Molecules undergoing extreme rotation

Figure 2. Angular distribution of the main fragments observed in the Multi Electron Dissociative Ionization (MEDI) of CO

PRL 82, 3420 (1999)

PRL 85, 542 (2000)

JCP 116, 10636 (2002)

Rotational Energy Level Clusters

1972 Dorney and Watson CH4 8-fold and 6-fold clusters

1978 Zhilinskii and Pavlichenkov H2O 4-fold clusters (Erb)

1978 Harter and Patterson Rotational energy surfaces and clusters

1991 Lehmann Local mode theory and clusters

1992 Kozin et al H2Se 4-fold clusters observed

1993 Kozin and Jensen H2Se 4-fold cluster theory (Erbs)

1994 Jensen and Bunker H2X 4-fold cluster symmetry

1996 Kozin et al H2Te 4-fold clusters (exp and theory)

1997 Jensen et al Review paper on 4-fold clusters

2000 Jensen Review paper on LMT and clusters

Emphasis is put on explaining the intimate relationship between local mode vibrations and the formation of both vibrational and rovibrational energy level clusters.

H2Te Rigid Rotor Energy Levels [E(JKaKc)-E(JJ0)]

JJ,0

JJ,1JJ-1,1

JJ-1,2

JJ-2,2

JJ-2,3

JJ-3,3

JJ-3,4

JJ-4,4

JJ,0JJ,1

JJ-1,1

JJ-1,2

J

Ae=6.26, Be=6.11, Ce=3.09 cm-1

4

4

Actual H2Te Energy Levels [E(JKaKc)-E(JJ0)]

J

JJ,0JJ,1JJ-1,1

JJ-1,2

JJ,0

JJ,1JJ-1,1

JJ-1,2

JJ-2,2

JJ-2,3

JJ-3,3

JJ-3,4

JJ-4,4

1R 1L

2L2R

1

2

1

11

22

2

JJ,0JJ,1JJ-1,1

JJ-1,2

in C2v(M)

Kinetic Tunneling

We can write

For one form (12), E*, and (12)* are not feasible. “A dynamical barrier”.

Thus the MS group is just {E} for each form and it must be chiral.

1L 1R 2R 2L

J even J odd

A1 B2

B1 A2

A2 B1

B2 A1

1R 1L

2L2R

2

11

11

2

2 2

WHAT ARE THE LIFETIMES OF SUCH “DYNAMICALLY” CHIRAL STATES

at t=0

at time t

Using

2

Probability of being in |1R> at time t is:

For high J: ∆J i.e.

(Half-life)

Time for probability to have decreased to 1/2

∆J as function of J∆J

Zhilinskiiand

Pavlichenkov

Half-life as function of J

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