Hydrated structure of ammonia–water molecule pair via the free energy gradient method: Realization of zero gradient and force balance on free energy surfaces

Abstract

The hydrated structure of ammonia molecule in aqueous solution was theoretically optimized as an ammonia–water molecule pair (H3N⋯H2O) by the free energy gradient (FEG) method [J. Chem. Phys. 113, 3516 (2000)]. The interaction between the pair and a solvent water molecule (TIP3P) [J. Chem. Phys. 79, 926 (1983)] was described by a hybrid quantum mechanical and molecular mechanical method combined with a semiempirical molecular orbital method at the PM3 level of theory. It is concluded that the present FEG method works quite well in spite of a simple steepest descent optimization scheme equipped with the adaptive displacement vector. The free energy stabilization was estimated −0.3 kcal/mol from the free energy for the same structure as that of the cluster in the gas phase. The optimized structure was found to be almost the same as that in the gas phase except for a longer OH bond length of the water molecule. However, its realization in aqueous solution is accomplished by virtue of the fulfillment of both “zero gradient” and “force balance” conditions. Finally, we discuss also the effect of microscopic “solvation entropy,” compared with the result by the conductorlike screening model method.

Transition-State Characterization of the Ammonia Ionization Process in Aqueous Solution via the Free-Energy Gradient Method

“…It should be noted that only one imaginary frequency was obtained at this structure by the normal-mode analysis on FES incorporated the effect from all of the ambient water molecules occurred by MD simulations. The average root-mean-square (RMS) force at the optimized TS geometry was 0.0086 hartree/bohr, which is satisfactory in comparison with the value at the SS, that is, 0.0043 hartree/bohr, 14 and the previous values of SS for glycine zwitterion, that is, 0.0025 hartree/bohr, 12 and of TS for a Menshutkin reaction, that is, 0.0010 hartree/bohr, 13 in aqueous solution. Additionally in Figure 2a, also shown are the solute potential energy V S changes in gas phase (O (PM3) and 0 (B3LYP/6-31G(d))) and that in aqueous solution by the COSMO method (2).…”

“…Hereafter, the present path-following procedure with an adaptive constant c i is called the adaptiVe steepestdescent-path scheme. 14 It is worth mentioning that at an optimized structure, in addition to the zero-gradient condition eq 2.18, the following force-balance condition must be fulfilled: 14 because the free-energetical optimization is accomplished in compensation for the balance between the solute potential energy gradient and the forces acting on each solute atom due to solvation. Precisely in Figure 1, this is a force balance between the restoring force on nuclei, which is to return back to the charge distribution of the bare solute molecule, that is, +f, and the force executed by solvent toward the charge distribution, that is, -f. Even if the geometrical change might be small in solution, the mechanism that maintains it microscopically could be fully different.…”

“…The structure that corresponds to the maximum of the FE curve (A FEG : b) at R(N1-H5) ) 1.512 Å in Figure 2a was taken to be the free-energetically optimized TS structure and is shown in Figure 3a together with the SS one (Figure 3b) obtained in our previous work. 14 In addition, the structure by the COSMO method that corresponds to the maximum on the closed triangle curve (A COSMO : 2) at R(N1-H5) ) 1.452 Å in Figure 2a is shown (Figure 3c). They all have the C s symmetry.…”

“…The former value obtained by the FEG method was estimated to be 14.7 kcal/ mol (300 K), which was estimated by the FE change ∆A FEG q between the FE value at the SS (R(N1-H5) ) 1.812 Å) 14 and that at the TS structure obtained in this work (R(N1-H5) ) 1.512 Å) (Figure 2a). To estimate the experimental value of …”

“…Development of theoretical methods to know stable or transition states in solution is, therefore, a crucial issue for deeply understanding these phenomena. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] However, by the necessity of taking a large number of solvent molecules into consideration, there are several theoretical restrictions to study even equilibrium thermodynamic characteristics of chemical reactions in solution.…”