Vibration-rotation Spectra Research Articles

Water line lists close to experimental accuracy using a spectroscopically determined potential energy surface for H2O16, H2O17, and H2O18

Line lists of vibration-rotation transitions for the H(2) (16)O, H(2) (17)O, and H(2) (18)O isotopologues of the water molecule are calculated, which cover the frequency region of 0-20 000 cm(-1) and with rotational states up to J=20 (J=30 for H(2) (16)O). These variational calculations are based on a new semitheoretical potential energy surface obtained by morphing a high accuracy ab initio potential using experimental energy levels. This potential reproduces the energy levels with J=0, 2, and 5 used in the fit with a standard deviation of 0.025 cm(-1). Linestrengths are obtained using an ab initio dipole moment surface. That these line lists make an excellent starting point for spectroscopic modeling and analysis of rotation-vibration spectra is demonstrated by comparison with recent measurements of Lisak and Hodges [J. Mol. Spectrosc. (unpublished)]: assignments are given for the seven unassigned transitions and the intensity of the strong lines are reproduced to with 3%. It is suggested that the present procedure may be a better route to reliable line intensities than laboratory measurements.

Solution of the Schrödinger Equation for a Diatomic Oscillator Using Linear Algebra

Computational experiment is proposed in which a linear algebra method is applied to the solution of the Schrödinger equation for a diatomic oscillator. Calculations of the vibration–rotation spectrum for the HCl molecule are presented and the results show excellent agreement with experimental data.

Rotational-vibrational energy spectra of triatomic molecules near relative equilibria

Complete Hamiltonian operators have been obtained in terms of internal coordinates on the basis of the fiber bundle theory in geometry [J. Math Phys. 44, 4411 (2003)]. In this article, the full Hamiltonian is specialized for a rigid and for a semirigid molecule. For the rigid molecule, all internal coordinates are fixed at constants, so that the Hamiltonian operator comes to take an ordinary matrix form, and accordingly, the Schrödinger equation becomes an algebraic eigenvalue equation. The eigenvalues then provide rotational energy spectra of the rigid molecule. For the semirigid molecule, the full Hamiltonian is expanded in the vicinity of an equilibrium position into a power series in an infinitesimal parameter, to which the perturbation method is applied to obtain energy spectra in the form of a power series in the infinitesimal parameter. Indeed, the energy spectra are calculated to the second order term in the infinitesimal parameter in both the cases where the unperturbed energy spectra are nondegenerate and where those are degenerate. It then turns out that the amount of the energy shift caused by the rotation, which is the sum of the pure rotational and the rotation-vibration coupling terms, is proportional to the total angular momentum eigenvalue. It is also observed that a vibrational energy shift occurs simultaneously, which is caused by the metric defined on the internal space. No symmetry is assumed on the shape of the molecule in equilibrium.

Non-adiabatic theory in terms of a single potential energy surface. The vibration–rotation levels of [formula omitted] and [formula omitted

The traditional formulation of a molecular wave function describing the motion of the electrons and the nuclei, in terms of the Born hierarchy, does not allow to account for the participation of the electrons in vibrational or rotational motions, except by recurring to a fully non-adiabatic treatment, abandoning completely the concept of a single potential energy surface for one electronic state of the molecule. An alternative approach has been presented recently, which is based on an exact separation in all possible dissociation limits, and which leads to a Hamiltonian for the nuclear motion with a geometry-dependent effective nuclear mass, that is different for vibration and rotation. This approach is now tested numerically. We account for the vibration–rotation spectrum of H 2 + and D 2 + in their electronic ground states in terms of a single potential energy curve, with spectroscopic accuracy, i.e. with errors of the order of a few hundredths of a cm −1. We byepass by far the accuracy that is achievable in terms of a geometry-independent effective mass.

An ab-initio study of multiple conformers of glycine

AbstractThe recent combination of new computational chemistry techniques and high performance computational hardware is allowing unprecedented levels of accuracy in the calculations of physical quantities such as potential energy surfaces and rotational-vibrational spectra. Previous results exist in the literature for the first three most stable conformers of glycine at the aug-cc-pVDZ basis set. In this work, we extend the known results, presenting calculations of the four most stable conformers of glycine using the aug-cc-pVQZ basis set. We compare our calculations to experimental values and show that our current calculations differ by <2% from measured values, much better than results from previous years. When searching for molecules in the Interstellar Medium this small difference suggests that computational methods are becoming well-suited for the task. The natural question to ask is: at what point will the small deviation from experimental values render our computations just as reliable as experiments? We feel that the current results show that we are indeed close to this goal.

Universal description of the rotational-vibrational spectrum of three particles with zero-range interactions

A comprehensive universal description of the rotational-vibrational spectrum for two identical particles of mass m and a third particle of mass m 1 in the zero-range limit of the interaction between different particles is given for arbitrary values of the mass ratio m/m 1 and the total angular momentum L. It is found that the number of vibrational states is determined by the functions L c(m/m 1) and L b(m/m 1). Explicitly, if the two-body scattering length is positive, the number of states is finite for L c(m/m 1) ≤ L ≤ L b(m/m 1), zero for L > L b(m/m 1), and infinite for L < L c(m/m 1). If the two-body scattering length is negative, the number of states is zero for L ≥ L c(m/m 1) and infinite for L < L c(m/m 1). For the finite number of vibrational states, all the binding energies are described by the universal function ɛLN(m/m 1) = (ξ, η), where ξ = (N − 1/2)/√L(L + 1), η = √m/[m 1 L(L + 1)], and N is the vibrational quantum number. This scaling dependence is in agreement with the numerical calculations for L > 2 and only slightly deviates from those for L = 1, 2. The universal description implies that the critical values L c(m/m 1) and L b(m/m 1) increase as 0.401 √m/m 1 and 0.563 √m/m 1, respectively, while the number of vibrational states for L ≥ L c(m/m 1) is within the range N ≤ N max ≈ 1.1√L(L + 1) + 1/2.

On the excited electronic state dissociation of nitramine energetic materials and model systems

In order to elucidate the difference between nitramine energetic materials, such as RDX (1,3,5-trinitro-1,3,5-triazacyclohexane), HMX (1,3,5,7-tetranitro-1,3,5,7-tetraazacyclooctane), and CL-20 (2,4,6,8,10,12-hexanitro-2,4,6,8,10,12-hexaazaisowurtzitane), and their nonenergetic model systems, including 1,4-dinitropiperazine, nitropiperidine, nitropyrrolidine, and dimethylnitramine, both nanosecond mass resolved excitation spectroscopy and femtosecond pump-probe spectroscopy in the UV spectral region have been employed to investigate the mechanisms and dynamics of the excited electronic state photodissociation of these materials. The NO molecule is an initial decomposition product of all systems. The NO molecule from the decomposition of energetic materials displays cold rotational and hot vibrational spectral structures. Conversely, the NO molecule from the decomposition of model systems shows relatively hot rotational and cold vibrational spectra. In addition, the intensity of the NO ion signal from energetic materials is proportional to the number of nitramine functional groups in the molecule. Based upon experimental observations and theoretical calculations of the potential energy surface for these systems, we suggest that energetic materials dissociate from ground electronic states after internal conversion from their first excited states, and model systems dissociate from their first excited states. In both cases a nitro-nitrite isomerization is suggested to be part of the decomposition mechanism. Parent ions of dimethylnitramine and nitropyrrolidine are observed in femtosecond experiments. All the other molecules generate NO as a decomposition product even in the femtosecond time regime. The dynamics of the formation of the NO product is faster than 180 fs, which is equivalent to the time duration of our laser pulse.

Enhanced Intensity Distribution Analysis of the Rotational–Vibrational Spectrum of HCl

Data are presented that indicates the best fit of intensity of the HCl vibrational�rotational FTIR spectrum, which includes a Boltzmann population profile, is accomplished by accounting for factors from the full transition moment integral and by relaxing the rigid-rotor approximation. Mathcad is used to generate intensity distributions. A typical HCl FTIR spectrum is shown and two methods are discussed for presenting the spectrum together with a calculated intensity distribution. The two methods are the use of transparencies or projection using PowerPoint to manipulate the images so that they overlay. A direct visual comparison can then be made by students in the classroom as to the quality of the fit. Information describing the HCl spectrum and the quality of these data, a description of intensity distributions using Boltzmann population profiles and how they are displayed, and techniques for employing both visualization methods in the classroom are presented in the Supplemental Material. Also available in the Supplemental Material is the HCl spectrum saved as an Excel file and the Mathcad file used to generate the intensity distributions.

Dihydrogen in zeolite CaX—An inelastic neutron scattering study

We report an inelastic neutron scattering (INS) study of the rotational–vibrational spectrum of dihydrogen sorbed by zeolite CaX. In the low energy (<200 cm −1) INS spectrum of adsorbed H 2 we observe the rotational–vibrational spectrum of H 2, where the vibration is that of the H 2 molecule against the binding site (i.e. H 2–X, not H–H). We have observed for the first time the vibrational overtones of the hydrogen molecule against the adsorption surface up to sixth order. These vibrations are usually forbidden in INS spectroscopy because of the selection rules imposed by the spin flip event required. In our case we are able to observe such a vibration because the rotational transition J(1 ← 0) convolutes the vibrational spectrum. This paper reports the effect for the first time.

Dihydrogen in cation-substituted zeolites X—an inelastic neutron scattering study

An inelastic neutron scattering (INS) study of the rotational–vibrational spectrum of dihydrogen sorbed by zeolite X having substituted sodium, calcium and zinc cations is reported. The rotational–vibrational spectrum of H2 was observed at low energy transfer (below ca. 25 meV, 202 cm−1); the vibration was that of the H2 molecule against the binding site (H2–X, not H–H). The vibration frequency was proportional to the polarising power of the cation (Na+ < Ca2+ < Zn2+). Polarisation of the H2 molecule dominated the interaction of H2 with this binding site. The total scattering intensity was proportional to the dihydrogen dose. However the vibrational intensities became constant at ca. 0.3 wt% showing that the H2 binding sites had saturated. Additional dihydrogen appeared as unbound or weakly bound dihydrogen exhibiting recoil.

First-principle studies of gaseous aromatic amino acid histidine

The properties of gaseous aromatic amino acid l-histidine depend on the structural forms it may take in gas phase. Systematic ab initio calculations were employed to characterize the conformational topology of the gaseous histidine. A total of 42 unique local minima conformers were located at the B3LYP/6-311G ∗ level of theory after geometry optimization of all possible single-bond rotamers. Single-point energy calculations of all conformers were performed at the levels of MP2/6-311++G(d,p), B3LYP/6-311++G(d,p) and B3LYP/6-311G(2df,p). The equilibrium distributions of the gaseous histidine conformers at various temperatures were obtained based on the principle of thermodynamics. Due to the big energy gap between the lowest energy conformer and the other conformers, the most stable conformer of histidine is dominant in the gas phase, a unique feature that is characteristically different from that of the other three aromatic amino acids, tryptophan, tyrosine and phenylalanine. The measurable quantities such as the rotational constants, dipole moments, vibrational spectra and ionization energies were also given for comparison with future experiments. In analyzing the structural characteristics, three types of H-bond (OH⋯N 3, OH⋯N 4 and N 3H⋯N 4) were identified and characterized in detail by the atoms in molecules (AIM) theory based upon the B3LYP/6-311++G(d,p) electron density ρ( r ). The H-bonding features of the two most stable conformers are similar for all the aromatic amino acids. The values of vertical ionization energies for all the conformers suggest that the ionization depends strongly on the type of intramolecular interaction in the neutral conformers. The average adiabatic ionization energy for the six lowest energy conformers is lower than the corresponding average vertical ionization energy by an amount of 0.45 eV due to the structural relaxations.

Millimeter-wave spectrum of 2,3-difluorobenzonitrile and ab initio DFT calculations

The ground vibrational state rotational spectrum of 2,3-difluorobenzonitrile has been reinvestigated in the frequency range 40.0–99.0 GHz. High J and K −1 ( J ⩽ 62 and K −1 ⩽ 20) transitions have been measured and analyzed to determine accurate rotational and centrifugal distortion constants. Finally, the experimental values were compared with the corresponding values computed at the DFT-B3PW91/6-31g(d,p) level of theory. A very good agreement has been found.

Ab initio prediction of the potential energy surface and vibration-rotation energy levels of BeH2

The equilibrium structure and potential energy surface of beryllium dihydride BeH(2) in its ground electronic state have been determined from highly accurate ab initio calculations. The vibration-rotation energy levels of three isotopomers BeH(2), BeD(2), and BeHD were predicted using the variational method. The calculated spectroscopic constants are in remarkably good agreement with the existing experimental data (sub-cm(-1) accuracy) and should be useful in a further analysis of high-resolution vibration-rotation spectra of all three isotopomers.

Laboratory spectroscopic calibration of infrared tunable laser spectrometers for the in situ sensing of the Earth and Martian atmospheres

This paper reports the laboratory spectroscopic calibration of near- and mid- infrared tunable laser spectrometers used to determine in situ trace gases in the middle atmosphere of the Earth or in development for the investigation of the Martian atmosphere. The use of infrared absorption spectroscopy to measure gas concentrations requires a proper knowledge of the rotation–vibration spectra of the targeted molecules as well as a proper investigation of the tunable laser spectral emission properties. This last point is of particular importance for the use of new-generation lasers like quantum-cascade lasers or room-temperature multi-quantum wells laser diodes emitting between 2 and 3 μm. Purposely, we have developed various laboratory tunable laser set-ups to obtain accurate line strengths and pressure-broadening coefficients of atmospheric molecules and to test the performances of cutting-edge laser technology for trace gas sensing. In this paper, the spectroscopic calibration work is described. Several atmospheric applications of tunable laser are reported to stress the impact on concentration retrieval of a proper spectroscopic calibration work.

Cross-orientational motion in liquid dichloromethane and trichloromethane (chloroform) by molecular dynamics simulation

Using molecular dynamics the l = 1 orientational auto- and cross-correlation functions of one of the C–H bond directions of neat dichloromethane at 273 K and that of chloroform between 301 and 438 K in its neat state and in solution with tetrachloromethane and liquefied methane (at 183 K) have been simulated. The simulations are confined to a model of singly rotating, individual molecules in the absence of induced absorption and translation-rotation coupling. It is found throughout that the orientational cross-correlation functions are equivalent to the auto-correlation functions, therefore bearing the same information content. On the basis of a simple thermodynamic argument, this phenomenon is extended to be generally valid to orientational correlation functions from vibration–rotation spectra of mobile liquids. Consequences of the equivalence are, first, that dilution does not break the symmetry between orientational auto- and cross-correlation functions of the solute species and, second, that the simulated auto-correlation functions of total and individual dipole moments of undressed dipoles in the system are indistinguishable.

Observation of a forbidden [formula omitted] infrared transition in 11BF 3

The forbidden 011 10 0–000 00 0 E ″ – A 1 ′ transition of 11BF 3 has been observed in absorption in the infrared near 2140 cm −1. Although weak, the entire band is observed and does not show any sign of intensity borrowing from nearby bands. The transitions obey the electric dipole allowed selection rules Δ k = ±2, Δ l = ∓1. As shown by the J and K dependence of the line intensities, the band appears to derive its intensity from terms in the dipole moment operator described by Aliev and Watson [M.R. Aliev, J.K.G. Watson, Higher-order effects in the vibration–rotation spectra of semirigid molecules, in: K. Narahari Rao (Ed.), Molecular Spectroscopy: Modern Research, vol. III, Academic Press, Inc., New York, 1985 (Chapter 1).] in their description of “Higher-order effects in the vibration–rotation spectra of semirigid molecules”. That theory is further developed and it is shown that, for this particular case, the intensity comes largely from the term in the dipole moment operator that governs the intensity of the 002 20 0–000 00 0 transitions and to a lesser extent from terms that govern the intensity of the 001 11 1–000 00 0 transitions and the fundamental bands.

Theory of the fundamental vibration-rotation-translation spectrum ofH2in aC60lattice

Calculations are presented for the fundamental vibration-rotation spectrum of ${\mathrm{H}}_{2}$ in fcc ${\mathrm{C}}_{60}$ (fullerite) lattices. The principal features are identified as lattice-shifted ``vibration-rotation-translation'' state absorption transitions. The level spacings of the ${\mathrm{H}}_{2}$ modes are calculated numerically for the potential function resulting from the summation of the individual $\mathrm{C}\text{\ensuremath{-}}{\mathrm{H}}_{2}$ potentials for all C atoms in the six nearest neighbor ${\mathrm{C}}_{60}$ molecules. The potential is approximately separable in Cartesian coordinates, giving a very good approximation to exactly calculated translational energies for the lower levels. The positions and relative strengths of the individual transitions are calculated from the eigenfunctions for this separable potential. The line shapes are assumed to be Lorentzian, and the widths are chosen so as to give good fits to the DRIFT spectrum of FitzGerald et al. [Phys. Rev. B 65, 140302(R) (2002)]. A theory of the $\mathrm{C}\text{\ensuremath{-}}{\mathrm{H}}_{2}$ induced dipole moment is developed with which to calculate intensities. In order to fit the observed DRIFTS transition frequencies it is found necessary to take the overlap part of the $\mathrm{C}\text{\ensuremath{-}}{\mathrm{H}}_{2}$ potential to be about 13% longer in range than the $\mathrm{C}\text{\ensuremath{-}}{\mathrm{H}}_{2}$ potential in graphene. Furthermore, differences in the theoretical spectra obtained with a near-optimal exp-6 potential and near-optimal Lennard-Jones 12-6 potential are clearly evident, with the exp-6 potential giving a better fit to observation than the Lennard-Jones potential. Similarly, Lorentzian line shapes assumed for the individual transitions yield better agreement with observation than Gaussian line shapes.

Infrared diode laser spectroscopy of the △ ν = 2 band of AlF

A vibrational–rotational spectrum of the △ ν = 2 transitions of a high-temperature molecule AlF was observed between 1490 and 1586 cm −1 with a diode laser spectrometer. Measurements were made on the ν = 3–1, 4–2, 5–3 and 8–6 bands at a temperature of 900 °C. Measured spectral lines were fitted to effective band constants ν 0, B ν and D ν for each band. Present measurements were made with only one Pb-salt laser diode. Physical significance of the effective band constants is discussed.

Vibration–rotation Fourier transform infrared spectrum of the C–D and C [tbnd]C stretching fundamental, ν1 and ν2, band systems of deuterated monobromoacetylene

A high resolution vibration–rotation spectrum of deuterated monobromoacetylene (DCCBr) has been recorded with a Bruker IFS 120 Fourier Spectrometer in the wavenumber region 1700–2800 cm −1, which covers the C–D and C C stretching fundamental ( ν 1 and ν 2, respectively) and the C C and C–Br stretching vibrational combination ( ν 2 + ν 3) band systems. The analysis of the spectrum provides accurate vibrational term values and rotational constant for 20 vibration–rotation bands for both isotopic species, DCC 79Br and DCC 81Br.

Insight into the rotational motion of [formula omitted] in Si from the IR spectrum of HD

The rotational–vibrational transitions of HD in Si are subject to less restrictive selection rules than for the homonuclear H 2 and D 2 molecules and give rise to a richer IR spectrum. IR lines for transitions between rotational–vibrational states of the interstitial HD molecule with rotational quantum numbers J = 0 , 1, and 2 have been observed. The assignment of the rotational–vibrational spectrum of interstitial HD, with additional transitions that occur for HD but not for H 2 or D 2 , is confirmed by uniaxial stress results.