Friday, January 23, 2009

Solvation energy of a diatomic molecule: continuous solvation energy test - I

Diatomic molecule is the simplest example of a realistic solvation energy calculation. Indeed, any reasonable solvation energy model gives exact value for a single atom.

Depending on the radii of the atoms involved the solvation energy of a pair may be a very good test of a solvation energy model and transferability of its parameters. In what follows we show the results of our Modified GB (MGB) approach for the test system. The graph below represents the solvation energies for similar and opposite charges pairs.

The upper (blue) solid curve represents the atom pair with opposite charges, whereas the lower (red) curve corresponds to the atoms with similar charges. First of all, the behavior of the two energies is easy to understand. At infinite separation both curves saturate at -0.125 (which is the Born solvation energy of the two charges of 0.5 and bare radii 2.). If the total charge is 0 (the opposite charges case, blue curve), at r=0 we have Es=0 as well. If the total charge is 2x0.5=1 (the red curve), then at r=0 we have Es=-0.25, as it should be for a combined charge within the sphere of radius 2.

Although the asymptotic values are OK, this does not mean the whole curve is fine. To compare our approach with true electrostatic we performed the calculation of the model system solving the Poisson equation as well as by two "classic" GB models (that of HCT and AGNP). The results for a diatomic molecule with zero total charge are represented on the last graph.

The electrostatic part of the solvation energy corresponds to the blue curve of the previous graph and is calculated either by a (surface-electrostatic) Poisson equation solver (blue), QUANTUM's MGB (cyan), AGBNP (yellow) and HCT GB model (yellow). As it is clear from here, all the approaches give very similar results for the "small" molecule and are practically indistinguishable. Indeed, it is well known that practically any sort of GB approximation gives good results for solvation energies of small molecules.

The difference between QMGB method and "classic" GB approaches and its relation to the exact solution becomes more obvious if we consider a charged diatomic molecule (a molecular ion with total charge, say, 1 placed on one of the atoms). The exact (blue) and QMGB (cyan), once again, are both in agreement with each other, whereas both "classic" GB approaches, HCT and AGBNP fail to recover correct asymptotic value at zero inter-atomic separation. The latter difference between GB solutions and the exact value of the solvation energy is not important for small molecules (low atom density) but is extremely important for ligand binding calculations (to be explained).

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