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 satisf ied for a variationally consistent construction of three-dimensional partit ions where a regional energy can be defined and the virial theorem satisfie d. These conditions have been previously found in terms of a nonhermitian m atrix P(1,1') (1 being a single particle index) which made its interpretati on very difficult. We have found a simple expression connecting the one-mat rix gamma(1,1') and P(1,1') in terms of the virial operator. We have also f ound a closed expression for the gradient fields based on the matrix P(1,1' ) and the one-particle density rho(1), which, in general, has very differen t structure. As an extension of our previous investigations for atoms and s imple diatomic molecules, we have applied these results to carry out a comp arison between the rho- and P-based schemes for one-electron diatomic speci es using three variationally related trial wavefunctions. For quasi-atomic fragments constructed in both schemes, we express our results in terms of t he fragment boundary shift as a function of a parameter, which is related t o the ratio of nuclear charges of the two nuclei. For our trial wavefunctio n, we obtain an explicit relationship for the boundary shift in both scheme s. We also performed a sensitivity analysis regarding the quality of the wa vefunction and found that the P-scheme is more robust than the rho-based on e for defining quasi-atoms. (C) 2000 Elsevier Science B.V. All rights reser ved.