Research
Themes

I.
Motivation
Highly
accurate predictions of condensedphase phenomena from firstprinciples
are rare. Current theoretical methods either cannot consistently
treat chemical reactions at a high level of accuracy, or are limited
by system size or the time scale of the process. To overcome such
obstacles, I will initiate a research program to devise better
linearscaling firstprinciples schemes to study interesting problems
in biological systems and materials science, with an equal emphasis
on theoretical advances and realworld applications. The ultimate
goal is to offer the scientific community a reliable vehicle to
qualitatively and quantitatively understand basic mechanisms in
complex systems, and to gain insights into aspects of nature that
cannot be easily probed by experimental means.

II. Ab Initio
Quantum Chemistry
The
success of ab initio quantum chemistry computational packages
(e.g., GAUSSIAN, MOLCAS, HONDO, MELD, etc.)
has made conventional ab initio theories essentially "household"
names in everyday chemistry. Despite their popularity, these methods
cannot be applied to many common chemical problems due to their
prohibitive scaling properties, i.e., scaling worse than
O(N^{4})
for postHartreeFock methods, where N is the "size"
of the system. Among various efforts to surmount this scaling
problem, working directly with loworder reduced density matrices
has the most promise: accurate energetics with relatively low
computational cost and without seriously sacrificing the quality
of the wave function. This research area will be one of our primary
interests.

III. DensityFunctional
Theory
In
addition to the popular KohnSham orbitalbased approach to densityfunctional
theory, there is a lessused HohenbergKohn orbitalfree densitybased
scheme. Though linearscaling KohnSham codes are available, they
are computationally expensive due to manipulations of basis sets
and KohnSham orbitals, including orbital orthonormalization and
orbital localization. In comparison, the orbitalfree HohenbergKohn
scheme is purely a densitybased, linearscaling method with none
of the overhead associated with basis sets and KohnSham orbitals.
The orbitalfree HohenbergKohn scheme also performs uniformly
well with linearscaling regardless whether or not the firstorder
reduced density matrix is "nearsighted" (diagonally
dominant).
With present computational
resources, systems of thousands of atoms can be studied with the
orbitalfree HohenbergKohn scheme; such a size is inconceivable
for the present orbitalbased ab initio and KohnSham methods.
In fact, the orbitalfree HohenbergKohn scheme is purely restricted
by the physical size of the system under investigation, not by
the number of electrons, and certainly has clear advantages over
the orbitalbased methods. Furthermore, with the help of linearscaling
summation techniques for longrange interactions, significantly
larger systems can be modeled dynamically within the densityfunctional
theory description using current computational power.
Hence, the orbitalfree HohenbergKohn scheme is a much better
choice in terms of efficiency and implementation. However, in
order to obtain accurate results via the orbitalfree HohenbergKohn
scheme, one must know all of the components in the total energy
density functional. Our task is to design nearly universal, highly
accurate, densityonly kineticenergy and exchangecorrelation
density functionals, such that the orbitalfree, linearscaling
HohenbergKohn scheme will become the preferred method of implementation
of densityfunctional theory in the near future.

IV.
Applications to Complex Systems
With
the advances mentioned in the previous two sections, we then merge
them into a coherent embedding formalism and methodology to study
chemical and physical processes in complex systems, especially
biological systems and condensedphase materials. The basic idea
behind such an embedding scheme is to treat the large surrounding
environment by a less computationally intensive method (e.g.,
densityfunctional theory), and to apply highlevel postHartreeFock
methods to the chemical reaction regions such that accurate energetics
are obtained. Ultimately, we will be able to develop highly accurate
linearscaling firstprinciples methods and apply them to reliably
predict the behavior of complex systems.

During the course of research, graduate students and postdoctoral
fellows will be equipped with a broad set of skills and knowledge
(physics, chemistry, mathematics, computation, biophysics, and
materials science), benefiting their future careers. 
