### Abstract:

Gas-phase electron-diffraction (GED) is an important analytical tool to experimentally determine thermally averaged bond distances. In recent years, improvements of spectroscopic techniques have largely phased out the use of GED techniques. We present improvements in GED calibration methods that enhance experimental precision and accuracy and show describe the experimental GED structural parameters of 1,1,3,3-tetramethylcyclobutene (TMCB) and spiropentane with the improved electron diffraction calibration methods above.
Calibration improvements that were conducted include of a precision transmission scanner in conjunction with powerful, public-domain image processing software (ImageJ). Procedures for finding an accurate center of the diffraction ring pattern are given and the software permits flexible determination of the intensity average of each radial circle or any chosen arc thereof. In addition, N2 is proposed as the ideal calibration molecule since at room temperature virtually all molecules are in the ground vibrational state. The result is ra = 1.10087 Å, with an uncertainty from fitting experiments of 0.00035 Å.
Data has been combined with recent spectroscopic rotational constants to determine the r0 structural parameters for spiropentane, C5H8. The structure has D2d symmetry and the results yield values of 1.105(2) Å for the CH bond length, 1.557(3) Ǻ for the distal CC bond length, and a somewhat smaller value of 1.482(1) Å for the four lateral CC bonds that connect to the central carbon atom. The HCH angle is 113.7(13) degrees and the HCH flap angle, defined as the angle of the HCH bisector and the distal CC bond, is 150.2(16) degrees. The results are in good accord with values from density functional calculations (B3LYP/cc-pVTZ) and resolve some questions about the structure reported in an earlier GED study, in particular about the HCH angle and anomalous rotational constants calculated for the structure.
According to theory, likely configurations of TMCB have either a planar ring of D2h symmetry or a nonplanar one of C2v symmetry. Our results suggest the D2h model is to be preferred. Dynamic averages (rα/Å; /deg), with estimated 2σ uncertainties, of the more important distances and angles in the D2h model are as follows. <C–H> = 1.080 (4), C1–C5 = 1.511 (8), C1–C2 = 1.563 (10), C2–C1–C4 = 88.4, C1–C2–C3 = 91.6 (7), C5–C1–C6 = 111.5 (12), and C2–C1–C5 = 113.8 (3). The large amplitude bending of the ring leads to a thermal average value of the folding equal to 22.8.

### Description:

The gas phase electron-diffraction (GED) technique has been the primary method used to expand our knowledge and understanding of gas-phase molecular structures. The technique yields interatomic distances and bond angles that are of use in both theoretical and experimental studies.
The GED structural parameters are thermal averages over all vibrational levels of a molecule that are occupied at the temperature of the experiment. Typical bond length accuracies are 0.01-0.004 Å and bond angles can be determined to a few tenths of a degree. In contrast, for small molecules, spectroscopic studies can give bond lengths of accuracy as good as 0.00001 Å for specific states, such as the vibrational ground state.
However spectroscopic measurements for a molecule can determine at most only three rotational constants, and hence only three structural parameters. Thus, for larger molecules, one would like to combine the results of both GED and spectroscopic experiments in determining the most accurate structures. To do this, one requires estimates of a number of small corrections which it is now possible to obtain from high-level quantum mechanical calculations. It is this approach that we have used in the work reported here.