First-Principles-Based Multiscale, Multiparadigm Molecular Mechanics and Dynamics Methods for Describing Complex Chemical Processes - Multiscale Molecular Methods in Applied Chemistry - page 5

The wavefunction is interpreted as the probability amplitude for different config-
urations, r , of the system at different times, i.e., it describes the dynamics of the n -
particles as a function of space, r , and time, t . In more abstract terms, (1) may also
be written as

H

c ¼ E c; (2)

and take several different forms, depending on the physical situation.
In principle, all properties of all materials, with known atomic structure and
composition, can be accurately described using (1) and one could then replace
existing empirical methods used to model materials properties by a first principles
or de novo computational approach design of materials and devices. Unfortunately,
direct first principles applications of QM is highly impractical with current meth-
ods, mainly due to the computational complexity of solving (1) in three dimensions
for a large number of particles, i.e., for systems relevant to the materials designer,
with a gap of ~10 20 !
There are numerous approaches to approximate solutions for (1), most of which
involve finding the system's total ground state energy, E , including methods that
treat the many-body wavefunction as an antisymmetric function of one-body
orbitals (discussed in later sections), or methods that allow a direct representation
of many-body effects in the wave function such as Quantum Monte Carlo (QMC),
or hybrid methods such as coupled cluster (CC), which adds multi-electron wave-
function corrections to account for the many-body (electron) correlations.
QMC can, in principle, provide energies to within chemical accuracy ( 2 kcal/

mol) [ 4 ] and its computational expense scales with system size as O(N 3 ) or better
[ 5 , 6 ], albeit with a large prefactor, while CC tends to scale inefficiently with the
size of the system, generally O(N 6 to N!) [ 7 ].
Nevertheless, we have shown how QMC performance can be significantly
improved using short equilibration schemes that effectively avoid configurations
that are not representative of the desired density [ 8 ], and through efficient data
parallelization schemes amenable to GPU processing [ 9 ]. Furthermore, in [ 10 ]we
also showed how QMC can be used to obtain high quality energy differences, from
generalized valence bond (GVB) wave functions, for an intuitive approach to
capturing the important sources of static electronic correlation. Part of our current
drive involves using the enhanced QMC methods to obtain improved functionals
for Density Functional Theory (DFT) calculations, in order to enhance the scalability
and quality of solutions to (1).
But for the sake of brevity, we will focus here on methods and applications that
are unique for integrating multiple paradigms and spanning multiple length- and
timescales, while retaining chemical accuracy, i.e., beyond direct use of conven-
tional QM approaches. The following section describes the general path to classical
approximations to (1), in particular to interatomic force fields and conventional
MD, which sacrifice electronic contributions that drive critical chemical properties,
and our departure from conventionalism to recover the missing physicochemical
details.