Transcript Methoxy2006_2.ppt

SIMULATION OF THE SPIN-VIBRONIC STRUCTURE IN THE
GROUND ELECTRONIC STATE AND EMISSION SPECTRA
INTENSITIES FOR CH3O RADICAL
VADIM L. STAKHURSKY
Radiation Oncology, Duke University Clinic,
DUMC 3295, Durham, NC 27710.
XIAOYONG LIU, VLADIMIR A. LOZOVSKY†, ILIAS SIOUTIS, C. BRADLEY
MOORE*, and TERRY A. MILLER
Laser Spectroscopy Facility, Department of Chemistry, The Ohio State University
120 W. 18th Avenue, Columbus OH 43210.
†Deceased
*Northwestern University, Evanston, IL, 60208-1108.
Motivation
1. Jahn-Teller distortion can significantly affect the
characteristics of the molecule, e. g. rotational and
vibrational spectra, partition function, rate of chem.
reaction, enthalpy
2. Because of the relatively small size we use methoxy as a
benchmark system for analysis of various effects of
coupling of electronic and vibrational motion, e. g. JahnTeller effect, Herzberg-Teller effect, etc..
3. We develop a generic throughput application for fast data
analysis of a wide variety of JT active systems.
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.
Vibrational frequencies of CH3O
2948a cm-1
1289 cm-1
662 cm-1
2840b cm-1
1362 cm-1
1047 cm-1
symmetric C-H stretch
CH3 umbrella
C-O stretch
3078 cm-1
1403 cm-1
930 cm-1
2774 cm-1
1487 cm-1
653 cm-1
asymmetric C-H stretch
scissors
CH3 rock
aD. E. Powers, M. B. Pushkarsky and T. A. Miller, J. Chem. Phys. 106, 6863 (1997).
bS.
C. Foster, P. Misra, T.-Y. Lin, C. P. Damo, C. C. Carter, and T. A. Miller, J. Phys. Chem. 92, 5914 (1988).
E
Pseudo Jahn-Teller
A
Optical transition
PJT Hamiltonian
E+
E-
6
H PJT   i L Q ,i
i 4
where coupling matrix elements i
can be calculated as
i 
2
A

Q ,i
2
E
and ladder operator L
2
C.F. Jackels, J. Chem. Phys. 76, 505 (1982).
A L
2
E 
2
A L
2
E  1
Same effect can be described via HerzbergTeller effect, that is when transitional dipole
moment has dependency along vibrational
coordinate:
d (r )  d (re ) 
a r
i 4..6
i i
i 
d (r )
ri r r
e
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 
2
2
L g iiQa i 
e-
jj
2
Less frequently used terms:
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
i,
Qa j , 
where
bij L Qs i Qa j , 
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 |v, l>
providing a tool for levels “labeling”
 Calculates UV spectrum for absorption or emission experiments
SOCJT input:
PES parameters up two third order:
Harmonic frequencies ωi and anharmonicities
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
Fermi iteraction terms Q3
Terms Q3 non-diagonal in the projection of the electronic orbital momentum
Spin-Orbit coupling parameter aze.
Establishing the PJT parameters, DF pumped via 35
PJT explains appearance of A1 and A2 levels of
vibrations v6, v5 and v4.
Simulations of DF spectrum pumped via 3141
PJT explains appearance of origin and CO
stretch progression in the spectrum
Establishing the PJT parameters, DF pumped via 3361
No significant difference
Establishing the PJT parameters, DF pumped via 3351
No significant difference
Determined constants and comparison with ab-initio
Ref. b
Ref. d
-108c
-134
1082
1116
1118
0.23
0.20
0.16
0.20
K6
-0.14
0.1
-0.146
-0.13
ω5
1401
1434
1509
1483
D5
0.058
0.02
0.01
0.02
K5
0.037
0.1
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
3065
3006
b14
53
-8.1
-9
Constant
This work
Aso
-139
ω6
1061
D6
Ref. a
2822
d ( r )
i 
ri r  r
e
Constant
This
work
6
-0.25
5
0.24
4
0.27
Aso, ωi (i=1, 4-6) and b14 in cm-1
aT.
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).
bU.
Conclusions and future work
1. We extended the SOCJT VIEW code to compute intensities of the vibronic
transitions with correction for pseudo Jahn-Teller effect. The coefficients for
coupling along different degenerate vibrational coordinates are extracted from
the experimental spectra.
2. The PJT corrections to intensities are important in analysis of DF spectrum
excited through symmetric level 35, and through CH stretch
fundamental 3141, but insignificant for simulations of spectra excited through
3351 and 3361.
2. The PJT correction approach has to be applied to the analysis of the vibronic
Spectra of CHD2O (NEXT TALK).
THANK YOU
ACKNOWLEDGMENTS
Ohio State University
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 Cnv molecule with up to 7
Jahn-Teller active vibrational modes and up to 5 non-active 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)
.