1. The Benzene Dimer
In collaboration with the FHI in Berlin
Melanie
Schnell
Undine
Erlekam
Gerard
Meijer
Gert von
Helden

2. Two key experimental results
IT IS POLAR:
Electric deflection of a Bz2 molecular beam: JCP 63, 1419 (1975)
RINGS ARE NOT EQUIVALENT:
Raman: JCP 97, 2189 (1992) IR: JCP 124, (2006).
Recent ab initio calculations
Cap
Stem
Szalewicz group: JPC A 110,10345 (2006)
Sherrill group: JACS 124, (2002)
DiStasio, von Helden, Steele and
Head-Gordon: CPL 437, 277 (2007)

3. Global minimum has 288 versions
Ab initio results
Global minimum Three saddle points of index 1
STEM
CAP
De = 980 cm-1
12 kJ/mol
2.8 kcal/mol
0.12 eV
5 cm-1
39 cm-1
147 cm-1
Cap
Torsion
Stem
Bend
Stem
Torsion
Global minimum has 288 versions
Chosen tunneling pathways have spectroscopic
consequencies. Use symmetry to probe this.

4. Global minimum has 288 versions
Ab initio results
Global minimum Three saddle points of index 1
STEM
CAP
De = 980 cm-1
12 kJ/mol
2.8 kcal/mol
0.12 eV
5 cm-1
39 cm-1
147 cm-1
Cap C6
Torsion
Stem
Bend
Stem C6
Torsion
Global minimum has 288 versions
Chosen tunneling pathways have spectroscopic
consequencies. Use symmetry to probe this.

5. MS group for nontunneling dimer1’ 2’ 6’ 3’ 5’ 4’ 4 3 2 5 6 1
(C1-H1)
MS group is Cs(M)
E (14)(23)(56)* A'
A''
Allowed transitions
A' A''
odd Kc A''
even Kc A'
6 cm cm cm-1

6. MS group allowing for cap-C6-torsion1’ 2’ 6’ 3’ 5’ 4’ 4 3 2 5 6 1
As for benzene-argon, MS group is now C6v(M)
E (123456) (135)(246) (14)(25)(36) (26)(35)* (14)(23)(56)*
(165432) (153)(264) (31)(46)* (25)(34)(61)*
(42)(51)* (36)(45)(12)*
6 cm cm cm-1

7. The correlation of C6v(M) to Cs(M)
A’+A’’
Cs(M)

8. The reverse correlation of Cs(M) to C6v(M)
Statistical weights for (12C6H6)2 in parentheses
Cs(M) C6v(M)
If V6 barrier = 0
Etorsion = F Ki2 E ΔE 3 1 Ki 3 2 1 9F 5
B1(896)
E2(1152)
E1(1408) 4F F
A´´
(4096)
A2(640)
If V6 barrier high (>20 cm-1) get ΔE 1 2
B2(896)
E2(1152)
E1(1408)
A1(640) 3 A´
(4096)
`` High barrier pattern’’
St. wt. ratios: 5/11/9/7
St. wts same for 12C6H6 cap on C6D6 stem

9. Alternatively, suppose is C2v at equilibrium1’
Allowed transitions:
A A2 B B2 2’ 6’ 3’ 5’ 4’
KaKc symmetry
ee A1
eo A2
oo B1
oe B2 4 5 6 3 2 1
Rigid molecule MS group is now C2v(M)
E (14)(25)(36)(2’6’)(3’5’) (14)(23)(56)* (26)(35)(2’6’)(3’5’)* A A B B
But now when we introduce cap torsion the MS group is G24

10. The structure of the group G24
G24 = C6v(M) x {E,(2´6´)(3´5´)}
{E,(2´6´)(3´5´)}
E (2´6´)(3´5´) As Aa
The 12 irreps are called A1s, A1a, A2s, A2a, etc.

11. Correlation of C2v(M) to G24
Statistical weights for (12C6H6)2 in parentheses
C2v(M) G24
C2v(M) G24
KaKc
KaKc
B1s(560)
E2a(432)
E1s(880)
A2a(240)
B2a(336)
E2s(720)
E1a(528)
oo B1
(2112)
ee A1
(1984)
A1s(400)
B1a(336)
E2s(720)
E1a(528)
A2s(400)
B2s(560)
E2a(432)
E1s(880)
A1a(240)
oe B2
(2112)
eo A2
(1984)
St. wt. ratios: 15/55/27/35
St. wt. ratios: 25/33/45/21

12. Correlation Cs(M) to C6v(M) to G24
Statistical weights for (12C6H6)2 in parentheses FOR Ka EVEN
Cs(M) C6v(M) G24
v(bend)=0 + v(bend)=1
B1(896)
E2(1152)
E1(1408)
B1a(336) + B1s(560)
E2s(720) + E2a(432)
E1a(528) + E1s(880)
A2s(400) + A2a(240)
A´´
(4096)
A2(640)
B2(896)
E2(1152)
E1(1408)
A1(640)
B2a(336) + B2s(560)
E2s(720) + E2a(432)
E1a(528) + E1s(880)
A1s(400) + A1a(240) A´
(4096)
St. wt. ratios: 5/11/9/ /3 or 3/5

13. h6-h6 Cs(M) C6v(M) C2v G24 Cs(M) C6v(M) G24 even Ka odd Ka even Ka21 45 33 25
odd Ka 35 27 55 15 7 9 11 5
Cs(M) C6v(M) G24
v=0/1 7 9 11 5
3/5
5/3
even Ka 7 9 11 5
5/3
3/5
odd Ka

14. MS group if stem-C6-torsion tunneling observed is G1441´ 2´ 3´ 4´ 4 3 2 1
6´ 5´ 5 6
(1´2´3´4´5´6´) and similar operations become feasible
MS group is G144
where G144 = Gcap x Gstem
See Spirko et al:
JCP 111, 572 (1999)
C6v(M) D6(M)
[A1,A2,B1,B2,E1,E2]
[A1,A2,B1,B2,E1,E2]
6 cm cm cm-1
Irreducible representations of G144: A1xA1, A1xA2, etc.
G144 has 16 1D, 16 2D, and 4 4D irreducible representations

15. h6-h6 Cs(M) C6v(M) C2v G24 Cs(M) C6v(M) G24 G24 G144 even Ka odd Ka21 45 33 25
odd Ka 35 27 55 15 7 9 11 5
Cs(M) C6v(M) G24
v=0/1
G G144 7 9 11 5
3/5
5/3
even Ka 13 9 11 7
even Ka 7 9 11 5
5/3
3/5 1 9 11 3
odd Ka
odd Ka

16. h6-h6 h6-d6 cap Cs(M) C6v(M) C2v G24 Cs(M) C6v(M) G24 G24 G144 even Ka21 45 33 25
odd Ka 35 27 55 15 7 9 11 5 7 9 11 5 28 45 44 25
h6-d6
cap 35 36 55 20
Cs(M) C6v(M) G24
v=0/1
G G144 7 9 11 5 7 9 11 5
3/5
5/3
4/5
5/4
even Ka 13 9 11 7 92
116
124 73
even Ka 7 9 11 5 7 9 11 5
5/3
3/5 1 9 11 3 38
116
124 46
odd Ka
odd Ka

17. d6-h6 d6-d6 cap Cs(M) C6v(M) C2v G24 Cs(M) C6v(M) G24 G24 G144 even Ka
odd Ka
119
248
232
130
119
248
232
130
d6-d6
cap
Cs(M) C6v(M) G24
v=0/1
G G144
119
248
232
130
119
248
232
130
3/5
5/3
4/5
5/4
even Ka 13 9 11 7 92
116
124 73
even Ka
119
248
232
130
119
248
232
130
5/3
3/5
5/4
4/5 1 9 11 3 38
116
124 46
odd Ka
odd Ka

18. h6-h6 h6-d6 d6-h6 d6-d6 Cs(M) C6v(M) G24 G24 G144 Cs(M) C6v(M) G24
Cap-stem
Cs(M) C6v(M) G24
G G144 7 9 11 5 7 9 11 5
3/5
5/3
4/5
5/4 13 9 11 7 92
116
124 73
h6-h6
even Ka
even Ka 1 9 11 3 38
116
124 46 7 9 11 5
h6-d6 7 9 11 5
5/3
3/5
odd Ka
odd Ka
Cs(M) C6v(M) G24
G G144
119
248
232
130
119
248
232
130
3/5
5/3
4/5
5/4 13 9 11 7 92
116
124 73
even Ka
even Ka
d6-h6 1 9 11 3 38
116
124 46
119
248
232
130
119
248
232
130
5/3
3/5
5/4
4/5
d6-d6
odd Ka
odd Ka