Invisible electronic states and their dynamics revealed by perturbations Anthony J. Merer Institute...
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Transcript of Invisible electronic states and their dynamics revealed by perturbations Anthony J. Merer Institute...
Invisible electronic states and their dynamics revealed by perturbations
Anthony J. Merer Institute of Atomic and Molecular Sciences, Taipei, Taiwan University of British Columbia, Vancouver, Canada
Don’t panic – there is an explanation!
There may not be enough information to allow youto work it out every time, but it is remarkable how often you can work it out, given a knowledge of the theory.
SO2: Regions of absorption
(0,0)
235 nm C1B2 and D1A1
~~
358 nm A1A2 and B1B1
~~
388 nm a3B1 and b3A2
~~
Upper electronic states
0 100 200 300 400 500
26000
27000
28000
29000
E / cm
K2
000
010020
100
110
120
200
002
012
300
210
Assigned a3B1, F3, N=K term values for S16O2 ~
= vibronic perturbation (K = 0)
v1v2v3
Vibronic perturbation (K=0)
0 100 200 300 400 500
26000
27000
28000
29000
E / cm
K2
000
010020
100
110
120
200
002
012
300
210
Assigned a3B1, F3, N=K term values for S16O2 and S18O2~
Vibronic perturbations (K = 0)
0 100 200 300 400 500
26000
27000
28000
29000
E / cm
K2
000
010020
100
110
120
200
002
012
300
210
Assigned a3B1, F3, N=K term values for S16O2 and S18O2~
001011
021101
b3A2
~
031
Vibrational structure of the perturbing state
N(N+1)0 200 400 600 800
E / cm
27000
27100
27200
27300
27400
27500
27600
27700 K=17
16
15
14
13
12
11
10
9
87
65
4
0
0,11,2
2,3
Vibronic (3 A 2
, 011)
Vibronic (3 A 2
, 021)
K=16
Spin-orbitK=15
K=12
Coriolis, 3 B1
, 011 K=10
K=11
Observed term values
S16O2, a3B1, 110 level~
Least squares gives ½(B+C) (3A2) = 0.329 cm.
Given A, from the slope of the N=K graph, the
geometric structure of the 3A2 state is
r(S-O) = 1.535 Å, (OSO) = 97o
The electron spin splittings are toosmall to be resolved at this scale.
K = ±2
43000 44000 45000 46000 47000 48000
Excitation spectrum of jet-cooled acetylene
31
32
33
212131
Trans bend C-C stretch
34
2132 2133
E / cm1
35
2134
A1Au (S1-trans) – X1+~g
~
Spectrum taken by Dr. Nami Yamakita
43000 44000 45000 46000 47000 48000
Excitation spectrum of jet-cooled acetylene
31
32
33
212131
Trans bend C-C stretch
34
2132 2133
E / cm1
2231
1131
IR-UV double resonance experiments by Utz et al. (1993) showed that the two bending fundamentals are nearly degenerate
and extremely strongly Coriolis-coupled (a = 0.707). They correlate with the 5 (cis-bend, u) vibration of the ground state.
The ungerade bending vibrations of C2H2, A1Au: 4 (torsion) and 6 (in-plane cis-bend)
~
H
C C
H
4 (au) torsion764.9 cm1
6 (bu)in-plane cis bend 768.3 cm1
H
H
C C
+
--
+
B = bending[31B1 = 3141 plus 3161]
11
E / cm 144440 44450 44460 44470 44480 44490 44500
K=1K=2 K=1
K=0 R
QP R
P
Q RQ R
bu K=2
123 4 5
6
1
2
3
4 53 1
3
1
2 35 14
243 25 1 43 5125 143
2 3 545
B3 polyad, low frequency part
2
P Q R2454 3
3 2
4 3
P K=3RQ65 64 235 434 5
Q35 1K=0
au5
IR-UV double resonance via the Q branch of 3+4″ (u)
A.J.Merer, N.Yamakita, S.Tsuchiya, A.H.Steeves, H.A.Bechtel, R.W.Field, J. Chem. Phys. 129, 054304 (2008)
A-axis Coriolis
Darling-Dennison
B-axis Coriolis
Final least squares fitto the interacting 31B3
and 2131B1 polyads
Dots are observed termvalues and lines are calculated. Some of thehigher-order rotational constants are not very realistic, but theyreproduce the J-structure!
= 0.045 cm1
Darling-Dennison resonance
3163
314162
3143
314261
213141
213161
k266 = 8.66 ± 0.16 cm1
k244 = 7.3 ± 1.1 cm1
3163 lies far belowthe rest of the polyad;x36 is very large!
Dynamics!
Assignment of interacting polyads
K assignment is given by the first lines of the branches. (Easy!)
Vibrational assignment requires that a full set of effective Coriolis, Darling-Dennison and anharmonicity parameters be determined from lower energy bending polyads. For example, 31B3 requires effective constants from 31, 31B1 and 31B2.
This is usually not far from the final set of constants. (Luckily!)Finally a full calculation of the rotational structure must be carried out.
Least squares fitting is tricky because of the difficulty of matching the calculated eigenvalues to the observed levels.
The four highest assigned K-stacksare not shown.
Observed rotational structures of the nine interacting vibrational levels from the 31B4, 2131B2 and 1131 polyads
Unassigned interloper
Observed rotational structures of the nine interacting vibrational levels from the 31B4, 2131B2 and 1131 polyads
C2H2, the 46200 cm band group
46185 46190 46195 46200 46205 46210E / cm
Q(22) P(18)Q00(21) Q(21) P(17)34Q(23) P(19)Q00(22)
(a)
(b)
RQP
RQ
12C2H2
H12C13CH
123456789102345
0 1 2 3 4 5QP
R13C2H2
0 1 2 3 4 5 6 7567 4 12323
0 1 2 34 123
Q(20)&P(16)
(Natural abundance)
C2H2: 13C isotope shifts of the 46192 cm1 band
A.J.Merer, A.H.Steeves, J.H.Baraban, H.A.Bechtel, R.W.Field, J. Chem. Phys. in press (2011)
Potential energy curves for cis and trans-bent acetylene
Energy (e.V.)
10
8
6
4
MR-CISD level calculations by E. Ventura, M. Dallos and H. Lischka, JCP 118, 1702 (2003)
60o 60o40o20o0o20o40o
Cis-bent Trans-bent
/ HCC/ HCC
1A2
3A2
1B2
3A2
1A2
3B2
3B2
1Au
3Au
1Bu
3Bu
1Au
3Bu
3Au
1u
3u
1u
3u
3u
A~ electron
configurationu
3 g1
(S1)
6000
4000
2000
0
E / cm1
Stanton et al. (1994) calculate that cis-trans isomerization of C2H2, A occurs via a half-linear transition state near 4700 cm1.
~
Cis-trans isomerization of C2H2, S1
More recent calculations by Baraban et al. (2011) have refined the numbers:
HHC C
178o
Cis Trans
3200 cm1
4700 cm1
1Au1A2
(1A2 – X1+g is forbidden)
~
4979 cm
2664 cm
0 cm
The 46200 cm1 band group of C2H2: a cis-well level?
The 13C shifts of the K=1 level are too small for its position within the trans well, but fit for a level in a potential well with minimum at higher energy.
The |g| value of the K=1 level (from Zeeman quantum beat studies) is only 0.089; it is not a triplet state.
The rotational selection rules are those of C2v symmetry (cis-C2H2), not C2h (trans-C2H2).
Its lifetime is much longer than that of nearby trans levels,consistent with a forbidden transition. (1A2 1+) g
Every vibrational level of the S1-trans well expected in this energy region has been accounted for.
Ab initio calculations predict no other singlet electronic states in this energy region.
0
1000
2000
3000
4000
5000
32
2131
22
33
34
23
2231
2132
B2
B3
B4
B5
B6
31B1
31B2
21B2
31B3
21B1
21B3
31B4
21B4
31B5
32B1
2131B1
22B1
22B2
32B2
2131B2
32B3
2131B3
22B3
32B4
33B1
33B2
2132B1
2231B1
2132B2
23B1
34B1
11B1
11B2
1131
1121
1131B1
1132
2133
35
22321121B1
51B1
3151
215151B2
3151B1
3251 2151B1
E /cm 1
042197.57 cm
S1-trans levels
Established by rotational analysisPredicted
S1-cislevels
a1
a1
a2
b2
Ab initio calculatedcis zero-point level
3141
623161
61 b2
S1-trans vibrational levels
Cis-trans perturbation in the S1 state:
cis-62, K=0 / trans-1131, K=0
W12 = 0.30 ± 0.02 cm1
(Hot bands from X, 4″in one-photon excitation)
~
C2H2: the cis-3161 band group (46200 cm1)
The isomerizationcoordinate combines
Q3 and Q6
H
H
C C
Q3 (trans bend)
Q6 (in-plane cis bend)
ag
bu
H
H
C C
Potential energy surface for the S1 state of acetylene
after Ventura et al (2003)
cis
trans cis
trans
linear saddlesaddle
saddle
saddle
0
60o
60o
60o
60o 0
Q3
Q6
26
3
6
Lowering of the effective 6 frequency by 3
G
/ cm1
nv3
Frequency intervals as a function of v3
3n62 – 3n
3n+1 – 3n
3n61 – 3n
The curvature representshuge cross anharmonicity,requiring large values ofx36, etc. to model the levels.
Conclusions
Perturbations often carry information about states that would otherwise be unobservable because of selection rules, e.g. the cis isomer of S1 acetylene.
The acetylene spectrum has shown, for the first time, the spectral signatures of cis-trans isomerization at high resolution.
Unexpected patterns of vibrational and rotational structure are the “fingerprints” of molecular dynamics in action.
K-staggering in the rotational structure. (At higher energy the levels rearrange into a new pattern.)
Huge cross-anharmonicity in vibrations involved in the isomerization coordinate.
Acknowledgements
Prof. Yoshiaki Hamada (Yokohama)Dr. Karl Hallin (U.B.C.)
Prof. Bob Field (M.I.T.)Dr. Nami Yamakita (Japan Women’s Univ.)Dr. Adam Steeves (M.I.T.)Dr. Hans Bechtel (M.I.T.)Mr. Josh Baraban (M.I.T.)
SO2
C2H2
$$: Academia Sinica, Taipei U.B.C.
Anharmonic interaction (k1244)plus b-axis Coriolis perturbation
Anharmonicity-transferredb-axis Coriolis perturbation
Finally, the missing 1
fundamental!
1.0 J(J+1)
Rotational structure of the 21B2 / 11 polyad
/ cm1
0 100 200 300 400 500
26000
27000
28000
29000
E / cm
K2
000
010020
100
110
120
200
002
012
300
210
Assigned a3B1, F3, N=K term values for S16O2 and S18O2~
Coriolis perturbations (K = ± 1)
3B1, 011
3B1, 001