Joint quantum chemical and polarizable molecular mechanics investigation of formate complexes with penta- and hexahydrated Zn2+: Comparison between energetics of model bidentate,monodentate, and through-water Zn2+ binding modes and evaluation of nonadditivity effects

In order to gain an understanding of the energetics of polycoordinated Zn²⁺ binding to the formate anion (the end side chain of the Asp and Glu residues of proteins), we compare three competing binding modes in the presence of five and six water molecules: a, bidentate binding of Zn²⁺ to both formate oxygens; b, monodentate binding of Zn²⁺ to one formate oxygen; and c, through-water binding of Zn²⁺ to formate, in which the cation remains bound to its first-hydration shell waters and interacts with both formate oxygens through three water molecules. We also investigate a complex d, which is similar to c, in which formate is protonated into formic acid and one water molecule is deprotonated. The computations are carried out using the ab initio self-consistent field/MP2 with three basis sets of increasing size density functional theory, semiempirical AM1 and PM3, and the sum of interactions between fragments ab initio computed (SIBFA) molecular mechanics procedures. The summed energies of the isolated molecules making up the complexes disfavor tautomer d compared to a–c. On the other hand, the ab initio computations give the ordering of intermolecular interaction energies as d formic acid tautomer >b monodentate >a bidentate >c through-water. Whereas the first-order energy E₁ favors both inner-shell Zn²⁺ complexes with formate over the outer-shell complex, the polarization and the charge-transfer components of the second-order energy E₂ both favor the outer-shell complex over the inner-shell one, despite the increased separation between the cation and the highly polarizable formate ion. Energy balances including continuum solvation enthalpies produce an equilibration of complexes a–d. The preference favoring the monodentate complex over the bidentate one is consistent with other ab initio results for formate binding by a fully coordinated Zn²⁺ cation and with structural results from X-ray crystallography. The SIBFA results are consistent with the ab initio results, and the computed interaction energy values match the ab initio ones to within 3%. The effects of nonadditivity are analyzed in the ab initio, SIBFA, and semiempirical computations. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1379–1390, 1999