Interactions from supermolecule calculations

Much effort has been devoted to other electrostatic representations of molecular interactions [89] using ab initio calculations based on the understanding that this component is the largest portion of the interaction energy [90]. A major application of the detailed analysis of intermolecular interactions provided by ab initio formulations has been an approximate expansion in terms of analytical functions that allow practical calculation for many different intermolecular distances [97], Alarge scale simulation of potential functions for solvated amino acids has been derived from supermolecule calculations based on one interacting water molecule [92],... 

Sanchez Marcos and Pappalardo have recently performed considerably more elaborate studies of the solvent influence on barriers and conformation equilibria of ni-troenamines . The solute cavity was modeled after the shape of the molecule, and the solvent was treated both as a continuum " and as a supermolecule with 15 methanol molecules per solute molecule. The solute-solvent interaction energy was obtained from the potential of a suitably defined surface charge density and the electron distribution in the solute from AMI calculations. The agreement between experimental and calculated free-energy barriers was excellent, whereas the Z-E equilibria were less well reproduced with AMI calculations. This discrepancy was diminished when conformation gas-phase energies from ab initio calculations were used. 

We choose a basis for the calculation of molecule A that seems suitable for our purpose. Inevitably it is incomplete, so our wavefunction for A is not exact. The same is true of the calculation for the isolated molecule B. Now we carry out a calculation on the complex A - B, and obtain a new energy that includes the interaction between the molecules. But in this calculation there are some new basis functions, belonging to molecule B, that were not present when we calculated the energy of the isolated A molecule, and they allow the wavefunction of molecule A to be improved variationally, so that its energy falls. This is quite separate from the true physical interaction it is a spurious effect that occurs because the basis set that we initially chose for A was not good enough to describe the wavefunction exactly. This is Basis Set Superposition Error, or BSSE, and it occurs in all supermolecule calculations. The effect is to make the interaction seem more attractive than it really is. 

One of the difficulties in performing calculations of intermolecular potentials is that it is very difficult to evaluate their accuracy. The calculation of measurable properties from a potential often involves approximations, and generally requires an integration over a large region of the potential surface, so that inaccuracies are smeared out. Errors may cancel, so an inaccurate potential may give better predictions than it deserves to. When there is disagreement between a calculated property and the experimental measurements it is often difficult to know what feature of the potential is at fault. It has often been assumed that supermolecule calculations provide a benchmark for model potentials, but we have seen that for weak interactions this assumption is untenable. 

The simplest discrete approach is the solvaton method 65) which calculates above all the electrostatic interaction between the molecule and the solvent. The solvent is represented by a Active molecule built up from so-called solvatones. The most sophisticated discrete model is the supermolecule approach 661 in which the solvent molecules are included in the quantum chemical calculation as individual molecules. Here, information about the structure of the solvent cage and about the specific interactions between solvent and solute can be obtained. But this approach is connected with a great effort, because a lot of optimizations of geometry with ab initio calculations should be completed 67). A very simple supermolecule (CH3+ + 2 solvent molecules) was calculated with a semiempirical method in Ref.15). 

The basis set used for calculations were the STO-3G, the 3-21G, and the 6-31G basis sets, as implemented by the Gaussian-88 computer program. The energies of interaction were computed by using the supermolecule approach where the sum of the energies of the subsystems are substracted from the energy of the complex. All the species were geometry optimized. 

The catalytic decomposition of N20 is regulated by the cycle Fc"/Fcm. N20 interacts with reduced Fe[[ site (Eq.16.1) to yield an extra-lattice oxygen Fe[[[-0 species, the so-called a-oxygen by Panov et al. (29). Most of studies have concluded that the removal of a-oxygen (Eq. 16.2) exhibits the lowest rate constant. The remarkable behavior of Fe exchanged in some zeolites could be ascribed to the occurrence of easily reduced and completely reversible Fe oxo-cation sites (28). TPR experiments by H2 and CO of N20-treated Fe-MFI (27) and Fe-BEA (33) have shown that such Fem-0 sites are much more reductible than those formed by 02 treatment. The influence of the zeolite on the reductibility of Fe species could be understand from quantum chemical calculations (DFT method) on model clusters of FAU and BEA containing Cu", Co" and Fe" cations (36). The calculations indicate that a charge transfer from zeolite to TM ion occurs of ca. one electron, and that the TM-zeolite system behaves like a supermolecule. Obviously, the addition of a reductant such as hydrocarbons (25, 26, 37, 38), CO (39, 40) or NH3 (41) boosts the N20 decomposition by a faster reduction of Fem-0 species. 

It does not appear that any attempt has been made to couple this BKO model to a means by which to calculate the CDS components of solvation, and this limits the model s accuracy, especially for solvents like water, where the CDS terms are not expected to be trivial. For water as solvent, studies have appeared that surround the solute with some small to moderate number of explicit solvent molecules, with the resulting supermolecule treated as interacting with the surrounding continuum. 23,230 Although such a treatment has the virtue of probably making the calculation less sensitive to the now-large cavity radius, it suffers from the usual explicit-solvent drawbacks of the size of the system, the complexity of the hypersurface, and the need for statistical sampling. 

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