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 you to work it out every time, but it is remarkable how often you can work it out, given a knowledge of the theory.

SO 2 : Regions of absorption (0,0) 235 nm C 1 B 2 and D 1 A 1 ~~ 358 nm A 1 A 2 and B 1 B 1 ~~ 388 nm a 3 B 1 and b 3 A 2 ~ ~ Upper electronic states

Vibronic perturbation (  K=0)

Vibronic perturbations (  K = 0)

b3A2b3A2 ~ 031 Vibrational structure of the perturbing state

Least squares gives ½(B+C) ( 3 A 2 ) = cm . Given A, from the slope of the N=K graph, the geometric structure of the 3 A 2 state is r(S-O) = Å,  (OSO) = 97 o

The electron spin splittings are too small to be resolved at this scale.  K = ±2

Excitation spectrum of jet-cooled acetylene Trans bendC-C stretch E / cm  A 1 A u (S 1 -trans) – X 1  + ~ g ~ Spectrum taken by Dr. Nami Yamakita

Excitation spectrum of jet-cooled acetylene Trans bendC-C stretch E / cm 

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 C 2 H 2, A 1 A u : 4 (torsion) and 6 (in-plane cis-bend) ~ H CC H  4 (a u ) torsion cm  1  6 (b u ) in-plane cis bend cm  1 H H CC

B = bending [3 1 B 1 = plus ] 1

IR-UV double resonance via the Q branch of ″ (  u ) A.J.Merer, N.Yamakita, S.Tsuchiya, A.H.Steeves, H.A.Bechtel, R.W.Field, J. Chem. Phys. 129, (2008)

A-axis Coriolis Darling- Dennison

B-axis Coriolis

Final least squares fit to the interacting 3 1 B 3 and B 1 polyads Dots are observed term values and lines are calculated. Some of the higher-order rotational constants are not very realistic, but they reproduce the J-structure!  = cm  1 Darling-Dennison resonance k 266 = 8.66 ± 0.16 cm  1 k 244 =  7.3 ± 1.1 cm  lies far below the rest of the polyad; x 36 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, 3 1 B 3 requires effective constants from 3 1, 3 1 B 1 and 3 1 B 2. 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-stacks are not shown. Observed rotational structures of the nine interacting vibrational levels from the 3 1 B 4, B 2 and polyads

Unassigned interloper Observed rotational structures of the nine interacting vibrational levels from the 3 1 B 4, B 2 and polyads

C 2 H 2, the cm  band group

C 2 H 2 : 13 C isotope shifts of the cm  1 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.) MR-CISD level calculations by E. Ventura, M. Dallos and H. Lischka, JCP 118, 1702 (2003) 60 o 40 o 20 o 0o0o 40 o Cis-bentTrans-bent / HCC 1A21A2 3A23A2 1B21B2 3A23A2 1A21A2 3B23B2 3B23B2 1Au1Au 3Au3Au 1Bu1Bu 3Bu3Bu 1Au1Au 3Bu3Bu 3Au3Au 1u1u 3u3u 1u1u 3u3u 3u3u A ~ electron configuration  u 3  g 1 (S 1 )

E / cm  1 Stanton et al. (1994) calculate that cis-trans isomerization of C 2 H 2, A occurs via a half-linear transition state near 4700 cm  1. ~ Cis-trans isomerization of C 2 H 2, S 1 More recent calculations by Baraban et al. (2011) have refined the numbers: H H CC 178 o Cis Trans 3200 cm  cm  1 1Au1Au 1A21A2 ( 1 A 2 – X 1  + g is forbidden) ~ 4979 cm  2664 cm  0 cm 

The cm  1 band group of C 2 H 2 : a cis-well level? The 13 C 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 C 2v symmetry (cis-C 2 H 2 ), not C 2h (trans-C 2 H 2 ). Its lifetime is much longer than that of nearby trans levels, consistent with a forbidden transition. ( 1 A 2  1  + ) g Every vibrational level of the S 1 -trans well expected in this energy region has been accounted for. Ab initio calculations predict no other singlet electronic states in this energy region.

Ab initio calculated cis zero-point level b2b2 S 1 -trans vibrational levels

Cis-trans perturbation in the S 1 state: cis-6 2, K=0 / trans , K=0 W 12 = 0.30 ± 0.02 cm  1 (Hot bands from X, 4 ″ in one-photon excitation) ~

C 2 H 2 : the cis band group (46200 cm  1 )

The isomerization coordinate combines Q 3 and Q 6 H H CC Q 3 (trans bend) Q 6 (in-plane cis bend) agag bubu H H CC   Potential energy surface for the S 1 state of acetylene after Ventura et al (2003) cis trans cis trans linear saddle   0  60 o  60 o  60 o 0 Q3Q3 Q6Q6

Lowering of the effective 6 frequency by 3 GG / cm  1 nv 3 Frequency intervals as a function of v 3 3 n 6 2 – 3 n 3 n+1 – 3 n 3 n 6 1 – 3 n The curvature represents huge cross anharmonicity, requiring large values of x 36, 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 S 1 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.) SO 2 C2H2C2H2 $$: Academia Sinica, Taipei U.B.C.

Anharmonic interaction (k 1244 ) plus b-axis Coriolis perturbation Anharmonicity-transferred b-axis Coriolis perturbation Finally, the missing 1 fundamental!  1.0 J(J+1) Rotational structure of the 2 1 B 2 / 1 1 polyad / cm  1

Coriolis perturbations (  K = ± 1) 3 B 1, B 1, 001