Theoretical prediction of vibrational spectra. Scaled quantum mechanical (SQM) force field for fluorobenzene

The complete harmonic force field of fluorobenzene has been determined from ab initio Hartree-Fock calculations using the 4–21 Gaussian basis set. As force constants are systematically overestimated at this level of theory, the directly calculated force field was scaled by empirical factors taken over from benzene and methylfluoride. Except for a slight overestimation of the CF stretching frequency, the scaled quantum mechanical (SQM) force field obtained in this way reproduces the experimental fundamental frequencies of the parent molecule and two deuterated isotopomers within 20 cm⁻¹ (with mean deviations below 12 cm⁻¹), and experimental assignments are analyzed on this basis. Theoretical i.r. intensities reproduce the main features of the spectra fairly well.     

Vibrational spectra of 1,3-dideuterioallene and normal mode calculations for allene

Infrared and Raman spectra of 1,3-d₂-allene were measured and fundamental frequencies were assigned. The frequencies were used with previously published data for the d₀, d₄, d₁ and 1,1,-d₂ isotopomers of allene in force field calculations. A new ab initio quantum mechanical force field calculated at the 6-31G** level was scaled to fit the anharmonic fundamental frequencies and used to provide some of the interaction constants for a second, conventionally refined force field.     

Theoretical prediction of vibrational spectra. The a priori scaled quantum mechanical (SQM) force field and vibrational spectra of pyrimidine

The complete harmonic force field of pyrimidine has been computed at the ab initio Hartree—Fock level using a 4–21 Gaussian basis set. In order to compensate the systematic overestimations of the force constants at the aforementioned level of quantum mechanical approximation, the theoretical force constants were empirically scaled by using nine scale factors. (The values of all these scale factors were previously determined by fitting the theoretical force field of benzene to the observed vibrational spectra of benzene.) The resulting a priori scaled quantum mechanical (SQM) force field is regarded as the most accurate and physically the most correct harmonic force field for pyrimidine. This force field was then used to predict the vibrational spectra of pyrimidine-h₄ and pyrimidine-d₄. On the basis of these a priori vibrational spectra uncertain assignments have been confidently resolved. After a few reassignments, the mean deviations between the experimental and calculated frequencies are below 9 and 18 cm⁻¹ for the non-CH stretching in-plane and the out-of-plane vibrations, respectively. Computed IR intensities are generally in agreement with experiments at a qualitative level.     

Vibrational spectra and a potential function for 3-chlorocyclopropene and its various deuterated modifications

I.r. and Raman spectra have been obtained for 3-chlorocyclopropene and 3-chlorocyclopropene-d₃ under a variety of experimental conditions. For mixtures of the two d₂ isotopic species and of the two d₂ isotopic species, only infrared spectra have been recorded. The pattern of gas-to-condensed-phase frequency shifts is interpreted as evidence of hydrogen bonding for the CH hydrogen atoms. A complete assignment of the vibrational fundamentals for the d₀ and d₃ species is derived from the spectra. For the d₀ species these frequencies (in cm⁻¹) are: (a′) 3171, 3029, 1633, 1266, 1141, 913, 713, 591, 345; (a″) 3140, 1034, 1017, 866, 840, 349. With guidance from normal coordinate calculations 59 of the 60 fundamentals for the d₁ and d₂ species are assigned. The full set of 89 observed frequencies has been used to fit an 18-parameter valence-type potential function. In comparison with the force constants for CC and CC stretching of cyclopropene and 3,3-difluorocyclopropene, the CC force constants of 3-chlorocyclopropene show changes similar to those expected for a substitution of a single fluorine atom. This finding is consistent with a σ-acceptor role for the mechanism of the interaction of fluorine and chlorine atoms with the cyclopropene ring system.     

Scaled quantum mechanical (SQM) vibrational analysis of AlCl3, Al2Cl6 and the free ion AlCl−4

A series of basis sets are evaluated for AlCl₃ and AlCl⁻₄, and a common scaling factor derived for these compounds was transferred to Al₂Cl₆. 6-31G* calculations, scaled with a common factor of 0.92, give a good fit to all vibrational frequencies for AlCl₃, AlCl⁻₄ and Al₂Cl₆, and there is also a qualitative fit between calculated and observed IR intensities. Extending the basis set does not lead to significant improvements, either for the geometry or for the vibrational frequencies. The calculations verify earlier assignments based on general valence force fields and predict frequencies for some unobserved bands. The SQM force fields for aluminium chlorides show large similarities with the isoelectronic thiophosphates; the main deviations can be attributed to more ionic bonds in the aluminium chlorides. A significant influence on the out-of-plane vibration in AlCl₃ by the basis set on the d-orbitals may indicate that π_dp bonding plays a role. A remarkable and unexpected basis set sensitivity is found for the ν₆(B_1g) ring vibration in Al₂Cl₆.     

Ab initio study of the vibrational assignment and force field of thiosemicarbazide-d0 and -d5

The complete harmonic force field and optimized geometry of thiosemicarbazide have been calculated at the ab initio Hartree—Fock level using the 3-21G basis set. On the basis of this, the frequencies of thiosemicarbazide-d₀ and -d₅ and their ¹⁵N isotopic molecules have been calculated. The calculated frequencies and their band assignments are utilized to critically examine our previous experimental assignments which were based on normal coordinate calculations. The theoretical IR and Raman intensities, together with qualitative experimental band intensities, are also presented.     

Vibrational spectra and normal coordinate analysis of CF3 compounds : XXXIV. The bis(trifluoromethyl)difluoroborate anion: X-ray structure of Cs[(CF3)2BF2]

The ¹⁰B and ¹¹B IR and Raman spectra of the [(CF₃)₂BF₂]^? anion are reported, assigned, and used to determine a quadratic local symmetry force field via a normal coordinate analysis. The crystal structure of Cs[(CF₃)₂BF₂] (P2₁/m, a 5.958(1), b 7.628(1), c 8.2997(9) Å, β 100.50(1)°, Z = 2, d_c 2.863 g cm^?3 has been determined by X-ray diffractometry. The most important force constants are f(BC) 3.68 × 10², f(BF) 4.17 × 10² and f(CF) 4.85 × 10² N/m, the respective mean bond lenghts being 1.618, 1.391 and 1.353 Å. The FBF and CBC bond angles are 108.1(4) and 113.6(5)°, respectively. Apparently because of Cs?F(B, C) interactions, one BC bond has a staggered and the other an eclipsed conformation in the solid state.     

Dynamic Jahn–Teller effect and average structure of dicyclopentadienylcobalt, (C5H5)2Co,studied by gas phase electron diffraction

The molecular structure of (C₅H₅)₂Co has been determined by gas phase electron diffraction. The best agreement between calculated and experimental intensity curves is obtained with a model with eclipsed C₅H₅ rings (symmetry D_5h), but a model with staggered rings (symmetry D_5d) cannot be ruled out. The mean CoC and CC bond distances are 2.119(3) Å and 1.429(2) Å respectively. The average angle between the CH bonds and the C₅ ring is 2.1(0.8)°. The value obtained for the CC vibrational amplitude, l(CC) = 0.055(1) Å, is significantly larger than the amplitude calculated from a molecular force field and the corresponding amplitudes in (C₅H₅)₂Fe and (C₅H₅)₂Ni determined by electron diffraction, and confirms the presence of a dynamic Jahn—Teller effect of the magnitude calculated from ESR data. The average structure is compared with those of the metallocenes of the other first row transition elements.     

Fourier transform infrared spectra of three titanium tetrachloride-ethyl benzoate complexes. Assignment based on five isotopic homologues and extension of the ethyl benzoate force field

FTIR spectra (200–1750 cm⁻¹) are given for (TiCl₄EB)₂, (TiCl₄)₂EB and TiCl₄EB₂, where EB is ethyl benzoate. A full assignment is given for (TiCl₄EB)₂ based on extension of an ethyl benzoate force field and four isotopically labelled complexes with ¹⁸Ocarbonyl-EB, d₅-EB, Ed₅-B and d₅-Ed₅-B. There is no evidence for bidentate complexation or complexation through the ether oxygen in any of the complexes. A strong coupling between the αCO stretching vibration and the ethyl group deformations can make simplified interpretations of differences between spectra misleading.     

Emission spectra of supersonically cooled methyldiacetylene cations

The ā²E → X?²E (Σ= + $\text{1}\text{2}$, - $\text{1}\text{2}$) electronic transitions of rotationally/vibrationally cooled CH₃CCCCH^- cation, as well as the d₁-/d₃-/d₄-substituted species, were studied by emission spectroscopy. Ion emission was obtained by electron impact on the neutral species seeded in a helium supersonic free jet. Vibrational frequencies in both electronic states are inferred to within ±1 cm^-1. Spin-orbit splittings are observed and interpreted on the basis of non-linear vibronic couplings. Rotational subbands are observed, yielding rotational and Coriolis parameters as well as rotational temperatures.     

Infrared and Raman spectra and normal coordinate analysis of trans-1,2-dicyanocyclopropane and its deuterated isotopomers

Infrared and Raman spectra are presented for trans-1,2-dicyanocyclopropane and its 1,2-d₂- and 3,3-d₂-isotopomers. Most of the d₀ assignments agree with previous assignments of Strumpf and Dunker encompassing 26 of the 27 fundamentals. The 1,2-d₂ assignments are similar, but for the 3,3-d₂ species only 11 bands could be assigned. A complete ab initio quantum mechanical force field has been calculated for this molecule at the 6-31G* basis set level. This force-field was scaled and least-squares optimized using eight parameters for functionally related diagonal force constants and their geometric mean for off-diagonals. Both theoretical minimum energy and “experimentally corrected” geometries were used with no significant difference in results. An earlier calculation with a 4-31G basis set gave a similar frequency fit but different scaling factors. As an alternative approach, the scaled ab initio force field, was also used as a starting point for a more conventional refinement of 27 force constants which had a significant influence on the potential energy distribution. The remainder were fixed at the scaled ab initio values. This empirical force field resulted in a fit to 65 fundamentals of d₀, 1,2-d₂ and 3,3-d₂ to < 1% average error.     

Theoretical study on the structures,force field,and vibrational spectra of cyclooctatetraene and cyclooctatetraene-d8

The structures and force field of 1,3,5,7-cyclooctatetraene (COT) have been studied using ab initio theory at the SCF level with the 4-21G basis set. The quadratic force field of the D_2d structure obtained by systematic scaling of the ab initio force constants successfully reproduces the observed frequencies of COT and COT-d₈ with a mean deviation of less than 10 cm⁻¹ for non-CH stretching modes. On the basis of the calculated results, assignments of the fundamental vibrations are examined. The normal mode υ₅ is reassigned to a weak band at 758 cm⁻¹ in the Raman spectrum of COT and to a weak band at 591 cm⁻¹ in the Raman spectrum of COT-d₈. The calculations favor the assignment of υ₂₆ given by Lippincott et al. [J. Am. Chem. Soc. 73, 3370 (1951)] over the revised assignment of Perec [Spectrochim. Acta 47A, 799 (1991)]. The calculations also furnish reliable prediction for the inactive A₂ fundamentals of COT and COT-d₈. The fundamental frequencies and IR and Raman intensities of ¹³CC₇H₈, which constitutes about 9% of COT in natural abundance, are also calculated. Only ν₁₀ (calculated at 908 cm⁻¹) of the formal inactive A₂ modes has appreciable Raman intensity (0.23 Å⁴/amu). A spectral feature due to this fundametal is identified in the liquid Raman spectrum of Tabacik and Blaise [C. R. Acad. Sci. Ser. II 303, 539 (1986)] as a weak peak at 908 cm⁻¹.     

Vibrational and conformational analysis of n-propylamine by means of i.r. spectroscopy and ab initio MO calculations

The gas-phase i.r. absorption spectra of normal and amino-deuterated n-propylamine were observed. Most of the observed bands were assigned with the help of ab initio MO calculations for the normal frequencies. The ab initio force constants were scaled to fit the observed spectrum by a least squares method. The existence of five rotational isomers is suggested from an analysis of the NH₂ wagging and torsion bands. The gauche-conformers about the CN axis are found to occupy about 70 % of all n-propylamine molecules, and the gauche-conformers about the CC axis are found to be more abundant than the trans-conformers.     

A vibrational molecular force field of model compounds with biological interest—III. Harmonic dynamics of α- and β-d-galactose in the crystalline state

The infrared spectra of α- and β-d-galactose were recorded, both in the mid-IR range (4000-500 cm⁻¹) and in the far-IR (500-50 cm⁻¹). The Raman spectra were also obtained. These spectra constitute the basis of a crystalline-state force field established for these two molecules through a normal coordinate analysis. A modified Urey—Bradley—Shimanouchi force field was combined with an intermolecular potential energy function which includes van der Waals interactions, electrostatic terms and an explicit hydrogen bond function. The force constants were varied, so as to obtain an agreement between the observed vibrational frequencies and the calculated ones of α-d-galactose. The force field obtained was then applied to α-d-galactose O-d5 and β-d-galactose, in order to test its transferability. The computed potential energy distribution was found to be compatible with previous assignments for d-glucose, particularly for the modes involving C6 and COH groups. For β-d-galactose the same force field was used with changing the force constants due to the C1 and C6 groups.     

Calculation of the in-plane force constants and vibrational spectra of pyridine and its deuterated derivatives by the CNDO/2 force method

The in-plane vibrations of pyridine and its deuterated derivatives (4-d₁, 2,6-d₂, 3,5-d₂, and d₅) have been studied with the CNDO/2 force method. The calculated values of the force field scaled by five empirical parameters yield good agreement with the experimental spectra. The results seem to permit the reassignment of some bands.     

Anharmonic calculation of bandwidths and frequency shifts in crystalline CO2

The bandwidths and the anharmonic frequency shifts of the optical lattice phonons of crystalline CO₂ are calculated as a function of temperature using three different intermolecular potentials. A previously available potential (MOSMD) which reproduces correctly the structure, energy and harmonic frequencies of the CO₂ crystal provides anharmonic, calculated bandwidths about 10 times larger than the experimental values. An improved potential (PRC-1) is obtained by moving inside the OC bonds the oxygen interaction center and by increasing the molecular quadrupole. This potential predicts bandwidths and shifts of the right order of magnitude but still too large. The third potential (PRC-2) is obtained from the previous one by using a non-collinear distribution of negative charges. The negative charges are localized on exagons around the OC bond at a distance d = 0.3 Å. This potential reproduces correctly the experimental bandwidths and yields small anharmonic shifts. The temperature dependence of the bandwidths and shifts is correctly reproduced in terms of three-phonon decay processes for the T⁺_g and for the T⁻_g phonons. In the case of the E_g phonon four-phonon processes are required in order to fit the experimental data.     

The vibrational spectrum of tetrafluoropropyne

The i.r. spectrum of gaseous tetrafluoropropyne has been measured from 4000 to 100 cm⁻¹, and all of the observed bands have been assigned. The e mode frequencies of the CF₃ group are similar to those of other CF₃CCX species, and even though the a₁ modes are less regular, the variations can be explained without changes in force constants other than those involving the CX bond. Several bands, particularly ν₁ and combinations with ν₁, show pronounced sequence structure due to excited levels of ν₁₀, the CCC skeletal bend.     

Structural and infrared spectroscopic characterization of Co6C(CO)12S2: a high-nuclearity carbido carbonyl cluster spontaneously formed from dicobalt octacarbonyl and carbon disulphide

Co₆C(CO)₁₂S₂ (I) has been isolated in crystalline form from the mixture of more than a dozen of carbonyl products formed when Co₂(CO)₈ reacts at room temperature with CS₂. Crystals of I are monoclinic with space group Cc, and lattice constants a  16.250(5), b  9.413(4), c  16.036(5) Å, β  116.77(4)°. Structure refinement gave R  0.034 for 1974 reflections. The CCo₆S₂ core of the molecule possesses idealized D_3h geometry. It is composed of a Co₆ trigonal prism, enclosing a C atom in the centre, and the triangular faces are capped symmetrically by the two S atoms. The core contains two sorts od CoCo distances: short one (2.432 Å) along the triangular edges, and long ones (2.669 Å) along the lateral edges. The average CoC distance is 1.94 Å, and the average CoS distance 2.192 Å.¹³CO-enriched samples were prepared photochemically and their IR spectra used in the assignment of the CO stretching frequencies. The CO stretching force constant was calculated to be 1670(2) Nm^-1.By the use of ¹³CS₂, I has also been obtained in a selectively carbido-¹³C-labelled form. The vibrational frequencies of the carbide atom were observed, and that at 819 cm^-1 (¹³C: 790 cm^-1) assigned to the species

, and that at 548 cm^-1 (¹³C: 535.5 cm^-1) to species E′. For the Co-C(carbide) force constant a value of 155 Nm^-1 was calculated. The cobalt—sulphur stretching frequencies were found at 309 cm^-1 (

) and 239 cm^-1 (E′). The CoS stretching force constant, 78 Nm^-1, is considerably lower than that obtained for SCo₃-(CO)₉, viz. 112 Nm^-1.     

Vibrational analysis of the trigonal bipyramidal NbCl5 and NbBr5 molecules

Vibrational normal coordinate analysis has been made for NbCl₅ and NbBr₅ molecules with D_3h symmetry and using Wilson's GF matrix method. The observed frequencies are quantitatively assigned on the basis of the calculated potential energy distribution values for each vibration. The values of force constants for NbCl′ (axial) and NbCl (equatorial) bonds in NbCl₅ equal 194 and 261 Nm⁻¹, respectively. The corresponding values for NbBr₅ are 142 and 217 Nm⁻¹. These values are discussed in view of the bonding and structure of both compounds.     

Etude structurale de composes organosilicies par diffusion rayleigh depolarisee : V. Proprietes acceptrices d'electrons du silicium dans les systemes SiOC et SiOSi

Among the characteristic properties of the SiOC and SiOSi systems relative to those of the corresponding COC systems, the optical anisotropy is a new example which shows the electron-acceptor ability of silicon by (p → d)π interaction in compounds of the type R₃SiO∑ (R = Me, Et, Pr; ∑ = H, Me, SiMe₃, CH₂-t-Bu, CHMe₂, CMe₃). Effectively, the existence of a linear relationship between the optical anisotropy or the principal optical polarisabilities of the OSiR₃ groups and the Taft's parameter σ^★ of the ∑ groups in this series of compounds, shows that the electron-accepting character of silicon increases with increasing electron-donating ability of the group ∑; this relationship simultaneously translates an increase of the electronic density and mobility perpendicular to the OSi axis to the detriment of the parallel direction. In application, we calculated the σ^★ values for the groups ∑ = SiEt₃, SiPr₃ and the OSiMe₃ optical anisotropy value in PhOSiMe₃.