Vibrational Energy States Research Articles

Temperature dependence of photoluminescence emission characteristics in a natural fluorite

The temperature dependence of photoluminescence emission of a natural fluorite has been studied in the wavelength region of 380–500 nm and in the temperature range of 17.5–300 K. The emission spectra of the sample show a broad emission band between 380 and 500 nm for temperatures above 100 K. At 100 K and below, vibronic lines appear on the emission band at approximately 413.3, 418.1, 419.3, 420.2, 423.9 and 427.1 nm. This broad emission band and the vibronic lines in fluorite are usually associated with phonon-coupled electronic transitions from 4f65d to 4f7 in the Eu2+ ion. Temperature dependences of the peak energy, intensity and full-width at half-maximum of the broad emission band are discussed, and the behaviour explained in terms of a configurational coordinate model. The excited state vibrational energy was obtained to be 0.023 ± 0.001 eV and this is lower than the LO phonon energy of 0.062 eV in pure fluorite. The activation energy of thermal quenching of the photoluminescence intensity was found to be 0.022 ± 0.002 eV.

The photoelectron spectrum of elusive cyclic-N3 and characterization of the potential energy surface and vibrational states of the ion

A potential energy surface is constructed for the ground X (1)A(1) electronic state of cyclic-N(3) (+) based on three-dimensional spline interpolation of ab initio points. The vibrational states of this molecular ion are calculated in the range up to 14 500 cm(-1) using hyperspherical coordinates and the coupled-channel (sector-adiabatic) approach. All the vibrational states are analyzed and assigned. The Franck-Condon overlaps of these states with the vibrational states of the neutral are calculated to predict the photoelectron spectrum of cyclic-N(3). Peak intensities are governed by the nodal structure of the vibrational wave functions and reflect the large geometric phase effect predicted for cyclic-N(3). Experimental validation may shed light on the existence of this elusive molecule and confirm the magnitude of the geometric phase effect.

Fluorescence excitation and single vibronic level emission spectroscopy of the ÃA″1←X̃A′1 system of CHCl

We report new fluorescence excitation and single vibronic level emission spectra of the A (1)A(")<-->X (1)A(') system of CHCl. A total of 21 cold bands involving the pure bending levels 2(0) (n) with n=1-7 and combination bands 2(0) (n)3(0) (1)(n=4-7), 2(0) (n)3(0) (2)(n=4-6), 1(0) (1)2(0) (n)(n=5-7), 1(0) (1)2(0) (n)3(0) (1)(n=4-6), and 1(0) (1)2(0) (n)3(0) (2)(n=4) were observed in the 450-750 nm region; around half of these are reported and/or rotationally analyzed here for the first time. Spectra were measured under jet-cooled conditions using a pulsed discharge source, and rotational analysis typically yielded band origins and rotational constants for both isotopomers (CH(35)Cl,CH(37)Cl). The derived A (1)A(") vibrational intervals are combined with results of Chang and Sears to determine the excited state barrier to linearity [V(b)=1920(50) cm(-1)]. The A (1)A(") state C-H stretching frequency is determined here for the first time, in excellent agreement with ab initio predictions. Following our observation of new bands in this system, we obtained the single vibronic level (SVL) emission spectra which probe the vibrational structure of the X (1)A(') state up to approximately 9000 cm(-1) above the vibrationless level. The total number of X (1)A(') levels observed is around three times than that previously reported, and we observe five new a (3)A(") state levels, including all three fundamentals. The results of a Dunham expansion fit of the ground state vibrational term energies, and comparisons with the previous experimental and recent high level ab initio studies, are reported. Our data confirm the previous assignment of the a (3)A(") origin, and our value for T(00)(a-X)=2172(2) cm(-1) is in excellent agreement with theory. By exploiting SVL spectra from excited state levels with K(a) (')=1, we determine the effective rotational constant (A-B) of the triplet origin, also in good agreement with theory. Our results shed new light on the vibrational structure of the X (1)A('), A (1)A("), and a (3)A(") states of CHCl, and, more generally, spin-orbit coupling in the monohalocarbenes.

First-principles potential energy surfaces and vibrational states of H∕Rh(111) at 0.25 and 1 monolayer coverages

Density functional theory calculations based on plane-wave expansion and a pseudopotential treatment have been carried out for atomic hydrogen adsorbed on Rh(111) at 0.25 and 1 monolayer (ML) coverages. The preferred binding site for hydrogen was found to be the fcc hollow site. The global three-dimension potential energy surfaces were obtained by spline interpolation. The calculated hydrogen diffusion barrier of 121meV at 0.25ML agrees well with the experimental result of 140meV at 0.3ML. The vibrational wave functions and the corresponding energies for atomic hydrogen on the calculated potentials were calculated by using the discrete variable representation and Lanczos method. The calculated results showed that the low-lying vibrational states exhibit strong localized characters, whereas the higher states show significant delocalized characters. The calculated vibrational frequencies agree well with the recent available experimental values. Particularly, the calculated blueshift of 10.6 (7.2)meV for the vibrational excitation parallel to the metal surface when the H(D) coverage is changed from 0.25ML to 1ML is in excellent agreement with the observed value of 11 (7)meV.

Fluorescence excitation and emission spectroscopy of the ÃA″1←X̃A′1 system of CHBr

We report fluorescence excitation and emission spectra of CHBr in the 450-750 nm region. A total of 30 cold bands involving the pure bending levels 2(0)(n) with n=2-8 and combination bands 2(0)(n)3(0)(1)(n=1-8), 2(0) (n)3(0)(2)(n=1-6), 2(0)(n)3(0)(3)(n=1-2), 1(0)(1)2(0)(n)(n=5-7), 1(0)(1)2(0)(n)3(0)(1)(n=4-6), and 1(0)(1)2(0)(n)3(0)(2)(n=5) in the A (1)A(")<--X (1)A(') system were observed, in addition to a number of hot bands. The majority of these are reported and/or rotationally analyzed here for the first time. Spectra were measured under jet-cooled conditions using a pulsed discharge source, and rotational analysis yielded band origins and rotational constants for both bromine isotopomers (CH (79)Br,CH (81)Br). The derived A (1)A(") vibrational intervals are combined with results of [Yu et al. J. Chem. Phys. 115, 5433 (2001)] to derive barriers to linearity for the 2(n), 2(n)3(1), and 2(n)3(2) progressions. The A (1)A(") state C-H stretching frequency is determined here for the first time, and the observed nu(3) dependence of the (79)Br-(81)Br isotope splitting in the A(1)A(") state is in good agreement with theoretical expectations. Our dispersed fluorescence spectra probe the vibrational structure of the X(1)A(') state up to approximately 9000 cm(-1) above the vibrationless level; the total number of levels observed is more than twice that previously reported. As first reported by [Chen et al. J. Mol. Spectrosc. 209, 254 (2001)], these spectra reveal numerous perturbations due to spin-orbit interaction with the low-lying a(3)A(") state. The results of a Dunham expansion fit of the ground state vibrational term energies, and comparisons with previous experimental and theoretical studies, are reported. Our results lead to several revised assignments, including the X (1)A(') C-H stretching fundamental. Globally, the vibrational frequencies of X(1)A('), a(3)A("), and A(1)A(") are in excellent agreement with theoretical predictions.

Deconstructing experimental rate constant measurements: Obtaining intrinsic reaction parameters, kinetic isotope effects, and tunneling coefficients from kinetic data for OH + methane, ethane and cyclohexane

Kinetic data for multiple OH–alkane reactions, including primary kinetic isotope data, can be fit simultaneously to extract constrained contributions from transition state vibrational activation, zero-point energy, and tunneling. We use data for single-pathway reactions: OH + methane, ethane, and cyclohexane, to obtain optimal ‘intrinsic’ parameters common to all reactions. This is possible because parameters specific to individual reactions, such as the pre-exponential term, can be accurately calculated with ease. Several intrinsic parameters – the barrier height, the tunneling temperature (imaginary frequency) and a transition state bending frequency (the radical attack angle) – scale together from reaction to reaction. This scaling is so precise that we can accurately fit data for OH + methane using intrinsic parameters derived for OH + ethane and OH + cyclohexane using only a single free parameter (the scaling factor). This strongly confirms our underlying hypothesis about the physics controlling the key transition state parameters and suggests that extrapolations in temperature and predictions for unmeasured reactions are potentially robust.

A reliable ab initio potential energy surface and vibrational states for the ground electronic state of HgH2(XΣg+1)

A three-dimensional global potential energy surface for the ground (X (1)Sigma(+)(g))electronic state of HgH(2) is constructed from more than 13,00 ab initio points. These points are generated using an internally contracted multireference configuration interaction method with the Davidson correction and a large basis set. Low-lying vibrational energy levels of HgH(2), HHgD, and HgD(2) calculated using the Lanczos algorithm are found to be in good agreement with the available experimental band origins. The majority of the vibrational energy levels up to 9000 cm(-1) are assigned with normal mode quantum numbers. Our results indicate a gradual transition for the stretching vibrations from the normal mode regime at low energies to the local mode regime near 9000 and 8000 cm(-1) for HgH(2) and HgD(2), respectively, as evidenced by a decreasing energy gap between the (0,0,n(3)) and (1,0,n(3)-1) vibrational states and bifurcation of the corresponding wave functions.

A first-principles potential energy surface and vibrational states for hydrogen on Cu(100).

Density-functional theory calculations based on plane-wave expansion and pseudopotential treatment were carried out for atomic hydrogen on a rigid Cu(100) surface. A global potential energy surface was then obtained by using a three-dimensional spline interpolation. It is found that the minimum of the potential is located at the fourfold hollow site with a diffusion barrier of 88 meV at the bridge site. The vibrational states of atomic hydrogen and deuterium on the Cu(100) surface were calculated on the potential surface. Our calculations show that the vibrational states A(1) (0), A(1) (1), E(1), and B(2) (1) of H/Cu(100) exhibit strong localized character and very narrow band widths, whereas other excited vibrational states have considerable delocalized character and broad band widths. The vibrational frequency of 71.2 (51.5) meV for H(D) in the perpendicular direction obtained in this study is in good agreement with the experimentally observed value of 70 (52) meV.

Partition sums and dissociation energy for 12C16O2 at high temperatures

Using the spectroscopic characteristic of the carbon dioxide molecule, direct calculations of the total internal and vibrational partition sums for the principal isotopologue 12C16O2 in the temperature range 400–10 000 K were carried out in steps of 200 K. The rotational–vibrational state energies were calculated utilizing an effective Hamiltonian, taking into account the rotational contribution to the Fermi resonance energy. The method of direct summation by conditions was employed, taking into account the effect of thermodissociation on the number of bound states of the molecule. It is demonstrated that, in order to accurately calculate the partition sum Q at high temperature, it is necessary to solve combined equations with regard to the partition sum Q as well as the energy of dissociation D T . The values of Q and D T calculated by means of an iterative process are compared with the results obtained using other calculations.

An ab initio potential energy surface and vibrational states of MgH2(1 1A′)

A three-dimensional global potential energy surface for the ground electronic state of MgH(2) is constructed from more than 3000 ab initio points calculated using the internally contracted multireference configuration interaction method with the Davidson correction at the complete basis set limit. Low-lying vibrational energy levels of MgH(2) and MgD(2) are calculated using the Lanczos algorithm, and found to be in good agreement with known experimental band origins. The majority of the vibrational energy levels up to 8000 cm(-1) are assigned with normal mode quantum numbers. However, our results indicate a gradual transition from a normal mode regime for the stretching vibrations at low energies to a local mode regime near 7400 cm(-1), as evidenced by a decreasing energy gap between the (n(1),0,0) and (n(1)-1,0,1) vibrational states and bifurcation of the corresponding wave functions.

The vibration–rotation spectrum of 12C 2HD: new overtone bands and global vibrational analysis

Two new bands, 2 ν 1+ ν 2+ ν 3+2 ν 5 and 5 ν 3 with origin at 12220.692 and 12496.158 cm −1, respectively, were identified on new FT-ICLAS spectra of 12C 2HD and rotationally analyzed. The rotational analysis of two known bands, with origin at 12038.538 and 12234.872 cm −1 was extended. Another band, 2 ν 1+2 ν 5 with origin at 7843.6622 cm −1, was identified for the first time and rotationally analyzed, from a high pressure conventional FT spectrum. Some 115 known vibrational state energies in the molecule, extending up to the visible range, were used to produce updated vibrational constants. Both a straightforward Dunham model and a global model accounting for a single anharmonic resonance, K 1/255, were used. The results are discussed.

Vibrational dynamics of SCCl2 from the zero point to the first dissociation limitElectronic supplementary information (ESI) available: Potential constants (table) conversion matrix from normal coordinates to Cartesian coordinates (table) and correlation between two normal coordinate force fields (figure). See http://www.rsc.org/suppdata/cp/b4/b403114h/

Over one thousand ← vibronic transitions of the SC35Cl2 and SC35Cl37Cl isotopomers, originating from eight state vibrational levels, have been measured by dispersed fluorescence spectroscopy and stimulated emission pumping. The observed ground state vibrational energy levels involve all six vibrational modes, and have up to 28 quanta of combined excitation. The energy window extends from the fundamental vibrations to beyond the molecular dissociation limit near E/h = 600 THz. 375 ground state vibrational levels of SC35Cl2 have been assigned and fitted to an effective Hamiltonian. 35–37 chlorine isotopomer splittings are regular except for a few resonances when v1 ≥ 7 and v4 ≥ 6. Regular progressions up to 600 THz indicate the conservation of at least two good vibrational quantum numbers at the SCCl–Cl and SC–Cl2 dissociation limits. A subset of over 100 transitions up to E/h = 240 THz was used to refine a 6-D ab initio potential surface represented in bond distance coordinates. This surface, together with a previously computed state potential surface and transition dipole surface, also reproduces the spectral intensities of the ν1–ν4 polyads up to E/h = 240 THz. SCCl2 is an excellent model system for intramolecular vibrational redistribution (IVR) among skeletal vibrations ranging from isolated resonances to extensively mixed quantum states. The newly extended spectra show that half of the 6-D quantum state space remains highly structured up to the first dissociation limit near 600 THz, resulting in sub-exponential IVR dynamics except at short times.

A computer assisted procedure of assignments of vibration–rotation bands of asymmetric and symmetric top molecules

An advanced graphically oriented interactive program package for assignments of complex (perturbed) vibration–rotation spectra of asymmetric and symmetric top molecules has been developed. In addition to the well known Loomis–Wood algorithm, the new procedure takes advantage of a precise knowledge of the lower (e.g. ground) vibrational state energies, works with a realistic approximation of effective Hamiltonians for lower as well as upper vibrational states, and allows an instant combination difference inspection of spectral lines by the graphical representation of the appropriate parts of the analyzed experimental spectrum. Being constrained to the combination difference checking, the new algorithm can directly assign the correct rotational quantum numbers as well as ‘quality weights’ estimating relative accuracies of the identified lines.

Vibrational Spectroscopic Database on Acetylene, X̃ 1Σg+ (12C2H2, C212D2, and C213H2)

Information on the vibrational energy states in acetylene (12C2H2, C212D2, and C213H2) is gathered: spectroscopic constants (vibrational frequencies and anharmonicities, vibration-rotation interaction parameters), observed vibrational energy states and complete sets of predicted vibrational energies and predicted principal rotational constants Bv for states of C212H2, C212D2, and C213H2 up to 15000, 10000, and 12000 cm−1, respectively. Statistical parameters (partition functions and integrated number of states) deduced from these predicted spectroscopic data are provided for the three isotopomers. The equilibrium geometrical structure is determined to be re(CH)=106.138(35) pm and re(CC)=120.292(13) pm from constants available for C212H2, C212D2, C213H2, and C212HD.

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 Nr = 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.

分子線赤外発光法によるPd単結晶表面上における定常的CO＋NO反応

The infrared chemiluminescence technique was applied to the steady-state CO oxidation by NO on Pd(111) and Pd(110) to measure the internal energy of CO2 desorbed from surfaces. In this paper, on the basis of the results of CO oxidation by O2, we elucidate the CO2 formation mechanism of CO + NO reaction. From the comparison of IR emission spectra of CO2 between CO + NO and CO + O2 reactions, it is found that the vibrational energy states of CO2 in CO + NO reaction are similar to those in CO + O2 reaction. This indicates that the reaction path of CO2 formation in CO + NO is the same as that in CO + O2. The vibrational states are much dependent on the surface structure: the CO2 molecules produced on flat Pd(111) were highly excited (especially bending mode) than those on Pd(110) which has atomically rough surface.

Elucidation of CO2 Formation Mechanism in CO + NO Reaction on Pd(111) and Pd(110) Surfaces Using IR Chemiluminescence Method

The infrared (IR) chemiluminescence technique was applied to steady-state CO oxidation by NO on Pd(111) and Pd(110). From a comparison of IR emission spectra of CO2 between the CO + NO and CO + O2 reactions, it was found that the vibrational energy states of CO2 in the CO + NO reaction were similar to those in the CO + O2 reaction. This indicates that the reaction path of CO2 formation in CO + NO is the same as that in CO + O2, although the vibrational states are very dependent on the surface structure.

Effective cross-sections for the thermal conductivity of diatomic gases

A new improved way for the inclusion of the vibrational degrees of freedom into the calculation of the thermal conductivity of dilute gases of diatomic molecules is proposed and has been tested for nitrogen and carbon monoxide. The effective cross-sections needed have been obtained using classical trajectory rigid-rotor calculations following the procedure by Heck and Dickinson on the basis of anisotropic ab initio potential energy hypersurfaces of both molecules. The calculations have been performed for the second-order approximation of the kinetic theory including corrections for the polarization effects of the rotational angular momentum according to Kagan and Maximov. The vibrational energy states have been taken into account by suitably chosen corrections of the effective cross-sections needed in the first-order approximation of the kinetic theory. In particular, the effective cross-section for the vibrational energy has been neglected, whereas the effective cross-section for the vibrational energy flux has been approximated by the effective cross-section for the particle flux connected with the self-diffusion coefficient.

Theoretical studies of the vibrational states of Ne2SH and Ne2OH (Ã 2Σ+)

Variational calculations of the 25 lowest energy vibrational states of the Ne2SH and Ne2OH (Ã 2Σ+) complexes are performed using potentials that are obtained by the pairwise addition of accurate neon dimer and Ne⋅XH potentials. The Ne2XH complexes are able to sample several local minima in their respective potentials at relatively low internal energies. Consequently, both complexes display average densities of states that exceed one vibrational state per cm−1 in the energy regime covered by this study. In spite of this, all of the calculated states are assigned to specific vibrational excitations, based on a structure of the complex that corresponds to one of the minima on the potential, and all of the minima are found to support progressions of bending states. In most cases, it is found that the wave functions have most of their amplitude in one of the potential minima, but the couplings between zero-order states that are localized in different minima increase as the internal energy is increased. The extent of mixing is found to depend on the symmetry of the wave functions with respect to the interchange of the two neon atoms. Effects of the differences in the anisotropies of the Ne⋅OH and Ne⋅SH potentials on the vibrational energies and wave functions are also investigated.

New implementation of the trajectory surface hopping method with use of the Zhu–Nakamura theory. II. Application to the charge transfer processes in the 3D DH2+ system

The newly implemented trajectory surface hopping (TSH) method for the collinear system with use of the Zhu–Nakamura semiclassical theory of nonadiabatic transition [C. Zhu, K. Nobusada, and H. Nakamura, J. Chem. Phys. 115, 3031 (2001)] is extended to treat 3D nonadiabatic reactions. Since the avoided crossing seam becomes a two-dimensional surface in the 3D system, the nonadiabatic transition region and the possibility of classically forbidden hops are enlarged very much in comparison with those in the collinear case. As a result, the contribution of the classically forbidden hops is quite a bit enhanced in the 3D system. Conservation of total angular momentum J is taken into account by slightly rotating the direction of momentum during the hop in the classically forbidden case. The method is tested by applying to the charge transfer processes in the 3D DH2+ system for J=0. Numerical results clearly demonstrate that the new TSH method works very well at all energies and for all initial vibrational states considered compared to the old TSH method based on the Landau–Zener formula. The significant discrepancy between the two TSH methods survives even at high collision energy and high vibrational states in contrast to the collinear case, indicating the importance of the classically forbidden hops in 3D systems. The new TSH method is considered to be a very promising method to deal with high dimensional nonadiabatic dynamics. It should also be noted that the new TSH method does not require any knowledge of nonadiabatic coupling and is based only on adiabatic potentials.