Mail:
Dept. of Chemistry
Ohio State University
100 W. 18th Ave.
Columbus, OH 43210
Office:
412 CBEC
Email:
herbert@
chemistry.ohio-state.edu
The past fifteen years have witnessed an explosion of activity in the field of fragment-based quantum chemistry, whereby ab initio electronic structure calculations are performed on very large systems by decomposing them into a large number of relatively small subsystem calculations, then reassembling the subsystem data in order to approximate supersystem properties. Most of these methods are based, at some level, on the so-called many-body (or "n-body") expansion, which ultimately requires calculations on monomers, dimers, ..., n-mers of fragments. To the extent that a low-order n-body expansion can reproduce supersystem properties, such methods replace an intractable supersystem calculation with a large number of easily-distributable subsystem calculations. This holds great promise for performing, e.g., "gold standard" CCSD(T) calculations on large molecules, clusters, and condensed-phase systems.
The literature is awash in a litany of fragment-based methods, each with their own working equations and terminology, which presents a formidable language barrier to the uninitiated reader. We have sought to unify these methods under a common formalism, by means of a generalized many-body expansion that provides a universal energy formula encompassing not only traditional n-body cluster expansions but also methods designed for macromolecules, in which the supersystem is decomposed into overlapping fragments. This formalism allows various fragment-based methods to be systematically classified, primarily according to how the fragments are constructed and how higher-order n-body interactions are approximated. This classification furthermore suggests systematic ways to improve the accuracy.
Whereas n-body approaches have been thoroughly tested at low levels of theory in small non-covalent clusters, we have begun to explore the efficacy of these methods for large systems, with the goal of reproducing benchmark-quality calculations, ideally meaning complete-basis CCSD(T). For high accuracy, it is necessary to deal with basis-set superposition error, and this necessitates the use of many-body counterpoise corrections and electrostatic embedding methods that are stable in large basis sets. Tests on small non-covalent clusters suggest that total energies of complete-basis CCSD(T) quality can indeed be obtained, with dramatic reductions in aggregate computing time. On the other hand, naïve applications of low-order n-body expansions may benefit from significant error cancellation, wherein basis-set superposition error partially offsets the effects of higher-order n-body terms, affording fortuitously good results in some cases. Basis sets that afford reasonable results in small clusters behave erratically in larger systems and when high-order n-body expansions are employed.
For large systems, and (H2O)N≥30 is large enough, the combinatorial nature of the many-body expansion presents the possibility of serious loss-of-precision problems that are not widely appreciated. Tight thresholds are required in the subsystem calculations in order to stave off size-dependent errors, and high-order expansions may be inherently numerically ill-posed. Moreover, commonplace script- or driver-based implementations of the n-body expansion may be especially susceptible to loss-of-precision problems in large systems. These results suggest that the many-body expansion is not yet ready to be treated as a "black-box" quantum chemistry method.