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Alumni ProjectNext-Generation, Explicitly-Correlated Electronic Structure Methods Wesley D. Allen and Henry F. Schaefer III SummaryThe 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 ( ) 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-body wavefunctions in regions of close electron proximity, leading to incomplete accounting of 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 merits of such “explicitly correlated” methods over conventional orbital-based descriptions.
Our SciDAC research has focused specifically on the development of “linear
R12” methods and competing schemes for achieving complete basis set limits of
electronic structure theory. The computer code developed in our group for evaluating
the nonstandard two-electron integrals [1] required by R12 theories employs a
sophisticated architecture effective for functions of arbitrarily high angular
momentum. This state-of-the-art integrals software has become part of an existing
massively parallel quantum chemical suite to take full advantage of terascale
computing facilities. Recently, we have executed novel computational partial wave
analyses [2,3] of molecular correlation energies to unprecedented levels to better
reveal the asymptotic structure of both R12 and conventional electronic wavefunctions.
This work entailed the construction of new, generally applicable one-particle basis
sets with angular momentum through l = 7 Continuing work within our group will pursue the development of new types of basis sets for explicitly-correlated theories, particularly non-Gaussian forms especially designed for the evaluation of three-and four-electron integrals, a daunting task which has been an obstacle to achieving the full promise of next-generation methods. We also plan continued work on R12 theories for open-shell species, both within less complicated unrestricted (UHF) formalisms and more difficult spin-adapted (ROHF) approaches. 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[5] of Allen and co-workers. Here we are involved in SciDAC collaborations with the Piecuch group, experts in high-order, renormalized coupled-cluster approaches for closely approximating exact correlation (FCI) limits. [1] E. F. Valeev and H. F. Schaefer, J. Chem. Phys. 113 ,
3990 (2000). For further information on this subject contact:
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