Quantum-mechanical explanation of intermolecular interactions

In the natural sciences, an intermolecular force is an attraction between two molecules or atoms. They occur from either momentary interactions between molecules (the London dispersion force) or permanent electrostatic attractions between dipoles. They can be explained using a simple phenomenological approach (see intermolecular force), or using a quantum mechanical approach. Hydrogen bonding, dipole–dipole interactions, and London (Van der Waals) forces are most naturally accounted for by Rayleigh–Schrödinger perturbation theory (RS-PT). In this theory—applied to two monomers A and B—one uses as unperturbed Hamiltonian the sum of two monomer Hamiltonians, H ( 0 ) ≡ H A + H B {displaystyle H^{(0)}equiv H^{A}+H^{B}} In the present case the unperturbed states are products Φ n A Φ m B {displaystyle Phi _{n}^{A}Phi _{m}^{B}quad } with H A Φ n A = E n A Φ n A {displaystyle quad H^{A}Phi _{n}^{A}=E_{n}^{A}Phi _{n}^{A}quad } and H B Φ m B = E m B Φ m B {displaystyle quad H^{B}Phi _{m}^{B}=E_{m}^{B}Phi _{m}^{B}} The early theoretical work on intermolecular forces was invariably based on RS-PT and its antisymmetrized variants. However, since the beginning of the 1990s it has become possible to apply standard quantum chemical methods to pairs of molecules. This approach is referred to as the supermolecule method. In order to obtain reliable results one must include electronic correlation in the supermolecule method (without it dispersion is not accounted for at all), and take care of the basis set superposition error. This is the effect that the atomic orbital basis of one molecule improves the basis of the other. Since this improvement is distance dependent, it easily gives rise to artifacts. The monomer functions ΦnA and ΦmB are antisymmetric under permutation of electron coordinates (i.e., they satisfy the Pauli principle), but the product states are not antisymmetric under intermolecular exchange of the electrons. An obvious way to proceed would be to introduce the intermolecular antisymmetrizer A ~ A B {displaystyle { ilde {mathcal {A}}}^{AB}} . But, as already noticed in 1930 by Eisenschitz and London, this causes two major problems. In the first place the antisymmetrized unperturbed states are no longer eigenfunctions of H(0), which follows from the non-commutation