Invisible electronic states and their dynamics revealed by perturbations Anthony J. Merer Institute of Atomic and Molecular Sciences, Taipei, Taiwan University.

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