Dept. of Chemistry
Ohio State University
100 W. 18th Ave.
Columbus, OH 43210

412 CBEC


John Herbert research group

Non-covalent interactions in many-body systems

Indinavir in the HIV-II protease binding pocket
Indinavir in the HIV-II protease binding pocket,
a large system with crucial non-covalent interactions


Accurate and efficient calculation of intermolecular interactions is a challenging problem for electronic structure theory. Although the van der Waals interaction is one of the most fundamental concepts in chemistry, from a quantum-mechanical point of view it arises purely from electron correlation, and thus demands a high-level theoretical treatments if it is to be described properly. However, such calculations are seldom amenable to large collections of monomers, and certainly not to liquids, and thus cannot be used to describe the important cooperative (non-additive or many-body) effects present in clusters and in the condensed phase. We are working to develop ab initio methods for many-body systems that exploit monomer-based SCF calculations whose cost scales linearly with the number of monomers. These calculations are then coupled to two- and three-body treatments of the intermolecular interactions, to obtain accurate many-body interaction energies (comparable to the best supersystem ab initio calculations) at dramatically reduced cost. We have written short reviews of many-body methods for non-covalent interactions. and "extended" symmetry-adapted perturbation theory (XSAPT).

Noteworthy Accomplishments

XPS(KS)+D timings
timings for polyadenine

We have recently introduced a systematically-improvable hierarchy of ab initio methods for computing interaction energies in many-body systems. This approach is based on a self-consistent, monomer-based treatment of polarization (the "explicit polarization" or "XPol" procedure),, which can be performed efficiently even in many-body systems, and which generates monomer wave functions that are polarized as appropriate for the many-body environment. These XPol monomer wave functions then form the basis states for a subsequent, pairwise version of symmetry-adapted perturbation theory (SAPT) to describe the remaining contributions to the intrmolecular interaction, primarily dispersion and exchange repulsion. The composite XPol+SAPT method extends the well-known SAPT methodology to systems composed of more than two monomer units.

Error statistics for dimer binding energies
Error statistics for binding energies
in the S66 data set

Furthermore, replacing the SAPT dispersion terms with an empirical potential facilitates the use of Kohn-Sham DFT as a low-cost means to treat intramolecular electron correlation. The resulting method, which we call XPol+SAPT(KS)+D, exhibits cubic-scaling cost, both with respect to the number of monomer units as well as with respect to the size of those monomer units. Moreover, by exploiting the embarrassingly parallel nature of the XPol+SAPT approach, the total wall time for XPol+SAPT(KS)+D calculations can be made to scale linearly with respect to the number of monomer units. Despite this favorable scaling, the accuracy of XPol+SAPT(KS)+D is better than 0.5 kcal/mol for the S22 and S66 databases of benchmark [CCSD(T)/CBS] non-covalent binding energies. This level of accuracy, which we achieve using modest double-ζ basis sets, rivals that of the best MP2- and CCSD-based methods, when those methods are extrapolated to the basis-set limit. MP2 and CCSD, however, exhibit O(N5) or O(N6) scaling with respect to the size of the total (super)system.

Finally, we have recently shown how to generalize the traditional many-body energy expansion (MBE) to cases where the monomer units overlap. In addition to clarifying connections between the vast menagerie of fragment-based methods that currently exist in the quantum chemistry literature, this generalized MBE formalism appears to offer a promising route toward high-accuracy, fragment-based calculations in large polyatomic molecules.

Representative Publications

Papers published prior to Sept. 1, 2012 are based upon work supported by the National Science Foundation under Grant No. CHE-0748448. Subsequent papers are based on work supported by the Dept. of Energy under Award No. DE-SC0008550. Calculations were performed primarily at the Ohio Supercomputer Center, under Project Nos. PAS0291 and PAA0003. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the funding agencies.

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