BREAKING THE SYMMETRY IN JAHN-TELLER ACTIVE MOLECULES BY ASYMMETRIC ISOTOPIC SUBSTITUTION: SPLITTING THE ZERO-POINT VIBRONIC LEVEL DMITRY G. MELNIK, JINJUN LIU AND TERRY A. MILLER The Ohio State University, Dept. of Chemistry, Laser Spectroscopy Facility, 120 W. 18th Avenue, Columbus, Ohio 43210 ROBERT F. CURL, Department of Chemistry and Rice Quantum Institute, Rice University, Houston, Texas 77005

Problem outline: Objective: analysis of the vibrational level structure of methoxy radicals study isotopic effects on vibrational energy level structure Motivation: vibrational (vibronic) level structure samples molecular PES with the isotopic substitution helps to study dynamics of unimolecular decomposition methoxy is a combustion intermediate, whose kinetics and thermodynamics depend on its PES. test case for systems exhibiting conical intersection.

Summary of the vibrational analysis Standard approach: formulate full Hamiltonian excluding rotational and translational parts in terms of the parameters characterizing molecular PES formulate isotopic relationships set up the Hamiltonian in the appropriate basis set adjust the parameters of the Hamiltonian to adequately predict experimentally observed energies. Challenges (methoxy): complex interaction pattern due to competing spin-orbit and Jahn-Teller interaction 9 vibrational modes makes the task computationally challenging rapidly increasing density of states makes vibrational assignment difficult

Spin-vibronic level structure of JT active molecule Sym Sym Sym Asym Asym Harmonic JT1 JT1+JT2 JT1+JT2 JT1+JT2 +SO v(E)=1 ? ? v=0 DE=E(A’)-E(A”) (a) T. Barckholtz and T. A. Miller, Intl. Rev. Phys. Chem., 17, 435 (1998)

Vibronic Hamiltonian R is a displacement vector in an arbitrary set of internal coordinates spanning 3N-6 space. R=0 indicates a “reference” nuclear configuration. Using the basis, the vibronic Hamiltonian writes in matrix form Harmonic part Jahn-Teller coupling Where At this point we disregard spin-orbit interaction, which can be trivially added later.

Hamiltonian reduction for the isotopic problem The values of can be measured experimentally. Suppose there is an isotopologue for which all three matrices are known. We will call it a “reference” isotopologue, and the corresponding values are labeled with “(0)”: “Potential reduction”: Hev can be rewritten for any isotopologue using unique sets of normal coordinates “Kinetic reduction”: Potential energy is unchanged upon isotopic substitution, but kinetic energy is:

Jahn-Teller interaction matrices Bilinear JT coupling A modes E modes Symmetric to sxz Quadratic and cross-quadratic JT coupling Antisymmetric to sxz Linear JT coupling Relationships to the experimentally observed values

Vibronic Hamiltonian for 3-mode (A+E) model (H3) A model with a single pair of A and E modes. 2. Normal modes are mass-weighted symmetry modes. 3. Transforming internal coordinates to symmetry coordinates, we write explicitly: y 2 R3 1 R1 x R2 3

Calculations of the vibronic level structure of isotopologues of H3 Parameters of Hev are chosen to approximately replicate fundamental frequencies and strength of vibronic coupling in v3+v6 pair in CH3O The Hamiltonian is set up in the vibrational basis vx,y,z = 0…10, resulting in the vibronic matrix 2000x2000. Vibrational matrix elements:

Calculations of the zero point splitting, DE = E(A’) – E(A”) DE(b,g;k=-1.75*104) DE(b,k;g=-9*104) H2D H2D HD2 HD2 Predicted by Scharf(a) and observed in CH3O(b) and C5H5(c) (a) B. Scharf et al, J. Chem. Phys, 77, 2226 (1982) (b) D. Melnik et al., J. Chem. Phys., submitted (c) L. Yu et. al., J. Chem. Phys., 98, 2682, (1993)

Isotopic problem for CH3O Use the “potential reduction” to obtain fundamental frequencies and Jahn-Teller parameters. Fundamental frequencies are square roots of the eigenvalues of GF matrix. Write potential energy as the function of the internal coordinates, RCO qj Ri jij 3. Fit f-parameters of the potential to the experimentally measured deperturbed fundamental frequencies of CH3O an CD3O. 4. Diagonalize G(k)F for all isotopologues, obtain U(k) and fundamental frequencies

Isotopic relationships for JT parameters in CH3O Transformation between the normal coordinates of different isotopologues: where U(m) is the unitary transformation which diagonalizes We can express parameters of one isotopologue (l), in terms those of another:

Vibrational parameters of CHD2O Fit fundamental frequencies PES parameters (dyn/cm) CH3O CD3O Predicted values of fundamental frequencies and JT coupling for CHD2O LJT QJT A’ A” (a) E. Wilson, J.D.Decius P.C.Cross, “Molecular Vibrations”

Vibrational level structure of CHD2O v5+v6+v8+v9 Experiment v4+v6+v8+v9

Summary Vibronic calculations for a simplified 3-mode molecule show semi-quantitative agreement with the observed splitting of the ground vibronic level. The ground vibronic level splitting is primarily cause by bilinear coupling, hence the latter needs to be included in the vibronic analysis to correctly analyze the vibrational level structure of JT-active moelcules. This necessitates the multimode approach. To correctly interpret spectra of the asymmetrically substituted molecules, all isotopologues need to be analyzed globally NEXT: set up multimode spin-vibronic problem and use nonlinear fit to obtain parameters of the PES that correctly predict the observed spectra.

Acknowledgements Colleagues: Dr. Gabriel Just, Dr. Phillip Thomas, Ming-Wei Chen, Terrance Codd, Neal Kline Rabi Chhantyal-Pun OSU NSF