T. G. Strand

Regularizing algorithm for determination of equilibrium geometry and harmonic force field of free molecules from joint use of electron diffraction, vibrational spectroscopy and ab initio data with application to benzene

Abstract A novel integrated algorithm is suggested for joint treatment of gas-phase electron diffraction and spectroscopic data. This algorithm develops the idea of the regularized quantum mechanical force field approach based on the theory of nonlinear illposed problems. The main advantage of the algorithm is that it provides a unique and stable solution for the equilibrium geometry and intramolecular harmonic force field of quasi-rigid systems. The check calculations were carried out with Oslo intensity data on benzene collected with improved precision. Infrared frequencies of benzene and its isotopomer were taken from the literature.

The molecular structure of benzene derivatives part 1. 4-Fluorobenzaldehyde by joint analysis of gas electron diffraction, microwave spectroscopy and ab initio molecular orbital calculations

Abstract The molecular structure of gaseous 4-fluorobenzaldehyde has been determined by a joint analysis of gas electron diffraction data, rotational constants from microwave spectroscopy, and constrained by results from ab initio calculations. The ab initio calculations have been performed at the HF 6-311 G ∗∗ and MP 2 6-31 G ∗ levels of theory. The planar Cs symmetry structure was found to be the only stable conformation. The torsion of the formyl group has been treated as a large-amplitude motion. The most important structure parameters (rg) from the joint analysis with estimates of 2σ (in parentheses) were: ( CC ) mean = 1.397(1) A , CF = 1.331(7) A , CC (= O ) = 1.488(7) A , CO = 1.195(5) A ,

Apparent wavelengths of the Oslo electron diffraction apparatus according to diffraction patterns from gaseous benzene

Abstract The electron wavelength of the short camera distance electron diffraction diagrams of benzene was calibrated against the CC distance of the molecule. This wavelength, when applied to the long camera distance data, repeatedly gives a CC distance about 0.3% longer than the applied calibration distance. The effect is demonstrated by the analysis of benzene data from eight plates recorded at each of the two applied camera distances. Our presently applied photometer procedures and numerical data reduction, which includes digital Fourier filtering of the photometer data, are described. A new variant of the autocorrelation power spectrum is illustrated for the benzene data.

Gas electron diffraction data: A representation of improved resolution in the frequency domain, a background correction for multiplicative and additive errors, and the effect of increased exposure of the photographic plates

Abstract An improved version of the previously proposed modified autocorrelation power spectrum is described. The enhanced resolution of this spectrum in the frequency domain is demonstrated for lead tetrachloride and benzene data. A background which may simultaneously correct gas electron diffraction data for both multiplicative and additive long periodic (low frequency) errors is suggested. Application of this background revealed systematic non-constant multiplicative errors in our data. The multiplicative corrections previously done to the calculated intensities of lead tetrachloride by modifications of the Pb scattering factor could now be substituted by a multiplicative background correction to the experimental intensities. For weakly exposed benzene data, the applied ‘blackness correction’ seemed to introduce a linear multiplicative correction of negative slope. The need for this correction disappeared for benzene data when the exposure of the photographic plates was increased.

The molecular structure of ortho- and meta-fluorobenzaldehyde by joint analysis of gas electron diffraction, microwave spectroscopy and ab initio molecular orbital calculations

Abstract The molecular structures of gaseous o -fluorobenzaldehyde and m -fluorobenzaldehyde have been determined by a joint analysis of gas electron diffraction data, rotational constants from microwave spectroscopy, and constrained by results from ab initio calculations (at HF/6-331G∗∗ level). The torsion of the formyl group has been treated as a large-amplitude motion. The most important structure parameters ( r g )) from the joint analysis with estimated total errors (in parentheses) are for o -fluorobenzaldehyde: ( C  C ) mean = 1.3999(2) A , C  F = 1.334(5) A , C  C ( O = 1.515(6) A , C  O = 1.216(3) A , ∠CC F C = 122.0(2)°, ∠CC CHO C = 120.3(6)° and for m -fluorobenzaldehyde: ( C  C ) mean = 1.394(2) A , C  F = 1.346(4) A , C  C ( O = 1.494(4) A , C  O = 1.201(2) A , ∠CC F C = 122.3(1)°, and ∠CC CHO C = 120.6(3)°. The scaled molecular force fields have been determined.

The molecular structure of a germacyclobutane by gas electron diffraction and ab initio molecular orbital calculations

Abstract The molecular structure of 1,1,3,3-tetramethylgermacyclobutane has been determined by gas electron diffraction supplemented by ab initio calculations at the HF/6–31G * and MP2/6-31G * levels. Structure refinement of a C S model with the differences between symmetry inequivalent Ge-C and C-C bond distances fixed at the HF values yielded the bond distances Ge-C = 197.5(3) and C-C = 156.7(2)pm (endocyclic) and Ge-C = 195.9(3) and C-C = 152.9(2)pm (exocyclic). The endocyclic valence angles are ∢CGeC = 75.3(2)°, ∢GeCC = 89.5(2)° and ∢CCC = 100.7(3)°. The exocyclic ∢CGeC = 108.8(8)°. The central ring is non-planar with a puckering angle of 24(2)°, the barrier to planarity is estimated to be V 0 = 4.2(8)kJ mol −1 . Optimisation of the structure of 1,1-dimethylgermacyclopropane at the HF/6-31G * level yields ∢CGeC valence angles of 47.5° (endocyclic) and 116.2° (exocyclic).

A digital fourier filter applied to the electron diffraction microphotometer data of gaseous benzene

Abstract A digital Fourier filter has been applied to the microphotometer data of six photographic plates of benzene. The sampling interval of the photometer corresponds to a maximum rotational frequency of about 73 A and frequencies above approximately 7.5 A are removed by the filter. Results from molecular intensities based on the filtered data are compared with results from the unfiltered ones. The average correlation has increased somewhat for the filtered data, but the reproducibility is improved. The least-squares standard deviations of the structure parameters are in general unchanged or smaller for the filtered data. Including contributions from three atomic scattering (single-double multiple scattering) according to theory, the agreement is improved by the expected amount and the structure parameters are unchanged. The possibility of systematic bonding effects beyond 5 = 6 rad A −1 are discussed in view of recent calculations for ethylene.