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.     

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.     

Scaled quantum mechanical (SQM) force field and theoretical vibrational spectrum for benzonitrile

The complete harmonic force field of benzonitrile has been determined by ab initio Hartree—Fock calculations using a 4–21 Gaussian basis set. As force constants are systematically over-estimated at this level, the directly calculated force field was scaled by empirical factors previously optimized for benzene and HCN. Frequencies calculated from this scaled quantum mechanical (SQM) force field confirm the published experimental assignments for benzonitrile, benzonitrile-p-d and benzonitrile-d₅. Aside from the CH (and CD) stretching frequencies, which are strongly affected by anharmonicity, the mean deviation between the observed and calculated frequencies is below 9 cm⁻¹ for each isotopomer. Theoretical i.r. intensities reproduce the main features of the spectra semiquantitatively.     

Modelling the vibrational behaviour of the cyclic carboxylic acid dimer. SQM force field of the formic acid dimer

The vibrational behaviour of the cyclic carboxylic acid dimer is modelled through the scaled quantum mechanical (SQM) force field of the cyclic formic acid dimer. The results indicate that the SQM force field technique is very well applicable to hydrogen bonded molecules. The frequency shifts observed on hydrogen bonding can be related to the shifts observed on lowering the temperature. This study also confirms that a clear distinction between cyclic carboxylic acid dimers and catamers can be made through the difference between infrared and Raman frequencies, and it is proved here that these conditions are also valid for weaker hydrogen bonded cyclic carboxylic acid dimers.     

Theoretical prediction of vibrational spectra: the harmonic force field and the vibrational spectrum of 4-methylpyridine

The geometry, complete harmonic force field and dipole moment derivatives have been computed for 4-methylpyridine at the Hartree-Fock level using a 4-21 basis set of Gaussian orbitals. A set of eleven scale factors, six of which were previously derived from benzene and the other five for the vibrational motions of the methyl group from toluene by fitting their computed force fields to their observed vibrational spectra, was used to scale the computed harmonic force constants of 4-methylpyridine. The vibrational frequencies and the associated infrared absorption intensities of 4-methyl -pyridine were then predicted from this scaled force field without any fitting to the experimental data of 4-methylpyridine. Comparison with experimental spectra permitted a few corrections to be made in previous experimental or semiempirical assignments. The mean-deviations between experimental and predicted frequencies was only 5.6 cm^-1 for the non-CH stretching frequencies or 8.3 cm^-1 overall. Computed intensities are qualitatively m agreement with experiment. The optimization of scale factors for the five methyl vibrational motions produced a trivial improvement in the fit.     

Vibrational spectra,scaled quantum-mechanical (SQM) force field and assignments for 4H-pyran-4-one

The gas phase i.r. spectrum of 4H-pyran-4-one (hereafter called γ-pyrone) has been recorded in the 4000-400 cm⁻¹ region by a Nicolet 7199 FTIR spectrometer and interpreted using a general valence force field calculated quantum mechanically at the ab initio level with a split-valence 4–21 basis. Assignment of certain fundamentals was facilitated by information gained from the i.r. and Raman spectra of the melt and from the i.r. spectrum of the saturated solution in CCl₄.To account for systematic computational errors, the theoretical ab initio force field was scaled using a set of constants derived by the empirical fitting of force fields computed for related molecules to their observed spectra. Either the scale factors derived for a family of open-chain molecules or, better, for benzene could be used to yield a scaled force field which gave unequivocal assignments for γ-pyrone. The method promises to be of general applicability for molecules of this complexity.     

A theoretical study of the vibrational spectra,geometry and force field of thiourea

A theoretical force field for the molecular vibrations of thiourea has been determined from ab initio calculations at the Hartree-Fock level using the 3-21G* basis set. The reliability of the force field is analyzed by calculating the vibrational frequencies for the deuterated and ¹⁵N isotopomers. Frequencies calculated from the force field are utilized to critically examine the experimental assignments for thiourea and deuterated thiourea. Theoretical geometry, the calculated IR and Raman band intensifies are analyzed.     

Efficiency of post-Hartree-Fock force field for the interpretation of vibrational spectra ofN,N-dimethylnitramine

Harmonic force fields for the molecule ofN,N-dimethylnitramine were calculated in the RHF/6-31G^* and MP2/6-31G^** approximations. Scaling of the force fields obtained made it possible to reliably interpret the vibrational spectra of light and perdeuterated compounds reported in the literature. The assignment is confirmed by good reproducibility of experimental isotope shifts upon¹⁵N-amino- and¹⁵N-nitrosubstitution. The frequencies of intramolecular vibrations in far IR and Raman spectra as well as in neutron inelastic scattering spectra for the light and perdeuterated samples of solidN,N-dimethylnitramine were identified using the force field calculated with the inclusion of electron correlation (MP2). Although general structures of the force fields calculated in the RHF and MP2 approximations are similar, considerable differences in the force constants of the NO and NN stretching vibrations and especially in the constants of the NO_str/NO_str and NO_str/NN_str interactions remain even after scaling the force fields.     

Solid-state vibrational spectra and theoretical study of alaninamide acetate

Solid-state IR and Raman spectroscopic elucidation of alaninamide acetate is preformed by means of the possibilities of linear-polarized IR and Raman methods. The experimental assignment is compared with theoretical vibrational analysis with the intention to explain the influence of intermolecular interactions in solid phase on the spectroscopic properties of the compound studied. The 1H and ¹³C NMR spectra in solution are compared with the corresponding ones of alanine, studying the amidation effect on the chemical shift signals in the alanine moieties.     

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.     

The computed force constants and vibrational spectra of toluene

The complete harmonic force field and dipole moment derivatives have been computed for toluene at the Hartree-Fock level using a 4-21G basis set. The six scale factors optimized for benzene were used to scale the computed harmonic force constants of toluene. The vibrational frequencies of toluene computed from this scaled quantum mechanical force field are quite good. After a correction was made to two previously proposed spectral assignments, the mean deviation from the experimental frequencies is only 7.8 cm^?1 except for the frequencies related to the methyl group. Five more scale factors for the vibrational modes of the methyl group were reoptimized. The final comparison showed an overall mean deviation of 7.5 cm^?1 between the theoretical spectrum and the experimental spectrum. Computed intensities are qualitatively in agreement with experiments. They are highly useful in the investigation of questionable assignments.     

Quantum chemical calculation of force constants and vibrational spectra

As a result of the development of direct derivative methods and improved computational facilities, ab initio quantum chemical calculations have become an increasingly important source of information for the determination of molecular force constants. Within the Hartree-Fock (H-F) SCF model and using moderate size basis sets such calculations are now economically feasible for molecules of up to 2o–3o atoms. At this level of theory, harmonic diagonal force constants are overestimated by 1o–3o%, corresponding to 5–15% in the frequencies. However, the largely systematic errors can be accounted for by simple empirical corrections. The resulting SQM (Scaled Quantum Mechanical) force fields are probably the most reliable ones available at present for larger molecules. Calculated infrared intensities are semi-quantitatively correct. Beyond the H-F model, large scale calculations including electron correlation give great improvements in the force constants, but there are still residual errors of a few percent.     

Interpreting the vibrational spectra of uracil molecules and their deuterated isotopomers using a scaled quantum-chemical quadratic force field

The quadratic force field of the uracil molecule is obtained by MP2(full) calculations using the cc-pVTZ and cc-pVQZ basis sets. Under the assumption that the most stable diketone form of the uracil molecule has a flat configuration with C _s symmetry, the available vibrational gas-phase spectra of uracil and the matrix isolation spectra of its seven N-, C-, and mixed N,C-deuterated derivatives are analyzed jointly for the first time by using Pulay??s force field scaling. Band assignments suggested earlier are corrected. It is shown that sets of 14 scaling factors allow us to reproduce the adjusted interpretation of the spectra and to obtain the most reliable quadratic force constant matrix for uracil among those available, based on joint consideration of the experimental and quantum-chemical calculation results.     

AB initio SQM FF calculations of vibrational frequencies of acetonitrile coordinated to Lewis acids

Experimental spectra of CH₃CN and CD₃CN were reproduced by scaling ab initio force constants calculated on HF/3-21G level. Scale factors obtained for acetonitrile molecule were used to calculate vibrational spectra of acetonitrile complexes with Lewis acids, such as AlCl₃, AlF₃ and Al(OH)₃. The observed increase of (CN) is due to both the growth in the CN-bond force constant and the kinematic coupling of CN and N-acid bonds.

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CH₃CN CD₃CN , 3–21G. , , AlCl₃, AlF₃ Al(OH)₃. , (CN) CN- CN -.

     

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.     

Size-extensive vibrational self-consistent field method

The vibrational self-consistent field (VSCF) method is a mean-field approach to solve the vibrational Schro?dinger equation and serves as a basis of vibrational perturbation and coupled-cluster methods. Together they account for anharmonic effects on vibrational transition frequencies and vibrationally averaged properties. This article reports the definition, programmable equations, and corresponding initial implementation of a diagrammatically size-extensive modification of VSCF, from which numerous terms with nonphysical size dependence in the original VSCF equations have been eliminated. When combined with a quartic force field (QFF), this compact and strictly size-extensive VSCF (XVSCF) method requires only quartic force constants of the ?(4)V/?Q(i)(2)?Q(j)(2) type, where V is the electronic energy and Q(i) is the ith normal coordinate. Consequently, the cost of a XVSCF calculation with a QFF increases only quadratically with the number of modes, while that of a VSCF calculation grows quartically. The effective (mean-field) potential of XVSCF felt by each mode is shown to be harmonic, making the XVSCF equations subject to a self-consistent analytical solution without matrix diagonalization or a basis-set expansion, which are necessary in VSCF. Even when the same set of force constants is used, XVSCF is nearly three orders of magnitude faster than VSCF implemented similarly. Yet, the results of XVSCF and VSCF are shown to approach each other as the molecular size is increased, implicating the inclusion of unnecessary, nonphysical terms in VSCF. The diagrams of the XVSCF energy expression and their evaluation rules are also proposed, underscoring their connected structures.     

Vibrational spectra and force field of terephtalonitrile

The IR and Raman spectra of the two molecules terephtalonitrile and terephtalonitrile-¹⁵N were recorded to permit the general assignment of the vibrational bands observed, in agreement with a D_2h symmetry for these molecules. The general quadratic force field was calculated by the semi-empirical MINDO/3 method from an optimized geometry obtained by the same method. The resulting force field was refined by employing the experimental vibrational frequency data of the two molecules and those of terephtalonitrile-d₄. The final differences between the calculated end experimentally observed frequencies for B_2g and B_3u terephtalonitrile species were within the range ± 0.1 cm⁻¹.     

Vibrational spectra and force field of dimethylphosphines

Vibrational spectra in the range 200–3000 cm^?1 are reported and assigned for the species (CH₃)₂PH, (CH₃)₂PD, (CD₃)₂PH, (CD₃)₂PD, CH₃CD₃PH and CH₃CD₃PD. The spectra in the range 1020–500 cm^?1 are complicated due to the coupling between δPH, ?Me and the skeletal modes of the molecule. Interpretation is only possible through a force field which is markedly different from an earlier one of dimethyl sulphide. This force field predicts uncoupled δPH frequencies of 835 (a) and 909 cm^?1 (a), couples PH bending largely to out-of-skeletal plane methyl rocking (?_i) and includes a low p¦¦(a) bending constant, a high skeletal bending constant and unusual signs for two interaction constants. In the crystalline phase at 78 K, the two methyl groups are non-equivalent.