The molecular packing of solid II cyclobutane by means of spectroscopic data and potential-energy calculations

Abstract

The molecular packing of solid II cyclobutane has been calculated starting from the knowledge of the site symmetry (point group D2) and of two possible symmetries of the primitive unit cell (D2 and D2h factor group symmetry), derived from analysis of the infrared and Raman spectra. Crystal potential energy has been calculated for 13 orthorhombic space groups using the packing program written by Williams. The calculation was based on a pairwise potential of Buckingam type, widely tested on a large number of hydrocarbon crystal structures and properties. The energy was calculated as a function of the unit cell parameters (length of the cell edges), considering the molecules as rigid bodies and leaving the crystal symmetry unchanged. The results show the packing corresponding to space group Ccca to have the lowest calculated potential energy. The spectroscopic results allowed some changes to be made in the previous assignment of the fundamental frequencies of cyclobutane and cyclobutane-ds. IntroductionSeveral low temperature infrared and Raman studies on molecular crystals have been carried out in recent years with the aim of determining the crystal structure when X-ray data were not available. In order to restrict the choice of the possible structures compatible with the spectral data, simple closest-packing arguments and, when available, the comparison between calculated and observed density, have often been used.A different approach to this problem concerns the calculation of the structure using the structural information obtained from the analysis of the crystal spectra. At any given temperature and pressure the most stable structure is governed by the arrangement of molecules that has the lowest free energy. Assuming the zero point lattice energy to be comparable for a number of possible close-packed structures, one can reasonably assume that the most probable structure is the one with the lowest calculated lattice energy.Cyclobutane offers an attractive possibility for this kind of investigation since: (i) the molecular geometry has been widely investigated; (ii) the molecule possesses only C and H atoms; (iii) infrared spectra in polarized E. CASTELLUCCI, M. G. MIGLIORINI AND P. MANZELLI 433 light of oriented crystals have been obtained, which are of help in deriving structural information. Point (ii) is very important for calculating the minimum energy crystal structure since different sets of semi-empirical atom-atom potential parameters exist in the literature which have been widely tested on a number of experimental crystal properties and structures of aromatic and aliphatic hydrocarbons (Williams, 1967). It is widely accepted that cyclobutane has a puckered equilibrium configuration with D2a symmetry and a dihedral angle of about 32 ° . The evidence for this has been given by electron diffraction experiments (Almenningen, Bastiansen & Skancke, 1961), by an unpublished vibrational analysis of Lord and Rea quoted by Lord & Nakagawa (L & N) (1963), by relative intensity measurements of CH2 rocking vibrat...

Spectra of Plastic and Disordered Crystals

“…These assignments are summarized in Table 6. The far infrared spectra were not as defmitive as the Raman spectra; however, the data were reasonably consistent with that previously reported by Castellucci et al [22]. For example, in the far infrared spectrum of the "light" compound, pronounced bands were observed at 100.3 and 86.7 cm-I with a possible additional one at 81.2 cm-I .…”

“…However, the spectral data reported by Castellucci et al [22] are in better agreement with our data than the data reported by Miller et al [23] Similarly, our data on cyclobutane-d8 (Fig. lOA) agrees well with that reported by Castellucci et al [22] for this isotope except that we did not observe the very weak line at 144 cm-I nor the weak broad line at 55 em-I. However, in our initial investigation we observed a weak line at 65 cm-l which disappeared with further purification of the sample.…”

“…For example, in the far infrared spectrum of the "light" compound, pronounced bands were observed at 100.3 and 86.7 cm-I with a possible additional one at 81.2 cm-I . These data were taken at 20 K and the frequencies for the two pronounced bands are about 5 cm-I higher than those reported previously [22] in which the spectrum was recorded with the sample at 77 K. These bands appeared to shift to 86.8, 75 and -69 cm-I with deuteration. The shift factors are consistent with these three bands being the infrared active librational modes.…”

“…[22] reported Raman lines at 249,220, 103,96 and 84 cm-l for cyclobutane in phase n at 77 K. At this temperature (75 K) we found lines at 255, 102, 89, 45 and 32 cm-l with no indication of a line at 220 cm-1 nor a third line between 80 and 105 em-I. However, the spectral data reported by Castellucci et al [22] are in better agreement with our data than the data reported by Miller et al [23] Similarly, our data on cyclobutane-d8 (Fig. lOA) agrees well with that reported by Castellucci et al [22] for this isotope except that we did not observe the very weak line at 144 cm-I nor the weak broad line at 55 em-I.…”

“…Castellucci. et al [22] investigated the molecular packing of solid phase IT cyclobutane and cyclobutane-dS by means of intramolecular spectroscopic data and concluded that the crystal was orthorhombic with space group Ceca (DJ:) with two molecules per primitive cell. In this study.…”