Results and Discussion

In Figure 2.2 the IR ion dip spectra, when exciting the 0⁰₀ transition of (C6H6)(C6D6) at 38044.0 cm⁻¹ (bottom spectrum) and at 38246.4 cm⁻¹ (top spectrum), are shown. These two IR spectra are found to be different, especially concerning the number of spectral signatures. Three important consequences arise from this observation: (1) In the two isomers of (C6H6)(C6D6) C6H6is located in two different sites and the C-H stretch spectra result from two sym-metrically inequivalent subunits. (2) The two benzene rings do not interchange on the timescale between IR excitation and UV excitation/ionization which is, in the present experiment, about 70 ns. (3) From the discussion on the symmetry properties conducted in section 1.5.3 and from the IR spectra shown in Figure 2.2 it can be concluded that the two spectral features at 38044.0 cm⁻¹ and at 38246.4 cm⁻¹in the 0⁰₀transition spectrum of (C₆H₆)(C₆D₆) (see Figure 1.10 (bottom)) are not the signatures of two different sites, but of the same site in two different substitution isomers . That is, the benzene dimer has a (distorted) T-shaped structure with a "stem" and a freely rotating "top" moiety (structures I or II in Figure 1.11).

If the two benzene molecules were equivalent and/or able to interchange on a 70 ns timescale, identical IR spectra would result when exciting the 0⁰₀ transition of (C₆H₆)(C₆D₆) at 38044.0 cm⁻¹ and at 38246.4 cm⁻¹. If the "top"

moiety was not freely rotating, the symmetries of both subunits and the two IR spectra would be equivalent. Therefore, the lower spectrum in Figure 2.2 results from a (distorted) T-shaped structure with C₆H₆in the "stem" position and C₆D₆ in the "top" position ((C₆H₆)^S(C₆D₆)^T) and the upper spectrum in Figure 2.2 results from the substitution isomer (C6D6)^S(C6H6)^T, where the

"stem" is deuterated and the "top" is protonated. Thus the C-H stretch spectra result from the "stem" and the "top" moiety, respectively.

The three well known IR transitions of the benzene monomer that occur in this range [53, 114, 123] are indicated as solid lines in Figure 2.2. These are theν₂₀fundamental mode (E_1usymmetry) at 3047.9 cm⁻¹, theν₁+ν₆+ν₁₉ combination band at 3078.6 cm⁻¹ and the ν₈+ν₁₉ combination band at 3101 cm⁻¹. Shown as dashed lines are the positions of two other, not IR active fundamental C-H stretch modes of the benzene monomer: theν7 mode (E2g

symmetry) at 3056.7 cm⁻¹[124, 125] and the ν2 mode (A1g symmetry) at 3073.9 cm⁻¹ [124, 125]. An overview over all experimentally determined values is given in Table 2.1.

In both (C₆H₆)(C₆D₆) benzene dimer spectra, the three resonances that are IR active in the bare benzene are observed. In all cases, they are, compared to the positions for the benzene monomer, redshifted by a few cm⁻¹. In the spectrum of (C6H6)^S(C6D6)^T additional resonances are observed, one at 3012.4 cm⁻¹, one at 3070.9 cm⁻¹ and a weak split peak (shown enlarged in the inset) at 3056.2 and 3057.3 cm⁻¹.

In the following, the nature of these transitions shall be discussed. Previous

(C₆D₆)^S(C₆H₆)^T

(C₆H₆)^S(C₆D₆)^T

3020 3040 3060 3080 3100

ab so rp ti on c ro ss s ec ti on [ a. u. ]

wavenumber [cm

]

3055 3056 3057 3058

ν₇(E_2g) ν₂(A_1g) ν₂₀(E_1u)

Figure 2.2: IR overview spectra in the region between 3010 and 3110 cm⁻¹of (C6D6)^S(C6H6)^T (top) and (C6H6)^S(C6D6)^T(bottom), corresponding to the two subunits of the benzene dimer, the "top" and the "stem", respectively. The positions of the IR active C-H stretch modes of the benzene monomer (D6h) are indicated as solid vertical lines and those of the two known IR inactive fundamental modes ν7 (E2g) and ν2 (A1g) as dashed vertical lines. In the inset the region between 3054 and 3059 cm⁻¹ is shown for (C6H6)^S(C6D6)^T, measured with a 10 times higher laser fluence. The red most absorption signal in the spectrum of (C₆H₆)^S(C₆D₆)^T is attributed to result from the so far unknownν₁₃(B_1u) fundamental mode of C₆H₆.

experiment theory ν (C6H6)^S(C6D6)^T (C6D6)^S(C6H6)^T C6H6 C6H6a C6H6b

13 (B_1u) 3012.4 - 3015^c 3159.2 2993.2^d

20 (E1u) 3044.8 3046.4 3047.9^e 3184.4 3030.1^d

7 (E2g) 3056.8 - 3056.7^c,f 3169.3 3034.8

2 (A1g) 3070.9 - 3073.9^c,f 3194.9 3053.2

aharmonic

banharmonic

cnot IR active

din Fermi resonance withν8+ν19 esee Reference [114]

fsee Reference [124, 125]

Table 2.1: Experimental and calculated (harmonic and anharmonic) wavenum-bers [cm⁻¹] for the benzene monomer and dimer.

spectra of (C₆H₆)₂show similar features. There, in one experiment two [53] and in another experiment all three [126] additional transitions have been observed as well. As tentative assignment for the two stronger additional transitions, combinations with intermolecular vibrations were suggested [53]. Here a different interpretation is proposed.

Our observation of two different IR spectra for the two benzene moieties is in agreement with a T-shaped geometry [55, 57] in which the "top" benzene molecule is freely rotating. Such a T-shaped geometry can be in its rigid form of C2v geometry as shown in Figure 1.9 (b) or it can haveCs symmetry as shown in Figure 1.9 (d). In the dynamic case both benzene dimer structures (of C2v

and Cs symmetry) become symmetrically equivalent (C6v); the symmetry of the "top" molecule is thenC_6v and that of the "stem" remains unchangedC_2v and C_s, respectively. Recentab initio calculations predict the benzene dimer of C_s symmetry to be the global minimum structure and the dimer of C_2v symmetry to represent a saddle point on the potential energy surface [70, 71].

The four fundamental modes of benzene in the range between 3010 and 3110 cm⁻¹ haveB1u, E1u,E2g andA1g symmetry in aD6h environment. In D6h, however, only theE1umode is IR allowed. It can be shown that in the reduced symmetry of the freely rotating "top" (C6v) theν2 mode hasA1symmetry and is IR allowed as well. When the symmetry is reduced toCs orC2v (monomer

→"stem"), all four fundamental modes are IR allowed, and additionally, the degeneracy of the E1u andE2g modes is lifted (see Table 2.2). Therefore it is possible, that the additional lines experimentally observed in the spectrum of the "stem" result from those modes that become IR active upon symmetry reduction. These symmetry considerations support the assignment of the upper

monomer "top" "stem"

D6h C6v C2v Cs

ν₁₃ B_1u B₁ A₁ A⁰

ν₂₀ E_1u E₁ A₁+B₁ 2A⁰

ν₇ E_2g E₂ A₁+B₁ 2A⁰

ν₂ A_1g A₁ A₁ A⁰

ν₁+ν₆+ν₁₉ B_1u+B_2u+E_1u B₁+B₂+E₁ 2A₁+ 2B₁ 4A⁰ ν8+ν19 B1u+B2u+E1u B1+B2+E1 2A1+ 2B1 4A⁰ Table 2.2: Symmetry properties of the four fundamental modes and two combi-nation bands of benzene C₆H₆ in the region between 3010 and 3110 cm⁻¹ in dependence of the symmetry environment. The correlation table is adapted from Reference [32]. The symmetry representations of IR active vibrational modes are underlined.

spectrum in Figure 2.2 to the "top" position in the benzene dimer and the lower spectrum to the "stem" position.

However, pure symmetry considerations do not reveal whether those newly activated IR transitions are strong enough to be observable and, if they are observable, whether they are significantly shifted from the positions of their unperturbed counterparts. Qualitatively, the strength of the symmetry reducing perturbation (i.e. the intermolecular interaction) will affect both, the strength and the frequency shift of the newly allowed transitions. For the benzene dimer the intermolecular interaction is very weak, compared to the intramolecular interactions. This is expected from theory [70, 71], and can also be seen from the shifts and splittings of the transitions in Figure 2.2. For the modes in the dimer that are IR active already in the monomer, the observed splittings are not larger than 2.5 cm⁻¹ and the absolute value of the redshifts (compared to the monomer) does not exceed 4 cm⁻¹. The mode at 3070.9 cm⁻¹ in the spectrum of (C6H6)^S(C6D6)^T is shifted by only -3 cm⁻¹ from the position of theν2A1g

mode in C6H6. The modes at 3056.2 and 3057.3 cm⁻¹ can be compared to the ν7E2gmode of C6H6at 3056.7 cm⁻¹. In the "stem" of the dimer the degeneracy is lifted (see Table 2.2) which might result in a splitting as the one observed.

Consistent with the (negligible) shift and splitting, the band appears to be very weak in the "stem" of the dimer. The third additional transition, observed at 3012.4 cm⁻¹, is thus assigned to the only other fundamental C-H stretch mode in benzene that is left in this energy range, theν₁₃mode ofB_1u symmetry.

To further test these assignments calculations of the vibrations of benzene that include the effects of anharmonicities have been performed with GAUS-SIAN03 [127] using the B3LYP DFT functional and the cc-pVTZ (correlation consistent polarized valence triple zeta) basis set. The resulting frequencies

for the C-H stretch modes are shown in Table 2.1. Relevant for the direct comparison to the experiment are the anharmonic modes, which also include the effect of Fermi resonances. Comparing those with the (experimentally) known bands (ν₂₀,ν₇, ν₂) of benzene shows that the calculated wavenumber values are between 0.6% and 0.7% too low for the individual modes. Correcting the calculated value for theν₂ B_1u mode at 2993.2 cm⁻¹ for the same amount, results in a predicted value of 3013.0 cm⁻¹for theB_1umode. This is in excellent agreement with the transition in the "stem" position of the dimer observed at 3012.4 cm⁻¹. Comparing now the experimentally observed transitions for the

"stem" in the benzene dimer to those for the monomer shows that in the dimer, transitions are up to 3 cm⁻¹ shifted to the red. This shift, which is due to van der Waals interactions between the two benzene molecules, is of course not known for the B1u mode, but it would be surprising if this shift was vastly different in this case. Therefore, an empirical shift of 2-3 cm⁻¹ is included for this band and it can be concluded that theν13fundamental mode of the benzene monomer is located at 3015⁺²₋₅ cm⁻¹.