Behavior of Occupied and Void Space in Molecular Crystal Structures at High Pressure

Abstract

We report a Monte Carlo algorithm for calculation of occupied (“network”) and unoccupied (“void”) space in crystal structures. The variation of the volumes of the voids and the network of intermolecular contacts with pressure sensitively reveals discontinuities associated with first- and second-order phase transitions, providing insights into the effect of compression (and, in principle, other external stimuli) at a level between those observed in individual contact distances and the overall unit cell dimensions. The method is shown to be especially useful for the correlation of high-pressure crystallographic and spectroscopic data, illustrated for naphthalene, where a phase transition previously detected by vibrational spectroscopy, and debated in the literature for over 80 years, has been revealed unambiguously in crystallographic data for the first time. Premonitory behavior before a phase transition and crystal collapse at the end of a compression series has also been detected. The network and void volumes for 129 high-pressure studies taken from the Cambridge Structural Database (CSD) were fitted to equation of state to show that networks typically have bulk moduli between 40 and 150 GPa, while those of voids fall into a much smaller range, 2–5 GPa. These figures are shown to reproduce the narrow range of overall bulk moduli of molecular solids ( ca. 5–20 GPa). The program, called CellVol, has been written in Python using the CSD Python API and can be run through the command line or through the Cambridge Crystallographic Data Centre’s Mercury interface.

Second Order Phase Transition and Stabilizing CH···H and CH···S Interactions in Naphthyl End-Capped Bithiophene at 3.5 GPa

“…As such, compression begins to favor the lower energy pathway along the chain direction from 4.0 GPa to accommodate the increasing repulsion terms formed between the chains as void space closes up. The transition in NaT2 at ∼3.5 GPa reflects a change in the compression pathway, rather than a well-defined structural change, a similar effect was seen in the prototypical fused-ring system, naphthalene at 2 GPa …”

“…The transition in NaT2 at ∼3.5 GPa reflects a change in the compression pathway, rather than a well-defined structural change, a similar effect was seen in the prototypical fused-ring system, naphthalene at 2 GPa. 51 The only structural feature differentiating phases I and I′, is that of the bifurcated S•••H interaction in contacts E′ and F′ (S1•••H2C2, 2.99 Å, ∠= 108°) as depicted in Figure 4. All other contacts remain relatively unchanged, only they become shorter (see Table 1).…”

The Effect of High Pressure on Polymorphs of a Derivative of Blatter’s Radical: Identification of the Structural Signatures of Subtle Phase Transitions

“…Structures were visualized in Mercury and DIAMOND. , The principal axes of strain were calculated using STRAIN and EoSFit7-GUI was used for equation of state fitting. The void space analyses were carried out with Mercury and CellVol …”

“…We refer to these as the "network" and "void" regions, respectively, and their volumes are V net and V void ; the structural signature of a high-pressure phase transition can be clearer in these quantities than in the overall unit cell volume or unit cell dimensions. 38 Attempts to fit V net and V void to third order Birch−Murnaghan and Vinet equations of state respectively are shown for each polymorph in Figures S8 and S9 in the Supporting Information, with numerical results presented in Table 4. The trends in the void volumes are smooth for both and adequately fitted to single equations of state with χ 2 values near unity.…”

Correction to “The Effect of High Pressure on the Crystal Structures of Polymorphs of l-Histidine”

“…Notwithstanding the errors outlined above, we remain of the view that the analysis of trends in void and network volumes remains a useful and sensitive means for the analysis of high-pressure crystal structures, with further information being available in ref .…”