accurate predictions of condensed-phase phenomena from first-principles
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
linear-scaling first-principles schemes to study interesting problems
in biological systems and materials science, with an equal emphasis
on theoretical advances and real-world 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
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
for post-Hartree-Fock methods, where N is the "size"
of the system. Among various efforts to surmount this scaling
problem, working directly with low-order 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
addition to the popular Kohn-Sham orbital-based approach to density-functional
theory, there is a less-used Hohenberg-Kohn orbital-free density-based
scheme. Though linear-scaling Kohn-Sham codes are available, they
are computationally expensive due to manipulations of basis sets
and Kohn-Sham orbitals, including orbital orthonormalization and
orbital localization. In comparison, the orbital-free Hohenberg-Kohn
scheme is purely a density-based, linear-scaling method with none
of the overhead associated with basis sets and Kohn-Sham orbitals.
The orbital-free Hohenberg-Kohn scheme also performs uniformly
well with linear-scaling regardless whether or not the first-order
reduced density matrix is "nearsighted" (diagonally
With present computational
resources, systems of thousands of atoms can be studied with the
orbital-free Hohenberg-Kohn scheme; such a size is inconceivable
for the present orbital-based ab initio and Kohn-Sham methods.
In fact, the orbital-free Hohenberg-Kohn 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 orbital-based methods. Furthermore, with the help of linear-scaling
summation techniques for long-range interactions, significantly
larger systems can be modeled dynamically within the density-functional
theory description using current computational power.
Hence, the orbital-free Hohenberg-Kohn scheme is a much better
choice in terms of efficiency and implementation. However, in
order to obtain accurate results via the orbital-free Hohenberg-Kohn
scheme, one must know all of the components in the total energy
density functional. Our task is to design nearly universal, highly
accurate, density-only kinetic-energy and exchange-correlation
density functionals, such that the orbital-free, linear-scaling
Hohenberg-Kohn scheme will become the preferred method of implementation
of density-functional theory in the near future.
Applications to Complex Systems
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 condensed-phase materials. The basic idea
behind such an embedding scheme is to treat the large surrounding
environment by a less computationally intensive method (e.g.,
density-functional theory), and to apply high-level post-Hartree-Fock
methods to the chemical reaction regions such that accurate energetics
are obtained. Ultimately, we will be able to develop highly accurate
linear-scaling first-principles 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.