A Variational Approach to London Dispersion Interactions without Density Distortion

Abstract

We introduce a class of variational wave functions that captures the long-range interaction between neutral systems (atoms and molecules) without changing the diagonal of the density matrix of each monomer. The corresponding energy optimization yields explicit expressions for the dispersion coefficients in terms of the ground-state pair densities of the isolated systems, providing a clean theoretical framework to build new approximations in several contexts. As the individual monomer densities are kept fixed, we can also unambiguously assess the effect of the density distortion on London dispersion interactions; for example, we obtain virtually exact dispersion coefficients between two hydrogen atoms up to C 10 and relative errors below 0.2% in other simple cases.

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

“…As we shall see, for closed-shell systems, this is almost always the case with CCSD pair densities, which yield in general good results, slightly underestimating C 6 , although there are exceptions. With HF pair densities, as it was already found in a preliminary result for the Ne–Ne case in ref ( 4 ), C 6 is, in the vast majority of cases, overestimated.…”

“…We consider two systems A and B separated by a (large) distance R having isolated ground-state wave functions and , where x denotes the spin-spatial coordinates ( r , σ) and denote the whole set of the spin-spatial coordinates of electrons in system A / B . The FDM framework is defined by the following constrained minimization problem 4 , 7 where T̂ is the usual kinetic energy operator acting on the full set of variables x̲ A , x̲ B , and With T 0 A / B we denote the ground-state kinetic energy expectation values of the two separated systems and where ρ 0 A ( B ) are the ground-state one-electron densities of the two systems. The constraint Ψ R → |Ψ 0 A | 2 ,|Ψ 0 B | 2 means that the search in eq 1 is performed over wave functions Ψ R ( x̲ A , x̲ B ) that leave the diagonal of the many-body density matrix of each fragment unchanged with repect to the ground-state isolated value.…”

“…The FDM approach has been found to yield exact results for the dispersion coefficients up to C 10 for the H–H case (and up to C 30 for the second-order coefficients), and very accurate results (0.17% error on C 6 ) for He–He and He–H. 4 This is achieved by reshuffling the contributions of kinetic energy and potential energy inside each monomer, as shown in Table 1 of ref ( 7 ). Another way to look at it is the following: dispersion between two systems in their ground states is a competition between a distortion of the fragments’ ground states (which raises the energy with respect to E 0 A + E 0 B ) and the interfragment interaction that can lower the energy of the two systems together.…”

“…We have recently introduced a class of variational wave functions that capture the long-range interactions between two quantum systems without deforming the diagonal of the many-body density matrix of each monomer. 4 The variational take on dispersion is certainly not new, as, for example, variational calculations of the dispersion coefficients have been performed in the context of (Hylleraas) variational perturbation theory 5 and variational calculations of the dispersion energy at finite intermonomer distance have been carried out in the framework of symmetry-adapted perturbation theory (SAPT) using orthogonal projection. 6 The distinctive feature of our approach is the reduction of dispersion to a balance between kinetic energy and monomer–monomer interactions only, providing an explicit expression for the dispersion energy in terms of the ground-state pair densities of the isolated monomers.…”

On the physical mechanisms underlying single molecule dynamics in simple liquids

“…Thus, building qualitative understanding of the essential connection between electron cloud distortion and single molecule viscous and self-diffusion forces represents an important task. Computational chemistry and biology 66 offer a number of techniques for visualizing distortion and modification of electron distributions that accompany various intermolecular interactions 67 , 68 . Unfortunately, while dispersive interactions are ubiquitous and must be accommodated to accurately capture, e.g., solvation-induced changes in polyatomic molecular structure 68 , development of predictive dispersion interaction models remains an open problem 68 .…”