We at Gaussian are saddened by the passing of Prof. George A. Petersson on January 22, 2026. George was a long time Gaussian collaborator, contributing the Complete Basis Set (CBS) high accuracy energy models and the Intrinsic Reaction Coordinate Maximum Energy (IRCMax) method for locating transition states to the Gaussian program. (See below for a brief description of Complete Basis Set extrapolation, the technique which underpins the CBS methods.) George was also a frequent instructor at Gaussian workshops.
George’s Life and Career
George grew up in Brooklyn, as it happens mere blocks from his scientific contemporary Ken Wiberg. He attended the City College of New York, graduating in 1964. He obtained his PhD at Caltech in 1970 and was then a postdoc with E. J. Corey at Harvard. He subsequently joined the Chemistry department at Wesleyan University, eventually becoming Professor of Theoretical and Computational Chemistry and Fisk Professor of Natural Science. After retiring from Wesleyan and moving to Philadelphia to be near his son, daughter-in-law and granddaughters, he became Distinguished Adjunct Professor of Chemistry at Temple University.
George’s research interests centered on high accuracy theoretical methods for the calculation of molecular energies and other properties, as well as methods applicable to transition states and potential energy surfaces for chemical reactions. He was also a frequent collaborator with experimental groups.
In his personal life, George was a devoted husband, father and grandfather. He and his wife Margaret took up ballroom dancing a few years before his retirement. He also enjoyed classical music, dance and theater, things available in abundance in Philadelphia, as well as the works of Salvador Dali. George was also a bit obsessed with his Ferrari.
A Note from Dr. Michael Frisch
George was a very thorough and systematic researcher, careful to understand where a particular models works well and when it fails as well as the underlying physics which is and which is not well represented in a model. His CBS methods are a series of models which are not only very accurate but also extremely reliable, in that their accuracy is consistent over a wide range of chemical systems. In this latter respect especially, George’s models have proved to be consistently superior to the alternatives while also requiring considerably fewer computational resources to achieve a given level of accuracy. They are used effectively by scientists working on a variety of problems in chemistry, chemical engineering and materials science, reflected in the high rate of citations for his key papers.
On a personal note, I thoroughly enjoyed and cherished my 30+ year friendship with George. I will miss him terribly.
— Mike Frisch
George’s Most Recent Papers
Two recent papers reflect his central interests:
The low-lying electronic states and ultrafast relaxation dynamics of the monomers and J-aggregates of meso-tetrakis(4-sulfonatophenyl)-porphyrins:
An experimental and theoretical study of UV absorption and emission of two species of meso-tetrakis(4-sulfonatophenyl)-porphyrins (TSPP), compounds which are key components of solar cells. The TD-DFT calculations revealed an infrared absorption at 1900 cm-1 for the singlet and triplet excited states that is absent in the ground state, allowing it to serve as a probe for subsequent transient IR absorption spectroscopy to study the excited state’s vibrational dynamics, yielding predictions for the lifetime of the S1 excited electronic state and other related properties.
H. Fang, M. J. Wilhelm, D. L. Kuhn, Z. Zander, H.-L. Dai, G. A. Petersson, J. Chem. Phys. 159 (2023) 154302; DOI:10.1063/5.0174368
Zero-point energies from bond orders and populations relationships:
Describes 2 new methods, ZPE-BOP1 and ZPE-BOP2, for calculating zero point energies from bond orders and orbital populations obtained from a B3LYP energy calculation with a very large basis set (6-311+(3d2f,2df,2p)) along with additional terms and fitting parameters. This work is part of an ongoing effort to approximate chemical properties without costly second derivative calculations.
B. Zulueta, C. D. Rude, J. A. Mangiardi, G. A. Petersson, J. A. Keith, J. Chem. Phys. 2025, 162, 084102. DOI:10.1063/5.0238831
The following list of articles provides a representative sample from each decade over the course of his long career:
Representative Publications from each Decade of George’s Career
1960s: Petersson, G. A.; McLachlan, A. D. Semiempirical Calculation of EPR Spin-Spin Coupling Constants. The Journal of Chemical Physics 1966, 45, 628. DOI:10.1063/1.1727619
1970s: Corey, E. J.; Petersson, G. A. Algorithm for machine perception of synthetically significant rings in complex cyclic organic structures. Journal of the American Chemical Society 1972, 94, 460–465. DOI: 10.1021/ja00757a023
1980s: Nyden, M. R.; Petersson, G. A. Complete basis set correlation energies. I. The asymptotic convergence of pair natural orbital expansions. The Journal of Chemical Physics 1981, 75, 1843. DOI:10.1063/1.442208
1990s: Wiberg, K. B.; Ochterski, J. W.; Petersson, G. A. A comparison of model chemistries. Journal of the American Chemical Society 1995, 117, 11299–11308. DOI:10.1021/ja00150a030
2000s: Petersson, G. A.; Zhong, S.; Montgomery, J. A.; Frisch, M. J. On the optimization of Gaussian basis sets. The Journal of Chemical Physics 2003, 118, 1101. DOI:10.1063/1.1516801
2010s: Frisch, M. J.; Petersson, G. A.; Austin, A.; Dobek, F. J.; Scalmani, G.; Throssell, K. A Density Functional with Spherical Atom Dispersion Terms. Journal of Chemical Theory and Computation 2012, 8, 4989–5007. DOI:10.1021/ct300778e
2020s: Zulueta, B.; Rude, C. D.; Mangiardi, J. A.; Petersson, G. A.; Keith, J. A. Zero-point energies from bond orders and populations relationships. J. Chem. Phys. 2025, 162, 084102. DOI: 10.1063/5.0238831
Complete Basis Set Extrapolation
The various members of the Complete Basis Set (CBS) family of high accuracy energy models all include a component that extrapolates from calculations using a finite basis set to the estimated complete basis set limit. The following excerpt from Exploring Chemistry with Electronic Structure Methods (pp. 496-97) briefly introduces this procedure. For a review, see [Petersson00].
The extrapolation to the complete basis set energy limit is based upon the Møller-Plesset expansion of the energy EMP= E(0)+ E(1)+ E(2)+ E(3)+ E(4)+ …. Recall that E(0)+ E(1)is the Hartree-Fock energy. We will denote E(3)and all higher terms as E(3→∞), resulting in this expression for E:
ECBS= E HF+ E(2)+ E(3→∞)
CBS extrapolation computes the second and third terms in this equation—the second-order and infinite-order corrections to the energy—via an extrapolation procedure [Nyden81, Petersson00]. No explicit extrapolation of the SCF energy is included because the CBS models begin with a large enough SCF calculation to obtain the desired level of accuracy.
Perhaps the most obvious way to extrapolate the MP2 energy term would be to calculate it using a set of increasingly large basis sets and then projecting the resulting series of values to the basis set limit. This would be very costly in terms of computation resources, depending as it does on large MP2 calculations. Moreover, careful analysis of the problem reveals the components of the Møller-Plesset second-order term (MP2) converge at different rates, which would cause the most lengthy parts to dominate the time required for any monolithic extrapolation scheme.
The CBS extrapolation process for the second-order correlation energy proceeds by decomposing it into a sum of pair energies, each of which represents the correlation energy for two of the electrons in the molecular system. This work draws on that of Schwartz [Schwartz62], who derived an expression for how the energy converges as successive s functions, p functions, d functions, f functions, and so on, are added to the description for a helium-like ion. Petersson and coworkers extended this two-electron formulation to many-electron atoms by writing the MP2 correlation energy as a sum of pair energies, each describing the energetic effect of the electron correlation between that pair of electrons.
In general, the process proceeds in this way:
- Perform an MP2 calculation. The basis set used depends on the specific CBS method and its target accuracy level. For example, the CBS-4 method uses the 6-31+G(d,p) basis set [Ochterski96, Montgomery00], and the CBS-QB3 method uses 6-311G(3d2f,2p) basis set [Montgomery99, Montgomery00] (with one fewer d and f function for first row atoms).
- Transform the orbitals and the MP2 amplitudes to the localized pair orbital formalism.
- For each electron pair:
- Compute the base pair energy (the contribution of that pair to the SCF energy).
- Calculate the second-order energy for each pair by adding in successive shells of virtual orbitals and extrapolating to the basis set limit.
- The sum of the extrapolated pair energies is the second-order correlation energy.
CBS extrapolation is illustrated in the following figure:
N is the number of orbitals in the expansion of the pair energy. The extrapolation begins at the top right, where the point N=1 corresponds to the uncorrelated pair energy, and it finishes in the lower left. The x-axis plots a quantity that is proportional to N-1, moving from right to left from 0 added virtual orbitals to the basis set limit: N→∞.
The circles indicate the contributions of each successive natural orbital to the pair energy; filled circles indicate complete shells. The extrapolation is linear in N when it corresponds to complete shells, and only these points are required for extrapolating to the complete basis set limit (indicated in red on the y-axis).
Computing the second-order energy by decomposition into pair energies is not only much faster than extrapolating the MP2 energy in toto, but it also produces a more accurate value for the basis set limit for a given basis set.
The E (3→∞) term in the equation above also requires only the extrapolated second-order energy because the ratio of the total full CI basis set truncation error to this term is known to be described by the following expression for incorporating the interference factor:
The denominator is the extrapolated second-order energy (the Δeij(2) are the pair orbital energies). C holds the coefficients of the virtual orbitals in the first-order perturbation wavefunction. The i and j indices run over the electron pairs, and the μ index runs over the virtual orbitals. In this way, when the MP2 CBS limit is known for a given basis set, the CCSD(T) CBS limit can be computed from a single CCSD(T) calculation with the same basis set. This is what is done in the CBS-QB3 compound model chemistry to obtain very accurate thermochemistry predictions at reasonable computational cost.
