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

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, 171101 (2006). Recent ab initio calculations Cap Stem Szalewicz group: JPC A 110,10345 (2006) Sherrill group: JACS 124, 10887 (2002) DiStasio, von Helden, Steele and Head-Gordon: CPL 437, 277 (2007)

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.

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.

MS group for nontunneling dimer 1’ 2’ 6’ 3’ 5’ 4’ 4 3 2 5 6 1 (C1-H1) MS group is Cs(M) E (14)(23)(56)* A' 1 1 A'' 1 -1 Allowed transitions A' A'' odd Kc A'' even Kc A' 6 cm-1 16 cm-1 38 cm-1

MS group allowing for cap-C6-torsion 1’ 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-1 16 cm-1 38 cm-1

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

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 1-3-1 pattern’’ St. wt. ratios: 5/11/9/7 St. wts same for 12C6H6 cap on C6D6 stem

Alternatively, suppose is C2v at equilibrium 1’ Allowed transitions: A1 A2 B1 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’)* A1 1 1 1 1 A2 1 1 -1 -1 B1 1 -1 -1 1 B2 1 -1 1 -1 But now when we introduce cap torsion the MS group is G24

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 1 1 Aa 1 -1 The 12 irreps are called A1s, A1a, A2s, A2a, etc.

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

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: 5/11/9/7 5/3 or 3/5

h6-h6 Cs(M) C6v(M) C2v G24 Cs(M) C6v(M) G24 even Ka odd Ka even Ka 21 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

MS group if stem-C6-torsion tunneling observed is G144 1´ 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-1 16 cm-1 38 cm-1 Irreducible representations of G144: A1xA1, A1xA2, etc. G144 has 16 1D, 16 2D, and 4 4D irreducible representations

h6-h6 Cs(M) C6v(M) C2v G24 Cs(M) C6v(M) G24 G24 G144 even Ka odd Ka 21 45 33 25 odd Ka 35 27 55 15 7 9 11 5 Cs(M) C6v(M) G24 v=0/1 G24 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

h6-h6 h6-d6 cap Cs(M) C6v(M) C2v G24 Cs(M) C6v(M) G24 G24 G144 even Ka 21 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 G24 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

d6-h6 d6-d6 cap Cs(M) C6v(M) C2v G24 Cs(M) C6v(M) G24 G24 G144 even Ka 357 476 1240 1240 696 928 650 650 odd Ka 595 595 744 992 1160 1160 390 520 119 248 232 130 119 248 232 130 d6-d6 cap Cs(M) C6v(M) G24 v=0/1 G24 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

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 G24 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 G24 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