Transcript MH10.ppt

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
1.
2.
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
JAHN-TELLER THEOREM
For any non-linear molecule
in a degenerate electronic state,
there exists a displacement of the
nuclei along at least one
non-totally symmetric normal
coordinate, that gives rise to a
distortion of the molecular
geometry with a concomitant
lowering of the energy.
Spin-vibronic Hamiltonian
e
Hˆ ev  Hˆ T  Vˆ  Hˆ SO
3
Standard:
6
6
e+
6
Vˆ1  Hˆ e   Hˆ h ,s ,i   Hˆ h ,a , j   Hˆ JT l , j   Hˆ JTq
i 1
j 4
j 4
j 4
1
Qs 2
2
1
 Qa 2
2
L k i Qa i 
e-
jj
const
2
2
L g iiQa i 
2
Additional term:
Vˆ2 
6
 Hˆ
i , j 4, i  j
1
2
g ij L Qa
2
3
JTq ij
6
6
6
  Hˆ JTb ij   Hˆ c iii  
i 1 j  4
i 1
6
 Hˆ
i 1 j 1, j i
6
c ijj

6
6
  Hˆ
i 1 j 1, j i k 1
k  j , k i
2
bij L Qs i Qa j , 
i ,  Qa j , 
where
2
cijk L Qi Q j Qk
e L e  1 and
2
or
cijk Eˆ Qi Q j Qk
e Eˆ e  1
c ijk
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
cijk Eˆ Qi Q j Qk
Terms non-diagonal in the projection of the electronic orbital momentum:
cijk L 2 Qi Q j Qk
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
2840a cm-1
symmetric C-H stretch
2774 cm-1
asymmetric C-H stretch
aS.
1362 cm-1
CH3 umbrella
1487 cm-1
scissors
1047 cm-1
C-O stretch
653 cm-1
CH3 rock
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 (v 1) with asymmetric CH stretch (v4)
Determined constants and comparison with ab-initio
aT.
Constant
This work
Aso
-139
ω6
1061
D6
0.23
K6
-0.14
ω5
1401
D5
0.058
K5
0.037
ω4
2852
D4
0.0012
K4
-0.025
ω1
2807
b14
53
Ref. a
Ref. b
Ref. d
-108c
-134
1082
1116
1118
0.20
0.16
0.20
-0.146
-0.13
1434
1509
1483
0.02
0.01
0.02
0.036
0.038
2891
3153
3109
<0.01
0.00016
0.0007
0.00514
0.00023
3065
3006
-8.1
-9
2822
A. Barckholtz and T. A. Miller, J. Phys. Chem. A 103, 2321 (1999).
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 work b.
dA. V. Marenich and J. E. Boggs, J. Chem. Phys. 122(2), 024308 (2005).
cU.
Comparison of experimental and calculated vibronic energies of CH3O (X~ 2 E ), including spin-orbit coupling effects
Assignment
Eexperimenta
Ecalcb
Ecalcc
Ecalcd
Assignment
Eexperimenta
Ecalcb
Ecalcc
Ecalcd
00
0
0
0
0
5161(e)
1995
2002
2170
2184
2008e
2009
2183
2193
62
61
62
68
2051
2235
2211
683
683
770
760
2161(a1)
2049
61(a1)
32(e)
2075
2074
2089
2221
61(a2)
945
935
1047
1023
2134
2135
2133
2287
31(e)
1045
1044
1046
1116
63(a1)
2188
2213
2353(62a1)
2360(61,2,3e)
1107
1105
1104
1186
5161(e)
2216
2236
2333(3161e)
2389(61,2,3e)
1226
1211
1314
1321
???
2230e
2255(3161(e))
1233
1228
1324
1335
5161(e)
2240
2261
2345(3161e)
2454(5161e)
51(a2)
1344
1340
1409
1515
2291f
2272(3161(e))
2441(63e)
2469(3161e)
21(e)
1367
1369
1411
1449
2327e
2303(2161(a2))
2460
2473(2161a2)
1414
1430
1449
1493
2369
2384(3151(a2))
51(a1)
1434
1429
1601
1447
2394
2437
51(e)
1519
1515
1581
1575
2451
2441(62e)
or
2425(2131e)
1524
1525
1562
1585
2475
2472(3151(a1))
1640e
1641
1770
1780
2475e,a
2486(2131(e))
1681e
1677
1815
1829
2519
2538
3161(a1)
1748
1727
1825
1891
5161(e)
1995
2002
2170
2184
61(e)
62(e)
62(a1)
63(e)
2393(61,2,3a1)
2516(3151e)
2504
2524
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
Conclusions and future work
1. 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