Dispersion without Many-Body Density Distortion: Assessment on Atoms and Small Molecules

Abstract

The “fixed diagonal matrices” (FDM) dispersion formalism [ 30865464 J. Phys. Chem. Lett. 2019 10 1537 ] is based on a supramolecular wave function constrained to leave the diagonal of the many-body density matrix of each monomer unchanged, reducing dispersion to a balance between kinetic energy and monomer–monomer interaction. The corresponding variational optimization leads to expressions for the dispersion energy in terms of the ground-state pair densities of the isolated monomers only, providing a framework to build new approximations without the need for polarizabilities or virtual orbitals. Despite the underlying microscopic real space mechanism being incorrect, as in the exact case there is density relaxation, the formalism has been shown to give extremely accurate (or even exact) dispersion coefficients for H and He. The question we answer in this work is how accurate the FDM expressions can be for isotropic and anisotropic C 6 dispersion coefficients when monomer pair densities are used from different levels of theory, namely Hartree–Fock, MP2, and CCSD. For closed-shell systems, FDM with CCSD monomer pair densities yield a mean average percent error for isotropic C 6 dispersion coefficients of about 7% and a maximum absolute error within 18%, with a similar accuracy for anisotropies. The performance for open-shell systems is less satisfactory, with CCSD pair densities performing sometimes worse than Hartree–Fock or MP2. In the present implementation, the computational cost on top of the monomer’s ground-state calculations is O ( N 4 ). The results show little sensitivity to the basis set used in the monomer’s calculations.

Density Functional Response Calculations of Dispersion Coefficients C6 and C9 of Closed- and Open-Shell Systems

“…A variety theoretical approaches, such as density functional theory (DFT), , linear-response time-dependent DFT (TD-DFT), ,,,,,− the DFT-based local response dispersion (LRD) method, time-dependent Hartree–Fock (TDHF), ,, Møller–Plesset perturbation theory (MPPT), − perturbation theory, ,− symmetry-adapted perturbation theory (SAPT), − other correlated wave function approaches , such as coupled cluster (CC) theory ,,− and the algebraic diagrammatic construction (ADC), and semiempirical approximations, − have been harnessed to calculate polarizabilities and dispersion coefficients. Static polarizabilities of closed- and selected open-shell atoms and small molecules may be computed accurately by quantum chemical techniques. ,,, Treating the frequency-dependent response is in principle straightforward, but requires additional method development effort.…”

The Strong Interaction Limit of the Møller-Plesset Adiabatic Connection

“…As mentioned before, density functionals often struggle with dispersion interactions due to these interactions being relatively weak, 18,[130][131][132] whereas most XC functionals are more accurate when describing stronger covalent bonds. Empirical dispersion corrections [133][134][135][136][137][138] have been used…”

“…A similar method, called the Tkatchenko-Scheffler method 139 , was also introduced although it differs in the fact that the dispersion coefficients and damping functions are now charge density dependent. Other strategies are the non-local functional correlation method [140][141][142][143][144] , the exchange dipole model 137,[145][146][147] and the fixed diagonal matrices dispersion method [130][131][132] .…”