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2013 Chemistry Newsletter
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2013 Beckman Scholars Program
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In the Herrick lab research is focused on theoretical chemistry and chemical physics, with emphasis on novel approaches to issues involving atomic and molecular structure. On the atomic side, this has included collision-induced angular momentum transfer in excited Rydberg atoms; energies and transitions of excited states in electric and magnetic fields; complex energy analysis of autoionization resonances; and electron correlation effects in two-electron excited states. Molecular interests have included electron correlation effects in excited states of conjugated polyenes; van der Waals clusters; Stern-Gerlach deflection spectra of magnetic molecules; and molecular pair potential energy functions from rotation-vibration spectroscopy.
A common theme and ongoing interest is the introduction of Lie algebraic theory [see Advances in Chemical Physics 52, 1–100 (1983)] to study and classify strong configuration interaction mixing effects in excited states from electron-electron repulsions or external fields. This exploits raising and lowering operators from mathematical groups to describe electron jumps between atomic orbitals in the atom, or between bonded atoms in molecules. Many-electron representations of these group operations then lead to correlated wave functions as a basis for exact solutions of the Schrödinger wave equation. This has involved groups such as O(4) for degenerate atomic orbitals or n-dimensional representations of SU(2) to describe delocalized molecular orbitals in a linear polyene CnHn+2.
We are studying new ways to represent molecular pair potentials V(R) in terms of the inverse function R(V). This shows up in semiclassical Rydberg-Klein-Rees theory for potentials from rotation-vibration energies, but we are using it for more accurate representations based on quantum mechanics. Starting with the virial theorem as a framework, the inverse potential is first represented as the solution of an integral equation or a differential equation [see Journal of Chemical Physics 109, 11 (1998)]. Fitting the parameters in these equations to spectroscopic data yields classes of elementary potential functions as exact solutions, which are then used as linear expansion bases to derive accurate molecular potentials consistent with experiment.
Another direction involves the application of effective potentials to study the structure and dynamics of rare gas atom clusters. These have the interesting property of forming icosahedral structures of 13, 55, 147, . . . atoms at low temperatures. We’re investigating tetrahedral symmetry-breaking pathways for large-amplitude vibrations over a barrier with cuboctahedral symmetry as a basis for internal rotations and fluid-like properties of individual clusters. Several aspects of this problem involve applications of group theory, including both traditional molecular point groups and continuous groups for the correlation of the n atoms in the cluster.
Other areas of recent interest have included the effects of perturbations on potential energy surfaces [see Journal of Chemical Education 79, 1372 (2002)], and a new theoretical approach that explains the long-standing empirical connection between the different electronegativity scales invented by Pauling and Mulliken [see Journal of Chemical Theory and Computation 1, 255 (2004)].
Top: Icosahedral atomic
clusters having “magic numbers” of rare-gas atoms.
Middle: Tetrahedral reaction path from icosahedral cluster to cuboctahedral cluster via concerted 30-degree internal rotation of equatorial atoms.
Bottom: Energy of concerted pathway between two icosaheral clusters. Cuboctahedral intermediate approaches fcc packing in limit of infinite cluster size.
"Connecting Pauling and Mulliken Electronegativities," David R. Herrick, J. Chem. Theory Comput. 2005, 1, 255-260.
Using Computer Graphics to Denonstrate the Origin and Applications of the “Reacting bond Rules,” David R. Tyler and David R. Herrick Journal of Chemical Education 79, 1372 (2002).
"Inverse Virial Symmetry of Diatomic Potential Curves", D.R. Herrick and Sean O'Connor, Journal of Chemical Physics 109 (1998) 11.
"Inflection Spacing Symmetry of Diatomic Potential Curves", D.R. Herrick and Sean O'Connor, Journal of Chemical Physics 109 (1998) 2071.
"New Symmetry Properties of Atoms and Molecules", D.R. Herrick, Advances in Chemical Physics 52 (1983) 1-115.
"Fully Resolved Zeeman Pattern in the Stern-Gerlach Deflection Spectrum of O2", J.J.Yang, N.A. Kuebler, M.B. Robin, A. Gedanken, and D.R. Herrick, Phys. Rev. A 38 (1988) 737.
"Theoretical Investigation of the Effects of Intramolecular Electron-spin Relaxation on Stern-Gerlach Deflection"s, D.R. Herrick, M.B. Robin, and A. Gedanken, Chemical Physics 130 (1989) 201.
"Spin-Rotation Effects in the Stern-Gerlach Deflection Spectra of Triplet-Sigma-Minus Molecules and their Complexes with Argon", D.R. Herrick, M.B. Robin, and A. Gedanken, Journal of Molecular Spectroscopy 133 (1989) 61.
"Strong Correlations in Simple Atoms and Molecules", D.R. Herrick, in "Electronic and Atomic Collisions," J.Eichler, I.V.Hertel, N. Stolterfoht (eds), Elsevier Science (1984) 487.
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