Planar and out-of-plane normal vibrations of nitro- and aminobenzenes

The normal vibrations of halogenobenzenes with a polyatomic para substituent (NO₂, NH₂ ) are reported.The specific vibrations of NO₂ and NH₂ groups and of the CN and CX bonds (X is F, Cl, Br, I) have been assigned using the G.F. method of Wilson. The potential energy distribution shows that the inplane and outofplane vibrations of CN bonds exhibit different behaviour in nitro and aminobenzenes. Indeed, the CN stretching and planar bending are vibrational modes coupled respectively with the symmetric deformation and rocking of NO₂ whereas in the case of the amino molecules they are coupled with the skeletal modes only. Consequently the CN planar bending vibrations have frequencies lower than the CX ones in the nitro compounds. In contrast, the CN bending frequencies are higher in the amino molecules. For the outofplane bending of amino and nitro molecules the γ(CN) frequencies are always higher than γ(CX) frequencies because there is no coupling with the wagging of the polyatomic substituent. Our experimental results by Raman spectroscopy are in good agreement with the theoretical calculations we have performed. They also agree with the spectra published by other authors. We have recorded the splitting of some NO₂ bands in pdinitrobenzene, which is probably due to isomeric positions of the two NO₂ groups relative to the plane of the skeleton.     

Model calculations of the vibrations of bonded water molecules

Model calculations have been made of the vibrational frequencies and normal modes of a water molecule vibrating in a combined internal and external field. A constant internal force field has been used together with an external central force field from four or three nearest-neighbour atoms to the water molecule. These neighbour atoms have been arranged either tetrahedrally or trigonally around the water molecule. The external force field has been further restricted by the use of five possible site symmetries for the water molecule, C_2v, C₂, C_s(σ_xz, C_s(σ_yz) and C₁. A series of calculations have been made where the external force constants have been varied within the range 1—80 Nm^?1.The nine calculated normal modes can be divided into three groups: intra-molecular, rotational and translational vibrations. Among the rotational vibrations it is found that, in the tetrahedral environment, the rocking mode occurs at lower frequencies than the twisting and wagging modes, whereas the opposite occurs for the trigonal environment. Frequency ratios have been calculated using the isotopic species H₂O, D₂O, HDO and H,¹⁸O. The twisting and wagging modes have the vH₂O/vD₂O ratio in the range 1.35-3-1.41 and the rocking mode in the range 1.26—1.41.     

A normal coordinate analysis of the vibrational modes of the three redox forms of methylviologen: Comparison with experimental results

A normal coordinate analysis of the three redox forms of methylviologen (MV) was accomplished using a simplified valence force field. The calculated band frequencies are compared with those observed experimentally. The plausibility of the assignments for the Raman A_g modes, as inferred from the normal coordinate analysis, is discussed. The assignments of several Raman A_g modes were checked by a comparison of the observed Raman spectra of viologens with different substituents, such as methyl group deuterated methyl viologen (DV), N-octyl-N′-methyl viologen (C₈MV), N-hexadecyl-N′-methyl viologen (C₁₆MV) and dibenzyl viologen (BV), with MV. The values of the root mean square (r.m.s.) amplitudes of vibrations between the bonded and the nonbonded atom pairs, and r.m.s. Cartesian displacements from the equilibrium geometry for MV²⁺ were computed. These data provide important insight with respect to the molecular geometry.     

Application of the dimer approach for the analysis of vibrational spectra of BEDT—TTF-based charge-transfer salts

The dimer approach was proposed for the normal coordinate analysis of BEDT—TTF⁺ molecular vibrations. It was shown that, within the framework of the approximation used, the appearance of additional bands in the IR as well as in Raman spectra may be explained as due to the reduction of symmetry of the dimerized system in comparison with the monomeric one. The strength of intermolecular interaction in the dimer was estimated by adjusting the calculated frequencies to the observed positions of intense “vibronic” bands recorded in the IR spectra of BEDT—TTF-based monovalent charge transfer salts. It was found that for the reproduction of “vibronic shifts” observed for some vibrations it should be assumed that the intermolecular interaction takes effect not only on the totally symmetric a_g modes, but also on the vibrations of other symmetry species.     

Nonradiative decay processes in benzene

We investigate the behavior of single vibronic level nonradiative decay rates in benzene and benzene-d₆. The effects of excitation in a promoting mode which undergoes frequency and geometry changes in the S₁ relaxation (to T₁ or S₀) are considered in detail. Calculated relative nonradiative decay rates are compared with experimental values and are used to assign triplet state vibrational frequencies to the ν_s, ν₁₀ and ν₁₆ vibrations. This comparison also indicates that none of these modes, nor the modes ν₁ and ν6, are likely to be the dominant promoting modes for the S₁ → T₁ decay. Some simple expressions are given which provide good estimates of the vibronic state dependence of the non-radiative decay rates. In conjuction with experimental decay rate data, these estimates can aid in guiding spectral assignments of vibronic bands. Simple but general theoretical criteria are derived which are useful in determining those vibrations which are poor (or good) accepting modes. Our previous theory is generalized to consider absolute nonradiative decay rates. The results are used to suggest a possible mechanism for the “channel three” decay process observed by Callomon . Although the numerical applications presented here are to benzene electronic relaxation processes, the theoretical developments also apply to and the calcultions illustrate general features of nonradiative decay in the statistical limit.     

Nonradiative transitions in benzene

A symmetric Rosen-Morse potential was assumed for the potential of the out-of-plane vibrations of benzene. Matrix elements and the respectiveS ₁ ?S ₀ nonradiative rates were calculated for several values of the anharmonicity constants and compared with the results obtained with a harmonic potential. Anharmonicities of the out-of-plane modes in benzene are found to decrease the values of the matrix elements and rates, thus leaving unresolved, a discrepancy between experimental and theoreticalS ₁ ?S ₀ rates for benzene. However, in molecules with distorted acceptor modes whose frequencies are higher in the optically excited, as compared to the acceptor state, increases of several orders of magnitude of the nonradiative rate could occur on introduction of Rosen-Morse type anharmonicities.     

Non-condon effects on radiationless triplet decay in benzene and naphthalene

Model calculations that avoid the Condon approximation are reported for T₁$\text{}\text{?}$ar S₀ intersystem crossing in normal and perdeuterated benzene and naphthalene. In both benzenes and in naphthalene-d₈, skeletal bending vibrations coupling T₁ to T₂ are found to be more efficient as accepting modes than CH-stretching vibrations.     

Electronic structures of organometallic complexes of f elements LXXVII: Complementary information of polarized Raman spectra of oriented single crystals and model calculations on the basis of density functional theory for assigning the vibrational spectra of decamethylferrocene

The far and mid infrared (FIR/MIR) spectra of powdered Fe(η⁵-C₅Me₅)₂ (FeCp1₂) as well as the polarized Raman spectra of an oriented single crystal (where the four FeCp1₂ molecules of D_5d symmetry in the unit cell are pairwise perpendicular to each other) have been recorded. The polarization selection rules were developed for this situation which allow the assignment of the observed Raman lines to irreducible representations (irreps) which agree well with the predictions of a calculation applying density functional theory. This finding suggests additional correlations to the observed (unpolarized) bands in the FIR/MIR spectra with the calculated wavenumbers (and their irreps) of IR active normal modes. Neglecting the νCH vibrations, a r.m.s. deviation of 7.0 cm^?1 for 41 assignments (IR and Raman) could be achieved. The frequencies of the calculated νCH vibrations, however, are on the average 55 cm^?1 higher than the experimental ones. Skeletal and intra-ligand vibrations could be separated and all previous assignments of the former had to be revised. Because of mixing, the graphical representations of the two skeletal modes of E_1u symmetry do not resemble the idealized ones of a typical sandwich complex but those of FeCp₂ shown in the literature. In-phase and out-of-phase intra-ligand motions of the Fe[(C₅C₅)]₂ moiety have calculated wavenumber differences between 3 and 42 cm^?1. Additionally, because of mixing with skeletal modes some of the low frequency intra-ligand vibrations display a noticeable dependence on the mass of the central atom which prevents the direct transfer of the identified βCCH₃ and γCCH₃ normal modes from MCp1₂ (M = Fe, Ru) to LnCp1₃ (Ln = La, Ce, Pr, Nd, Sm) complexes.     

Molecular vibrations of complexes with trigonal ligands: Part IX. Zr(BH4)4

The molecular vibrations of Zr(BH₄)₄ are analysed on the basis of a T_d model. Symmetry coordinates are described and classified into those of ligand vibrations and central-part vibrations. A simple force field is deduced, which gives satisfactory agreement with experimental vibrational frequencies and mean amplitudes of vibration. A continuation of the work by considering the probably more realistic T model is suggested.     

Raman spectra of single H2O molecules isolated in cavities of crystals

The vibrational (Raman) spectra of H₂O molecules isolated in cavities of beryl, cordierite, bikitaite, natrolite, scolecite, lawsonite, and hemimorphite have been measured in the temperature range of 4–295 K. The influence of van der Waals and hydrogen bonds on the values of frequency, intensity, and half-width of stretching and bending modes of H₂O is considered. The spectra of translational vibrations of H₂O molecules in crystal cavities are discussed. For the firsts time, the ratio between the frequencies of translation and stretching vibrations of H₂O and the dependence of frequencies of bending vibrations on the angle H-O-H in H₂O molecule are presented.     

Spectres de vibration de composés MIIMo6X14

Infrared and Raman spectra of compounds M^IIMo₆X₁₄ with M^II = Fe, Cd, Pb and X = Cl or Br were recorded in the solid state and interpreted. It was shown that if the highest infrared frequency depends only of the nature of X, the other vibrations, especially for the three lower, are complex modes, the frequencies of which vary both with the nature of X and M^II. Despite this, the Raman frequencies are unaffected by the nature of M^II and the Ag₁ mode of the MoMo vibration is situated at 104 ± 4 cm⁻¹ for all the compounds.     

Vibrational analyses of silacyclopentanes

The complete infrared and Raman spectra of 1,1-difluoro-1-silacyclopentane and 1,1-dichloro-1-silacyclopentane have been recorded and analyzed. Furthermore, a number of the vibrational frequencies of the silacyclopentane and silacyclopentane-1, 1-d₂ molecules have been reassigned.A normal coordinate calculation for each of these molecules was carried out and this demonstrated the validity of the assignments. Considerable mixing of the modes was found especially where ring vibrations and SiX₂ motions were involved.     

A DFT analysis of the vibrational spectra of nitrobenzene

Raman and FTIR, spectra of nitrobenzene, nb, and its isotopomers, nb-¹⁵N, nb-¹³C₆ and nb-d₅, were obtained and the fundamental vibrational modes assigned with the aid of a B3LYP/6-311+G** calculation, without the need for scaling of the force constants. The changes in vibrational coupling between the nitro and benzene groups upon certain isotopic substitutions are well modelled by the calculation, which is able to reproduce the isotopic shifts in frequencies for the nitro vibrations, as well as changes in IR intensities.     

Vibrational analysis of l-alanine and deuterated analogs

Raman spectra of the polycrystalline l-alanine analogs CH₃CH(NH⁺₃)COO^?, CH₃CH(ND⁺₃)-COO^?, CD₃CD(NH⁺₃)COO^?, and CD₃CD(ND⁺₃)COO^? have been obtained. A normal coordinate analysis is carried out based on the experimental frequencies of the four isotopic analogs and a 34 parameter valence-type force field defined in terms of local symmetry coordinates. The final refinement, in which five stretching force constants are constrained to fixed values obtained from bond length data, results in an average error of 7 cm^?1 (0.9%) for the observed frequencies of the four isotopically substituted molecules. Band assignments are given in terms of the potential energy distribution for local symmetry coordinates. For non-deuterated l-alanine, the vibrations above 1420 cm^?1 and below 950 cm^?1 may be described as localized group vibrations. By contrast, the eight modes in the middle frequency range, viz. the three skeletal stretching, the COO^? symmetric stretching, one NH⁺₃ rocking, the symmetric CH₃ deformation, and the two methyne CH deformation vibrations, are very strongly coupled to one another. Some decoupling appears to take place in the perdeutero molecule, and all but five modes can be described as localized group vibrations.     

Vibrational Spectra of the Cyclic SN-Compounds S4N4, S4N4H4 and S3N3Cl3

The IR and Raman spectra of solid and dissolved S₄N₄, S₄N₄H₄, S₄N₄D₄ and S₃N₃Cl₃ have been recorded and are assigned according to D_2d, C_4v and C_3v symmetry respectively. In the solid state, many forbidden bands and splittings of degenerate vibrations are observed because of the symmetry lowering in the crystals. Due to the different size and shape of the rings and to strong coupling of the normal modes there is no clear correlation between the SN ring stretching vibrations and the strength of the SN bonds, except for the one of the E modes. However, the stretching force constant show the trend expected from changes in interatomic distances.     

An inverse sum rule for isotopic frequencies

A rule relating to the square of the inverse harmonic frequencies of a set of isotopically substituted molecules is developed. The rule is

where Λⁱ_x. is the square of the Xth harmonic frequency of the ith isotopic species, and σⁱ is a weighting factor for the ith species, taken so that

for all a, where Mⁱ_a is the mass of the ath atom in the ith species. An upper bound for the residue (Res)_i can be evaluated from the frequencies of the ith species alone. If the rule is not satisfied, no harmonic force field is compatible with the set of assigned frequencies. The rule is applied to ethylene. The rule is most sensitive to the assignment of the low frequencies. The rule is shown to apply to the vibrations of crystals, including the lattice modes, and if the sum is taken over K = K' ≠ 0 modes, the residue→ 0.     

Vibrational spectra of halogen substituted cyclopropanes—V. Trans-1,2-dichlorocyclopropane

The i.r. spectra of gaseous trans-1,2-dichlorocyclopropane were measured from 4000 to 400 cm⁻¹ and to 200 cm⁻¹ in the liquid phase. The Raman spectrum of the liquid was obtained from 4000 to 50 cm⁻¹. An assignment of all 21 normal vibrations was proposed on the basis of i.r. vapour phase band contours, Raman depolarization ratios, expected group frequencies and comparison with closely related molecules. There is excellent agreement with the normal modes previously assigned for the cis and trans isomers of the chloro, bromo and iodo analogues. The data indicate little interaction between the two CHCl moieties.     

Infrared and Raman spectra and normal coordinate calculations for methylisothiocyanate

The infrared spectra (3200-50 cm^?1) of gaseous and solid CH₃NCS and CD₃NCS and the Raman spectra (3200-10 cm^?1) of the liquids and solids have been recorded. The spectra have been interpreted on the basis of a “pseudo-symmetric top” with C_3v symmetry. An assignment of the fundamental vibrations in both molecules, based on their infrared band contours, depolarization values and group frequencies, is given and discussed. Particularly interesting is the low-frequency region where band maxima were observed at 152 and 80 cm^?1 for CH₃NCS and 139 and 71 cm^?1 for CD₃NCS in the infrared spectra of the gases. A normal coordinate analysis has also been carried out based on C_3v symmetry. Considerable mixing was found between the C_αN stretch and NCS symmetric stretch in both isotopic species. The other normal modes in CH₃NCS are reasonably pure but, for the CD₃NCS molecule, considerable mixing was found between the CD₃ stretches and NCS antisymmetric stretch. The proposed vibrational assignment and the results of the normal coordinate calculations are discussed and compared with the results obtained for similar molecules.     

The vibrational spectra of N-Cl maleimide

The infrared spectra of N-Cl maleimide as a Nujol mull and dissolved in various solvents were recorded between 4000 and 30 cm^?1. Raman spectra of the crystalline solid and saturated solution in CH₃CN were recorded and semiquantitative polarization measurements were made.The fundamental frequencies have been tentatively assigned in terms of C_2V symmetry, based upon Raman polarization data and analogies with the spectra of maleimide and maleic anhydride. A force field was derived by initially transferring force constants from maleimide. After small iterations a satisfactory correspondance was achieved between the observed and calculated in-plane modes whereas larger discrepancies remained for some of the out-of-plane vibrations.     

A joint local mode and normal mode interpretation of vibrational anharmonicity in methyl bromide

The gas-phase i.r. spectrum of CH₃Br has been studied up to 14 000 cm⁻¹. Some 32 new vibration levels are located accurately, involving up to 5 quanta (V= 5) of excitation in CH stretching. Reproduction of a total of 72 vibration levels is achieved through a joint treatment of CH stretching vibrations in a local mode basis, other vibrations in a normal mode basis, and with the inclusion of two Fermi resonances. The local mode approach satisfactorily accounts for the effects of the large Darling—Dennison vibrational interactions which occur between CH stretching modes. Fermi resonances between CH stretching and overtones of both methyl group deformation vibrations (ν₂ and ν₅) are treated explicitly. Interacting levels become quasi-degenerate at V = 3 in the case of 2ν₅, and at V = 5 in the case of 2ν₂. The analysis permits the determination of a complete set of 27 physically representative anharmonicity constants for CH₃Br, four of which are interrelated through the local mode model. Data reproduction between 600 and 14 000 cm⁻¹ is achieved with an r.m.s. error of 2.55 cm⁻¹.