Experimental Equilibrium Structures: Application of Molecular Dynamics Simulations to Vibrational Corrections for Gas Electron Diffraction

Abstract

A general method is described that allows experimental equilibrium structures to be determined from gas electron diffraction (GED) data. Distance corrections, starting values for amplitudes of vibration and anharmonic "Morse" constants (all required for a GED refinement) have been extracted from molecular dynamics (MD) simulations. For this purpose MD methods have significant advantages over traditional force-field methods, as they can more easily be performed for large molecules, and, as they do not rely on extrapolation from equilibrium geometries, they are highly suitable for molecules with large-amplitude and anharmonic modes of vibration. For the test case Si(8)O(12)Me(8), where the methyl groups rotate and large deformations of the Si(8)O(12) cage are observed, the MD simulations produced results markedly superior to those obtained using force-field methods. The experimental equilibrium structure of Si(8)O(12)H(8) has also been determined, demonstrating the use of empirical potentials rather than DFT methods when such potentials exist. We highlight the one major deficiency associated with classical MD--the absence of quantum effects--which causes some light-atom bonded-pair amplitudes of vibration to be significantly underestimated. However, using C(3)N(3)Cl(3) and C(3)N(3)H(3) as examples, we show that path-integral MD simulations can overcome these problems. The distance corrections and amplitudes of vibration obtained for C(3)N(3)Cl(3) are almost identical to those obtained from force-field methods, as we would expect for such a rigid molecule. In the case of C(3)N(3)H(3), for which an accurate experimental structure exists, the use of path-integral methods more than doubles the C-H amplitude of vibration.

Functionalized Bis(pentafluoroethyl)phosphanes: Improved Syntheses and Molecular Structures in the Gas Phase

“…On the one hand, it is well known that classical MD underestimates vibrational amplitudes and corrections for light atom pairs (see ref. [29,30] ), but corrections for C-C pairs (which have reduced masses even smaller than C-F) are in very good agreement with SHRINK. On the other hand, in our experience, SHRINK calculations with a cubic force field can sometimes produce unreasonably large corrections for bonded distances in molecules with low-frequency vibrational modes.…”

“…A novel approach involves calculating vibrational corrections by using molecular dynamics (MD). [29,30] The last two methods were applied in the two structure determinations in this contribution, and the MD method has been further developed in this context.…”

“…It is also interesting to compare the anharmonic vibrational corrections computed by two approaches, namely by molecular dynamics [29,30] and the SHRINK procedure, [31] by using potential energy third derivatives. The corrections (k = r a -r e ) for all the bonded distances in (C 2 F 5 ) 2 PH calculated by these two methods are available in the Supporting Information.…”

Predicting anisotropic displacement parameters using molecular dynamics: density functional theory plus dispersion modelling of thermal motion in benzophenone

“…However, the principal disadvantage of LD calculations is that they are nearly always performed in the harmonic limit. At high temperatures, attempting to fit an anharmonic potential with a harmonic one may lead to spurious results, as we have seen for an equivalent situation in the gas phase (Wann et al, 2008(Wann et al, , 2009.…”

“…It is common in gas electron diffraction studies to use theoretically determined vibrational and structural information as restraints (Blake et al, 1996;Brain et al, 1996;Mitzel & Rankin, 2003) and corrections (McCaffrey et al, 2007;Sipachev, 1985Sipachev, , 2001Sipachev, , 2000Wann et al, 2009) to counter the limited nature of the data. Our recent work on vibrations in crystals has focused on using molecular dynamics (MD) simulations to probe the nature of anharmonic thermal motion, providing corrections that convert time-averaged experimental structures to equilibrium ones (Reilly et al, 2007(Reilly et al, , 2010b, as well as model data sets for assessing new anharmonic Debye-Waller factors Reilly, Morrison, Rankin & McLean, 2011).…”