Supermolecular methods

We have used the supermolecular method to compute the total energy of the system the interaction (complexation) energy is obtained by subtraction of the energies of the constituent molecular fragments. This method is theoretically straightforward and can be improved successively by an increase in the theoretical sophistication. The wavefunction used in this procedure gives the molecular properties directly. 

A weakness of this model is that the separation of the electrostatic and the so-called specific solute-solvent interactions is not defined. In practice, two main approaches are used to account for solvent effects on the spin-spin coupling constants the continuum and the supermolecular methods. The combined MD/QM approach is rarely used for the purpose, since calculations of the spin-spin coupling constants are much more time consuming than those of the shielding constants and the MD/QM approach is too expensive for the former. 

In the variational method (also known as supermolecular method), the interaction energy A B is calculated from... 

Keywords intermolecular forces, Born-Oppenheimer approximation, supermolecular method, polar-... 

There are two approaches often used for computing interaction energies supermolecular and perturbation methods (for reviews see Chalasihski and Gutowski, 1988 Chalasihski and Szczqsniak, 1994). In the supermolecular method the interaction energy of a pair of molecules is the difference between the energy of the pair and the energy ofthe individual molecules... 

The interaction energy of each molecular pair was then computed using the supermolecular method [Eq. (1)] at the 1IF/6-311 -F-l-G(3d,2p) level at the separation and orientation obtained in the previous step. 

The next level of sophistication is to include inter- as well as intracorrelation effects using, as advocated by Pople , M011er-Plesset perturbation theory , a true supermolecular method subject to BSSE (cf Section V). We restrict our discussion here to the frequently applied second-order variant (MP2). 

Good and Bad News About the Supermolecular Method Perturbational Approach (A)... 

In the supermolecular method, the interaction energy is calculated from its definition [Eq. (13.1) using any reliable method of the eleetronic energy calculation. For the sake of brevity, we will consider the interaction of only two subsystems A and B. 

Fig. 13.4. In the supermolecular method, we subtract two large numbers that differ only slightly and lose accuracy in this way. In order not to obtain a result like 240 kg or so. we have to have at our disposal a very accurate method of weighing things.

Interaction energy of two molecules (at a given geometry) may be calculated within any reliable quantum mechanical method by subtracting from the total system energy the sum of the energies of the subsystems. This is called a supermolecular method. 

In the supermolecular method, there is a need to compensate for what is called the basis set superposition error (BSSE). The error appears because due to the incompleteness of the atomic basis set b)> Ihe individual subsystem A with the interaction switched off profits from the basis set only, while when interacting, the energy is lowered due to the total 2 U 2g basis set (the same pertains to any of the subsystems). As a result a part of the calculated interaction energy does not come from the interaction, but from the problon of the basis set used (BSSE) described above. A remedy is called the counter-poise method, in which aU quantities (including the energies of the individual subsystems) are calculated within the 2 1 U basis set. 

Supermolecular methods compute the interaction AT (and their parts, e.g., dispersion) as a difference of total energies F,q, for the aggregate (complex AB) and the fragments (A and B) as... 

The majority of these models have their origin in a physical analysis of the solutions but, with the passage of time, they have acquired a more chemical coimotation, they have centered the analysis more on the molecular aspect. As well as this, recourse is more and more being made to combined strategies which use the best of each of flic methods referred to in pursuit of a truer reproduction of the solute-disolvente interactions. Specially useful has been shown to be a combination of the supermolecular method, used to reproduce the specific interactions between the solute and one or two molecules of the solvent, with those of continuum or of simulation, used to reproduce the global properties of the medium. 

Good and bad news about the supermolecular method Perturbational approach... 

There are two principal methods of calculating the intermolecular interactions the supermolecular method and the perturbational method. Both assume the Born-Oppenheimer approximation. 

GOOD AND BAD NEWS ABOUT THE SUPERMOLECULAR METHOD Two deficiencies... 

A big advantage ot the supermolecular method is its applicability at any intermolecular distance, i.e. independently of how strong the interaction is. 

The supermolecular method has at least one important advantage it works independently of the interaction strength and of the intennoleailar distance. The method has the disadvantage that due to the subtraction, a loss of accuracy occurs and no information is obtained about the structure of the interaction energy. 

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