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The two-body interaction energy
The interaction energy of a pair of interacting molecules is defined as
Eint=EAB−EA−EB.
If we calculate all three energies using a suitable electronic structure method---some of which will be described later---this definition provides a simple method for calculating the interaction energy of a pair of interacting molecules. This approach, known as the //supermolecular// method, provides us with a single number: the interaction energy Eint. We gain considerable physical insight into Eint by evaluating it not as the difference in energies suggested by the above definition, but through //perturbation theory//, which enables us to partition Eint into physical components: the electrostatic, induction (or polarization), dispersion and exchange-repulsion energies. This breakup proves invaluable not only as an aid to interpretation, but also forms the basis for all analytic atom--atom potentials (See //Intermolecular Forces// by Anthony Stone, OUP (2012)).
Consider the dimer Hamiltonian partitioned as
H(λ)=H0+λV,
where H0=HA+HB is the sum of the Hamiltonians of the unperturbed monomers A and B, and V is the intermonomer interaction operator that consists of electron-electron, electron-nuclear, and nuclear-nuclear interactions between the monomers. We may now carry out a symmetrized Rayleigh-Schrodinger perturbation theory ((Jeziorski, Moszynski & Szalewicz, Chem. Rev. 1994)) using as our zeroth-order wave function the unsymmetrized product Φ0=ΦA0ΦB0 and applying a suitable projection to retain only the fully antisymmetric states.
The zeroth-order energy is then E0=EA0+EB0. The interaction energy appears at first and higher orders in perturbation theory (setting λ=1):
Eint=E(1)elst+E(1)exch+E(2)ind+E(2)disp+⋯
As indicated, at first and second order the terms take on well-defined physical meanings.