Joel Bowman



Joel Mark Bowman is an American physical chemist and educator. He is the Samuel Candler Dobbs Professor of Theoretical Chemistry at Emory University.

Publications, honors and awards
Bowman is the author or co-author of more than 600 publications and is a member of the International Academy of Quantum Molecular Sciences. He received the Herschbach Medal. He is a fellow of the American Physical Society and of the American Association for the Advancement of Science.

Research interests
His research interests are in basic theories of chemical reactivity. His AAAS fellow citation cited him “for distinguished contributions to reduced dimensionality quantum approaches to reaction rates and to the formulation and application of self-consistent field approaches to molecular vibrations.”

Bowman is well known for his contributions in simulating potential energy surfaces for polyatomic molecules and clusters. Approximately fifty potential energy surfaces for molecules and clusters have been simulated employing his permutationally invariant polynomial method.

Permutationally invariant polynomial (PIP) method


Simulating potential energy surfaces (PESs) for reactive and non-reactive systems is of broad utility in theoretical and computational chemistry. Development of global PESs, or surfaces spanning a broad range of nuclear coordinates, is particularly necessary for certain applications, including molecular dynamics and Monte Carlo simulations and quantum reactive scattering calculations.

Rather than utilizing all of the internuclear distances, theoretical chemists often analytical equations for PESs by using a set of internal coordinates. For systems containing more than four atoms, the count of internuclear distances deviates from the equation 3N−6 (which represents the degrees of freedom in a three-dimensional space for a nonlinear molecule with N atoms). As an example, Collins and his team developed a method employing different sets of 3N−6 internal coordinates, which they applied to analyze the H+ CH4 reaction. They addressed permutational symmetry by replicating data for permutations of the H atoms. In contrast to this approach, the PIP method uses the linear least-square method to accurately match tens of thousands of electronic energies for both reactive and non-reactive systems mathematically.

Methodology
Generally, the functions used in fitting potential energy surfaces to experimental and/or electronic structure theory data are based on the choice of coordinates. Most of the chosen coordinates are bond stretches, valence and dihedral angles, or other curvilinear coordinates such as the Jacobi coordinates or polyspherical coordinates. There are advantages to each of these choices. In the PIP approach, the N(N − 1)/2 internuclear distances are utilized. This number of variables is equal to 3N −6 (or 3N − 5 = 1 for diatomic molecules) for N = 3, 4 and differs for N ≥ 5. Thus, N = 5 is an important boundary that affects the choice of coordinates. An advantage of employing this variable set is its inherent closure under all permutations of atoms. This implies that regardless of the order in which atoms are permuted, the resulting set of variables remains unchanged. However, the main focus pertains to permutations involving identical atoms, as the PES must be invariant under such transformations.



PIP utilizing Morse variables of the form $$y_{ij}=exp(-r_{ij}/a)$$, where $$r_{ij}$$ is the distance between atoms $$i$$ and $$j$$ and $$a$$ is a range parameter) offers a method for mathematically characterizing high-dimensional PESs. By fixing the range parameter in the Morse variable, the PES can be determined through linear least-squares fitting of computed electronic energies for the system at various structural arrangements. The adoption of a permutationally invariant fitting basis, whether in the form of all internuclear distances or transformed variables like Morse variables, facilitates the attainment of accurate fits for molecules and clusters.

Selected publications

 * Vibrational Dynamics of Molecules, World Scientific Publishing, 2022.
 * Vibrational Dynamics of Molecules, World Scientific Publishing, 2022.
 * Vibrational Dynamics of Molecules, World Scientific Publishing, 2022.
 * Vibrational Dynamics of Molecules, World Scientific Publishing, 2022.
 * Vibrational Dynamics of Molecules, World Scientific Publishing, 2022.