Vibration-rotation-tunneling states of the benzene dimer: An ab initio study. At the Fritz-Haber Institute Berlin: A. van der Avoird, P. R. Bunker, M. Schnell, G. von Helden and G. Meijer At the University of Delaware: R. Podeszwa and K. Szalewicz At Université Montpellier: C. Leforestier At Radboud University Nijmegen: R. van Harrevelt PCCP, 2010 DOI: /c002653k

Early experiments: It is a polar molecule The electric deflection of molecular beams of (C 6 H 6 ) 2 produced by adiabatic expansion, has been measured by Klemperer’s group. JCP 63, 1419 (1975) and JCP 70, 4940 (1979).

More experiments IDS Raman, Felker et al JCP 97, 2189 (1992): The monomers are inequivalent Very many reasons, one of which is that there are two [C 6 H 6 ν 1 ] resonances in C 6 H 6 -C 6 D 6

F. T. Microwave spectrum Arunan and Gutowsky, JCP 98, 4294 (1993) More than a hundred lines in the 2.5 to 6 GHz region. 22 fitted to J+1,K J,K symmetric-top expression J = 6 5, K=1 EXAMPLE All 22 have quartet structure which is the signature of V 6 tunneling through a significant barrier 2 11 splittings

F. T. Microwave spectrum Arunan and Gutowsky, JCP 98, 4294 (1993) More than a hundred lines in the 2.5 to 6 GHz region. 22 fitted to J+1,K J,K symmetric-top expression J = 6 5, K=1 EXAMPLE All 22 have quartet structure which is the signature of V 6 tunneling through a significant barrier 2 11 splittings

Unpublished Hannover measurements on COBRA. Erlekam and Uwe-Grabow J+1,K J,K experimental intensity ratios 5,0 4,0 37.8/25.4/24.4/12.4 = 3.1/2.1/2.0/1.0 5,1 4,1 34.3/28.1/25.5/12.1 = 2.8/2.3/2.1/1.0 7,0 6,0 38.5/23.1/25.5/13.0 = 3.0/1.8/2.0/1.0 7,1 6,1 41.7/20.7/25.2/12.3 = 3.4/1.7/2.1/1.0 So statistical weights are roughly 3/2/2/1 for even or odd K

Cap Stem Podeszwa, Bukowski and Szalewicz: JPC A 110,10345 (2006) DiStasio, von Helden, Steele and Head-Gordon: CPL 437, 277 (2007) Recent ab initio calculations of global minimum structure SAPT(DFT) at 491 points rigid C 6 H 6

Oncomodulin Science, 229, 23 (1985)

Podeszwa et al., JPCA 2006,110, cm cm cm -1 STEM CAP Global minimum Three saddle points of index 1 D e = 980 cm kJ/mol 2.8 kcal/mol 0.12 eV = E h Cap Torsion Stem Bend Stem Torsion Chosen tunneling pathways have spectroscopic consequencies. Use symmetry to probe this. Global minimum has 288 versions

5.6 cm cm cm -1 STEM CAP Global minimum Three saddle points of index 1 D e = 980 cm kJ/mol 2.8 kcal/mol 0.12 eV = E h Cap Torsion Stem Tilt Stem Torsion Global minimum has 288 versions Podeszwa et al., JPCA 2006,110,10345 Also cap-turnover and stem-cap interchange

[T + V ]Φ vrt = E vrt Φ vrt Set up in appropriate coordinates Analytical function fitted to ab initio points ’pot3’ Must solve the VRT Schrödinger Equation 9 dimensional To solve need basis set and good diagonalization methodology Improvement on Podeszwa et al., 3 rd order SAPT(DFT)

Kinetic energy operator and basis set

C and H nuclear positions plus 13 off-nuclear sites for each monomer 92 fitting parameters. 479 geometries The analytical fitting of V

Basis functions symmetry adapted to 54 irreps of MS group G 576 Diagonalization methodology JCP 101, 7357 (1994)

Molecular symmetry group MS Odutola, Alvis, Curtis and Dyke, Mol. Phys., 42, 267 (1981) Schmied and Lehmann, J. Mol. Spec., 226, 201 (2004) Spirko et al., J. Chem. Phys., 111, 572 (1999) St. Wts C 6 H 6 C 6 D 6 E. Bright Wilson Jr., (1935) GAP

5.6 cm cm cm -1 STEM CAP Global minimum Three saddle points of index 1 Cap Torsion Stem Tilt Stem Torsion pot3. JPCA 2006,110, rd order KiKi v tilt Cap Turnover 54 cm -1 Δ ~ 1 kHz

K i = v tilt = 1 v tilt = 0 6 = K i 5 4 v tilt = 1 v tilt = 0

A 1a A 1s G 24 symmetries and st. wts added E 1s E 1a E 2a E 2s B 2s B 2a Boltzmann factor ~ 0.1 at 2 K for level at 3 cm -1 ASIDE: Small cap-turnover splitting calculated. Tunneling path not found cm -1

Microwave spectrum JCP 98, 4294 (1993) More than a hundred lines in the 2.5 to 6 GHz region. 22 fitted to J+1,K J,K symmetric-top expression J = 6 5, K=1 EXAMPLE All 22 have quartet structure which is the signature of V 6 tunneling 2 11 splittings Need V 6 barrier of greater than 40 cm -1 to get structure

Hannover measurements J,K J+1,K experimental intensity ratios 4,0 5,0 37.8/25.4/24.4/12.4 = 3.1/2.1/2.0/1.0 4,1 5,1 34.3/28.1/25.5/12.1 = 2.8/2.3/2.1/1.0 6,0 7,0 38.5/23.1/25.5/13.0 = 3.0/1.8/2.0/ ,1 41.7/20.7/25.2/12.3 = 3.4/1.7/2.1/1.0 K even: 0.8/1.8/1.3/1.0 K odd: 2.3/1.8/3.7/1.0 Theory G 24 st.wts. in order K i =3,2,1,0 High frequency component is K i = 0 transition from JTH

A 1a A 1s G 24 symmetries and st. wts added E 1s E 1a E 2a E 2s B 2s B 2a How do we get quartets with 1/2/2/3 st.wts? And how do we get symm top with linear Stark effect? Boltzmann factor ~ 0.1 at 2 K for level at 3 cm -1

F. T. Microwave spectrum Arunan and Gutowsky, JCP 98, 4294 (1993) More than a hundred lines in the 2.5 to 6 GHz region. 22 fitted to J+1,K J,K symmetric-top expression J = 6 5, K=1 EXAMPLE All 22 have quartet structure which is the signature of V 6 tunneling through a significant barrier 2 11 splittings MORE EXPERIMENTAL RESULTS NEEDED TO CONFIRM OUR THEORY!