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Despite the importance of non-singlet molecules in chemistry, most variational second order density matrix calculations have focused on singlet states. Ensuring that a second order density matrix is derivable from a proper N-electron spin state is a difficult problem because the second order density matrix only describes one- and two-particle interactions.… (More)

The variational determination of the two-particle density matrix is an interesting, but not yet fully explored technique that allows us to obtain ground-state properties of a quantum many-body system without reference to an N-particle wave function. The one-dimensional fermionic Hubbard model has been studied before with this method, using standard two- and… (More)

- An Ghysels, H Lee Woodcock, Joseph D Larkin, Benjamin T Miller, Yihan Shao, Jing Kong +4 others
- Journal of chemical theory and computation
- 2011

The calculation of the analytical second derivative matrix (Hessian) is the bottleneck for vibrational analysis in QM/MM systems when an electrostatic embedding scheme is employed. Even with a small number of QM atoms in the system, the presence of MM atoms increases the computational cost dramatically: the long-range Coulomb interactions require that… (More)

We discuss how semidefinite programming can be used to determine the second-order density matrix directly through a variational optimization. We show how the problem of characterizing a physical or N-representable density matrix leads to matrix-positivity constraints on the density matrix. We then formulate this in a standard semidefinite programming form,… (More)

Based on the so-called Hirshfeld atom in the molecule scheme, a new AIM method is presented. The method is similar to the Hirshfeld-I scheme, with the AIM weight function being constructed by minimizing the information loss upon formation of the molecule, but now requiring explicitly that the promolecular densities integrate to the same number of electrons… (More)

The Faddeev Random Phase Approximation is a Green's function technique that makes use of Faddeev-equations to couple the motion of a single electron to the two-particle–one-hole and two-hole–one-particle excitations. This method goes beyond the frequently used third-order Algebraic Diagrammatic Construction method: all diagrams involving the exchange of… (More)

Standard normal mode analysis becomes problematic for complex molecular systems, as a result of both the high computational cost and the excessive amount of information when the full Hessian matrix is used. Several partial Hessian methods have been proposed in the literature, yielding approximate normal modes. These methods aim at reducing the computational… (More)

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