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Schlagwörter:
PolarizabilityDensity functional theoryMany body problemsDisperse systemsAdiabatic theoremEigenvaluesDatabasesElectric dipole momentsEnergy efficiencyTensor methods
Zusammenfassung:
Interatomic pairwise methods are currently among the most popular and accurate ways to include
dispersion energy in density functional theory calculations. However, when applied to more than two
atoms, these methods are still frequently perceived to be based on ad hoc assumptions, rather than
a rigorous derivation from quantum mechanics. Starting from the adiabatic connection fluctuationdissipation
(ACFD) theorem, an exact expression for the electronic exchange-correlation energy, we
demonstrate that the pairwise interatomic dispersion energy for an arbitrary collection of isotropic
polarizable dipoles emerges from the second-order expansion of the ACFD formula upon invoking
the random-phase approximation (RPA) or the full-potential approximation. Moreover, for a system
of quantum harmonic oscillators coupled through a dipole-dipole potential, we prove the equivalence
between the full interaction energy obtained from the Hamiltonian diagonalization and the ACFDRPA
correlation energy. This property makes the Hamiltonian diagonalization an efficient method
for the calculation of the many-body dispersion energy. In addition, we show that the switching
function used to damp the dispersion interaction at short distances arises from a short-range screened
Coulomb potential, whose role is to account for the spatial spread of the individual atomic dipole
moments. By using the ACFD formula, we gain a deeper understanding of the approximations made
in the interatomic pairwise approaches, providing a powerful formalism for further development of
accurate and efficient methods for the calculation of the dispersion energy. © 2013 American Institute
of Physics.
