Variation of the energy functional of the reduced first-order density operator

Dispersion interactions within the Piris natural orbital functional theory: The helium dimer

The authors have investigated the description of the dispersion interaction within the Piris natural orbital functional (PNOF) theory. The PNOF arises from an explicit antisymmetric approach for the two-particle cumulant in terms of two symmetric matrices, Delta and Lambda. The functional forms of these matrices are obtained from the generalization of the two-particle system expressions, except for the off-diagonal elements of Delta. The mean value theorem and the partial sum rule obtained for the off-diagonal elements of Delta provide a prescription for deriving practical functionals. In particular, the previous employed approximation {Jpp/2} for the mean values {Jp*} affords several molecular properties but it is incapable to account for dispersion effects. In this work, the authors analyze a new approach for Jp* obtained by factorization of the matrix Delta within the bounds on its off-diagonal elements imposed by the positivity conditions of the two-particle reduced density matrix. Additional terms for the matrix elements of Lambda proportional to the square root of the holes are again introduced to describe properly the occupation numbers of the lowest occupied levels. The authors have found that the cross products between weakly occupied orbitals must be removed from the functional form of Lambda to obtain a correct long-range asymptotic behavior. The PNOF is used to predict the binding energy as well as the equilibrium distance of the helium dimer. The results are compared with the full configuration-interaction calculations and the corresponding experimental data.

A NATURAL ORBITAL FUNCTIONAL STUDY FOR THE ELECTRIC RESPONSE PROPERTIES OF MOLECULES

This paper presents dipole moments, static isotropic polarizabilities and polarizability anisotropies of 20 molecules calculated in the framework of a new natural orbital functional method. All calculations have been performed using a finite field approach. Comparison with other correlated methods (CCSD(T), B3LYP) shows a reasonable agreement in the prediction of electric response properties by this new functional.

Effective potential for natural spin orbitals

For the first time the explicit form of the effective nonlocal potential for the natural spin orbitals is derived and analyzed. It is shown that in the case of the degenerate one-electron reduced density matrix the potential is not unique. The knowledge of the effective potential allows one to establish one-electron equations for the natural spin orbitals that may be of great value for efficient density matrix functional theory calculations.