5.76 Lecture #36S Isomeric Forms Page 1 of 10 pages

5.76 Lecture #36S Isomeric Forms Page 1 of 10 pages

Lecture #36 Supplement: C2H2 Has Many Isomeric Forms

C2

aKa( ) C

2

cKc( )STRUCTURE MOLECULAR E* (PARITY)

SYMMETRY SUBGROUP OF

G8 [SYMMETRY OPERATION?PERMUTE H’s? PERMUTE C’s?] yes, no, no yes, no, no

no, no, no yes, yes, yes Rc(π)

no, no, no no, yes, yes (–1)Kc Rc(π)

yes, yes, no no, ?, no Rc(π)

no, no, no no, yes, yes — (Near

D!h

a

C2h

c

C2v

b

C2v

a

C2

b

CIS)

C2

c no, no, no yes, yes, yes —

(Near Trans)

a,b,c: CORRESPONDENCE BETWEEN Cn SYMMETRY AXIS AND a,b,c INERTIAL AXES

CLASSIFY IN CNPI GROUP (G8) BECAUSE PERMUTATIONS AND INVERSIONS ARERIGOROUS SYMETRY OPERATIONS.

THE BEST (ONLY?) WAY TO DEAL WITH TRANSITIONS BETWEEN ISOMERIC FORMS(LARGE AMPLITUDE MOTIONS)




THE NON-PLANAR (NEAR-CIS) E!1

A STATE OF ACETYLENE

I. E! ! X! , E! !A! , AND A! ! X! , ALL ARE ELECTRIC DIPOLE ∴ E! IS NON-CENTRO-SYMMETRIC A. E

! ! X!

A! ! X!

E! !A!

f ≈ 0.06 VERY STRONG B. ZEEMAN POLARIZATION QUANTUM BEATS C. QQ || VS. ⊥

II. E! !A! : OBSERVE Ka = 1 ←Ka = 1 (a-TYPE)

E!SIGN OF ASYMMETRY SPLITTING IN Ka = 1

∴ IN PLANAR LIMIT

ALREADY RULED OUT

ELECTRONICALLY FORBIDDEN

III. ROTATIONAL SELECTION RULES FOR

TRANS!BENT 1Bg

OR

CIS!BENT 1A2

"

#$

%$

1Bg ! X!

1

"g

+ 1Ag( )

1A2 ! X!

1

"g

+ 1A1( )

E!! A!

a-TYPE FROM Ka = 1

b-TYPE FROM Ka = 0, 2Ka NUMBERING CONFIRMED BY

WILKINSON’S A0 ! 8 cm–1

! 1A2 BUT ELECTRONICALLY FORBIDDEN

FRANCK-CONDON FORBIDDEN 00

0 BAND

IV. NONPLANAR (NEAR-CIS) WITH TUNNELING THROUGH CIS BARRIER HOT BANDS EXPLAINED

V. INERTIAL DEFECT ⇒ NONPLANAR

E! ! X! ! ""#

4+ ""#

5


E! -STATE IS NON-CENTRO-SYMMETRIC

E!! X!A. OBSERVED BY WILKINSON* IN ABSORPTION f ≈ 0.06 TOO STRONG TO BE MAGNETIC DIPOLE: f < 10–3

B. A!! X! ZEEMAN POLARIZATION QUANTUM BEATS

B-FIELD

Z Z

X

B-FIELD

E-FIELD

ELECTRIC DIPOLE: !MJ = ±1

MAGNETIC DIPOLE: !MJ = 0

! POLARIZED

LIGHT

EXCITE WITH

SHORT PULSE

LASER

M

M

µm

M+1

M–1

µe

M X!

A!

INDUCED

POLARIZATION

ROTATES IN XY

PLANE!

QUANTUM BEATS

NO ROTATING

POLARIZATION!

NO BEATS

OBSERVED BY EVAN ABRAMSON AND PETER GREEN

Ix

t

Iy

t

Expected if A!! X! were electric dipole allowed.

Ix

OR

Iy

t

Expected if A!! X! were magnetic dipole allowed.

* P. G. Wilkinson, J. Mol. Spectrosc. 2, 387 (1958).


C. E!! A! POLARIZATION DEPENDENT PQR INTENSITIES

E!

A!

X!

µ!M M

2

NM

–J +J0

–J +J0

–J +J0–J +J0

|| "

Excitation sequence:

# QQ || STRONG

QQ " WEAK

A!

X!

ELECTRIC DIPOLE SELECTION RULE: g↔u

u

u

g X!

A!

E!

E! CAN BE NEITHER g NOR u because it

is excited from both rigorously g and

rigorously u initial states.

! E! IS NOT CENTROSYMMETRIC

g


HCCH

E! v = 0" Ka = 1 ! A (0 0 2 0 0 0) Ka = 1

THE ONLY E! " A! BAND WITH

RESOLVABLE J-STRUCTURE

* MUST BE A Ka ≠ 0 LEVEL BECAUSE OF THE PRESENCE OF PQR BRANCHES.

* INTENSITY RATIO PQR IMPLIES K′ a = 1 and a-type ROTATIONAL SELECTION RULES


PLANAR LIMIT

Ag Au Bg Bu A1A2 B1 B2

211

212

a–

a– a–

a–

s+

s+

s+

211

212

a+

s–

J = 2 a+ ! a–

s– ! s+

A! 1Au

X means NO

a–LEVELS

IN Ka = 1

TRANS CISKa = 1 LEVELS

s+

IF TRANSITION TERMINATES IN Ka = 1, IT MUST BE a-TYPE. ∴ IT MUST GO TO LOWER ASYMMETRY COMPONENT (CONFIRMED BY TERM VALUE PLOT.)

E! IS 1Bg OR 1A2

RULED

OUT

ELECTRONICALLY

FORBIDDEN FROM

X!

1

!g

+ 1A1( )

So it seems as though planar symmetry is ruled out!


SPECIFIC EXAMPLES

SELECTION RULE a+ → a– s– → s+

ONLY POSSIBLE FINAL STATES

b-type

b-type

b-type

a-typeAll nuclear permutationallowed levels must be either a+ or s–.


Inertial Defect vs. A Rotational Constant

E!1

A

110°

H

H

75°

(ASSUMING SAME RCH AND RCC AS A! -STATE)

A! 1Au

120°

H

180°

H

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5.76 Lecture #36S Isomeric Forms Page 1 of 10 pages