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Dynamic analysis of the molecules with large-amplitude motions (LAM) based on the pseudo-conformer approach has been successfully applied to various molecules. Floppy linear molecules present a special class of molecular structures that possess a pair of conjugate LAM coordinates but allow one-dimensional treatment. In this paper, previously developed treatment for the semirigid molecules is applied to the carbon suboxide molecule. This molecule characterized by the extremely large CCC bending has been thoroughly investigated by spectroscopic and ab initio methods. However, the earlier electron diffraction investigations were performed within a static approach, obtaining thermally averaged parameters. In this paper we apply a procedure aimed at obtaining the short list of self-consistent reference geometry parameters of a molecule, while all thermally averaged parameters are calculated based on reference geometry, relaxation dependencies and quadratic and cubic force constants. We show that such a model satisfactorily describes available electron diffraction evidence with various QC bending potential energy functions when r.m.s. CCC angle is in the interval 151 ± 2°. This leads to a self-consistent molecular model satisfying spectroscopic and GED data. The parameters for linear reference geometry have been defined as re(CO) = 1.161(2) A and re(CC) = 1.273(2) A.

There exists a noticeable disagreement in the difference of axial and equatorial bond lengths in D 3h symmetry arsenic and phosphorus pentafluorides between the GED data and high level quantum chemical results. In order to resolve this disagreement, a new structural analysis of the original experiment of (Clippard & Bartell, Inorg. Chem., 9 (1970) 805–811) was undertaken on the basis of modern approach incorporating spectroscopic evidence and quantum chemical information and allowing for intramolecular large-amplitude motion. The results of the analysis prove the internal insufficiency of the experimental material in the description of the accurate positions of the peaks on the radial distribution function. Additional experimental investigation of pentahalide molecules, especially at high temperatures, is of interest.

The equilibrium structure of the 2-chloro-3-nitrothiophene molecule and the internal rotation of the nitro group have been studied in gas phase using electron diffraction data and quantum chemical calculations in the framework of the large-amplitude motion model for internal rotation. Quantum chemical calculations at the MP2 and B3LYP levels of theory with various Pople and Dunning basis sets predict the planar minimum energy molecular conformation, with the internal rotation barrier height in the interval 1140–1560 cm −1 . The experimental GED data are consistent with the dynamic model governed by the twofold cosine potential energy function with the barrier height in the range from 600 to 1400 cm −1 . The main equilibrium structure parameters are as follows (values in parentheses correspond to 3 times standard deviations): r e (N O) = 1.225/1.227(3) A, r e (C − C)/ r e (C − N) = 1.362/1.376/1.403/1.438(3) A, r e (C − Cl)/ r e (C − S) = 1.700/1.712/1.715(2) A, ∠ e C2SC5 = 92.2 (5)°, ∠ e C3C2S = 110.8 (6)°, ∠ e C4C5S = 111.3 (5)°, ∠ e C3C4C5 = 113.0 (7)°, ∠ e C2C3C4 = 112.7 (8)°, ∠ e C3NO11 = 116.9(6)°, ∠ e C3NO10 = 118.5 (6)°, ∠ e SCCl = 118.6 (5)°, ∠ e C4C3N = 121.8 (7)°, ∠ e ONO = 124.6(6)°, ∠ e C2C3N = 125.1 (6)°, ∠ e C3C2Cl = 130.7 (6)°. Thermally averaged parameters are provided for comparison with the results of traditional studies.

In this paper, the equilibrium structural parameters of the 2-nitropropane molecule and the barrier of internal rotation of the nitrogroup are determined from the gas electron diffraction data, with the use of quantum chemistry calculations and experimental vibrational frequencies, in the framework of the large-amplitude motion model for internal rotation. Quantum chemistry calculations at the MP2 and B3LYP levels of theory with various Pople and Dunning basis sets unambiguously predict the same minimum energy molecular conformation, with relatively close values of internal rotation barrier (375–525 cm −1 ). The results of present analysis show that the minimum of the potential function of the nitrogroup internal rotation is located in syn -H position when one of the oxygen atoms eclipses hydrogen atom that does not belong to any of CH 3 groups (dihedral angle H–C–N–O is zero). It has also been found that internal rotation is hindered, with the barrier height in the range of 220–560 cm −1 (0.6–1.6 kcal/mol) with the most probable value near 380 cm −1 (1.1 kcal/mol). The main equilibrium structure parameters in syn -H configuration are as follows (values in parentheses correspond to 3 times standard deviations): r e (C–C) = 1.516(5) A, r e (C–N) = 1.501(5) A, r e (N O) = 1.225(4) A, ∠ C–C–N = 108.7 ( 1.0 ) ° , ∠ O N O = 124.8 ( 0.4 ) ° . We also provide thermally averaged parameters for comparison with the results of previous studies.

Studies of the molecular structure and spectra of the lower nitroalkanes are complicated due to hindered internal rotation of the nitro group around the C N bond. In the present work, the structure of nitroethane molecule is determined from electron diffraction (ED) data supplemented by results of quantum chemical calculations within the model accounting for the large-amplitude motions and anharmonicity of vibrations in the rigid fragments. Quantum chemical calculations at the MP2, QCISD and B3LYP levels of theory result in contradictory conclusions regarding the location of the minimum of internal rotation potential energy function and potential barrier height. In the ED analysis, parameters of equilibrium geometry were refined simultaneously with scaling of quantum chemical force matrix aimed at fitting experimental vibrational frequencies. The data processing has shown the minimum of the potential energy function of internal rotation of NO 2 group corresponding to the syn -C molecular configuration with torsional angle τ (C C N O) = 0°. Rotation of the nitro group was found to be slightly hindered, with potential energy barrier height in the range of 50–200 cm −1 (with the most probable value near 120 cm −1 ). The refined parameters of equilibrium molecular configuration are the following: r e (C C) = 1.509(3) A, r e (C N) = 1.503(3) A, r e (N O) = 1.213(3) and 1.215(3) A, ∠ e (C C N) = 112.3(9)°, ∠ e (O N O) = 125.9(5)°.

A flexible self-consistent approach based on the adiabatic separation between large- and small-amplitude motions has been developed for the joint treatment of gas-phase electron diffraction (ED) and spectroscopy data. The Hamiltonian developed gains versatility by directly proceeding from assumed model properties to energy levels and wavefunctions. In addition to the vibrational terms, it explicitly includes rotational effects as well as interactions between overall rotation and intramolecular motion. A particular form of a Hamiltonian is specified by the system to be considered. If the vibrational energy is much higher than rotational energy, the latter can be separated and treated conventionally as perturbation. Six-membered ring planar floppy molecules 1,4-cyclohexadiene and 1,4-dioxin (1,4-dioxacyclohexa-2,5-diene) were selected for illustration. Large-amplitude approach described below and previously developed technique based on the general framework of rigid molecules with account for anharmonicity have been compared in predicting theoretical ED intensities for these molecules. We conclude that no noticeable deviations between ED intensities obtained using the two mentioned theoretical approaches have been observed when large-amplitude vibrations were governed by the approximately quadratic potential function (the case of 1,4-cyclohexadiene) while the case of quartic potential (for 1,4-dioxin) resulted in significantly different ED patterns.

Equilibrium and thermal average structure of 1,4-disilacyclohexa-2,5-diene (DSCHD) was determined by applying procedures that have been recently developed for joint treatment of gas phase electron diffraction and molecular spectroscopy data guided by ab initio calculations. Both large amplitude motion and anharmonic vibrational effects were taken into account. Similar structural results were obtained by considering DSCHD molecule as a unique equilibrium conformer and as a set of quasi-conformers describing large amplitude motion. The determined equilibrium structural parameters for DSCHD (planar configuration) are: r e ( Si – C )=1.861(2) A , r e ( CC )=1.346(3) A , r e ( Si – H )=1.498(10) A , r e ( C – H )=1.074(10) A , ∠(C–Si–C)=109.9(3)°, ∠(H–CC)=116.7(10)°, and ∠(H–Si–H)=107.9(10)°. Uncertainties given in parentheses include three times standard deviation and a systematic error.

The equilibrium molecular geometry of thiophene has been determined from a combination of gas-phase electron diffraction, vibrational and microwave data and ab initio and DFT calculations. The quadratic and cubic force constants of thiophene calculated theoretically and empirically improved by harmonic scale factors were incorporated in the analysis in which equilibrium distances and harmonic scale factors were refined simultaneously. The diffraction intensities were calculated by the use of first-order perturbation theory. The commonly used r a distances and amplitudes of vibration were also estimated and found to agree reasonably well with those from an earlier investigation. Anharmonic phase shift parameters for all atom pairs and the various distance correction terms are presented.

The use of ab initio methods has been investigated for obtaining physically meaningful anharmonic force fields applicable in structure analysis of molecules by electron diffraction. The quadratic and cubic force constants for the sample molecule SF 6 chosen as a suitable test case were theoretically estimated and improved by an empirical scaling based on a quadratic force constant scale factors. It was confirmed that if theoretical calculations are made with well selected basis sets the accuracy of the individual values of the computed cubic constants established by reference to precise spectroscopic data is practically sufficient to experimentally determine the accurate equilibrium S–F distance and to theoretically estimate the amplitudes of vibration and the phase shift parameters for all internuclear distances. Calculations based on a Morse-like anharmonic model function were also performed for comparison. The present calculations show that determination of an accurate equilibrium molecular structure by electron diffraction is possible through the appropriate combination of experimental and theoretical data. The best equilibrium geometry results, if empirically scaled ab initio quadratic and cubic force constants are used in a regularizing algorithm developed earlier for the effective interaction of electron diffraction with vibrational and microwave spectroscopy techniques.

The previously developed integrated algorithm for the joint treatment of gas-phase electron diffraction and vibrational spectroscopic data is extended to include systems with large-amplitude oscillatory motion. In addition, the treatment is augmented by the inclusion of microwave rotational constants. As in the previous work, the analysis of data from experimental sources is guided by quantum mechanical molecular geometry and force field optimization results. The computed force field matrix can be corrected empirically with the aid of suitable scale factors. Centrifugal distortion corrections to interatomic distances are included. The standard deviations of the parameters determined and the correlation coefficients can now be estimated. The principal design of the developed computer program is outlined, and some methodological problems associated with diffraction analysis of molecules with large-amplitude motion are discussed. To provide an example of a problem susceptible to attack by the present method an account is made of the re-analysis of diffraction data for 4-fluorobenzaldehyde collected earlier on the Balzers apparatus in Oslo.

An approximate method for diffraction analysis of equilibrium geometries of molecules which extensively uses dynamical information from computational sources is developed. The method obviates refinement of the harmonic force field of a molecule by using the eigenvector matrix obtained from mopac semiempirical calculations of the PM-3 type and spectroscopically observed or scaled mopac vibrational frequencies. The frequency scale factors were adjusted in the course of the analysis of diffraction data. A simple account for anharmonicity was also made by the aid of the Morse oscillator potential function. The method was checked against analysis of diffraction data for the sample molecules CO 2 , SO 2 and SF 6 .

An approximate approach to the structural analysis of molecules exerting moderately anharmonic motion based on the model potential function involving only a single Morse-like parameter for the bonded atom pair is developed. Also suggested is the simplified “quasi-diatomic” approximation. The natural curvilinear internal coordinates were used in formulating the molecular potential function. The check calculations were performed with non-photographic intensity data on CO2 and SO2 taken from the literature. It is shown that a sufficiently reliable determination of equilibrium geometry of molecules in anharmonic approximation is feasible provided that the diffraction technique is supplemented by spectroscopic methods.

A method of analysis of molecules by electron diffraction in terms of the intramolecular potential function is presented. The method is based on the cumulant representation of the molecular scattering function and a perturbation solution of the vibrational problem. Special care has been taken in difficulties involving Fermi resonances. A test of the performance of the devised theory is provided by comparison of the calculated temperature dependence of ra distances in SF6 with available experimental data. The proposed scheme of diffraction analysis, providing due facility for incorporation of relevant spectroscopic information, is checked by treatment of published intensity data for SO2 and SF6.