First-Principles-Based Multiscale, Multiparadigm Molecular Mechanics and Dynamics Methods for Describing Complex Chemical Processes - Multiscale Molecular Methods in Applied Chemistry - page 7

(see [ 22 ] for a recent review). A form of MC-SCF useful for interpreting electron
correlation and bonding is the GVB method, [ 23 - 25 ] which leads to the best
description in which every orbital is optimized for a single electron. These are
referred to as ab initio methods as they are based directly on solving (1), without
any empirical data. Many methods, which rely on empirical data to obtain approxi-
mate descriptions for systems too large for ab initio methods, have also been proved
useful. [ 26 ]
A non-empirical alternative to ab initio methods that now provides the best
compromise between accuracy and cost for solving Schrodinger's equation of
large molecules is DFT. The original concept was the demonstration by Hohenberg
and Kohn [ 27 ] that the ground state properties of a many-electron system are
uniquely determined by the density, r

, as a function of nuclear coordinates, r , and
hence all the properties of a (molecular) system can be deduced from a functional
of r ( r ), i.e.,

E ¼ erð ½ r Þ : (4)

DFT has evolved dramatically over the years, with key innovations including the
formulation of the Kohn-Sham equations [ 28 ] to develop a practical one-particle
approach, while imposing the Pauli principle, the Local Density Approximation
(LDA) based on the exact solution of the correlation energy of the uniform electron
gas, the generalized gradient approximation (GGA) to correct for the gradients in
the density for real molecules, incorporating exact exchange into the DFT. This
has led to methods such as B3LYP and X3LYP that provide accurate energies
(~3 kcal/mol) and geometries [ 29 ] for solids, liquids, and large molecules [ 30 , 31 ].
Although generally providing high accuracy, there is no prescription for improving
DFT when it occasionally leads to large errors. Even so, it remains the method
of choice for electronic structure calculations in chemistry and solid-state physics.
We recently demonstrated improved accuracy in DFT by introducing a universal
damping function to correct empirically the lack of dispersion [ 32 ].
An important area of application for QM methods has been determining and
describing reaction pathways, energetics, and transition states for reaction pro-
cesses between small species. QM-derived first and second derivatives of energy
calculated at stable and saddle points on PES can be used under statistical
mechanics formulations [ 33 , 34 ] to yield enthalpies and free energies of structures
in order to determine their reactivity. Transition state theory and idealized ther-
modynamic relationships (e.g.,

kTln[P/P 0 ]) allow temperature and
pressure regimes to be spanned when addressing simple gas phase and gas-surface
interactions.
On the other hand, many applications involve interactions between solutes and
solvent, which utterly distinguish the condensed phase from in vacuo, free energy
surfaces. To tackle this challenge, we describe below a unique multiparadigm
strategy to incorporate the effects of a solvent when using QM methods to deter-
mine reactivity in organic and organometallic systems.

D G[P 0 ! P] ¼