*Physical Chemistry:** Computational quantum mechanics emphasizing ab-initio electronic structure theory. Developing new methods for computational thermochemistry with applications to predictions of the absolute rates of chemical reactions. *

My group develops improved theoretical methods for the calculation of molecular energies. We are particularly interested in methods applicable to transition states and potential energy surfaces for chemical reactions. Our work has included the integration of these methods into variational transition state theory and the prediction of absolute rates for chemical reactions. Our complete basis set (**CBS**) methods for molecular energies and our intrinsic reaction coordinate maximum energy (**IRCMax**) method for transition states are available in the computer program Gaussian 09^{TM}.

The slow convergence of the correlation energy with the one-electron basis set expansion has provided the motivation for several attempts to extrapolate to the complete basis set limit. Our complete basis set extrapolations are based on the asymptotic convergence of pair natural orbital (PNO) expansions of the first-order wave function:

(1)

The essential idea is conveyed by a graph of *e _{ij}(N) vs N*

^{-1}*,*where the intercept is the CBS limit. Note that only certain closed-shell sets of pair natural orbitals (denoted by filled red circles in Figure 1) are useful for the extrapolation.

The accurate calculation of molecular energies requires convergence of both the one-particle (basis set) expansion and the *n*-particle (CI, perturbation, or coupled-cluster) expansion. However, the order-by-order contributions to chemical energies, and thus the number of significant figures required, generally decrease with increasing order of perturbation theory. The general approach for our CBS-*n* models is therefore to first determine the geometry and ZPE at a low level of theory, and then perform a high level single point electronic energy calculation at this geometry using large basis sets for the SCF calculation, medium basis sets for the MP2 calculation, and small basis sets for the higher-order calculations through order *n*. The components of each model have been selected to be balanced so that no single component dominates either the computer time or the error. Our sequence of CBS computational models are denoted CBS-4, ROCBS-QB3, and CBS-QCI/APNO. The RMS errors for a standard test set of 125 chemical energy differences are 2.5, 1.3, and 0.7 kcal/mol respectively.

The absolute rates of chemical reactions present a formidable challenge to theoretical predictions. The difficulty lies in the extreme sensitivity of the predicted rate constant to small errors in the activation energy. An error of only 1.4 kcal/mol leads to an error of an order-of-magnitude in the reaction rate at room temperature. Our IRCMax method reduces errors in transition state geometries by as much as a factor of five and errors in barrier heights by as much as a factor of ten.

More than sixty years ago, Eyring proposed the use of statistical mechanics to evaluate the absolute rate constant:

(2)

The challenge is to accurately determine all the quantities required to evaluate this equation. We employ an adaptation of Truhlar’s “zero curvature variational transition state theory” (**ZC-VTST**) to our CBS models through use of the IRCMax technique. Arrhenius plots for five hydrogen abstraction reactions are given in the Figure 2. The barrier heights for these reactions range from 1.3 kcal/mol (H_{2 }+ F) to 20.6 kcal/mol (H_{2}O + H). We include temperatures from 250 K to 2500 K. The rate constants range from 10^{-18} up to 10^{-10} cm^{3}/ molecule sec. If we include variations of the zero-point energy along the reaction path (*i.e.* variational transition state theory), all absolute rate constants obtained from our CBS-QCI/APNO model are within the uncertainty of the experiments. The dashed curves and open symbols for H_{2 }+ H, H_{2} + D, and D_{2} + H represent the least-squares fits of smooth curves to large experimental data sets in an attempt to reduce the noise level in the experimental data. The close agreement with theory suggests that this attempt was successful.

Our more recent work has included establishing rigorous complete basis set limits to provide benchmarks for the calibration of a new generation of more accurate CBS models (Figure 3), devising more efficient methods for optimizing Gaussian basis sets and using these methods to develop the *n*ZaP family of basis sets, and developing a new density functional with physically correct dispersion terms.

The APF-D functional employs a *spherical atom model* (SAM) for instantaneous dipole – induced dipole interactions. This model is based on the interaction between two polarizable spherical shells:

(3)

which corrects the effective interatomic distance, *R _{AB}* for the size of the atoms,

*r*(

_{s}*A*) and

*r*(

_{s}*B*). It is comparable in accuracy to including

*C*

_{6}

*R*

^{–6},

*C*

_{8}

*R*

^{–8}, and

*C*

_{10}

*R*

^{–10}, terms in a point multipole expansion. The attraction between the hydrophobic side chains of amino acids plays an important role in protein folding. This new DFT describes these interactions within the currently known accuracy (Figure 4).

Dispersion forces can also play an important role in determining the relative energies of conformational and configurational isomers. For example, the *cis*-halopropenes are more stable than the trans-isomers, due in part to the dispersion attractions. Hartree-Fock calculations predict that only the *cis*-fluoropropene is more stable than the trans-isomer (Table 1). The B3LYP functional reduces the rms error by a factor of two and correctly predicts that all three *cis*-halopropenes are more stable than the trans-isomers. The M05-2X functional again cuts the errors in half, while the APF-D model reduces the errors well below the level of second-order many-body perturbation theory. The APF-D functional will provide a valuable new tool for structural studies.

## Awards

- Kitasato Medal from the Kitasato Institute, Tokyo, Japan 2005.
- The Gold Award – First Place: 308 – 328 Class – Concorso Ferrari, Hartford Connecticut 2006.
- The John S. Burlew Award from the Connecticut Valley Section of the American Chemical Society 2009-2010.

## Selected Publications

- “Substituent Effects on O-H Bond Dissociation Enthalpies. A Computational Study,” Kenneth B. Wiberg, G. Barney Ellison, J. Michael McBride, and George A. Petersson,
*J. Phys. Chem.*,**117**, 213 (2013). - “A Density Functional with Spherical Atom Dispersion Terms,” Amy Austin, George A. Petersson, Michael Frisch, Frank Dobek, Giovanni Scalmani, and Kyle Throssell,
*Journal of Chemical Theory and Computation*,**8**, 4989 (2012). - “A Computational Study of the Properties and Reactions of Small Molecules Containing O, S and Se,” Kenneth B. Wiberg, William F. Bailey, and George A. Petersson,
*Journal of Chemical Theory and Computation*, 115, 12624 (2011). - “MP2/CBS atomic and molecular benchmarks for H through Ar,” Ericka C. Barnes, and George A. Petersson,
*J. Chem. Phys.***132**, 114111 (2010). - “Spin unrestricted coupled-cluster and Brueckner-doubles variations of W1 theory,” Ericka C. Barnes, George A. Petersson, Michael J. Frisch, John A. Montgomery, Jr., and Jan Martin,
*Journal of Chemical Theory and Computation***5**, 2687 (2009). - “Intramolecular nonbonded attractive interactions: 1-substituted propenes,” Kenneth B. Wiberg, Yi-gui Wang, George A. Petersson, and William F. Bailey,
*Journal of Chemical Theory and Computation***5**, 1033 (2009). - “Uniformly Convergent
*n*-tuple-z Augmented Polarized (*n*ZaP) Basis Sets for Complete Basis Set Extrapolations. I. Self-consistent Field Energies,” Shijung Zhong, Ericka C. Barnes, and George A. Petersson,*J. Chem. Phys.***129**, 184116 (2008). - “The CCSD(T) Complete Basis Set Limit for Ne Revisited,” Ericka C. Barnes, George A. Petersson, David Feller, and Kirk A. Peterson,
*J. Chem. Phys.***129**, 194115 (2008). - “A restricted-open-shell complete-basis-set model chemistry,” Geoffry P. F. Wood, Leo Radom, George A. Petersson, Ericka C. Barnes, Michael J. Frisch, and John A. Montgomery Jr,,
*J. Chem. Phys.***125**, 94106 (2006). - “The Convergence of CASSCF-CISD Energies to the Completer Basis Set Limit,” George A. Petersson, David K. Malick, Michael J. Frisch, and Matthew Braunstein,
*J. Chem. Phys*.**125**, 44107, (2006). - “The Convergence of CASSCF Energies to the Completer Basis Set Limit,” George A. Petersson, David K. Malick, Michael J. Frisch, and Matthew Braunstein
*J. Chem. Phys***123**, 74111, (2005). - “On the Optimization of Gaussian Basis sets,” G. A. Petersson, S. Zhong, J. A. Montgomery, Jr., and M. J. Frisch,
*J. Chem. Phys.***118**, 1101 (2003). - “An Overlap Criterion for Selection of Core Orbitals,” Amy J. Austin, Austin, Michael J. Frisch, J. A. Montgomery, Jr., and George A. Petersson,
*Theor. Chem. Acc.***107**, 180-186 (2002). - “A Complete Basis Set Model Chemistry. VII. Use of the Minimum Population Localization Method,” J. A. Montgomery, Jr., M. J. Frisch, J. W. Ochterski, and G. A. Petersson,
*J. Chem. Phys.***112**, 6532 (2000). - “A Journey from Generalized Valence Bond Theory to the Full CI Complete Basis Set Limit,” G. A. Petersson and M. J. Frisch,
*J. Phys. Chem.***104**, 2183 (2000). - “Perspective on “
*The Activated Complex in Chemical Reactions,” H. Eyring, J. Chem. Phys.,*” George A. Petersson,**3**, 107 (2000),*Theor. Chem. Acc.,***103**, 190 (2000). - “A Complete Basis Set Model Chemistry. VI. Use of Density Functional Geometries and Frequencies,” J. A. Montgomery, Jr., J. W. Ochterski, M. J. Frisch, and G. A. Petersson,
*J. Chem. Phys.***110**, 2822 (1999). - “Complete Basis Set Thermochemistry and Kinetics,” G. A. Petersson, In
*Computational Thermochemistry*, Karl K. Irikura and David J. Frurip Eds., ACS Symposium Series No.**677**, p237, Washington, D. C., 1998. - “Transition States for Chemical Reactions. I. Geometry and Barrier Height,” David K. Malick, G. A. Petersson, and John A. Montgomery, Jr.,
*J. Chem. Phys*.**108**, 5704 (1998). - “A Complete Basis Set Model Chemistry. V. Extensions to Six or More Heavy Atoms,” J. W. Ochterski, G. A. Petersson and J. A. Montgomery, Jr.,
*J. Chem. Phys.***104**, 2598 (1996). - “A Complete Basis Set Model Chemistry. IV. An Improved Atomic Pair Natural Orbital Method,” J. A. Montgomery, Jr., J. W. Ochterski and G. A. Petersson,
*J. Chem. Phys.***101**, 5900 (1994). - “Vinylidene and the Hammond Postulate,” G. A. Petersson, T. G. Tensfeldt and J. A. Montgomery, Jr.,
*J. Am. Chem. Soc.***114**, 6133 (1992). - “Complete Basis Set Correlation Energies. I. The Asymptotic Convergence of Pair Natural Orbital Expansions,” Marc R. Nyden and G. A. Petersson
*J. Chem. Phys.***75**, 1843 (1981).

## Education

B.Sc. 1964 City College of New York

Ph.D. 1970 California Institute of Technology

Research Fellow 1970-1971 Harvard University

M.A.A.E. 1986 Wesleyan University