Critical evaluation of anharmonic corrections to the equilibrium isotope effect for methyl cation transfer from vacuum to dielectric continuum

Harmonic and anharmonic vibrational frequencies are computed for isotopologues of methyl cation in vacuum and in a polarised continuum model (PCM) dielectric continuum (? = 80) within Gaussian09. Comparison of results in vacuum for two methods (B3LYP and second-order Møller–Plesset perturbation theory) and three basis sets (6-31+G(d), cc-aug-PVDZ, cc-aug-PVQZ) with published anharmonic frequencies obtained from an accurate vibrational configuration interaction (VCI) method shows the smallest root mean square error in the frequencies from B3LYP/6-31+G(d) with anharmonic corrections. Using this method to calculate isotopic partition function ratios (IPFRs) for all six pairs of CH₃⁺, CH₂D⁺, CHD₂⁺ and CD₃⁺ gives better results for anharmonic frequencies than for unscaled harmonic frequencies, but scaled harmonic frequencies give even better results for less cost. The scaling factor is simply the ratio of the sum of the anharmonic VCI frequencies to the sum of the harmonic B3LYP/6-31+G(d) frequencies, which corresponds to the dominance of zero-point energy changes in determining the IPFRs. Both the scaled and unscaled harmonic frequencies provide reasonable estimates for the equilibrium isotope effects (EIEs) upon transfer of methyl cation from vacuum to PCM ‘water’, but the anharmonic PCM calculations give erratic results. The use of scaled B3LYP/6-31+G(d) harmonic frequencies is recommended for the estimations of EIEs rather than expensive anharmonic corrections.     

The two-dimensional anharmonic oscillator: Vibration-rotation constants of fulminic acid,HCNO

The lowest-wavenumber vibration of HCNO and DCNO, ν₅, is known to involve a largeamplitude low-frequency anharmonic bending of the CH bond against the CNO frame. In this paper the anomalous vibrational dependence of the observed rotational constants B(v₅, l₅), and of the observed l-doubling interactions, is interpreted according to a simple effective vibration-rotation Hamiltonian in which the appropriate vibrational operators are averaged in an anharmonic potential surface over the normal coordinates (Q_5x, Q_5y). All of the data on both isotopes are interpreted according to a single potential surface having a minimum energy at a slightly bent configuration of the HCN angle (～170°) with a maximum at the linear configuration about 2 cm^?1 higher. The other coefficients in the Hamiltonian are also interpreted in terms of the structure and the harmonic and anharmonic force fields; the substitution structure at the “hypothetical linear configuration” determined in this way gives a CH bond length of 1.060 Å, in contrast to the value 1.027 Å determined from the ground-state rotational constants.We also discuss the difficulties in rationalizing our effective Hamiltonian in terms of more fundamental theory, as well as the success and limitations of its use in practice.     

Towards an explanation of collisionless multiple-photon laser dissociation of SF6

The rapidity and high degree of molecular vibrational excitation by the absorption of ir laser light in SF₆ and other molecules may be due in large part to the anharmonic splitting of excited vibrational states. Anharmonic splitting of an overtone or combination vibrational level (i) is possible only in molecules with degenerate vibrational states, (ii) can be comparable in magnitude to the net anharmonic shift of the level, (iii) is generally much larger than the rotational shifts which have previously been proposed as an explanation for the dissociation of SF₆. We find that consecutive nearly resonant transitions are possible in SF₆ up to υ₃ = 5 to 10.     

Pressure dependence of phonon energies at critical points in the Brillouin zone in KTaO3 measured with differential second order raman scattering

Wavelength modulated Raman scattering was used to study the effects of pressure on the second order spectrum of KTaO₃. The pressure results lend support to previous identifications of structures in the second order differential Raman spectrum in terms of pairs of phonons from critical points in the Brillouin zone. Using these identification mode Grüneisen parameters are obtained for several vibrational modes. Strong anharmonic behavior of of the TA(X) mode is observed when we correlate the results from pressure measurements with previous studies of the effects of temperature.     

New results on vibrational population decay in simple liquids

The population lifetimes of the symmetric CH₂-stretching mode of several methylene halides were measured after infrared excitation by spontaneous anti-Stokes Raman scattering of delayed picosecond probe pulses. Data ranging from 6.5 to 45 ps are reported. The results give evidence for vibrational energy transfer via anharmonic coupling to neighbouring vibrational combination bands and overtones.     

Energy level clusters for ν2 + ν3 type combination bands of tetrahedral molecules

Clustering of tetrahedral levels is shown to occur in ν₂ + ν₃ type combination bands of spherical top molecules due to Coriolis and vibrational anharmonic interactions. Cluster correlation diagrams are shown for cases where the vibrational splitting is both large and small compared to the Coriolis splitting, and cluster approximations are given for both cases.     

Electrons in dry DNA from density functional calculations

The electronic structure of an infinite polyguanine-polycytosine DNA molecule in its dry A-helix structure is studied by means of density functional calculations. An extensive study of 30 nucleic base pairs is performed to validate the method. The electronic energy bands of DNA close to the Fermi level are then analysed in order to clarify the electron transport properties in this particularly simple DNA realization, probably the best suited candidate for conduction. The energy scale found for the relevant band widths, as compared with the energy fluctuations of vibrational or genetic-sequence origin, makes highly implausible the coherent transport of electrons in this system. The possibility of diffusive transport with subnanometre mean free paths is, however, still open. Information for model Hamiltonians for conduction is provided.     

Effects of anharmonic splitting upon collisionless multiple-photon laser excitation of SF6

Qualitative agreement of the dependence of molecular excitation upon laser frequency, between non-perturbative quantum-mechanical calculations and experimental measurements of the collisionless multiple-photon excitation of a few vibrational quanta in SF₆ by a CO₂ laser, results when anharmonic splitting of the vibrational energy levels is taken into account.     

Calculation of vibrational energy levels of triatomic molecules with the C2v and Cs symmetries by summing divergent series of the Rayleigh-Schr?dinger perturbation theory

The Rayleigh-Schr?dinger perturbation theory is applied to calculation of vibrational energy levels of triatomic molecules with the C _2v and C _s symmetries: SO₂, H₂S, F₂O, HOF, HOCl, and DOCl. Particular attention is given to the states coupled by anharmonic resonances; for such states, the perturbation theory series diverge. To sum these series, the known methods of Padé, Padé-Borel, and Padé-Hermite and the method of power moments are used. For low-lying levels, all the summation methods give satisfactory results, while the method of quadratic Padé-Hermite approximants appears to be more efficient for high-excited states. Using these approximants, the structure of singularities of the vibrational energy, as a function in the complex plane, is studied.     

The anharmonic force fields of PH3, PHF2, PF3, PH5, and H3PO

The cubic and quartic force fields of the title compounds are determined from ab initio SCF calculations using 6-31G^** and TZP/TZ2P basis sets. The computed geometries, vibration-rotation interaction constants, l-doubling constants, anharmonicity constants, and vibrational wavenumbers are compared with the available experimental data, especially for PH₃ and PF₃. Many experimentally unknown spectroscopic constants are predicted. A scaling procedure based on calculated harmonic and anharmonic force fields is proposed for predicting the vibrational wavenumbers of unknown molecules such as PH₅.     

Experimental and theoretical study of the ν(HF) absorption band structure in the H2O…HF complex

The νHF absorption band shape of the H₂O…HF complex is studied in the gas phase at a temperature of 293 K. The spectra of H₂O/HF gaseous mixtures in the range 4000–3400 cm^?1 are recorded at a resolution of 0.2–0.02 cm^?1 with Bruker IFS-113v and Bruker IFS-120 HR vacuum Fourier spectrometers in a 20-cm cell. The spectra of the H₂O…HF complex in the region of the ν₁(HF) absorption band are obtained by subtracting the calculated spectra of free H₂O and HF molecules from the experimental spectrum. The ν₁ band of the H₂O…HF complex has an asymmetric shape with a low-frequency head, an extended high-frequency wing, and a characteristic vibrational structure. Two approaches are used to calculate the ν1 band shape as a superposition of rovibrational bands of the fundamental and hot transitions involving the low-frequency modes of the complex. The first approach is based on a simplified semiempirical procedure. The second approach relies on a nonempirical anharmonic calculation of the vibrational energy levels, the frequencies and intensities of the corresponding transitions, and the rotational constants. These parameters are obtained by calculating ab initio the potential energy and dipole moment surfaces in the second-order Möller-Plesset approximation and using the variational method to solve one-, two-, and three-dimensional anharmonic vibrational problems. The absorption spectrum of the complex in the range 3600–3720 cm^?1, reconstructed using the nonempirical electro-optical parameters, reproduces rather well the main features of the experimental spectrum, including the relative intensities of peaks of the vibrational structure. However, the interpretation of most of the structural features of the spectrum differs from that adopted in the semiempirical scheme. First of all, it follows from the results of nonempirical calculation that the central, most intense, maximum of the experimental spectrum should correspond to the v ₁=1←0 transition from the ground vibrational state. This fact gives rise to a new value of the vibrational transition frequency ν ₁ ⁰ in the H₂O…HF complex equal to 3635 cm^?1, which is higher than the commonly accepted value of 3608 cm^?1.     

Vibrational corrections to electric properties of weakly bound systems

The pure electronic and vibrational contributions to electric dipole moments, dipole polarizabilities, and first hyperpolarizabilities have been evaluated for the HF and H₂O dimers. The zero-point vibrational average corrections to dipole moments and dipole polarizabilities turn out to be relatively small. However, the corresponding contributions to the first hyperpolarizability are found to be of the same magnitude as the pure electronic values. The so-called pure vibrational corrections to the dipole polarizability and first hyperpolarizability of hydrogen bonded dimers are exceptionally large and indicate that the perturbation theory method used for their evaluation fails to account properly for the high mechanical and electric anharmonicities present in these systems. The analysis of different harmonic and anharmonic contributions to the pure vibrational correction to the first hyperpolarizability shows explicitly the importance of the low frequency intermolecular modes.     

Molecular dynamics calculations of anharmonic properties of the vibrational spectrum of BCC zirconium under pressure

The structural stability and lattice dynamics of the high-pressure bcc phase of Zr at a constant temperature T = 500 K are studied for various volumes using molecular dynamics simulation with the Animalu pair pseudopotential. Dispersion curves of the vibrational spectrum calculated by the molecular dynamics method for various volumes are compared to the phonon spectrum obtained in the harmonic approximation. It is demonstrated that, as the volume decreases, all frequencies of the vibrational spectrum increase gradually and bcc zirconium remains strongly anharmonic along all high-symmetry directions of the Brillouin zone over the entire range of volumes studied. The strongly anharmonic N _T1 phonon is significantly softened near the point of structural instability of bcc-Zr at T = 500 K and V = 0.87V ₀. As the volume decreases to V = 0.73V ₀ under pressure, the anharmonic corrections for this phonon decrease by almost an order of magnitude and the phonons near the H point of the Brillouin zone become anharmonic. The damping of the T ₁ phonon mode along the [110] direction is calculated as a function of pressure.     

New approach to nonlinear dynamics of fullerenes and fullerites

A new type of nonlinear (anharmonic) excitations—bushes of vibrational modes—in physical systems with point or space symmetry is discussed. All infrared-active and Raman-active bushes for C₆₀ fullerene are found by means of special group-theoretical methods.     

Experimental determination of vibrational anharmonic contributions

This article deals with the experimental determination of separate vibrational anharmonic contributions to the self‐energy of phonons in any crystals based on temperature dependence of their Raman spectra. We propose a new approach to find each anharmonic contribution by using special temperature points. We apply the approach to diamond, silicon, and crystalline α‐S₈ and show that our results for summarized anharmonicity in diamond and silicon are in good agreement with the values obtained previously for these systems by other researchers. Copyright © 2013 John Wiley & Sons, Ltd.     

Anharmonic force fields of cis- and trans-S1 C2H2

We calculate second-order vibrational perturbation theory (VPT2) anharmonic force fields for the cis and trans conformers of S₁ C₂H₂, and compare the results to experiment. The vibrational assignments of recently observed levels belonging to the cis well are of particular interest. A refined estimate of the cis origin position (44,870?±?10?cm^?1) is proposed, and preliminary low-energy fits to the global J?=?K?=?0 trans level structure are also described. The performance of perturbation theory in this isomerizing system is examined, and both surprising successes and failures are encountered. We examine these and their causes, and offer practical suggestions for avoiding the pitfalls of applying perturbation theory to systems with large amplitude motions.     

IR Vibrational spectra of H-bonded complexes of adenine, 2-aminopurine and 2-aminopurine<Superscript>+</Superscript> with cytosine and thymine: Quantum-chemical study

Using theoretical study on the B3LYP/6-311++G(d,p) level of theory, we have compared vibrational spectra of 2-aminopurine (as neutral or protonated at N1 atom species) with adenine and H-bonded complexes of 2-aminopurine (as neutral or protoned at N1 atom species) · cytosine or 2-aminopurine · thymine with adenine · cytosine and adenine · thymine base pairs. The nature of the base pairing between adenine, 2-aminopurine, 2-aminopurine⁺ and cytosine or thymine have been investigated by means of quantum-mechanical calculations. We have investigated the effect of the hydrogen bond formation on the vibrational spectra of the investigated base pairs. The main differences in the vibrational spectra as for bases so for base pairs have been observed in the high-frequency region.     

Anharmonic spectra of methanol and silanol: A comparative study

Anharmonic vibrational spectra of methanol and silanol as well as of some of their deuterated isotopomers are analysed using the vibrational self-consistent field approximation corrected by second order perturbation theory (cc-VSCF). Experimental frequencies in the case of methanol and its isotopomers are in general reproduced and anharmonic effects in their vibrational spectra are suitably explained. The similar species containing Si, i.e., silanol, is very unstable. Experimental data about its vibrational spectra are rare in the literature and the only theoretical data available come from the harmonic approach. Thus, to predict further anharmonic effects in its vibrational spectra, we extend our results on methanol to the silanol molecule.     

On the Hulburt-Hirschfelder potential function for the Ar2 molecule

The modified Morse potential function known as the Hulburt-Hirschfelder function has been used for the Ar₂ molecule using experimental values for the spectroscopic constants. The consistency of this potential is checked by recalculating the vibrational levels using Cashion's method. The results are satisfactory. The potential may be useful for calculating the anharmonic properties of crystalline argon.     

Application of the algebraic approach to molecular thermodynamics and quantum deformations

An algebraic model based on Lie-algebraic techniques is applied to vibrational molecular thermodynamics. The model uses the isomorphism between the SU(2) algebra and the one-dimensional Morse oscillator. A vibrational high-temperature partition function and the related thermodynamic properties are derived in terms of the parameters of the model. The anharmonic vibrations are described as anharmonic q-bosons using a first-order expansion of a quantum deformation. It is shown, that this quantum deformation is related to the shape of the Morse potential.