dmitry g. melnik 1 ming-wei chen 1, jinjun liu 2, and terry a. miller 1, and robert f. curl 3 and c....
TRANSCRIPT
DMITRY G. MELNIK1 MING-WEI CHEN1, JINJUN LIU2, and TERRY A. MILLER1, and ROBERT F. CURL3 and C. BRADLEY MOORE4
EFFECTS OF ASYMMETRIC DEUTERATION ON THE ROTATIONALLEVEL STRUCTURE OF JAHN-TELLER ACTIVE METHOXY
RADICALS
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.
Motivation
• Jahn-Teller active molecule with spin-orbit interaction
• High resolution spectroscopy: characterize the effects of lowering of the nuclear symmetry on the rotational level structure
• Connect the spectra of the molecule to intrinsic geometric properties and the properties of the electronic wavefunction
• Use isotopic relationships and the data obtained from the study of the normal species to facilitate the analysis
Methoxy spectroscopy
1/ 2E
3/ 2E 2X E
21 6;A A
21 3;2A A
LIF –Rotational structure
of E3/2 state (=50MHz)P = -1, 0, +1
LIF –Rotational structure
of E3/2 state (=50MHz)P = -1, 0, +1
Direct microwave absorption –rotational structure of E3/2 state
across paritystacks (=1 MHz)
=0P=0
p: +1 <-> -1
Direct microwave absorption –rotational structure of E3/2 state
across paritystacks (=1 MHz)
=0P=0
p: +1 <-> -1
SEP –rotational structure
of E1/2 state(=70 MHz)
Pump+Dump:= -1
p = +1<-> +1 -1<->-1
SEP –rotational structure
of E1/2 state(=70 MHz)
Pump+Dump:= -1
p = +1<-> +1 -1<->-1
Rotational level reflection parity:p = +1p = -1
32915 32920 32925 32930 32935 32940
Pa
inte
nsity
(a.
u.)
frequency / cm-1
LIF of CHD2O,
32
0 band of A2A
1-X 2E
3/2
high-res moderate-res
Pb
32915 32920 32925 32930 32935 32940
Pa
inte
nsity
(a.
u.)
frequency / cm-1
LIF of CHD2O,
32
0 band of A2A
1-X 2E
3/2
high-res moderate-res
Pb
32845.4 32845.6 32845.8 32846.00.58
0.60
0.62
0.64
0.66
0.68
0.70
0.72
0.74
0.76
0.78
norm
aliz
ed L
IF
frequency / cm-1
Depletion: ~15%
Linewidth (FWHM): ~200MHz
Freq. Accuracy (1): <100MHz
*
SEP dip by Pa
* LIF excited by dump laser32845.4 32845.6 32845.8 32846.0
0.58
0.60
0.62
0.64
0.66
0.68
0.70
0.72
0.74
0.76
0.78
norm
aliz
ed L
IF
frequency / cm-1
Depletion: ~15%
Linewidth (FWHM): ~200MHz
Freq. Accuracy (1): <100MHz
*
SEP dip by Pa
* LIF excited by dump laser
~2
3/2EX
~2
1AA
~2
1/2EX
LIF
SEP
Experimental data: LIF and SEP (CHD2O)
178995.3 MHz 199614.5 MHz
1.8 MHz
183250.5 MHz
2.7 MHz 3.2 MHz
1.2 MHz
187131.0 MHz
5 1, ; 1
2 2J P
7 3, , 1
2 2J P
7 1, , 1
2 2J P 5 1
, , 12 2
J P
CHD2OCHD2O
CH2DOCH2DO
Experimental data: microwave spectra
C3vCs
EA
A
00
0 0
1
22 21
2 2 2
e
SVEe
a d E evEH
a dEE ev
E
(a)
aI.Kalinovsky Ph.D. Thesis, U.of California, Berkeley, (2001)
0 0
0 0
10.31
2
10.3
0.95
0.95 12
ev ev ev
ev ev ev
1
1
| | | |
47 cm
62 cm
e
e
E a d
E
a d
• Treat nuclear asymmetry effects as perturbation.
• Use C3v vibronic functions.
• Ignore the effects of the totally symmetric modes (i.e. limit the discussion to the components of doubly-degenerate modes)
Spin-Vibronic problem
0EV JTSVE SO ASYMHH HH H
Basis set:
-- eigenfunctions of
in unsubstituted (normal)species
ev
0EV EV JTH H H
Difference in ZPE along A” and A’ components
1. Traditional treatment, principal 2. Axis system with z axis placed axis system (PAS): along C-O bond, or “internal axis system” (IAS)
a
c
D
D
H
D
DH
z
2 2 2ROT a b c
a a a a
H AR BR CR
R J S L
2 2
2 ( )
ROT z y
x xz z x x z
H A
B R R R R
R BR
CR
cos sina xzJ J J 12
( )xJ J J
x
D.Melnik, J. Liu, R.F. Curl and T.A.Miller et al Mol.Physics, 105, 529 (2007)
Choice of the axis system
General form:HEFF = HSO + HROT + HCD + HCOR + HSR + HJT + HCDJT+ HSRJT+ HASYM
Basis set:
Effective Rotational Hamiltonian
1/ 2, 1 2 ( 1)J P SJPS p e JP S e J P S
Two types of rotational matrix elements:
,ˆˆ
R Sev S J P Oe e PO J S
Matrix element of the vibronic part of microscopic rotational Hamiltonian
,ˆ(ˆ 1)ev R SS J P O J P S
J P
e
S
O e
-diagonal in vibronic component, or“parity-independent”
-off-diagonal in vibronic component, or“parity-dependent”. In the absecne of vibronic interaction all parity-dependentterms vanish.
Expressions for HROT and HJT
2 2 21 2 1
1
0 2 0 0 0 0
2
1
2
2
2 2 0
12
81
2
1 1 1,
4 4
4
1
2
12
8
4
R
JT z z A
xx yy xy
xz yz
xx yy x
OT
zz z yy xx yy xx
z
z
y
z B
x
xz
H
H h N h N N h
N N N N N
h ev i ev
h ev i ev
h ev i ev
h ev i
N
N h N N h N h N
N
N
N
1
21
2
yz
A zz
B xx yy
ev
h ev ev
h ev ev
Nuclear asymmetry-induced terms. These terms
vanish in the limit of symmetric molecule
Spin-rotation in an asymmetrically substituted molecule
00
(2) . .COR SO
i
COR SOR
i iiS
e H i i e H i i H e
E
H e
EH c c
EE
Spin-rotation interaction is dominated by the second order contribution:
The parity-independent part: derived using relationships by J. Brown, T.J. Sears and J.K.G. Watson (a)
The parity dependent part. Only two types of the interactionin C3v group(b):
-- with nondegenerate states
-- with doubly degenerate states
The isotopic substitution does not alter the electronic wavefunctions,therefore we expect exactly the same number of independent spin-rotationalparameters in the isotopically substituted species!
2 2
2 1
10 0
20
2
i i
xx yy
i ii i
i iz
zzi i
A L e A L eB Ba
E E E E
e L E E L eaB
E E
(a) J.M. Brown, T.J. Sears, J. K. G. Watson, Mol. Phys. 41, 173, (1980)(b) J. T. Hougen, J. Mol. Spectroscopy, 81, 73 (1980)
Effective spin-rotational Hamiltonian
2 2 2 2 2 21 2 2
2 21
2 22
21
1 1
4 8
, ,4 4
SR zz z z xx yy xx yy
xz zxz z
SRJT a z z b z z
a z z
a z z
b
H N S N S N S N S N S
N N S S S N
H L N S L N S L N S L N S L N S L N S
L L N S
L N S L N S
L N
2
2 22
2 2, ,
b z z
S L N S
L N S L N S
L N N S L N N S
Parity-independent terms, incl. asymmetry-induced
Parity-dependent terms in normal species
Nuclear asymmetry-induced parity-dependent terms. None of these parameters are independent.
(a) J. T. Hougen, J. Mol. Spectroscopy, 81, 73 (1980)
Parameter constraints
HSR :
2
2
xx yy
xx yy
xzxz zz
zz
xzzx xx yy
xx yy
xx yy
xx yy xx yyxx yy
nbcn
B B
B
B
B
B B
B B
B B
B
11
2 2
2xx yy
zza
nn
an
B
A
B B
B
HSR :
1 2
2 1
1 1
2 2
12
2
2
2
2 4
xza a
zz
xza
xx yy
xx yy
b
xx yy
xx yy
b azz
xz aa
zz
B
B
B
B B
B B
B B
B B
B
B
B
Additional constraints: HCD
Parameters are derived from the corresponding values in the normal species using 2nd order PT (a)
• A total of 18 ground state parameters were constrained in the actual fits.
N NK K D e e t K tD D D a d
(a) R. N. Zare, Angular Momentum (Wiley Interscience, New Yourk, 1988)
1 2, , ,n n n naA B Where are the values of the
corresponding parameters in normal species
Numerical analysis: statistics
CH2DO CHD2O
Number of assigned transitions:
MW 13 14
LIF 126 165
SEP 8 6
Fit standard deviation (MHz)
MW 0.26 0.36
LIF 38 36
SEP 55 54
Number of independently fit parameters
17 17
5 5
5 5
2
21 3
21 6
2
X E
A A
A A
Experimental accuracy: MW: 1 MHzLIF: 50 MHzSEP: 70 MHz
1
2
1
2
94900(15) 95180
/ 2 23884(5) 23917
/ 4 271(3) 253
4339(92) 4482
27638(13)
1722481(1
Parameter Value (exp) Valu
55)
26757(
72(4) 85.5
1011
29(1) 0
136(26) 234
41) 2
e
66
(pre
90
d)
zz
xx yy
yy xx
xz
zz t
e
zz
B
B B
B B
B
B
h
h
h
h
h
a d
299(15) 1144
19(1) 25.8
1301843(204)
A
Bh
E
1
2
1
2
119028(20) 119171
/ 2 25836(7) 25876
/ 4 434(3) 426
6350(97) 6577
36989(12)
Parameter Value (exp) Value (
1790517(2
79(11) 84.3
1221
26(2) 1
17)
31660(60) 33475
p
7
269(2
red)
zz
xx yy
yy xx
xz
zz t
e
zz
B
B B
B B
B
B
a d
h
h
h
h
6) 321
1003(21) 2329
10(1) 0
1367281(288)
A
B
h
h
E
Molecular constants of the ground state
CH2DO CHD2O
NOTE: for brevity, CDJT terms are not shown
Conclusions
• A simple mechanical model is used to construct the effective rotationalHamiltonian of the asymmetrically substituted methoxy radical.
• The parameters of this model are shown to have straightforward physicalmeaning by relation to the corresponding parameters in the symmetric species.
• The model is successfully used to calculate a number of parameters tobreak correlations in the fit procedure and reduce dimensionalityof the problem.
• The model is used to describe all available high resolution spectra to the experimental error.
Acknowledgements
• Colleagues:
Gabriel Just,Dr. Phillip Thomas,Rabi Chhantyal PanTerrance Codd,Neal Kline
•OSU
•NSF
Calculation of the asymmetry-induced HJT terms
• Electronic PES is insensitive to isotopic substitution• h1, h2 etc. terms characterize the geometry of the molecule in JT minimum (Watson)
Structural parameters from fit of () to experimentalvalues of A,B,h1 and h2of C3v species:
r
1 1 2
1 1 2
2 2
cos sin cos
sin cos sin
cos sin
xx xz
yy
xz
B h h B h
h B h h
B h h A
3
2
1.36039(8)
1.10697(9)
3.67(6) 10
107.76(1)
3.13(40) 10
3.26(20)
4.44(11)
o
o
CO
CH
CH CD
Parameter Value
R A
R A
R R A
HCH
r
Substitute to the expressionof for asymmetric species,calculate assymetry-inducedterms in HJT
Rotational Hamiltonian HROT and HJT
A’ A’’
“O”
Qa
“A”z
xx
y y
zz
y
x
“B”“O”
,
,
1( )
1( )
( )2
0
( )2
ROT JTROT JT
A BJT R A R A
R
JT ROT
J
OT R A R A
a
T
H H
H HH
H H
ev
ev H
H H ev H ev
e
e
v
i
Q
H
v
Undistorted configuration at
conical intersection