Intermolecular interaction energy supermolecular approach

Within the supermolecular approach, the total intermolecular interaction energy (AE) of a complex A---B is evaluated as the difference between the energy of the complex (EA" B) and the sum of the energies of its subsystems (EA, EB) ... 

Contrary to the previously described supermolecular approach, perturbation theory treatment allows for the partition of the interaction energy into physically interpretable components. The most frequently used method for this purpose is symmetry-adapted perturbation theory (SAPT) [13]. More recently, great effort has also been invested in the development of DFT-SAPT [14-16], In the present contribution, we use the variational-perturbational scheme [17-20], In this approach, the intermolecular interaction energy components are determined based on the wave functions of the subsystems evaluated in the dimer-centered basis set. Thus, both interaction energy and its components are BSSE-free. More details about this scheme can be found elsewhere [21-23]. The total intermolecular interaction energy at the MP2 level of theory can be expressed as follows ... 

After generating optimized clusters, the intermolecular interaction energies between pair molecules a and / ( ) in the cluster were calculated using the supermolecular approach ... 

For quantitative description of H-bond interactions in solution or in gas phase, it is a common practice to define the H-bond energy by intermolecular interaction energy. In the supermolecular approach, H-bonding energies are described by the free energy of the complexation reaction (3.1), which is estimated according to the following equation ... 

We also focused [156] on the Coulomb energy between atoms in supermolecules. We proposed an atom-atom partitioning of the Coulomb interaction, which should not be confused with the electrostatic component of the intermolecular interaction, defined within the perturbation approach. Instead, this atom-atom Coulomb interaction energy uses the total molecular (in the case of a single, covalently boimd molecule) or the supermolecular (in... 

An alternative to the supermolecular approach is symmetry adapted perturbation theory (SAPT) that computes the interaction energy directly (Chipman and Hirschfelder 1980 Jeziorski et al. 1978, 1980). The SAPT method has been shown to be suitable for studying weak intermolecular interactions and, in general, provides results similar to the current gold standard CCSD(T) (see below). Although this method has been instrumental to the understanding of weak intermolecular interactions, we have omitted details to rein in the scope of the chapter. 

An alternative to the supermolecular approach is symmetry-adapted perturbation theory [19-21]. hi SAPT, the interaction energy is computed directly rather than by subtraction. SAPT provides both the conceptual framework and the computational techniques for describing intermolecular interactions, including the dispersion energy. However, the computer resources required by SAPT, similar to those of the methods with high-level treatment of correlation used in the supermolecular approach, make appHcations to monomers with more than about ten atoms impractical at the present time. For ten-atom or smaller molecules, SAPT has been very successful see [20,21], and Sect. 7 for a review of applications. 

The resulting SAPT(DFT) potential energy curves turn out to be very accurate in the wide range of intermolecular separations. For the benzene dimer225,228 the results are very close to those of the much more expensive CCSD(T) treatment. For systems of the size of the benzene dimer and for the triple-zeta quality basis sets, a SAPT(DFT) calculation actually takes less time than a conventional supermolecular DFT calculation. Due to the favorable computational scaling the SAPT(DFT) approach is applicable to much larger molecules than any method used thus far for a reliable calculation of dispersion-dominated interaction potential. 

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