Conformational Distribution of Gas-phase Glycerol Riccardo Chelli, Francesco L. Gervasio, Cristina Gellini, Piero Procacci,* Gianni Cardini, and Vincenzo Schettino UniVersita` di Firenze, Dipartimento di Chimica, Via Gino Capponi 9, 50121 Firenze, Italy, and European Laboratory for Nonlinear Spectroscopy (LENS), Largo E. Fermi 2, 50125 Florence, Italy ReceiVed: July 26, 2000; In Final Form: September 20, 2000 Combining ab initio and statistical mechanics calculations we have determined the conformational distribution of gas-phase glycerol at different temperatures. The obtained results are consistent with infrared spectroscopy and electron diffraction measurements and are in excellent agreement with previous molecular dynamics simulation data. In a recent paper 1 we have calculated the infrared absorption of various conformers of glycerol using density functional theory. These conformers are shown in Figure 1. The ab initio data were used in a fitting procedure of the experimental infrared spectrum of gas-phase glycerol. 2 The results indicated that, at 498 K, glycerol is present as a mixture of two conformers, namely RR and Rγ. Unfortunately the fit was not able to give quantitative results because of the large computational error (see discussion in ref 1). However, our conclusions were qualitatively similar to those obtained with electron diffraction measurements 3 and with molecular dynamics simulations 4 using empirical potential models. At variance with these conclusions, the best fit to the supersonic jet rotational spectrum of a gas sample at 423 K was obtained assuming a distribution of γγ and Rγ conformers. 5 Although the independent experimental measurements of the vibrational infrared and rotational microwave spectra refer to comparable thermodynamic conditions, they give contradictory indications on the conformational distribution that cannot be explained on the basis of the temperature difference. In view of this discrepancy, we thought it useful to search for an additional independent evidence for the conformational com- position of gas-phase glycerol. In this paper we report on a quantitatively reliable estimate of the conformational distribution of glycerol in gas phase, by computing the molecular partition function and the equilibrium constants using the results of accurate ab initio data. In gas-phase glycerol, for any pair of conformational species I and J, the following conformational equilibrium holds In the hypothesis of an ideal mixture, the equilibrium constant K IJ can be determined from the knowledge of the molecular partition functions 6 where N J and N I are the molar concentrations. The d I and d J factors correspond to the structural degeneracy of the conform- ers, namely to the number of different conformational enanti- omers. For all of the considered conformers (see Figure 1) d ) 2, except for RR3(d ) 1) because of the presence of a symmetry plane. In the Born-Oppenheimer approximation and neglecting vibro-rotational coupling, the molecular partition function can be factorized into its translational, rotational, vibrational, electronic, and nuclear parts, i.e., q ) q trans q rot q vib q elec q nucl . The translational and nuclear partition functions are identical for all of the species and therefore they are irrelevant for the equilibrium constant of eq 2. The rotational partition function for an asymmetric top such as any glycerol conformer I is given by 6 where I A (I) , I B (I) , and I C (I) are the principal moments of inertia, h is the Planck constant and  ) 1/(k B T). The vibrational partition function is given by where j goes over the 36 vibrational frequencies ν j (I) . Finally the electronic partition function is given by where E g (I) is the (non degenerate) ground-state electronic energy of the Ith conformer. Using the factorization property of the molecular partition function, the equilibrium constant K IJ (eq 2) can be written as Using the ab initio data relative to the various conformers (all the ab initio data were obtained by the Gaussian98 package 7 ), i.e., inertia moments, vibrational frequencies, and ground-state electronic energies, the gas-phase partition func- tions (eqs 3-5) can be calculated. From these, via eq 6, the * To whom correspondence should be addressed. E-mail: procacci@ chim.unifi.it I h J (1) N J N I ) d J q J d I q I ) K IJ (2) q rot (I) ) π 1/2 ( 8π 2 h 229 3/2 (I A (I) I B (I) I C (I) ) 1/2 (3) q vib (I) ) ∏ j exp(-hν j (I) /2) 1 - exp(-hν j (I) ) (4) q elec (I) ) exp(-E g (I) ) (5) K IJ ) K rot K vib K elec ) q rot (J) q rot (I) q vib (J) q vib (I) q elec (J) q elec (I) (6) 11220 J. Phys. Chem. A 2000, 104, 11220-11222 10.1021/jp002677e CCC: $19.00 © 2000 American Chemical Society Published on Web 11/04/2000