SIMULATIONS OF VIBRONIC LEVELS IN DEGENERATE ELECTRONIC STATES IN THE PRESENCE OF JAHN-TELLER COUPLING – EXPANSION OF PES THROUGH THIRD ORDER VADIM L. STAKHURSKY, VLADIMIR A. LOZOVSKY, C. BRADLEY MOORE, TERRY A. MILLER Laser Spectroscopy Facility, Department of Chemistry, The Ohio State University 120 W. 18th Avenue, Columbus OH 43210.

Motivation Jahn-Teller distortion can significantly affect the characteristics of the molecule, e. g. rotational and vibrational spectra, partition function, rate of chem. reaction, enthalpy There is a group of C3v molecules exhibiting Jahn-Teller effect (CH3O, CF3O, CH3S, CF3S, in the ground X2E state CdCH3, MgCH3, ZnCH3 in the excited A2E state); D3h molecules Na3, Ag3, Au3 with JT distorted structure 3. Their vibronic structure is not completely understood, partially because of the computational complexity of the Jahn-Teller problem

Harmonic potential JT distorted potential

Spin-vibronic Hamiltonian e Standard: e+ e- const Additional term: where

SOCJT(*) as a tool for JT problem analysis What is SOCJT? Fortran code for multidimensional Jahn-Teller problem with/without spin-orbit interaction SOCJT gives: Positions of spin-vibronic levels of the molecule in degenerate electronic state Insight into composition of the level in terms of harmonic oscillator quantum numbers |n, l> providing a tool for “labeling”of the levels Calculates vibronic spectrum for absorption or emission experiments (A-E electronic transition, some limitations apply) SOCJT input: PES parameters up two third order: Harmonic frequencies ωi and anharmonisities Linear JT parameters Di Quadratic JT parameters Ki and cross-quadratic terms for interaction of degenerate vibrations Bilinear terms for coupling of symmetric and degenerate modes bij Fermi iteraction terms Terms non-diagonal in the projection of the electronic orbital momentum: Spin-Orbit coupling parameter aze.

SOCJT GUI hybrid capabilities SOCJT code is interfaced to spectra simulation and visualization package SpecView The features of the product: Simulate vibronic structure in degenerate electronic state of a C3v molecule with up to 3 Jahn-Teller active e vibrational modes and up to 3 totally symmetric a modes Simulate intensities of vibrational features observed in dispersed fluorescence (DF) and absorption spectra Fast calculation of spectra (2-5 sec for region up to 3000 cm-1 in methoxy) Ability to run non-linear least square fit of simulated lines to frequencies of observed features (Levenberg-Marquardt method) .

Vibrational frequencies of CH3O 1362 cm-1 1047 cm-1 2840a cm-1 symmetric C-H stretch CH3 umbrella C-O stretch 2774 cm-1 653 cm-1 1487 cm-1 asymmetric C-H stretch scissors CH3 rock aS. C. Foster, P. Misra, T.-Y. Lin, C. P. Damo, C. C. Carter, and T. A. Miller, J. Phys. Chem. 92, 5914 (1988).

Dispersed Fluorescence spectra of methoxy radical 3361 pumped Experiment Simulation 3351 pumped Experiment Simulation Energy relative to vibrationless level, cm-1

Dispersed Fluorescence spectra of methoxy radical 35 pumped Experiment Simulation 3341 pumped Experiment Simulation Energy relative to vibrationless level, cm-1

Numerical calculations Dispersed Fluorescence spectrum of methoxy radical, 3141 pumped experiment b14= 53 cm-1 b14= 35 cm-1 b14= 15 cm-1 b14=0, K4=0.025 Spin-orbit, No JT b14 – bilinear parameter of coupling of symmetric CH stretch (v1) with asymmetric CH stretch (v4)

Determined constants and comparison with ab-initio This work Ref. a Ref. b Ref. d Aso -139 -108c -134 ω6 1061 1082 1116 1118 D6 0.23 0.20 0.16 K6 -0.14 -0.146 -0.13 ω5 1401 1434 1509 1483 D5 0.058 0.02 0.01 K5 0.037 0.036 0.038 ω4 2852 2891 3153 3109 D4 0.0012 <0.01 0.00016 0.0007 K4 -0.025 0.00514 0.00023 ω1 2807 2822 3065 3006 b14 53 -8.1 -9 aT. A. Barckholtz and T. A. Miller, J. Phys. Chem. A 103, 2321 (1999). cU. Höper, P. Botschwina and H. Köppel, J. Chem. Phys. 112, 4132 (2000) and J. Schmidt-Klügmann, H. Köppel, S. Schmatz and P. Botschwina, Chem. Phys. Lett. 369, 21 (2003). cThis value was introduced phenomenologically to match the separation of the vibrationless spin-doublet in workb. dA. V. Marenich and J. E. Boggs, J. Chem. Phys. 122(2), 024308 (2005).

Comparison of experimental and calculated vibronic energies of CH3O ( ), including spin-orbit coupling effects Assignment Eexperimenta Ecalcb Ecalcc Ecalcd 00 62 61 68 61(a1) 683 770 760 61(a2) 945 935 1047 1023 31(e) 1045 1044 1046 1116 1107 1105 1104 1186 61(e) 1226 1211 1314 1321 1233 1228 1324 1335 51(a2) 1344 1340 1409 1515 21(e) 1367 1369 1411 1449 1414 1430 1493 51(a1) 1434 1429 1601 1447 51(e) 1519 1581 1575 1524 1525 1562 1585 62(e) 1640e 1641 1770 1780 1681e 1677 1815 1829 3161(a1) 1748 1727 1825 1891 5161(e) 1995 2002 2170 2184 Assignment Eexperimenta Ecalcb Ecalcc Ecalcd 5161(e) 1995 2002 2170 2184 2008e 2009 2183 2193 2161(a1) 2049 2051 2235 2211 32(e) 2075 2074 2089 2221 2134 2135 2133 2287 63(a1) 2188 2213 2353(62a1) 2360(61,2,3e) 2216 2236 2333(3161e) 2389(61,2,3e) ??? 2230e 2255(3161(e)) 2393(61,2,3a1) 2240 2261 2345(3161e) 2454(5161e) 2291f 2272(3161(e)) 2441(63e) 2469(3161e) 2327e 2303(2161(a2)) 2460 2473(2161a2) 2369 2384(3151(a2)) 2516(3151e) 62(a1) 2394 2437 2451 2441(62e) or 2425(2131e) 2504 2475 2472(3151(a1)) 2475e,a 2486(2131(e)) 2524 63(e) 2519 2538 a SEP data by Temps and coworkers6, if not marked otherwise b current work, the constants were slightly adjusted to compensate for a wrong sign of the K5 constant in work by T. Barckholtz et al.20 c J. Schmidt-Klugmann et al.22 d A. Marenich et al.23 e Analysis of the DF data in this work f Averaged position from this DF work and work by Foster et al.12

THANK YOU Conclusions and future work We extended SOCJT Fortran code to include potential energy surface terms up to third order. High-throughput GUI C++/Fortran hybrid is developed for the simulation of the vibrational structure of the electronic transitions (2A-2E) 2. In our future work we will extend the approach to allow for high-throughput simulations of the 2E-2E electronic transitions THANK YOU

ACKNOWLEDGMENTS Ohio State University