George A. Petersson

George A. Petersson, Ph.D.

Professor Theoretical and Computational Chemistry

Fisk Professor of Natural Science

(860) 685-2508

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 recent work includes 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 98^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:

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 the figure) are useful for the extrapolation.¹
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^3-5 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.

    The CBS-n single point energy is evaluated at a geometry determined at a lower level of theory (e.g. CBS-4//UHF/3-21G). Our sequence of CBS computational models are denoted CBS-4, CBS-Q, and CBS-QCI/APNO.^3-5 The RMS errors for the 125 chemical energy differences of the G2 test set are 2.5, 1.3, and 0.7 kcal/mol respectively.^5,7
    The absolute rates of chemical reactions present a formidable challenge to theoretical predictions. The principal 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.
    The potential energy surface (PES) for a typical bimolecular chemical reaction includes valleys (leading to the reactants and products) connected at the transition state (TS), which is a first-order saddle point (i.e. a stationary point with exactly one negative force constant). Calculated energies along the coordinates with positive force constants behave very much like their counterparts in stable molecules. However, the energy changes along the reaction coordinate are much more difficult to predict. It is the variation of the energy along this coordinate that is very sensitive to (and thus requires the inclusion of) the correlation energy, as demonstrated by the figure at the right (UHF without electron correlation vs MP2 with electron correlation).
    Based on these observations, we have developed⁸ the "IRCMax transition state method," in which we select the maximum of the high-level Energy[Method(1)] (MP2/6-31G* in the example in the figures) along the low-level IRC obtained from the Geom[Method(2)] (UHF/3-21G in the figures) calculations. The IRCMax transition state extension of the CBS-n models takes advantage of the enormous improvement (up to two orders-of-magnitude) in computational speed achieved by using the low-level, Geom[Method(2)] (UHF/3-21G in our example), IRC calculations. We then perform several single point higher level, Energy[Method(1)] (MP2/6-31G* in our example), calculations along the Geom[Method(2)] reaction path to locate the Energy[Method(1)] transition state, that is, the maximum of Energy[Method(1)] along the Geom[Method(2)] IRC. The 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.⁸
    More than sixty years ago, Eyring proposed the use of statistical mechanics to evaluate the absolute rate constant:

The challenge we face 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.^8-10

Arrhenius plots for five hydrogen abstraction reactions are given in the figure to the right. The barrier heights for these reactions range from 1.3 kcal/mol (H₂+ F) to 20.6 kcal/mol (H₂O + H). We include temperatures from 250 K to 2500 K. The rate constants range from 10^-18 up to 10^-10 cm³/ 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 H₂+ H, H₂ + D, and D₂ + 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.^{9,
10}
Our CBS-4 model is applicable to much larger species. We are currently investigating the /\⁵-3-ketosteroid isomerase catalyzed conversion

of /\⁵-androstene-3,17-dione to the conjugated isomer, /\⁴-androstene-3,17-dione (the hydrogens transferred between the androstene-3,17-dione and the aspartic acid are labeled with purple).

Our calculatons indicate that the aspartic acid residue, Asp38, by itself can reduce the barrier, /\G⁺, for this reaction from 60 to 30 kcal/mol. Inclusion of the other important interactions known to be present in the active site will undoubtedly provide additional lowering of this barrier. The goal here is to expand the range of applicability of the CBS methods by combining them with Morokuma's ONIOM methods and Tomasi's PCM model of solvation. The critical portion of the reacting species (ball and bond with HOMO in the above figure) can be treated at the CBS-QB3 level of theory, while the modifications resulting from the remainder of the steroid substrate (tubes in the above figure) are treated at the CBS-4 level of theory, and the rest of the enzyme active site (wire frame above) is included through some combination of DFT, semiempirical quantum mechanics, and molecular mechanics. Bulk effects will then be treated with the PCM model.

Selected Publications

"Complete Basis Set Correlation Energies. I. The Asymptotic Convergence of Pair Natural Orbital Expansions," M. R. Nyden and G. A. Petersson, J. Chem. Phys. 75, 1843 (1981).
"Vinylidene and the Hammond Postulate," G. A. Petersson, T. G. Tensfeldt and J. A. Montgomery, Jr., J. Am. Chem. Soc. 114, 6133 (1992).
"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).
"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).
"Photoelectron Spectroscopy of the NCN- and HNCN- Ions," E. P. Clifford, P. Wenthold, W. C. Lineberger, G. A. Petersson and G. B. Ellison, J. Phys. Chem. A, 101, 4338 (1997).
"Calibration and comparison of the G2, CBS, and DFT methods for computational thermochemistry," G. A. Petersson, D. K. Malick, W. G. Wilson, J. W. Ochterski, J. A. Montgomery, Jr., and M. J. Frisch, J. Chem. Phys., 109, 10570 (1998).
"Transition States for Chemical Reactions. I. Geometry and Barrier Height," D. K. Malick, G. A. Petersson, and John A. Montgomery, Jr., J. Chem. Phys., 108, 5704 (1998).
"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.
"Computational Study of the Kinetics of Hydrogen Abstraction from Fluoromethanes by the Hydroxyl Radical," M. Schwartz, P. Marshall, R. J. Berry, C. J. Ehlers, and G. A. Petersson, J. Phys. Chem., 102, 10074 (1998).
"Properties of Diazocarbene [CNN] and the Diazomethyl Radical [HCNN] via Ion Chemistry and Spectroscopy," E. P. Clifford, P. G. Wenthold, W. C. Lineberger, G. A. Petersson, K. M. Broadus, S. R. Kass, S. Kato, C. H. DePuy, V. M. Bierbaum and G. B. Ellison, J. Phys. Chem., 102, 7100 (1998).
"Comment on Assessment of complete basis set methods for calculation of enthalpies of formation [J. Chem. Phys. 108, 692 (1988)]" J. A. Montgomery, Jr., M. J. Frisch, J. W. Ochterski, G. A. Petersson, K. Raghavachari, and V. G. Zakrzewski, J. Chem. Phys., 109, 6505 (1998).
"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).
"Perspective on "The Activated Complex in Chemical Reactions," H. Eyring, J. Chem. Phys., 3, 107 (2000)," G. A. Petersson, Theor. Chem. Acc., 103, 190 (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).
"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 Comparison of Algorithms to Construct Sequences of Gaussian Basis Sets" Abstracts of Papers of the American Chemical Society Zhong, S.J. and Petersson, G.A. 223, U477-U477 (2002).
"An Overlap Criterion for Selection of Core Orbitals: Theoretical Chemistry Accounts, Austin, A.J., Frisch, M.J., Petersson, G.A., et al., 107, 180-186 (2002).
"On the Optimization of Gaussian Basis Sets" Journal of Chemical Physics, Petersson, G.A., Zhong, S.J. et al. 118, 1101-1109 (2003).
"The Convergence of CASSCF Energies to the Completer Basis Set Limit," Petersson, G.A., Malick, D. K., Frisch, M. J., and Braunstein, M., J. Chem. Phys. 123, 74111, (2005).
"The Convergence of CASSCF-CISD Energies to the Completer Basis Set Limit," Petersson, G.A., Malick, D. K., Frisch, M. J., and Braunstein, M., J. Chem. Phys. 125, 44107, (2006).
"A restricted-open-shell complete-basis-set model chemistry," Wood, G. P. F., Radom, L., Petersson, G. A., Barnes, E. C., Frisch, M. J., and Montgomery Jr, J. A. and Martin, J., J. Chem. Phys. 125, 94106 (2006)
"The CCSD(T) Complete Basis Set Limit for Ne Revisited." Barnes, E. C., Petersson, G. A., Feller, D. and Peterson, K.A. J. Chem. Phys. 129, 194115 (2008).
"Uniformly Convergent n-tuple-z Augmented Polarized (nZaP) Basis Sets for Complete Basis Set Extrapolations. I. Self-consistent Field Energies." J. Chem. Phys. 129, 184116 (2008).
"Intramolecular nonbonded attractive interactions: 1-substituted propenes." J. Chem Theory Comput. 1033, 2009.

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

[Chemistry][Wesleyan]

Last updated: July 16, 2009 (GAP/rncb)