First-Principles-Based Multiscale, Multiparadigm Molecular Mechanics and Dynamics Methods for Describing Complex Chemical Processes - Multiscale Molecular Methods in Applied Chemistry - page 8

Application Example: Solvent and pH Effects on Reactivity

Interactions critical to the rate and selectivity of reactions include the relaxation of
a wavefunction or zwitter-ionic geometry in response to a polarizable solvent,
hydrogen bonding, and reversible proton transfer. It is necessary in these cases to
introduce solvation effects explicitly through the inclusion of solvent molecules,
and/or implicitly through a continuum representation of the medium. Adding
explicit solvent molecules increases the cost of already expensive QM calcula-
tions, while implicit solvation models vary in their degree of parameterization and
generality.
One approach assigns an empirical surface free energy to each exposed atom
or functional group in a solute. More general algorithms combine an electrostatic
term based on atomic charges and solvent dielectric constant with empirical
corrections specific to functional groups and solvent cavitation energies. In the
Poisson-Boltzmann (PB) model [ 25 ], solvent is represented as a polarizable

continuum (with dielectric ) surrounding the solute at an interface constructed

by combining atomic van der Waal radii with the effective probe radius of the
solvent. Charges are allowed to develop on this interface according to the
electrostatic potential of the solute and

e

through the solution of the Poisson-
Boltzmann equation. Charges representing the polarized solvent are then included
in the QM Hamiltonian, such that the wavefunction of the complex is relaxed self-
consistently with the solvent charges via iterative solution of

e

the PB and

Schr odinger equations. Implicit models offer the advantage over explicit solvation

that degrees of freedom corresponding to solvent motion are thermally averaged;
thus the number of particles in a QM simulation (which typically scales as N 3 or
worse) is not significantly increased.
In spite of the success of implicit solvation models, it is often easier and more
precise to take advantage of the tabulated free energies of solvation of small,
common species such as proton, hydroxide, halide ions, and so on [ 35 , 36 ]. To
screen new potential homogeneous catalysts for favorable kinetics and elucidate
mechanisms of existing systems, we have typically employed the following expres-
sion for free energies of species in solution:

€

G ¼ E elec þ ZPE þ H vib TS vib þ G solv ; (5)

which includes an electronic energy, E elec , a temperature-dependent enthalpy,
TS vib , entropy contributions, H vib , the zero-point-energy, ZPE, and a solvation
free energy, G solv , provided by a PB continuum description [ 14 ].
An example of fundamental transformations that cannot be modeled without
accurate accounting of changes in electronic structure (on the order of 100 kcal/
mol), solvation of multiply charged species (~100 kcal/mol), and the macroscopic
concentration of protons (~10 kcal/mol) is the pH-dependent oxidation of acidic
metal complexes. Figure 2 compares experimentally determined pKas and oxida-
tion potentials [ 33 ]of trans -(bpy) 2 Ru(OH 2 ) 2 2 þ to values computed with (5). Maxi-
mum errors are 200 mV and 2 pH units, despite the large changes in the components