Transcript RI09.ppt

THE ANALYSIS OF HIGH RESOLUTION SPECTRA
OF ASYMMETRICALLY DEUTERATED METHOXY
RADICALS CH2DO AND CHD2O
(RI09)
MING-WEI CHEN1, JINJUN LIU2, DMITRY G. MELNIK1 and
TERRY A. MILLER1, and ROBERT F. CURL3 and C. BRADLEY
MOORE4
1Laser
Spectroscopy Facility Department of Chemistry The Ohio State University,
2Laboratory of Physical Chemistry ETH, Zurich, Switzerland
3Department of Chemistry and Rice Quantum Institute, Rice University,
4Department of Chemistry, University of California, Berkeley.
Outline
The goal:
•Understand the molecular properties of methoxy radicals “beyond numbers”
•Built the relationship between the molecular properties of different isotopomers
•Study the effect of symmetry reduction on the molecular parameters
Methods:
•Comparison of the molecular parameters of the symmetric methoxy species, CH 3O
and CD3O .
•High resolution spectroscopic study of asymmetrically deuterated methoxy
species, CHD2O and CH2DO.
•Extension of global analysis to experimentally determined molecular parameters
of substituted species.
The Benefits of the Isotopic Studies
The potential hypothetical molecule
along normal mode q
Isotopic scaling of rotationally resolved spectra:
• Molecular properties manifest themselves
through the effective parameters of the
rotational Hamiltonian:
V (q)
E ( J , P, S,...)   X i fi ( J , P, S,...)
i
• The Xi are the effective parameters that are
co-factors to the terms with the unique functional
dependence on quantum numbers fi(J, P,S, etc...).
• Parameters Xi have different contributions:
X i  X i1  X i2 e  X i2 v
q
Levels of
Isotopomer 1
X 1  ev X ev  F 1 (r , m,...)
Levels of
Isotopomer 2
Interactions with excited vibrational states
Interactions with excited electronic states
X i2 e  F e ( Ee ; A, B,...)
X i2 v  F v ( Ev ; A, B,...)
• If F1, Fe and Fv have different functional
dependence, they can be separated, e.g. through
studying the isotopic dependencies.
Hamiltonian parameters and corrections
HEFF = HROT + HCOR + HSO + HSR + HJT + HCD
X
A
B
h1
h2
 aa
 bc
1
 2a
 2b
X1
mH1K11

B 2 m1/H 2 K 21[3  5]
ABm1/H 2 K 31[5]





X 2 v[2]
A2 K12 v
B 2 K 22 v


aA e K12 v




X 2 e[1]
4 A2 K12 e
B 2 K 22 e
B 2 K 32 e
2 ABK 42 e
4aAK12 e
aBK 22 e
aBK 32 e
aAK 42 e
aBK 42 e
A,B – rotational constants,
mH – mass of the hydrogen isotope
a – spin-orbit coupling constant
 – the ratio of the average vibational
frequency of the protonated isotopomer
( H ) to that of the species in question
(  I ).

H
I
Dominating terms are highlighted
[1]
J.Mol.Spectrosc., 81, 73 (1980)
J.Mol.Spectrosc., 140,112 (1990)
[3] J. Chem. Phys, 42, 2283 (1965)
[4] Can.J.Phys, 59, 428 (1981)
[5] This work
[2]
Note: we assume that the ratio  of the
vibrational frequency wi of the normal and
substituted species is approximately the same
for all modes.
Isotopic Dependence and Structural Parameters
Experimentally obtained values and their ratios:
Experiment vs. estimation
X
A
B
h1
h2
 aa
 bc
1
 2a
a e d
t
13
CH 3O
CH 3O[ a ]
154800(50)
154800
27930.36(4)
27283.9(38)
77.7(21)
73.9(24)
1326(3)
1370(318)
37375(88)
40870(12664)
1111(3)
1312(260)
172.65(13)
167(3)
534(86)
2204(9158)
1843703(113) 1849175(11461)
0.3375(8)
0.342(8)
X 13 / X 12 , cal
1

0.954
0.977
1.0
0.977
0.977
1.0


X 13 / X 12 , obs
CD3O
1
78391(23)
0.97687(8)
22194.05(2)
0.95(5)
88.7(1)
1.03(23)
847(1)
1.09(31)
23097(71)
1.18(20)
841(2)
0.97(2)
142.09(15)
-4(16)
192(42)
1.003(6)
1648732(101)
1.01(2)
0.2844(6)
X D / X 12 , cal
0.500

1.171
0.650
0.650
0.795
0.795
0.500


X D / X 12 , obs
0.5064(2)
0.794621(1)
1.142(31)
0.639(1)
0.618(2)
0.757(2)
0.823(1)
0.359(97)
0.8941(1)
0.8427(24)
[a] parameters obtained from re-fitting the 13CH3O data by Momose et al, J.Chem. Phys. 88, 5338 (1988)
Experimentally obtained structural parameters of methoxy radical*:
rCH  rCD rCH  rCD  0.003 A
1.1063(25)
1.1099(13)
Parameter
rCH , A
rCH , rCD varied
1.1137(16)
rCD , A
1.1075(5)
1.1063
1.1069
rCO , A
1.3597(8)
1.3637(2)
1.3618(1)
OCH  OCD,deg
111.1(1)
110.6(2)
110.8
What Happens When the Symmetry is Reduced (CHD2O)?
Vibronic eigenfunctions:
Cs
C3v
A
E
H SO  H ASYM
E
A
Basis set:
ev |   1| vu , u 
u
 a e d
 2

 E

 2
E   ev S  1 
 

2 
2 

a e d  
1 

  ev S  
2 
2 
1
 ( A)  0.95 ev  0.31 ev  S 
2
E  47 cm1
a
a e d  62 cm1
| E || a e d | 
1
 ( A)  0.95 ev  0.31 ev  S 
2
The effective rotational Hamiltonian:
HEFF = HROT + HCOR + HSO + HSR + HJT + HCD + HASYM
Vibronic problem:
“asymmetry” Hamiltonian
H ASYM
aJ.

 0

 E

 2
E 
2 

0 

Mol.Struct. 780, 163 (2006)
H ASYM 
E 2
L  L2 

2
• Treat asymmetry effects as perturbation.
• Use C3v vibronic functions.
• Use the obtained isotopic dependence to predict the properties
of the asymmetrically substituted species.
Coordinate System for Rotational Hamiltonian (CHD2O)
1. Traditional treatment, principal
axis system (PAS):
2. Axis system with z axis placed
along C-O bond, or “internal axis
system” (IAS)
z
a
a
c
x
D
H
H
D
D
J a  J z cos a  J x sin a
H ROT  ARa2  BRb2  CRc2
Ra  J a  Sa  La
Mol.Physics, 105, 529 (2007)
D
Jx 
1
2
(J  J )
H ROT  ARz2  BRy2 
CRx2  Bxz ( Rz Rx  Rx Rz )
Diagram of the Levels Accessed by the Measurements.
Rotational level parity:
even
odd
A2 A1;2 3
SEP –
rotational structure
of E1/2 state
(s=70 MHz)
A A1; 6
2
LIF –
Rotational structure
of E3/2 state (s=50MHz)
E1/ 2
Direct microwave absorption –
rotational structure of E3/2 state
across parity
stacks (s=2 MHz)
E3/ 2
X 2E
Microwave Spectra.
CHD2O
1.8 MHz
178995.3 MHz
5
1
J   , P  ;  1
2
2
2.7 MHz
199614.5 MHz
CH2DO
7
3
J   , P  ,  1
2
2
3.2 MHz
1.2 MHz
183250.5 MHz
5
1
J   , P   ,  1
2
2
187131.0 MHz
7
1
J   , P   ,  1
2
2
LIF and SEP Spectra (CHD2O)
~
A 2 A1
LIF
SEP
~
X 2 E1/2
~
LIF of CHD2O,
2
2
X 2 E3/2
Pa
0.78
2
30 band of A A1-X E3/2
high-res
moderate-res
normalized LIF
0.74
Pb
intensity (a.u.)
*
0.76
0.72
0.70
0.68
0.66
SEP dip by Pa
0.64
Depletion: ~15%
0.62
Linewidth (FWHM): ~200MHz
Freq. Accuracy (1s): <100MHz
* LIF excited by dump laser
0.60
0.58
32915
32920
32925
32930
frequency / cm
32935
-1
32940
32845.4
32845.6
32845.8
frequency / cm
-1
32846.0
Parameters of the Effective Hamiltonian (CHD2O)
Parameter
A
Number of assigned
transitions:
• microwave
• LIF
• SEP
14
165
6
Exp. accuracy
MHz
[std deviation],
• microwave*
• LIF
• SEP
2.0 [ 1.52 ]
50 [ 36 ]
70 [ 76 ]
Number of parameters
used:
2
X E
16
A2 A1 2 3
A2 A1  6
B  C/ 2
B  C/ 4
Value
94721(93)
23954(44)
Bxz
240(23)
5252(640)
A t
27631(14)
a e d
1721677(804)
26800(50)
 aa
 bc
 bb   cc  / 4
 xz
1
 2a
907
fixed
87(15)
2349(57)
153
fixed
230
fixed
5
h1
h2
65(6)
1399(117)
5
E
1302844(1050)
* due to partially unresolved hyperfine structure, centers-of-mass of transitions were used
Molecular Parameters, Isotopic Trends
Isotopic trends of some of the effective Hamiltonian parameters
Parameter
A
B  C/ 2
B  C/ 4
Bxz
h1
h2
 aa
a e d
t
CH 3O
CD3O
CHD2O, pred
154800(50)
78391(23)
95232
27930.36(4)
22194.05(2)
23894
0.0
0.0
253
0.0
0.0
4486
77.7(21)
88.7(1)
84
1326(3)
847(1)
1031
37375(88)
23097(71)
29403
1843703(113) 1648372(101)

0.3375(8)
0.2844(6)

CHD2O , obs
94721(93)
23954(44)
239(16)
5252(640)
65.5(63)
1399(117)
26800(50)
1721677(804)
0.2917(2)
Parameters used to predict values of CHD2O
Parameter
rCO , A
Value
1.3597
rCH , A
1.1137
rCD , A
1.1075
OCH  OCD,deg
111.1
 (CHD2O)   (CD3O) / 2
m   5/ 3 mH
Asymmetry effects in Rotational Jahn-Teller Hamiltonian
C3v case, effective Jahn-Teller Hamiltonian

H JT  h1  L2 N2  L2 N2   h2 L2  N N z   L2  N N z 



Cs case, effective Hamiltonian:


H JT  h1  L2 N 2  L2 N 2   h2 L2  N  N z   L2  N  N z  




h1  L2 N 2  L2 N 2   h2 L2  N  N z   L2  N  N z   ...


The potential sources of discrepancies
between the prediction and experiment:
• Neglect of the coupling between the
qua components of the Jahn-Teller
active modes with totally symmetric
modes when the symmetry is reduced:
A
A1
The values of h1 and h2 are modified:
h1  h1 1  f1 (E , Ba ) 
A
us
h2  h2 1  f 2 (E , Ba ) 
us
E
A
us
where fi (E, Ba ) are functions of derivatives of the
Components of tensor of inertia with respect to normal
Coordinates and energy difference E. These functions
vanish in the C3v limit.
• Vibronic coupling in the system with
reduced symmetry (new type of X2v
contributions).
h1, h2
terms?
Summary
Accomplished:
• The isotopic dependencies of various parameters of the effective rotational
Hamiltonian are summarized end extended, including the h1 and h2 Jahn-Teller
terms.
• The global analysis of the symmetric species is performed. Its results allowed
to approach the problem of the analysis of the asymmetrically substituted molecules.
• The analysis of the CHD2O is reasonably successful within the approximation
of the model used. The higher order treatment is needed to achieve the agreement
of the theory with observed data within the experimental error.
Future development:
• Refine the analysis of the Jahn-Teller terms in the asymmetrically substituted
species.
• Global analysis of both asymmetric species with symmetric ones.
Acknowledgements
Colleagues:
Gabriel Just
Phillip Thomas
Linsen Pei
Rabi Chhantyal-Pun
Shenghai Wu (alumni)
Patrick Rupper (alumni)
John T. Yi (alumni)
Jinjun Liu (alumni)
Erin Sharp (alumni)
Funding: NSF