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Direct variational calculation of two-body density matrix and a calculation of particle--hole states determined by two-body density matrix of the ground state

Miodrag V. Mihailović, Judit Németh

Published Jan 1, 1974• 0 citations
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New truncation scheme for a time-dependent density-matrix approach applied to the ground state of O16

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F. Catara, M. Grasso, G. Piccitto +1 more

We develop a procedure recently proposed for the treatment of correlations in finite Fermi systems in a more consistent way than the random phase approximation (RPA). The one-body density matrix in the correlated ground state is now no more assumed to be diagonal in the Hartree-Fock basis. An expression is rather provided where this quantity is expressed in terms of the X and Y amplitudes of the particle-hole phonon operators. A set of RPA-like equations depending only on the one-body density matrix is then constructed by means of the method of linearized equations of motion and solved via an iterative procedure. The procedure is employed to calculate spectra and strength distributions of several neutral and charged Na and Li metal clusters within the jellium approximation. Improvements are observed with respect to standard RPA calculations.

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Physical Interpretation of the Two-Body Density Matrix

Theoretical chemistry•Jan 1, 1976•0 citations
The ground state of 16O^{16}\mathrm{O}16O is calculated by using a time-dependent density-matrix approach derived from a new truncation scheme of the Bogoliubov--Born--Green--Kirkwood--Yvon hierarchy for reduced density matrices, where a three-body density matrix is approximated by an antisymmetrized product of two-body density matrices. The new scheme is compared with a simpler truncation scheme previously used for the calculation of the ground state of 16O^{16}\mathrm{O}16O where the three-body density matrix is neglected and only two-particle--two-hole elements of the two-body density matrix are considered. It is shown that the results obtained from the two truncation schemes agree well with the exact solution.
We develop a procedure recently proposed for the treatment of correlations in finite Fermi systems in a more consistent way than the random phase approximation (RPA). The one-body density matrix in the correlated ground state is now no more assumed to be diagonal in the Hartree-Fock basis. An expression is rather provided where this quantity is expressed in terms of the X and Y amplitudes of the particle-hole phonon operators. A set of RPA-like equations depending only on the one-body density matrix is then constructed by means of the method of linearized equations of motion and solved via an iterative procedure. The procedure is employed to calculate spectra and strength distributions of several neutral and charged Na and Li metal clusters within the jellium approximation. Improvements are observed with respect to standard RPA calculations.