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For the Hirshfeld-I atom in the molecule (AIM) model, associated single-atom energies and interaction energies at the Hartree-Fock level are efficiently determined in one-electron Hilbert space. In contrast to most other approaches, the energy terms are fully consistent with the partitioning of the underlying one-electron density matrix (1DM). Starting from… (More)

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)

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)

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)

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)

- D Van Neck, Y Dewulf, M Waroquier
- 2001

New lower bounds for the binding energy of a quantum-mechanical system of interacting particles are presented. The new bounds are expressed in terms of two-particle quantities and improve the conventional bounds of the Hall-Post type. They are constructed by considering not only the energy in the two-particle system, but also the structure of the pair wave… (More)

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