Die Eigenschwingungen des Metall-Hydratkomplexes in BeSO4·4H2O und BeSO4·4D2O

Infrared reflection spectra of single crystals of BeSO₄·4H₂O and BeSO₄·4D₂O have been obtained in polarized light at 300°K and at 14°K in the region between 4000 cm^?1 and 300 cm^?1. By a Kronig-Kramers analysis, the frequencies of the infrared active transitions have been calculated. These transitions are attributed to internal vibrations of the water molecules and sulfate ions and, in the region between 1000 cm^?1 and 300 cm^?1, especially to internal and external vibrations of the tetrahedral Be⁺⁺·4aqu-complexes. The vibrational modes of these complexes consist of a superposition of translational and librational modes of the water molecules and translational modes of the central Be⁺⁺-ion. The vibrational frequencies and normal modes of this complex have been calculated in a central-force model, and force-constants have been determined by fitting the calculated frequencies to the observed spectra. The calculations have shown that the modes, which comprise mainly translational motions of the water molecules, are strongly coupled with librational motions of the water molecules. On the other hand, there exist pure librational modes with practically no admixture of translational motions. The optimum sets of force constants for the BeSO₄·4H₂O crystal and the BeSO₄·4D₂O crystal differ in a manner which can be understood under the assumption that the dimensions of the Be(D₂O)₄ complex are about 0.1 Å larger than those of the Be(H₂O)₄ complex. Some arguments supporting this conclusion will be discussed.     

Fourier Transform Vibrational Spectra of Magnesium Hydrogenphosphate Trihydrate. I. The O-H Stretching Region∗

Abstract

The Fourier transform (FT) infrared and Raman spectra of newberyite, MgHPH₄ - 3H₂O are studied in the region where the stretching vibrations of the water molecules (protiated and deuterated) and the O-H/O-D stretches of the hydrogenphosphate anions are expected to appear. The O-H stretching vibrations give rise to a complex feature known as the A,B,C trio. Since neither of the maxima found below 3000 cm^?1 represents a true band arising from a given fundamental, it is pointless to correlate their frequencies with the observed O…O distances. In the water stretching region, the two bands with highest frequencies undoubtedly correspond to the anti symmetric and symmetric stretch of one type of the water molecules. The stretching vibrations of one of the remaining two types of H₂O molecules are clearly uncoupled and the O-H oscillator involved in the weaker hydrogen bond is responsible for a band at 3376 cm^?1 whereas the rest of the water stretchings are apparently overlapped yielding the complex band below 3320 cm^?1. Thus the situation is again complicated and the correlations between the frequencies and the O_w…O distances are inappropriate. The two bands at highest frequencies (3522 and 3483 cm^?1 at RT) exhibit a positive temperature coefficient.

     

Raman spectroscopic study of the antimonate mineral lewisite (Ca,Fe, Na)2(Sb,Ti)2O6(O,OH)7

The mineral lewisite, (Ca, Fe, Na)₂(Sb, Ti)₂O₆(O, OH)₇, an antimony-bearing mineral, has been studied by Raman spectroscopy. A comparison is made with the Raman spectra of other minerals, including bindheimite, stibiconite, and roméite. The mineral lewisite is characterised by an intense sharp band at 517 cm^?1 with a shoulder at 507 cm^?1 assigned to SbO stretching modes. Raman bands of medium intensity for lewisite are observed at 300, 356, and 400 cm^?1. These bands are attributed to OSbO bending vibrations. Raman bands in the OH stretching region are observed at 3200, 3328, 3471 cm^?1, with a distinct shoulder at 3542 cm^?1. The latter is assigned to the stretching vibration of OH units. The first three bands are attributed to water stretching vibrations. The observation of bands in the 3200–3500 cm^?1 region suggests that water is involved in the lewisite structure. If this is the case then the formula may be better written as (Ca, Fe²⁺, Na)₂(Sb, Ti)₂(O, OH)₇ xH₂O.     

Absolute line wavenumbers in the near infrared: 12C2H2 and 12C16O2

40 absolute line wavenumbers in the 3v ₃ band of ¹²C¹⁶O₂ between 6927 cm^?1 and 6989 cm^?1 and 626 absolute line wavenumbers in the near infrared absorption spectrum of ¹²C₂H₂ between 7060 cm^?1 and 9900 cm^?1 have been measured using high resolution Fourier transform spectroscopy. The calibration of the CO₂ line wavenumbers relied on heterodyne frequencies available in the v ₁ + v ₃ band of ¹²C₂H₂ near 6556 cm^?1. The absolute uncertainty of the calibrated CO₂ line wavenumbers is estimated to 0.000 08 cm^?1. The acetylene spectra were calibrated using heterodyne frequencies available in the 2—0 band of ¹²C¹⁶O and the line wavenumbers obtained in the 3v ₃ band of ¹²C¹⁶O₂. The absolute uncertainty of the calibrated acetylene line wavenumbers is estimated to range from 0.0003 cm^?1 to 0.006 cm^?1 for strong to very weak isolated lines. Comparison with absolute line wavenumbers obtained independently at JPL in the 3v ₃ band of ¹²C₂H₂ near 9649 cm^?1, calibrated using absolute wavenumbers available in the 2—0 and 3—0 (near 6350 cm^?1) bands of ¹²C¹⁶O, shows very good agreement. Also, the vibration—rotation constants for the observed upper vibrational states of ¹²C₂H₂ were determined, but without accounting for the perturbations affecting these states.     

Vibrational Spectroscopic and Theoretical Studies of Urea Derivatives with Biochemical Interest: N,N′-Dimethylurea,N,N,N′,N′-Tetramethylurea,and N,N′-Dimethylpropyleneurea

Abstract

Mid-infrared, far-infrared, and Raman vibrational spectroscopic studies were combined with density functional theory (DFT) calculations and normal coordinate force field analyses for N,N′-dimethylurea (DMU), N,N,N′,N′-tetramethylurea (TMU), and N,N′-dimethylpropyleneurea (DMPU: IUPAC name 1,3-dimethyltetrahydropyrimidin-2(1H)-one). The equilibrium molecular geometry of DMU (all three conformers), TMU, and DMPU and the frequencies, intensities, and depolarization ratios of their fundamental infrared (IR) and Raman vibrational transitions were obtained by DFT calculations. The vibrational spectra were fully analyzed by normal coordinate methods as well. A starting force field for DMPU was obtained by adapting corresponding force constants for DMU and TMU, resulting after refinements in the stretching force constants C=O (7.69, 7.30, 7.68 N·cm^?1), C–N (5.16, 5.55, 5.05 N·cm^?1), and C-Me (5.93, 4.00, 4.22 N·cm^?1) for DMU, TMU, and DMPU, respectively. The dominating conformer of liquid DMU was identified as trans-trans, strong intermolecular hydrogen bonding was verified in solid DMU, and weak dipole–dipole association was found in liquid TMU and in DMPU. Special attention was paid to analyzing the methyl group frequencies, which revealed deviations from local C_3v symmetry. A linear correlation was found between the CH stretching force constants and the inverse of the CH bond lengths (1/r ²). The averaged NH stretching frequencies of gaseous, dissolved, and solid urea and of DMU, with variations for hydrogen bonding of different strength, are linearly correlated to the NH stretching force constants. Characteristic skeletal vibrations were assigned for a broad variety of urea derivatives and also for pyrimidine derivatives, which all contain the N₂C=O entity. The very strong IR bands of C=O stretching (1,676 ± 40 cm^?1) and asymmetric CN₂ stretching (1,478 ± 60 cm^?1), and the very intense Raman feature of symmetric CN₂ stretching or ring breathing (757 ± 80 cm^?1), can be recognized as fingerprint bands also for the pyrimidine derivatives cytosine, thymine, and uracil, which all are nucleobases in DNA and RNA nucleotides.     

The integrated number of vibrational states in acetylene (12C2H2, 13C2H2, 12C2D2)

A calculated exhaustive set of vibrational state energies in ¹²C₂H₂, ¹³C₂H₂ and ¹²C₂D₂ has been used to analyse the evolution of the integrated number of states with increasing vibrational energy N(E) up to 15000 cm^?1, 12000cm^?1 and 10000 cm^?1 in each isotopomer, respectively. The regular contribution to N(E) was modelled analytically and numerical parameters were fitted. The other expected contribution to N(E), which is of oscillatory nature, was quantified and is discussed using energyand time-dependent theories. Related periods of oscillation and temporal recurrences are interpreted consistently in terms of the constant of the motion N_r = 5v₂ + 3v₂ + 5v₃ + v₄ + v₅ and of an average vibrational quantum. More pragmatically, the vibrational dynamics appear to be dominated by the bending vibrations, i.e., by the slowest oscillators.     

Fourier Transform Infrared Spectroscopic Investigation of the Binary and Ternary Cyanide Adducts of the Oxidized Horseradish Peroxidase: Identification of a Second Stretching Mode for the Carbon-Nitrogen Bond of the Bound Cyanide Ion

The binary and ternary cyanide adducts of the ferric horseradish peroxidase were investigated by Fourier transform infrared spectroscopy. The carbon-nitrogen bond of the bound cyanide ion in the binary ferric cyanohorseradish peroxidase exhibits two stretching vibrations at 2130 cm^?1 and 2127 cm^?1 with the latter mode being observed in this work for the first time. This finding supports the results of the resonance Raman study of cyanohorseradish peroxidase, which identified two iron-carbon-nitrogen bending vibrations and two iron-carbon stretching vibrations, proving the existence of two conformational states. The identification of the latter carbon-nitrogen stretching frequency allowed the assignment of all of the vibrational modes of the iron-carbon-nitrogen groups of the two conformational states of the ferric cyanohorseradish peroxidase. The first conformer is characterized by a carbon-nitrogen stretch at 2130 cm^?1, an iron-carbon stretch at 453 cm^?1, and an iron-carbon-nitrogen bending mode at 405 cm^?1. The second state has a carbon-nitrogen stretch at 2127 cm^?1, an iron-carbon stretch at 360 cm^?1, and an iron-carbon-nitrogen bending mode at 422 cm^?1. The iron-carbon stretching band is weakly sensitive to pH changes, but it is sensitive to H₂O/D₂O substitution, indicating that the bound cyanide ion in cyanohorseradish peroxidase is hydrogen bonded to the surrounding protein. The two states were attributed to variation in the extent of hydrogen bonding of the iron-carbon-nitrogen groups in the two states. The carbon-nitrogen stretching vibrations of the ternary complexes of cyanohorseradish peroxidase with ferulic acid, benzamide, and benzhydroxamic acid have been investigated for the first time. The binding of the substrate to cyanohorseradish peroxidase does not always lead to the vanishing of one of the conformational states as in the carbon monoxide adducts of the ferrous horseradish peroxidase, but can cause shifts in the νC-N frequency and in the relative population of both conformational states.     

Hydrogen-bonded OH and OD overtone bands and potential energy curve of methanol

The absorption spectra of CH₃OH, CH₃OD, CD₃OH, and CD₃OD as pure liquids and as carbon tetrachloride solutions were measured in the 3,850 – 16,600cm^?1 region. In addition to the various combination bands, the higher overtone bands of the hydrogen-bonded OH stretching vibration of self-associated methanols were observed at ～6470, 9300–9700, and 12,200 – 12,700 cm^?1 with broad half-widths of ～700, ～1200, and ～1800 cm^?1, respectively, and those of the OD stretching vibration, at ～4900, 7200–7400, and 9200–9600 cm^?1 with half-widths of ～370, ～700, and ～1200 cm^?1, respectively. With the aid of the observed frequencies, we determined the single minimum potential energy curve for the hydrogen-bonded OH and OD stretching vibrations of self-associated methanols. Furthermore, the absorption band due to double excitation of two neighboring OH groups linked together by a hydrogen bond was quantitatively analyzed by using the isotopic isolation technique. The double excitation band of CH₃OH as pure liquid was found to appear at 6730 cm^?1 with an absorbance of 0.08 at 1 mm light path length.     

The Application of Raman Spectroscopy to the Study of the Uranyl Mineral Coconinoite Fe2Al2(UO2)2(PO4)4(SO4)(OH)2 · 20H2O

ABSTRACT

Raman spectra of the uranyl-containing mineral coconinoite, Fe₂Al₂(UO₂)₂(PO₄)₄(SO₄)(OH)₂ · 20H₂O, are presented and compared with the mineral's infrared spectra. Bands connected with (UO₂)²⁺, (PO₄)^3?, (SO₄)^2?, (OH)^?, and H₂O stretching and bending vibrations are assigned. Approximate U?O bond lengths in uranyl, (UO₂)²⁺, and O?H…O hydrogen bond lengths are calculated from the wavenumbers of the U?O stretching vibrations and (OH)^? and H₂O stretching vibrations, respectively, and compared with published data for similar natural and synthetic compounds.     

Raman spectroscopic study of the uranyl titanate mineral betafite (Ca,U)2(Ti,Nb)2O6(OH): effect of metamictization

Raman spectra of the uranyl titanate mineral betafite were obtained and related to the mineral structure. A comparison is made with the spectra of uranyl oxyhydroxide hydrates. Observed bands are attributed to the (UO₂)²⁺ stretching and bending vibrations, U–OH bending vibrations and H₂O and (OH)^? stretching, bending and libration modes. U–O bond lengths in uranyls and O?H···O bond lengths are calculated from the wavenumbers assigned to the stretching vibrations. Raman bands of betafite are comparable with those of the uranyl oxyhydroxides. The mineral betafite is metamict as is evidenced by the intensity of the UO stretching and bending modes being of lower intensity than expected and by bands that are significantly broader.     

The fluctuation hypothesis of hydrogen bonding

To describe the distortion perturbations of the water molecules in solutions the quantum-mechanical method of partial oscillators has been developed. This method allows one to separate in a simple manner two types of influences on vibrations of OH oscillators, viz. the intermolecular perturbations resulting in the different strengths of hydrogen bonds and intramolecular coupling between stretching vibrations. Here the coupling is treated quite strictly, whereas the intermolecular perturbations are introduced phenomenologically. The calculation of the distribution of distortions among molecules in liquid H₂O and D₂O induced by non-equivalency of the two hydrogen bonds of the water molecule has been made on the basis of the method developed, and the parameters of the mean statistical molecule have been found from the experimental spectrum of HOD. The depolarization ratios of vibrations in Raman spectra of the mean statistical molecules H₂O and D₂O have been computed as an illustration of the possibilities of the proposed calculation method. All the estimates show that the stretching oscillators of H₂O and D₂O molecules are significantly coupled in spite of the great distortion of the symmetry of water molecules in the liquid state.     

Ethylene adsorption on the Pt-Cu bimetallic catalysts. Density functional theory cluster study

The adsorption of ethylene on Cu₁₂Pt₂ clusters has been studied within the density functional theory (DFT) approach to understand the high ethylene selectivity of Cu-rich Pt-Cu catalyst particles in the reaction of hydrogen-assisted 1,2-dichloroethane dechlorination. The structural parameters for Cu₁₂Pt₂ clusters with D_4h, D_2d, and C_3v symmetry have been calculated. The relative stability of the isomeric Cu₁₂Pt₂ clusters follows the order: C_3v > D_2d > D_4h. Each isomer has an active site for ethylene adsorption that consists of a single Pt atom surrounded by Cu atoms. The interaction of ethylene with the active site yields a π-C₂H₄ adsorption complex. The strongest π-C₂H₄ complex forms with the cluster of C_3v symmetry; the bonding energy, ΔE_π(C₂H₄), is −15.6 kcal mol⁻¹. The bonding energies for the π-C₂H₄ complex with Cu₁₄ and Pt₁₄ clusters are −6.5 and −18.8 kcal mol⁻¹, respectively.The addition of Pt to Cu modifies the valence spd-band of the cluster as compared to a Cu₁₄ cluster. The DOS near the Fermi level increases when C₂H₄ adsorbs on the Cu₁₂Pt₂ cluster. As well, the center of the d-band shifts toward lower binding energies. Ethylene adsorption also induces a number of states below the d-band. These states correspond to those of gas-phase C₂H₄.The vibrational frequencies of C₂H₄ adsorbed on the clusters of D_4h and C_3v symmetry have been calculated. The phonon vibrations occur below 250 cm⁻¹. The intense bands around 200 cm⁻¹ are attributed to stretching vibrations of the Pt-Cu bonds normal to the cluster surface. The stretching vibrations of the Pt-C bonds depend on the local structure of the active site: ν_s(Pt-C) = 268 cm⁻¹ and ν_as(Pt-C) = 357 cm⁻¹ for the cluster of the D_4h symmetry; ν_s(Pt-C) = 335 cm⁻¹ and ν_as(Pt-C) = 397 cm⁻¹ for the cluster of the C_3v symmetry. Bands in the range of 800-3100 cm⁻¹ are attributed to vibrations of the adsorbed C₂H₄ molecule. The signature frequencies of the π-C₂H₄ adsorption complex are the δ_s(CH₂) deformation vibration at ∼1200 cm⁻¹ and the ν(C-C) stretching vibration at ∼1500 cm⁻¹. These vibration are absent for di-σ-C₂H₄ adsorption complexes.     

Raman spectroscopic study of the antimonate mineral brandholzite Mg[Sb2(OH)12]·6H2O

Raman spectra of brandholzite Mg[Sb₂(OH)₁₂]·6H₂O were studied, complemented with infrared spectra, and related to the structure of the mineral. An intense Raman sharp band at 618 cm⁻¹ is attributed to the SbO symmetric stretching mode. The low‐intensity band at 730 cm⁻¹ is ascribed to the SbO antisymmetric stretching vibration. Low‐intensity Raman bands were found at 503, 526 and 578 cm⁻¹. Corresponding infrared bands were observed at 527, 600, 637, 693, 741 and 788 cm⁻¹. Four Raman bands observed at 1043, 1092, 1160 and 1189 cm⁻¹ and eight infrared bands at 963, 1027, 1055, 1075, 1108, 1128, 1156 and 1196 cm⁻¹ are assigned to δ SbOH deformation modes. A complex pattern resulting from the overlapping band of the water and hydroxyl units is observed. Raman bands are observed at 3240, 3383, 3466, 3483 and 3552 cm⁻¹; infrared bands at 3248, 3434 and 3565 cm⁻¹. The Raman bands at 3240 and 3383 cm⁻¹ and the infrared band at 3248 cm⁻¹ are assigned to water‐stretching vibrations. The two higher wavenumber Raman bands observed at 3466 and 3552 cm⁻¹ and two infrared bands at 3434 and 3565 cm⁻¹ are assigned to the stretching vibrations of the hydroxyl units. Observed Raman and infrared bands in the OH stretching region are associated with O‐H···O hydrogen bonds and their lengths 2.72, 2.79, 2.86, 2.88 and 3.0 Å (Raman) and 2.73, 2.83 and 3.07 Å (infrared). Copyright © 2009 John Wiley & Sons, Ltd.     

The assignment of Co-C bond stretching vibrational frequency of CH3Co(DH)2H2O in IR and Raman spectra

Abstract

In order to aid assignment of Co-C bond stretching vibrational frequency of CH₃Co(DH)₂H₂O (DH=dimethylgIyoximato monanion) in IR and Raman spectra, its isotopic substitution CD₃Co(DH)₂H₂O has been synthesized and normal coordinate analyses on the two complex have been made. The bands were assigned in terms of potential energy distribution. The results provide definitive band assignment of the Co-C bond and Co-N bond stretching modes which are coupling at 511 cm^?1.     

Raman spectroscopic study of the uranyl mineral pseudojohannite Cu6.5[(UO2)4O4(SO4)2]2(OH)5·25H2O

Raman spectra of pseudojohannite were studied and related to the structure of the mineral. Observed bands were assigned to the stretching and bending vibrations of (UO₂)²⁺ and (SO₄)²⁻ units and of water molecules. The published formula of pseudojohannite is Cu_6.5(UO₂)₈[O₈](OH)₅[(SO₄)₄]·25H₂O. Raman bands at 805 and 810 cm⁻¹ are assigned to (UO₂)²⁺ stretching modes. The Raman bands at 1017 and 1100 cm⁻¹ are assigned to the (SO₄)²⁻ symmetric and antisymmetric stretching vibrations. The three Raman bands at 423, 465 and 496 cm⁻¹ are assigned to the (SO₄)²⁻ν₂ bending modes. The bands at 210 and 279 cm⁻¹ are assigned to the doubly degenerate ν₂ bending vibration of the (UO₂)²⁺ units. U O bond lengths in uranyl and O H···O hydrogen bond lengths were calculated from the Raman and infrared spectra. Copyright © 2009 John Wiley & Sons, Ltd.     

Absorptionsspektrum des Ce3+-Ions und Schwingungsspektrum im CeCl3·7H2O und CeCl3·7D2O

The absorption spectra of CeCl₃·7 H₂O, LaCl₃·7 H₂O, CeCl₃·7 D₂O and LaCl₃·7 D₂O have been measured at low temperatures in the region of the 4 f→4 f infrared transitions. The energy levels of the Ce³⁺-ion in these compounds have been derived. The infrared phonon transitions have also been determined from the reflection spectra of these crystals measured in the region between 4000 cm^?1 and 50 cm^?1. Some of the energy levels of the Ce³⁺-ions in the deuterated crystals are shifted for about 10 wavenumbers against those in CeCl₃·7 H₂O. These shifts are probably due to an interaction of the electronic levels with resonant phonon-states in one or the other of the two compounds.     

Vibrational Spectroscopic Studies of Molecules with Biochemical Interest: The Cysteine Zwitterion

Abstract

The L-cysteine zwitterions in the orthorhombic crystal structure and in aqueous solution, including the deuterated isotopologues HSCD₂CH(NH₃ ⁺)COO^?, DSCH₂CH(ND₃ ⁺)COO^?, and DSCD₂CH(ND₃ ⁺)COO^?, have been studied by mid-infrared, far-infrared, and Raman spectroscopy. Density functional theory (DFT) calculations were performed for an equilibrium molecular geometry of the cysteine zwitterion to obtain vibrational frequencies of fundamental modes, infrared (IR) and Raman intensities, and the depolarization ratio of the Raman bands and combined with normal coordinate force field analyses. The force field obtained for dissolved (in H₂O and D₂O) cysteine, based on the 4 × 36 experimental fundamental modes of the four isotopologues, was successfully transferred to the two conformers in the solid state. The experimentally observed multiple bands (generally doublets) of L-cysteine and its deuterated isotopologues in the solid state were interpreted based on the coexistence of two conformers in the unit cell. The calculated frequencies were used for full assignments of the fundamental IR and Raman vibrational transitions, including an attempt to interpret all low-frequency vibrations (below 400 cm^?1) of the zwitterion also in the solid state. In particular, the hydrogen bonding effects on conformation, bond lengths, and force constants were studied, including those of the distorted NH₃ ⁺ amino group. The –S-H and -S-D stretching vibrations were found to be local modes, not sensitive to deuterium substitution of the -CH₂ and -NH₃ ⁺ groups in the molecule or to the H(D)-S-C-C torsional angle. The two major -S-H or -S-D stretching bands observed in the solid state correspond to different S-H/D bond lengths and resulted in the force constants K _SH = 3.618 N·cm^?1 and 3.657 N·cm^?1 for the SH^… S and SH^… O hydrogen-bonded interactions. A remarkable result was that the S(H)^… O interaction was weaker than the S(H)^… S interaction in the solid state and even weaker in aqueous solution, K _SH = 3.715 N·cm^?1, possibly due to intramolecular interactions between the thiol and amino groups. A general correlation between the S-H/D bond length and vibrational frequency was developed, allowing the bond length to be estimated for sulfhydryl groups in, for example, proteins. The C-S stretching modes were fitted with different C-S stretching force constants, K _CS = 3.213 and 2.713 N·cm^?1, consistent with the different CS bond lengths for the two solid-state conformers.     

Excess thermodynamic quantities of D<Subscript>2</Subscript>O water calculated from its Raman O−D stretching spectra

Excess thermodynamic functions of D₂O water have been calculated from the vibrationally decoupled O−D stretching spectra of very dilute solutions of HOD in H₂O. Comparison of the results with reference calorimetric data for water showed a good correspondence for excess heat capacity above the melting point of ice. The excess enthalpy at the melting point also coincides well with latent heat of melting.     

Fundamental and combination bands of CO2–C2H2 and CO2–C2D2 in the mid-infrared region

Spectra of the weakly bound CO₂–C₂H₂ and CO₂–C₂D₂ complexes are observed in the regions of CO₂ ν₃ (≈ 2349 cm^?1) and C₂D₂ ν₃ (≈ 2440 cm^?1) fundamental vibrations, using an infrared optical parametric oscillator to probe a pulsed supersonic slit-jet expansion. Five bands are measured and analysed: the fundamental asymmetric stretch of the C₂D₂ component, two combination bands involving the out-of-plane torsional vibrations (C₂D₂ ν₃ + torsion and CO₂ ν₃ + torsion) for CO₂–C₂D₂, and two combination bands involving an intermolecular in-plane bending vibration for CO₂–C₂H₂ and CO₂–C₂D₂. The resulting intermolecular frequencies are 61.408(1), 54.5(5), 39.9(5), and 39.961(1) cm^?1 for CO₂–C₂H₂ and CO₂–C₂D₂ in-plane vibrations, and CO₂–C₂D₂ out-of-plane torsional vibrations in CO₂ and C₂D₂ regions, respectively. This is the first experimental determination of these intermolecular vibrational frequencies.     

Potential models and local mode vibrational eigenvalue calculations for acetylene

Two potential models for acetylene are developed and tested by comparison between variational calculations for the stretching vibrational term values and available spectroscopic data. The first model based on local bond potentials with harmonic interbond coupling gives root mean square deviations of 6 cm^?1 for C₂H₂ and 3 cm^?1 for C₂D₂. The second model is more ambitious, being designed to reproduce the dissociation characteristics of the molecules, and the calculated root mean square deviations from the experimental vibrational term values are larger, 32 cm^?1 for C₂H₂ and 24 cm^?1 for C₂D₂. The eigenvalue spectrum of C₂H₂ is shown to differ from that of C₂D₂ in showingmarked local mode features and this difference in behaviour is underlined by means of a correlation diagram. Finally it is shown how the known normal mode frequencies and anharmonic constants may be introduced into a simple model in order to predict the excited term values of C₂H₂, again with a root mean square deviation of 6 cm^?1.