Transcript TJ06_v3.ppt

THE ANALYSIS OF THE GROUND STATE OF ASYMMETRICALLY
DEUTERATED METHOXY RADICALS: AN ALTERNATIVE APPROACH
DMITRY G. MELNIK AND ROBERT F. CURL,
The Department of Chemistry and Rice Quantum Institute, Rice University,
Houston, Texas 77005;
JINJUN LIU, JOHN T. YI AND TERRY A. MILLER
The Ohio State University, Dept. of Chemistry, Laser Spectroscopy Facility,
120 W. 18th Avenue, Columbus, Ohio 43210;
Motivation and goals
1. An interesting spectroscopic problem of symmetry reduction
(C3v to Cs) in Jahn-Teller active molecule
2. Previously proposed model (I.Kalinovsky and C.B.Moore)a was
introduced to describe moderate resolution cold spectra with relatively
small number of the accessed levels in the ground electronic state.
The goal:
To develop a theoretical model which:
a. is physically meaningful
b. allows for reliable computational analysis (e.g. stable numerical fit)
c. has the predictive power.
a I.Kalinovsky,
“Laser Induced Fluorescence Spectroscopy of CHD2O and CH2DO and High Resolution
Spectroscopy of CH3O and HFCO'', Ph.D. Thesis, U. of California, Berkeley, 2001
Previously proposed model
Kalinovsky and Moore:
HEFF = HSO + HCOR + HJT + HSR + HROT + HASYM
H ASYM
  E
0   e x
2


 0
  E   e y

2




or
H ASYM
The matrix element of the new term (Hund’s case a):
J , P, ; p H ASYM J ,  P, ; p  (1)
J  P  S 
p
E
E 
 0
 e  
2





 E

e


0 


2


 e
e   (2)  (1/ 2) e x  i e y
e   (2)  (1/ 2)
x
 i e y


2
p – parity with respect to (12)* transformation
Ground state
Computational analysis by Kalinovsky and Moore:
E = -47.15 cm-1
1. E is expected to correlate strongly with spin-orbit
interaction term azed
2. The nature of experimental data allowed Kalinovsky
and Moore to handle the problem successfully
with the addition of a single new parameter.
E1/2
70-80
cm-1
E3/2
Available experimental data
23
Kalinovsky and Moore(CHD2O):
Rotationally resolved LIF data,
7 vibronic bands,
over 200 transitions,
Experimental accuracy 2000 MHz.
These studies (CHD2O):
6’
14 microwave transitions with partially
resolved hyperfine structure,
experimental accuracy 1.0 MHz
High resolution
(HF structure average).
UV LIF
High resolution LIF spectra,
2 vibronic bands,
170 transitions,
Experimental accuracy 50 MHz.
Levels accessed (ground state):
J= 0.5…5.5
P=-1.5…2.5
microwave
Ground state
(E3/2)
p=-1
p=+1
The choice of the system of coordinates
1. Traditional treatment, principal
axis system (PAS):
2. Axis system with z axis placed
along C-O bond, or “bond axis
system” (BAS)
CHD2O
z
a
a
D
H
c
H
D
D
J a  J z cos a  J x sin a
H ROT  ARa2  BRb2  CRc2
Ra  J a  Sa  La
D
Jx 
1
2
(J  J )
H ROT  Pzz Rz2  Pyy Ry2 
Pxx Rx2  Pxz ( Rz Rx  Rx Rz )
Modification of the symmetric case Hamiltonian
Starting with the Hamiltonian used by Watsona and Hirotab, adding new terms
due to the asymmetry:
asym
H ROT
 Pxz [( J x  Lx  S x )( J z  Lz  S z )]
(rotation)
1
asym
H SR
  xz ( Rx S z  S x Rz  Rz S x  S z Rx )
2
(spin-rotation)
and the new term introduced by Kalinovsky and Moore:
H ASYM 
E
2
 e

e   e  e 

The corresponding matrix elements are:
asym
asym
J , P  1, ; p H SR
 H ROT
J , P, ; p  [ Pxz {( P  12 )  }  12  xz ] J ( J  1)  P( P  1)
asym
asym
J , P  1, ; p H SR
 H ROT
J , P, ; p  [ Pxz {( P  32 )  }  12  xz ] J ( J  1)  P( P  1)
asym
asym
J , P, ; p H SR
 H ROT
J , P, ; p  [ Pxz  12  xz ](1  P)
E
J ,  P, ; p H ASYM J , P, ; p  (1) J  P  S  p
2
a
b
J.K.G.Watson, , J.Mol.Spectroscopy, 103, 125 (1984)
Y.Endo, S.Saito, E.Hirota, J.Chem. Phys., 81, 122 (1984)
Numerical analysis: combination differences vs. global fit
Combination difference
analysis scheme
1. Combination differences: not all of the
available data is used.
2. Ambiguity: a large number of local minima
that predict the accessed levels energies
accurately but fail to predict the other energies
consistently.
Excited state
3. The computation problem is highly nonlinear and
prone to diverge if the initial guess is too far away
from the solution.
p=-1
Ground state
p=+1
4. Data correlation: combination differences derived
from a set of more than two transitions to the
same upper state level are affected by a single
mismeasured or misassigned transition
5. The global fit: the amount of data used more than
doubles at the expense of the addition of the
parameters of the two relatively simple and wellbehaved excited states (184 transitions in global
fit vs. 79 combination differences)
Global analysis
1. Ground state: used Hund’s case (a) Hamiltonian described above
2. Excited states: used Hund’s case (b) Hamiltonian (S-reduction) by
Brown and Searsa and Watsonb.
3. Did not calculate intensities of transitions, rather, relied on the
assignments made by J.Liu and co-workers [TJ05]
4. Used Levenberg-Marquadt fitting procedure
a
J.M.Brown and T.J.Sears, J. Mol.Spectroscopy, 75, 11 (1979)
J.K.G.Watson, “Aspects of Quadratic and Sextic Centrifugal Distortion Effects
on Rotational Energy Levels”, in Vibrational Spectra and Structure, Vol.6., Chap. 1,
ed. by J.R.Durig (Elsevier, Amsterdam, 1977).
b
Numerical analysis: preliminary results
Nonlinear fit summary:
Data: 14 MW lines, 170 UV LIF lines
Standard deviation: MW: 0.8 MHz, UV LIF: 35 MHz
Molecular constants of CHD2O. All constants in MHz, except as noted
~
~2 A(2 )
A
3
X 2E
az e d
Az t
Pzz
( Pyy  Pxx ) / 2
( Pyy  Pxx ) / 4
 zz
( yy   xx ) / 2
( yy   xx ) / 4
 xz
1
h1K
h2
E
Pxz
-59.15(47) cm-1
20059(4)
95057(10)
23765(7)
307 (2)
-50515 (fixed)
-1000 (fixed)
3187(87)
-3217(152)
-18842(490)
-11.8(15)
1315(22)
-44.94(35) cm-1
2347(138)
0
A
(B  C) / 2
(B  C) / 4
DK
( bb   cc ) / 2
( bb   cc ) / 4
32888.99(29) cm-1
90157(12)
18879.6(8)
315.4(7)
-9.3(28)
350(3)
12.9(4)
~2 A( )
A
6
0
A
(B  C) / 2
(B  C) / 4
( bb   cc ) / 2
32368.16(29) cm-1
90981(2)
19422.0(7)
213.4(5)
328(3)
Correlation and error analysis
1. Confidence interval (“error bars”) for a varied Hamiltonian parameter ai:
 ai   Cii
where C is the covariance matrix C=B-1, B being the normal matrix on the
last successful iteration
2. The correlation between the two parameters could be estimated as
Cor (ai , a j ) 
Cij
Cii C jj
If ai is large and |Cor(ai, aj)| is close to 1, then ai cannot be accurately determined
independently of aj. The potential solutions of such case:
i. Refining the model
ii. Fixing one of the correlated parameters to an a priori known value
iii Obtaining discriminating experimental data
3. In this case:
Cor (az e d ,  E )  0.999858
Cor (( xx   yy ) / 4, 1 )  0.999331
Cor ( Pxz ,  xz )  0.974
Summary and the future work
1. A theoretical and computational approach to the solution of the
problem of asymmetrically deuterated methoxy radical has been
developed.
2. The model still requires fine adjustment, which can be achieved by
error and correlation analysis of the obtained results
3. The application of the developed procedure on CH2DO radical
is underway
4. The analysis of the spectra involving the levels of E1/2 component
of the ground state may serve as a test for the method presented.
Acknowledgements
Rice University
Welch Foundation
NSF