Self-consistent geometry in the computation of the vibrational spectra of molecules

An exact and general approach to study molecular vibrations is provided by the Watson Hamiltonian. Within this framework, it is customary to omit the contribution of the terms with the vibrational angular momentum and the Watson term, especially for the study of large systems. We discover that this omission leads to results which depend on the choice of the reference structure. The self-consistent solution proposed here yields a geometry that coincides with the quantum averaged geometry of the Watson Hamiltonian and appears to be a promising way for the computation of the vibrational spectra of strongly anharmonic systems.

[Ag(NH3)(2)]ClO4: Crystal structures, phase transition, and vibrational spectra

[Ag(NH3)(2)](ClO4) is obtained from a solution of AgClO4 in cone. ammonia as colourless single crystals (orthorhombic, Pnmn, Z = 4, a = 795.2(1) pm, b 617.7(1) pm, c = 1298.2(2) pm, R-all = 0.0494). The structure consists of linearly coordinated cations, [Ag(NH3)(2)](+), stacked in a staggered conformation and of tetrahedral (ClO4)(-) anions. A first order phase transition was observed between 210 and 200 K and the crystal structure of the low-temperature modification (monoclinic. P2/m, Z = 4, a = 789.9(5) pm, b = 604.1(5) pm, c = 1290.4(5) pm, beta = 97.436(5)degrees, at 170 K, R-all = 0.0636) has also been solved. Spectroscopic investigations (IR/Raman) have been carried out and the assignment of the spectra is discussed.

On the treatment of singularities of the Watson Hamiltonian for nonlinear molecules

The applicability of the Watson Hamiltonian for the description of nonlinear molecules—especially triatomic ones—has always been questioned, as the Jacobian of the transformation that leads to the Watson Hamiltonian, vanishes at the linear configuration. This results in singular behavior of the Watson Hamiltonian, giving rise to serious numerical problems in the computation of vibrational spectra, with unphysical, spurious vibrational states appearing among the physical vibrations, especially in the region of highly excited states. In this work, we analyze the problem and propose a simple way to confine the nuclear wavefunction in such a way that the spurious solutions are eliminated. We study the water molecule and observe an improvement compared with previous results. We also apply the method to the van der Walls molecule XeHe2.

DFT studies of long-chain FAMEs: theoretical justification for determining chain length and unsaturation from experimental Raman spectra

Density functional calculations, using B3LPY/6-31G(d) methods, have been used to investigate the conformations and vibrational (Raman) spectra of a series of long-chain, saturated fatty acid methyl esters (FAMEs) with the formula CH2nO2 (n = 5-21) and two series of unsaturated FAMEs. The calculations showed that the lowest energy conformer within the saturated FAMEs is the simple (all-trans) structure and, in general, it was possible to reproduce experimental data using calculations on only the all-trans conformer. The only exception was C6H12O2, where a second low-lying conformer had to be included in order to correctly simulate the experimental Raman spectrum. The objective of the work was to provide theoretical justification for the methods that are commonly used to determine the properties of the fats and oils, such as chain length and degree of unsaturation, from experimental Raman data. Here it is shown that the calculations reproduce the trends and calibration curves that are found experimentally and also allow the reasons for the failure of what would appear to be rational measurements to be understood. This work shows that although the assumption that each FAME can simply be treated as a collection of functional groups can be justified in some cases, many of the vibrational modes are complex motions of large sections of the molecules and thus would not be expected to show simple linear trends with changes in structure, such as increasing chain length and/or unsaturation. Simple linear trends obtained from experimental data may thus arise from cancellation of opposing effects, rather than reflecting an underlying simplicity.

Conformations, vibrational frequencies and Raman intensities of short-chain fatty acid methyl esters using DFT with 6-31G(d) and Sadlej pVTZ basis sets

Density functional calculations, using B3LPY/6-31G(d) methods, have been used to investigate the conformations and vibrational (Raman) spectra of three short-chain fatty acid methyl esters (FAMEs) with the formula CnH2nO2 (n = 3-5). In all three FAMEs, the lowest energy conformer has a simple 'all-trans' structure but there are other conformers, with different torsions about the backbone, which lie reasonably close in energy to the global minimum. One result of this is that the solid samples we studied do not appear to consist entirely of the lowest energy conformer. Indeed, to account for the 'extra' bands that were observed in the Raman data but were not predicted for the all-trans conformer, it was necessary to add-in contributions from other conformers before a complete set of vibrational assignments could be made. Provided this was done, the agreement between experimental Raman frequencies and 6-31G(d) values (after scaling) was excellent, RSD = 12.6 cm(-1). However, the agreement between predicted and observed intensities was much less satisfactory. To confirm the validity of the approach followed by the 6-3 1 G(d) basis set, we used a larger basis set, Sadlej pVTZ, and found that these calculations gave accurate Raman intensities and simulated spectra (summed from two different conformers) that were in quantitative agreement with experiment. In addition, the unscaled Sadlej pVTZ, and the scaled 6-3 1 G(d) calculations gave the same vibrational mode assignments for all bands in the experimental data. This work provides the foundation for calculations on longer-chain FAMEs (which are closer to those found as triglycerides in edible fats and oils) because it shows that scaled 6-3 1 G(d) calculations give equally accurate frequency predictions, and the same vibrational mode assignments, as the much more CPU-expensive Sadlej pVTZ basis set calculations.

Dissociation of H2+ from a short, intense, infrared laser pulse: proton emission spectra and pulse calibration

The proton energy spectrum from photodissociation of the hydrogen molecular ion by short intense pulses of infrared light is calculated. The time-dependent Schrödinger equation is discretized and integrated. For few-cycle pulses one can resolve vibrational structure, arising from the experimental preparation of the molecular ion. We calculate the corresponding energy spectrum and analyse the dependence on the pulse time delay, pulse length and intensity of the laser for ? ~ 790 nm. We conclude that the proton spectrum is a sensitive probe of both the vibrational populations and phases, and allows us to distinguish between adiabatic and nonadiabatic dissociation. Furthermore, the sensitivity of the proton spectrum from H2+ is a practical means of calibrating the pulse. Our results are compared with recent measurements of the proton spectrum for 65 fs pulses using a Ti:Sapphire laser (? ~ 790 nm) including molecular orientation and focal-volume averaging. Integrating over the laser focal volume, for the intensity I ~ 3 × 1015 W cm-2, we find our results are in excellent agreement with these experiments.

Positron annihilation in large polyatomic molecules. The role of vibrational Feshbach resonances and binding

We analyse the process of rapid positron annihilation in large polyatomic molecules due to positron capture into vibrational Feshbach resonances. Resonant annihilation occurs in molecules which can bind positrons, and we analyse positron binding to alkanes using zero-range potentials. Related questions of spectra of annihilation gamma quanta and molecular fragmentation following annihilation, are discussed briefly.

The role of vibrational doorway states in positron annihilation with large molecules

Positron annihilation rates in many polyatomic molecular gases are anomalously high. Qualitatively, this can be explained by positron capture in vibrational Feshbach resonances, which can occur for molecules with positive positron a?nities [Gribakin, Phys. Rev. A 61 (2000) 022720]. To verify this idea quantitatively, we examine the densities of vibrational excitation spectra of alkanes. To understand the energy dependence of the annihilation rates for alkanes, we propose that positron capture is mediated by vibrational doorway states, in which positron binding is accompanied by the excitation of fundamentals.

RESONANCE RAMAN-SPECTRA OF THE TRIPLET-STATE OF FREE-BASE TETRAPHENYLPORPHYRIN AND 6 OF ITS ISOTOPOMERS

The resonance Raman spectra of the ground state and the lowest excited tripler state of free-base tetraphenylporphyrin and six of its isotopomers have been obtained using two-color time-resolved techniques. Ground-state spectra were recorded using low-energy 447 nm probe laser pulses, and triplet-state spectra were probed, with similar pulses, 30 ns after high-energy excitation with 532 nm pump pulses. Polarization data on both the ground and triplet states are also reported. The resonance Raman spectrum of the triplet is very different from that of the ground state but the combination of extensive isotope substitution with polarization data allows bands in the ground state to be assigned and corresponding bands in the tripler state to be located. Isotope shifts of the same bands in the S-0 and T-1 states are similar, implying that the compositions of the vibrational modes do not change significantly on excitation. Two of the strongest bands in the T-1 spectra are associated with phenyl ring substituents; these are shifted less than 5 cm(-1) between the S-0 and T-1 states so that bonding in the phenyl substituents is barely affected by excitation to the T-1 state. The changes in position of the porphyrin ring bands are larger, but still only tens of cm(-1) or less, the main changes in the spectra being due to differences in relative band intensities in the two states. The relatively small shifts in the porphyrin ring band positions which are observed show that the excitation energy is not localized on a single small region of the molecule but is delocalized over the entire porphyrin skeleton. This picture of an excited species with high chemical reactivity, but with individual bonds only slightly perturbed from the ground state, is contrasted with molecules, such as benzophenone, where excitation causes a large perturbation in the bonding within a single functional group.

Temperature dependence of the Raman spectra of carbon nanotubes

We report on a temperature dependence of the frequency of all the major peaks in the Raman spectra of carbon nanotubes, using different excitation laser powers at the sample. The frequency decreases with increasing temperature for all peaks, and the shifts in Raman frequencies are linear in the temperature of the sample. In comparison, a similar dependence is found in active carbon, but no shift is observed for the highly ordered pyrolytic graphite within the same range of variation in laser power. A lowering of frequency at higher temperature implies an increase in the carbon-carbon distance at higher temperature. The relatively strong temperature dependence in carbon nanotubes and active carbon may be due to the enhanced increase in carbon-carbon distance. This enhancement may originate from the heavy defects and disorder in these materials. (C) 1998 American Institute of Physics. [S0021-8979(98)05219-0].

Pressure effect on vibrational frequency and dephasing of 1-alkyl-3-methylimidazolium hexafluorophosphate ionic liquids

Raman spectra in the range of the totally symmetric stretching mode of the [PF6]− anion, νs(PF6), have been measured for 1-alkyl-3-methylimidazolium ionic liquids [CnC1im][PF6], for n = 4, 6, and 8, as a function of pressure at room temperature. The ionic liquids [C6C1im][PF6] and [C8C1im][PF6] remain in an amorphous phase up to 3.5 GPa, in contrast to [C4C1im][PF6], whichcrystallizes above ∼0.5 GPa. Equations of state based either on a group contribution model or Carnahan-Starling-van der Waals model have been used to estimate the densities of the ionic liquids at high pressures. The shifts of the vibrational frequency of νs(PF6) with density observed in [C6C1im][PF6] and in [C8C1im][PF6] have been calculated by a hard-sphere model of a pseudo-diatomic solute under short-range repulsive interactions with the neighboring particles. The stochastic model of Kubo for vibrational dephasing has been used to obtain the amplitude of vibrational frequency fluctuation, ⟨Δω 2⟩, and the relaxation time of frequency fluctuation, τ c , as a function of density by Raman band shape analysis of the νs(PF6) mode of [C6C1im][PF6] and [C8C1im][PF6].

Extreme ultraviolet emission lines of Ca XV in solar and laboratory spectra

New R-matrix calculations of electron impact excitation rates in Ca XV are used to derive theoretical electron density diagnostic emission line intensity ratios involving 2s(2)2p(2)- 2s2p(3) transitions, specifically R-1 = I(208.70 Angstrom)/I(200.98 Angstrom), R-2 = I(181.91 Angstrom)/I(200.98 Angstrom), and R-3 = I(215.38 Angstrom)/I(200.98 Angstrom), for a range of electron temperatures (T-e = 10(6.4)-10(6.8) K) and densities (Ne = 10(9)-10(13) cm(-3)) appropriate to solar coronal plasmas. Electron densities deduced from the observed values of R-1, R-2, and R-3 for several solar flares, measured from spectra obtained with the Naval Research Laboratory's S082A spectrograph on board Skylab, are found to be consistent. In addition, the derived electron densities are in excellent agreement with those determined from line ratios in Ca XVI, which is formed at a similar electron temperature to Ca XV. These results provide some experimental verification for the accuracy of the line ratio calculations, and hence the atomic data on which they are based. A set of eight theoretical Ca XV line ratios involving 2s(2)2p(2)-2s2p(3) transitions in the wavelength range similar to140-216 Angstrom are also found to be in good agreement with those measured from spectra of the TEXT tokamak plasma, for which the electron temperature and density have been independently determined. This provides additional support for the accuracy of the theoretical line ratios and atomic data.