Intermolecular interaction operator

Although Eqs. (1-109) and (1-114) represent the very same multipole expansion of the intermolecular interaction operator, the expressions for the transformations... 

The dispersion nonadditivity Eib arises from the coupling of intermonomer pah-correlations in subsystems XY and YZ via the intermolecular interaction operator Vzx. This contribution can be expressed as a generalized Casimir-Polder formula,... 

We wish to end this section by saying that similarly as in the two-body case, nonadditive induction, induction-dispersion, and dispersion terms have well defined asymptotic behaviors from the multipole expansions of the intermolecular interaction operators. For instance, the leading term in the multipole expansion of the three-body dispersion energy for three atoms in a triangular geometry is given by the famous Axilrod-Teller-Muto formula311,312,... 

In practical applications of the sapt approach to interactions of many-elect ron systems, one has to use the many-body version of sapt, which includes order-by-order the intramonomer correlation effects. The many-body SAPT is based on the partitioning of the total Hamiltonian as H = F+V+W, where the zeroth-order operator F = Fa + Fb is the sum of the Fock operators for the monomers A and B. The intermolecular interaction operator V = H — Ha — Hb is the difference between the Hamiltonians of interacting and noninteracting systems, and the intramonomer correlation operator W = Wa + Wb is the sum of the Moller-Plesset fluctuation potentials of the monomers Wx — Hx — Fx, X — A or B. The interaction operator V is taken in the non-expanded form, i.e., it is not approximated by the multipole expansion. The interaction energy components of Eq. (1) are now given in the form of a double perturbation series,... 

Let us examine the processes described in the reactant channel (1) corresponding to the collision pair R1+R2. Elastic scattering effects are hidden in Hn. To see this, one uses with the asymptotic Hamiltonian (HR1+HR2) to represent the 1-state. The Hamiltonian H = Ku + Hm (T) can be written in terms of the asymptotic system Hm = HR1 + HR2 + WR1R2. The term WR1R2 is the intermolecular interaction operator measured from the local stationary frames whose origins are... 

In the SAPT method, the total Hamiltonian H of the dimer is partitioned dsH = Ha + Hb + V, where Hx, X = A or B, is the total Hamiltonian for monomer X, and V is the intermolecular interaction operator. The operator V collects Coulomb interactions of all the particles of monomer A with those of monomer B. This partition means that the unperturbed operator is chosen as Ha = Ha + Hb and V is the perturbation. The interaction energy is then obtained directly in the form of a perturbation series in V,... 

From the perturbation theory, the Hamiltonian of the dimer (H) can be written in terms of the unperturbed Hamiltonian (Hq) and the intermolecular interaction operator V ... 

The quantity Gaa, for example, is often referred to as containing the solute-solute interaction. In this book, we reserve the term interaction for the direct intermolecular interaction operating between two particles. Thus, two hard-sphere solutes of diameter a do not interact with each other at a distance R > a, yet the solute-solute affinity conveyed by Gaa may be different from zero. Furthermore, the use of the term solute-solute interaction for Gaa some misinterpretations. Consider, for... 

The intermolecular interaction operator V defined through O Eq. 6.5 can be written as... 

A solution to this problem is to use a multi-centered multipole expansion, more commonly called a distributed multipole expansion. In principle the centers could be arbitrarily chosen, but it is convenient to use the atomic nuclei as centers. The distributed multipole expansion of the intermolecular interaction operator V is... 

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