Dispersion interactions in density-functional theory: An adiabatic-connection analysis

Abstract

We present an analysis of the dispersion interaction energy and forces in density-functional theory from the point of view of the adiabatic connection between the Kohn-Sham non-interacting and fully interacting systems. Accurate coupled-cluster singles-doubles-perturbative-triples [CCSD(T)] densities are computed for the helium dimer and used to construct the exchange-correlation potential of Kohn-Sham theory, showing agreement with earlier results presented for the Hartree-Fock-Kohn-Sham method [M. Allen and D. J. Tozer, J. Chem. Phys. 117, 11113 (2002)]. The accuracy of the methodology utilized to determine these solutions is checked by calculation of the Hellmann-Feynman forces based on the Kohn-Sham densities, which are compared with analytic CCSD(T) forces. To ensure that this comparison is valid in a finite atomic-orbital basis set, we employ floating Gaussian basis functions throughout and all results are counterpoise corrected. The subtle charge-rearrangement effects associated with the dispersion interaction are highlighted as the origin of a large part of the dispersion force. To recover the exchange-correlation components of the interaction energy, adiabatic connections are constructed for the supermolecular system and for its constituent atoms; subtraction of the resulting adiabatic-connection curves followed by integration over the interaction strength recovers the exchange-correlation contribution relevant to the density-functional description of the dispersion interaction. The results emphasize the long-ranged, dynamically correlated nature of the dispersion interaction between closed-shell species. An alternative adiabatic-connection path is also explored, where the electronic interactions are introduced in a manner that emphasizes the range of the electronic interactions, highlighting their purely long-ranged nature, consistent with the success of range-separated hybrid approaches in this context.

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“…12 This approach has proved to be fruitful in many contexts, including dispersion interactions (Strømsheim et al, 2011). It was around this time that Bader (1990) began his studies of the topology of the density distribution that he pursued for many years.…”

Study of adiabatic connection in density functional theory with an accurate wavefunction for two‐electron spherical systems

“…Exchange‐correlation potential and the local energies were also obtained using nonlinear adiabatic connections . The adiabatic connection has also been used to analyze dispersion forces in density functional theory. Recently, an alternative representation of the correlation energy has been given by kinetic‐energy based adiabatic connection.…”

Density-functional theory for internal magnetic fields

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