsuji’s density equations of the first and the second orders together with the decoupling approximation of the 3- and 4-RDMs are solved numerically to examine the properties of the correlation energy functional. This functional, defined as the solution of the set of equations, satisfies Levy’s homogeneous coordinate scaling and the particle-hole symmetry and reproduces about 95% of the correlation energies of several molecules. By expanding these equations in perturbation series the leading term of the correlation energy functional is identified. Numerical analysis shows that this simplified functional, which contains one fitting parameter, reproduces the energies of several molecules accurately. The direction of further study is discussed.