Pressure and temperature effects on the vibrational frequencies of crystalline polymethylenes. II. Lattice anharmonicity and the equation of state

The lattice anharmonicity of crystalline polymethylene is interpreted from the observed pressure and temperature dependence of Raman active interchain lattice frequencies of the n-paraffins C₂₃H₄₈ and C₄₄H₉₀. The temperature dependence of the L_c′ interchain lattice frequency is separated into quasiharmonic and self-energy shifts. The former is due to the volume dependence of the force constant of the oscillator. The latter is due to the anharmonicity of the dynamic potential, and is obtained as a function of volume and phonon population. The setting angle of the carbon skeleton is predicted to be temperature-sensitive. While the potential surface of the crystal is asymmetric along the L_c′ normal coordinate, it is essentially symmetrical along the T_b′ coordinate. The well-known Mie–Gruneisen equation of state is generalized to include anharmonicities of oscillators through the temperature dependence of their vibrational frequencies.     

Low-frequency vibrational modes and temperature dependence of NQR frequencies in 1,2,4,5-tetrabromobenzene

A temperature variation study of the nuclear quadrupole resonance (NQR) frequencies for the two resonance lines in 1,2,4,5-tetrabromobenzene was carried out in the range 77–300 K. The far-infrared spectrum of 1,2,4,5-tetrabromobenzene was recorded and the low-frequency vibrational modes noted. From the nine observed frequencies, the torsional modes contributing to the change in NQR frequencies with temperature are identified by correlating the calculated values of the NQR frequencies at different temperatures with the observed values.     

Intramolecular vibrational coupling contribution to temperature dependence of vibrational mode frequencies

High-frequency vibrational modes in molecules in solution are sensitive to temperature and shift either to lower or higher frequencies with the temperature increase. These frequency shifts are often attributed to specific interactions of the molecule and to the solvent polarization effect. We found that a substantial and often dominant contribution to sensitivity of vibrational high-frequency modes to temperature originates from anharmonic interactions with other modes in the molecule. The temperature dependencies were measured for several modes in ortho-, meta-, and para-isomers of acetylbenzonitrile in solution and in a solid matrix and compared to the theoretical predictions originated from the intramolecular vibrational coupling (IVC) evaluated using anharmonic density functional theory calculations. It is found that the IVC contribution is essential for temperature dependencies of all high-frequency vibrational modes and is dominant for many modes. As such, the IVC contribution alone permits predicting the main trend in the temperature dependencies, especially for vibrational modes with smaller transition dipoles. In addition, an Onsager reaction field theory was used to describe the solvent contribution to the temperature dependencies.     

Cation effects on the vibrational frequencies of adsorbed thiocyanate on platinum

Infrared spectra of thiocyanate adsorbed on a platinum electrode surface were obtained in the presence of perchlorate electrolytes of various alkali metal cations. It was discovered that the vibrational frequency of the C-N stretching mode is dependent upon the nature of the supporting electrolyte cation. Two bands were observed in the 2050 to 2150 cm⁻¹ range; one band was attributed to nitrogen-bound thiocyanate, and the other to species adsorbed via the sulfur atom. Each of these bands demonstrated independent frequency dependencies on cation nature and on the applied electric field within the interfacial region. Differences were also observed in the intensity dependence of the bands on the applied potential. The results were explained in terms of changes in the distance between the outer Helmholtz plane (OHP) and the surface of the electrode, and also in terms of the possible influence of coadsorbed alkali metal cations on the vibrational frequency of thiocyanate species adsorbed through the nitrogen atom. The effects that variations in the OHP-electrode distance impart on the magnitude of the potential drop across the interface, and the influence of small changes in this potential field on the C-N stretching frequency of N- and S-adsorbed thiocyanate species, are discussed.     

The calculation of the vibrational frequencies of crystalline compounds and its implementation in the CRYSTAL code

The problem of numerical accuracy in the calculation of vibrational frequencies of crystalline compounds from the hessian matrix is discussed with reference to alpha-quartz (SiO(2)) as a case study and to the specific implementation in the CRYSTAL code. The Hessian matrix is obtained by numerical differentiation of the analytical gradient of the energy with respect to the atomic positions. The process of calculating vibrational frequencies involves two steps: the determination of the equilibrium geometry, and the calculation of the frequencies themselves. The parameters controlling the truncation of the Coulomb and exchange series in Hartree-Fock, the quality of the grid used for the numerical integration of the Exchange-correlation potential in Density Functional Theory, the SCF convergence criteria, the parameters controlling the convergence of the optimization process as well as those controlling the accuracy of the numerical calculation of the Hessian matrix can influence the obtained vibrational frequencies to some extent. The effect of all these parameters is discussed and documented. It is concluded that with relatively economical computational conditions the uncertainty related to these parameters is smaller than 2-4 cm(-1). In the case of the Local Density Approximation scheme, comparison is possible with recent calculations performed with a Density Functional Perturbation Theory method and a plane-wave basis set.     

15N isotope effects on the vibrational frequencies of aniline and assignments of the frequencies of its nh2 group

Abstract-Infrared absorptions of aniline in which 31·9 per cent of nitrogen is ¹⁵N and 68·1 per cent is ¹⁴N were examined in dilute CCl₄ and CS₂ solutions by means of a grating instrument. For five bands at 3481·4, 3395·2, 1618·9, 1276·1 and 1114·6 cm⁻¹ appreciable isotope shifts were observed. It was shown that these bands are to be assigned, respectively, to NH₂ antisymmetric stretching, NH₂ symmetric stretching, NH₂ bending, C-N stretching and NH₂ rocking (or twisting) vibrations.     

Van der Waals interaction and hydrogen bond effects on molecular vibrational frequencies

The frequency shift of an AZ two-atomic fragment upon molecule transfer from gas to solution or matrix is investigated. The nearest neighbour ligands are considered to form a cluster. The coupling of the ν_s(AZ) mode with the cluster low-frequency oscillators (ν_Q) is taken into account. One such oscillator can be the ν_σ(AZ…B) intermolecular stretching frequency oscillator in the H-bonded or charge transfer complex. A general expression for the ν_s(AZ) frequency shift (Δω) is obtained, which allows for both the usual van der Waals interaction and the (ν_s, ν_σ) and (ν_s, ν_Q) mode couplings. When the former prevails, the relative frequency shift Δω/ω_f is invariant to the Z → Z* (e.g., H → D) isotopic substitution. When the mode coupling prevails, the quantity Δω/ω²_f is invariant what is typical for H bonds. If the H-bonded or charge transfer complexes are absent, the frequency shift Δω is proportional to α(ϱ_AZ + ϱ_L)⁻⁶ where α is the polarizability of the ligand, ϱ_AZ and ϱ_L are the van der Waals radii of AZ and ligand, respectively. The additional ν_s(AH) frequency shift upon transfer of the AH…B complex from the gas to solution seems to be caused by (ν_s, ν_Q) mode coupling.     

A new way of analyzing vibrational spectra. I. Derivation of adiabatic internal modes

A new way of analyzing measured or calculated vibrational spectra in terms of internal vibrational modes associated with the internal parameters used to describe geometry and conformation of a molecule is described. The internal modes are determined by solving the Euler–Lagrange equations for molecular fragments ϕ_n described by internal parameters ζ_n. An internal mode is localized in a molecular fragment by describing the rest of the molecule as a collection of massless points that just define molecular geometry. Alternatively, one can consider the new fragment motions as motions that are obtained after relaxing all parts of the vibrating molecule but the fragment under consideration. Because of this property, the internal modes are called adiabatic internal modes, and the associated force constants k_a, adiabatic force constants. Minimization of the kinetic energy of the vibrating fragment ϕ_n yields the adiabatic mass m_a (corresponding to 1/G_nn of Wilson's G matrix) and, by this, adiabatic frequencies ω_a. Adiabatic modes are perfectly suited to analyze and understand the vibrational spectra of a molecule in terms of internal parameter modes in the same way as one understands molecular geometry in terms of internal coordinates. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 67 : 1–9, 1998     

Effect of amorphous sequences on the longitudinal acoustic modes in partially crystalline polymers. I. Transfer matrix method

A novel theoretical scheme is developed which enables the determination of the LAM-like vibrations of polymer chains made up of crystalline and amorphous parts as they occur in partially crystalline structures. The boundary conditions effective at the junction points are formulated in terms of the compliances of the associated amorphous sequences. These compliances can be derived from their eigenfrequencies and eigenvectors in a disconnected state. The treatment uses a matrix formalism which can be extended to include bending and torsional motions in a general state of vibration of the crystalline stem. A first numerical example demonstrates that the LA mode of a crystalline stem can be strongly perturbed by the coupling to the adjacent amorphous sequences. Interpretation of frequencies and line shapes of observed LA modes should always include these coupling effects; their neglect can lead to considerable errors.     

Characteristic vibrational frequencies of the SOS group

The assignment of frequencies for the three vibrations of the SOS groups in molecules of the type X_nSOSX_n is discussed. It is shown that a consistent assignment can be given for all ten molecules of this type for which data are available. This assignment gives reasonable values of force constants in a simple valence force-field calculation. It is shown that there are linear relationships between the frequencies of the symmetrical stretching and bending modes of the SOS group and the square-root of the mass of the groups SX_n attached to the oxygen atom.     

Solvent effects on the vibrational frequencies of the phenolate anion, the para-cresolate anion, and their radicals

The effects of aqueous solvation on the structure and vibrational frequencies of phenol, para-cresol, and their respective radicals are calculated at the B3LYP/6-31+G(d,p) level of theory using the conductor-like polarizable continuum model (C-PCM) alone and in combination with an explicit water molecule H-bonded to the phenolic oxygen. Calculated vibrational frequencies are compared to experimental frequencies obtained in aqueous buffer at high pH. For all models, the C-PCM provides the best overall agreement between theory and experiment at a modest computational effort, as demonstrated by the lowest mean absolute deviations in the computed frequencies. In addition, the C-PCM provides anion Wilson mode 7a (18)O isotope shifts in excellent agreement with experiment and improves agreement between the computed and observed radical Wilson mode 7a (2)H isotope shift. On the basis of a quantitative comparison of the anion and radical normal modes by vibrational projection analysis and total energy decomposition, an alternative criterion for distinguishing the anion and radical Wilson modes 7a and 19a using the relative phasing of the carbon-oxygen and carbon-carbon bond stretches is presented.     

Coupled calculation of vibrational frequencies and intensities

The combination of normal coordinate analysis with intensity calculations gives quantitative information about molecular force fields and the assignments of vibrational frequencies. Calculations of vibrational intensities by means of a standard CNDO/2 version give rise to satisfactory results for the IR intensities. However, the calculated Raman intensities often differ strongly from the experimental data. Inclusion of 2p-polarization functions on hydrogen in the usually used valence basis set is quite successful to obtain improved molecular polarizabilities as well as Raman intensities.     

Structure and vibrational frequencies of 2-butanimine

The conformational behavior and structural stability of 2-butanimine were investigated by utilizing ab initio calculations with 6-311++G** basis set at HF, MP2, B3LYP and BLYP levels. The vibrational frequencies of 2-butanimine were computed. Complete vibrational assignments were made on the basis of normal coordinate calculations for stable conformer of the molecule. HF results without scaled quantum mechanical (SQM) force field procedure considered are in bad agreement with experimental values. Of the two DFT methods, BLYP reproduces the observed fundamental frequencies most satisfactorily with the mean absolute deviation of the non-CH stretching modes less than 21.3 cm(-1). The results indicate that BLYP calculation is a very promising approach for understanding the observed spectral features.     

IR frequencies and intensities of the vibrational modes of Cx Hy fragments bonded to metal complexes. Relationship with structure,bonding and reactivity

The following organometallic complexes were studied as models of the coordination between metal atoms and different C_x H_y ligands: Co₂Fe(CO)₉(CCH₂), Co₂Ru(CO)₉(CCH₂), Os₃(H)₂(CO)₉(CCH₂) and Co₂Fe(CO)₉(CC(H)CH₃) (η₃-η₂-vinylidene or μ₃-η₂-methylvinylidene group); Fe₂(C₅H₅)₂(CO)₃(CCH₂) (μ₂-η¹-vinylidene group); Os₃(μ-H)(CO)₉(CHCH₂) (μ₂-η²-vinyl group); CH₃Mn(CO)₅ (η¹-methyl group); Os₃(μ-H)₂(Co)₁₀(CH₂) and Fe₂(CO)₈(CH₂) (μ₂-η¹-methylene group); Co₃(CO)₉(CH) (μ₃-methyne group); CO₃(CO)₉(CCH₃) (μ₃-η¹-ethylidyne group); Os₃(H)(CO)₉(C₂H) (μ₃-η²-acetylide group). The infrared frequencies and intensities associated with the main vibrational modes of the ligands (CC and CH stretchings, CH deformations) were evaluated and compared with those of appropriate model molecules. Both the frequency and intensity data can be usefully correlated with structural parameters (e.g. CC and CH bond distances and HCH bond angles) and provide information on the charge distribution on the ligands. It is therefore possible to discuss the type of metal—ligand interaction and the balance between the σ and π contributions to the bond.     

Relating normal vibrational modes to local vibrational modes with the help of an adiabatic connection scheme

Information on the electronic structure of a molecule and its chemical bonds is encoded in the molecular normal vibrational modes. However, normal vibrational modes result from a coupling of local vibrational modes, which means that only the latter can provide detailed insight into bonding and other structural features. In this work, it is proven that the adiabatic internal coordinate vibrational modes of Konkoli and Cremer [Int. J. Quantum Chem. 67, 29 (1998)] represent a unique set of local modes that is directly related to the normal vibrational modes. The missing link between these two sets of modes are the compliance constants of Decius, which turn out to be the reciprocals of the local mode force constants of Konkoli and Cremer. Using the compliance constants matrix, the local mode frequencies of any molecule can be converted into its normal mode frequencies with the help of an adiabatic connection scheme that defines the coupling of the local modes in terms of coupling frequencies and reveals how avoided crossings between the local modes lead to changes in the character of the normal modes.     

Effect of electron correlation on theoretical vibrational frequencies

Theoretical HF /6-31G * (Hartree–Fock, 6-31G * basis set) and MP 2/6-31G * (second-order Møller–Plesset, 6-31G * basis set) vibrational frequencies based on complete quadratic force fields have been obtained for a set of 36 one- and two-heavy-atom molecules comprising first-row elements for which experimental spectroscopic data are available. Frequencies calculated at the HF /6-31G * level are an average of 12.6% higher than experimental values. Partial treatment of electron correlation via the perturbation method of Møller and Plesset, terminated at second order, leads to a significant reduction in this error, although theoretical MP 2/6-31G * frequencies are still larger than the experimental quantities by 7.3%. Part of the difference may be traced to the restriction of quadratic force fields, as comparison with experimental harmonic frequencies shows deviations of only 9.5% and 4.7% for the two levels, respectively. The calculated frequencies are used in conjunction with the corresponding theoretical equilibrium structures to obtain absolute molecular entropies, which may in turn be used to yield entropies of reaction. These latter quantities are generally in good accord with entropies derived using experimental structures and frequencies.     

The anharmonic vibrational potential and relaxation pathways of the amide I and II modes of N-methylacetamide

We investigate the influence of isotopic substitution and solvation of N-methylacetamide (NMA) on anharmonic vibrational coupling and vibrational relaxation of the amide I and amide II modes. Differences in the anharmonic potential of isotopic derivatives of NMA in D2O and DMSO-d6 are quantified by extraction of the anharmonic parameters and the transition dipole moment angles from cross-peaks in the two-dimensional infrared (2D-IR) spectra. To interpret the effects of isotopic substitution and solvent interaction on the anharmonic potential, density functional theory and potential energy distribution calculations are performed. It is shown that the origin of anharmonic variation arises from differing local mode contributions to the normal modes of the NMA isotopologues, particularly in amide II. The time domain manifestation of the coupling is the coherent exchange of excitation between amide modes seen as the quantum beats in femtosecond pump-probes. The biphasic behavior of population relaxation of the pump-probe and 2D-IR experiments can be understood by the rapid exchange of strongly coupled modes within the peptide backbone, followed by picosecond dissipation into weakly coupled modes of the bath.     

Excited-state geometries and vibrational frequencies studied using the analytical energy gradients of the direct symmetry-adapted cluster-configuration interaction method. I. HAX-type molecules

In this series of studies, we systematically apply the analytical energy gradients of the direct symmetry-adapted cluster-configuration interaction singles and doubles nonvariational method to calculate the equilibrium geometries and vibrational frequencies of excited and ionized states of molecules. The harmonic vibrational frequencies were calculated using the second derivatives numerically computed from the analytical first derivatives and the anharmonicity was evaluated from the three-dimensional potential energy surfaces around the local minima. In this paper, the method is applied to the low-lying valence singlet and triplet excited states of HAX-type molecules, HCF, HCCl, HSiF, HSiCl, HNO, HPO, and their deuterium isotopomers. The vibrational level emission spectra of HSiF and DSiF and absorption spectra of HSiCl and DSiCl were also simulated within the Franck-Condon approximation and agree well with the experimental spectra. The results show that the present method is useful and reliable for calculating these quantities and spectra. The change in geometry in the excited states was qualitatively interpreted in the light of the electrostatic force theory. The effect of perturbation selection with the localized molecular orbitals on the geometrical parameters and harmonic vibrational frequencies is also discussed.     

Pressure and temperature effects on the excess deuteron and proton conductance

The limiting molar conductances ° of deuterium chloride DCl in D₂O were determined as a function of pressure and temperature in order to examine the proton-jump mechanism in detail. The excess deuteron conductances °_E(D ⁺), as estimated by the equation [°_E(D ⁺) = °(DCl/D ₂ O) – °(KCl/D ₂ O)], increases with an increase in the pressure and temperature as well as the excess proton conductance [°_E(H ⁺) = °(HCl/H ₂ O) – °(KCl/H ₂ O)]. The isotope effect on the excess conductances, however, depends on the pressure and temperature contrary to the model proposed by Conway et al.: °_E(H ⁺)/°_E(D ⁺) decreases with increasing pressure and temperature. The magnitude of the decrease with pressure becomes more prominent at lower temperature. These results are discussed in terms of the pre-rotation of adjacent water molecules, the bending of hydrogen bonds with pressure, and the difference in strength of hydrogen bonds between D₂O and H₂O.