In press (DOI:10.1016/j.molstruc.2012.07.051) in the Journal Of Molecular Structure. May go down in history as a hardest-fought paper acceptance. In a similar line of research as the -annulene study, but exploring the infinite limit of geometry and bond length alternation energy barrier for this infinite case. If the numbers are correct, the infinite polyene chains (polyacetylene) do not exhibit bond length alternation because the Peierls' barrier between the single-double and double-single bond alternate minima is below the vibrational zero-point level. Plenty of ramifications.
Bruce S. Hudson and Damian G. Allis
Abstract. The potential energy of the infinite periodic chain model of polyacetylene (pPA) is symmetric with two equivalent minima separated by the Peierls' stabilization barrier. In this work it is shown how an energy scale and vibrational energy levels for this highly anharmonic Peierls' degree of freedom can be estimated. Attention is given to the potential energy increase for large deformations. The Born-Karman treatment of translational symmetry is applied. Two empirical methods and a direct periodic boundary condition (PBC) density functional theory (DFT) calculations are in semi-quantitative agreement, each leading to the conclusion that pPA has a zero-point level that is above the Peierls' barrier. The argument does not depend critically on the barrier height or the other parameters of the model or the computation method. It is concluded that pPA will not exhibit bond alternation and that the zero-point average geometry does not preclude possible conductivity.
In press (DOI:10.1016/j.molstruc.2012.05.016) in the Journal Of Molecular Structure (Volume 1023, 12 September 2012, Pages 212-215) in the special issue: MOLECULAR VIBRATIONS AND STRUCTURES: THEORY AND EXPERIMENT â€” A collection of papers dedicated to Professor Jaan Laane on the occasion of his 70th birthday.
This paper on the "actual" geometry of -annulene is part of several larger stories addressing a larger polyene (or larger-polyene) issue. First among these is the meaning of experimental results obtained by various spectroscopic methods (in this case, using previous X-ray, Raman (with the C2 (blue) and D6h (red) simulated spectra shown in the image above), IR, and NMR data that produce different results within the limitations of the methods to study the single molecule). Second is the quality of the theoretical method for reproducing certain types of spectroscopic data. In the case of the [N]-annulene series, the ever-present B3LYP density functional is found to produce the time-average geometry of -annulene found in X-ray data, but another density functional (in this case, KMLYP), finds that bond-alternate minima exist. Third is the importance of the zero-point level in the treatment of systems for which bond-alternate geometries exist with transition-state barriers calculated to be below the zero-point level in the classical approximation of nuclear positions (the Born-Oppenheimer Approximation).
NOTE 1: The KMYLP density functional is called in Gaussian with the following keyword set:
BLYP iop(3/76=1000005570) iop(3/77=0000004430) iop(3/78=0448010000)
NOTE 2: Optimization and Frequency calculations must be performed as TWO SEPARATE CALCULATIONS. The iop-called density functional does not carry itself over between opt + freq (or other properties) in the same input file. If you opt + freq in the same input file, you will Opt with KMLYP but freq with BLYP. This will be obvious by the number of imaginary modes.
Bruce S. Hudson and Damian G. Allis
Abstract. -annulene has been of great interest from the structural point of view of its bond alternation. High-level calculations based on structures selected for agreement with NMR spectra lead to a bond-alternate C2 form over a non-alternating planar D6h structure deduced from diffraction, infrared (IR) and electronic spectral studies. Here it is shown that computed Raman spectra for the D6h and C2 forms are expected to be very different. However, two equivalent non-D6h bond-alternate minima of D3h or C2 geometries are separated by only a small barrier along a motion that involves CC stretching and compression. It is shown here that the zero-point level is above the barrier for this species. In light of that fact, the NMR calculations are reconsidered with inclusion of zero-point level averaging.