Alumni Project
Next-Generation, Explicitly-Correlated
Electronic Structure Methods
Wesley D. Allen and Henry F. Schaefer
III
Center for Computational Quantum Chemistry,
University of Georgia, Athens, GA 30622
Summary
The quantum chemical wavefunction methods in current use for electronic
structure computations have accuracy limits arising from their fundamental
inability to properly describe electron-electron cusp behavior. Our
work is devoted to the development and dissemination of rigorous, “explicitly-correlated”
methods that solve the electron cusp problem and deliver potential energy
hypersurfaces for chemical systems of exceptional accuracy (±0.1
kcal mol-1) in terascale computing environments.
The revolutions in physics in the early decades of the past century
provided essentially exact, predictive theories for all chemical properties
and processes. However, the mathematical intractability of the Schrödinger
and Dirac equations of molecular quantum mechanics prevented the computation
of accurate numerical solutions for chemical systems until the past
two decades. Carried by a synergy between breathtaking improvements
in computer hardware and groundbreaking innovations in mathematical
formulations and algorithms, computational quantum chemistry has established
a burgeoning presence in chemical research, owing both to the elucidation
of complex phenomena it provides and its cost effectiveness vis-à-vis
experimental methods.
Virtually all ab initio methods of quantum chemistry in some
way involve the orbital approximation, wherein the many-electron molecular
wavefunction (Y) is represented as superpositions of antisymmetrized
products of single-particle functions. Such methods, frequently aided
by empirical corrections, have been quite successful in approaching
or reaching “chemical accuracy” (1-2 kcal mol-1) for relative energies
of modestly-sized molecules. Moreover, the elementary bonding principles
of interpretive chemistry are built on longstanding orbital concepts.
However, order of magnitude improvements to “subchemical accuracy” (0.1-0.2
kcal mol-1) are needed to expand the world’s thermochemical (and spectroscopic)
database into inaccessible realms, establish its building blocks beyond
dispute, and supersede more expensive experimental approaches.
Theoretical methods built on the orbital approximation have fundamental
accuracy limits and fall short of the subchemical accuracy target
for all but the simplest molecules. The essential flaw in these methods
is their inability to correctly describe the mathematical cusp behavior
of many-electron wavefunctions in the vicinity of coalescence points,
and hence to fully account for instantaneous, short-range correlation
among electrons. Achieving the subchemical accuracy dream will require
next-generation methodologies that solve the electron cusp
problem by explicitly incorporating interelectronic variables (r12)
into molecular wavefunctions, or equivalently by constructing Y
from two-particle components (geminals). Figure 1 is a scheme depicting
the superiority of such “explicitly correlated” methods over conventional
orbital-based descriptions.
Figure 1. Superiority of explicitly correlated (R12) methods
in the cusp regions of many-electron wavefunctions.
Our SciDAC research has been directed specifically toward the development
of “linear R12” methods. We have written a new computer code to evaluate
the plethora of nonstandard two-electron integrals[1] required by R12
theories by means of a sophisticated architecture effective for functions
of arbitrarily high angular momentum. This state-of-the-art integrals
software is the centerpiece of our new integral-direct R12 package,
which is now being incorporated by colleagues into an existing massively
parallel quantum chemical suite to take full advantage of terascale
computing facilities. Our R12 research has already resulted in several
chemical applications[2] exhibiting unparalleled convergence of predictions
toward the complete basis set (CBS) limit, including studies to pinpoint
the problematic barriers to linearity of H
2O and SiC
2, and the heats
of formation of HNCO and NCO.
Continuing work within our group will pursue the development and implementation
of explicitly-correlated perturbation and coupled-cluster theories for
open-shell species, both within less complicated unrestricted
(UHF) formalisms and more difficult spin-adapted (ROHF) approaches.
Such open-shell methods promise to have a particular impact for critical
computations on combustion and atmospheric chemistry. In addition, we
are working to solve certain technical deficiencies in the standard
approximations for many-electron integrals in R12 theory and thereby
to usher in the full promise of the methodology.
To reach the ab initio limit of molecular quantum mechanics
most efficiently, we conjoin lower-order, explicitly-correlated methods
with high-order conventional correlation treatments via the focal-point
scheme[3] of Allen and co-workers. Here we are involved in SciDAC collaborations
with the Head-Gordon and Piecuch groups to find better means of obtaining
auxiliary high-order, conventional coupled-cluster predictions and thereby
to more reliably infer exact correlation (FCI) limits. In addition,
to address issues of chemical reaction dynamics with our next-generation
electronic structure methods, we are working with the Thompson group
to develop improved methods for generating and representing large regions
of potential energy hypersurfaces.
[1] E. F. Valeev and H. F. Schaefer, J. Chem. Phys. 113,
3990 (2000).
[2] See E. F. Valeev, W. D. Allen, H. F. Schaefer, and A. G. Császár,
J. Chem. Phys. 114, 2875 (2001) and other papers to
appear in 2003 in the same journal.
[3] See, for example, A. G. Császár, W. D. Allen, and
H. F. Schaefer, J. Chem. Phys. 108, 9751(1998).
For further information on this subject contact:
Dr. Wesley D. Allen, CCQC, Univ. of Georgia;
wdallen@ccqc.uga.edu or
www.ccqc.uga.edu.
back to project page
