Generalized virial partitions and the one-particle density matrix

We address the problem of expressing, in terms of an equation involving the one-particle density matrix, the boundary conditions that should be satisfied for a variationally consistent construction of three-dimensional partitions where a regional energy can be defined and the virial theorem satisfied. These conditions have been previously found in terms of a nonhermitian matrix P(1,1') (1 being a single particle index) which made its interpretation very difficult. We have found a simple expression connecting the one-matrix γ(1,1') and P(1,1') in terms of the virial operator. We have also found a closed expression for the gradient fields based on the matrix P(1,1') and the one-particle density ρ(1), which, in general, has very different structure. As an extension of our previous investigations for atoms and simple diatomic molecules, we have applied these results to carry out a comparison between the ρ- and P-based schemes for one-electron diatomic species using three variationally related trial wavefunctions. For quasi- atomic fragments constructed in both schemes, we express our results in terms of the fragment boundary shift as a function of a parameter, which is related to the ratio of nuclear charges of the two nuclei. For our trial wavefunction, we obtain an explicit relationship for the boundary shift in both schemes. We also performed a sensitivity analysis regarding the quality of the wavefunction and found that the P-scheme is more robust than the ρ- based one for defining quasi-atoms. (C) 2000 Elsevier Science B.V.