Energy Level Pattern Research Articles

Infrared spectroscopy of 15ND3: The ν2 and ν4 bending fundamental bands

The infrared spectrum of the ammonia isotopologue 15ND3 has been investigated by high resolution Fourier transform spectroscopy in the region from 450 to 1600cm−1. In total, 2217 transitions involving the (s) and (a) inversion–rotation–vibration levels have been identified and assigned to the ν2 and ν4 bending fundamentals. The assigned transitions have been fitted simultaneously using an inversion–rotation–vibration effective Hamiltonian which includes all symmetry allowed interactions between and within the excited state levels. The adopted model has been successful in rationalizing the complicated energy level pattern. Accurate values for the vibration and rotation spectroscopic constants, including 11 interaction coefficients, have been obtained for both inversion levels of the v2=1 and v4=1 states. The standard deviation of the fit, 0.00071cm−1, is about two times the estimated measurement precision.

Modeling of photoacoustic Raman spectroscopy with dissipation

Photoacoustic Raman spectroscopy (PARS) is a technique used to identify chemical species mixed in a gas or liquid based on their pattern of vibrational energy levels. Raman spectroscopy differs from the more familiar absorption spectroscopy by using a nonlinear two-photon process that can be more sensitive to small differences in vibrational energy levels. Thus it can detect defect sites in solid-state optical materials, or low concentrations of chemical species in gases. The Raman scattering process generates acoustic pulses that can be detected with a microphone. In this talk we present an overview of PARS and present an updated model that includes dissipation for the production of acoustic pulses from the energy deposited in the medium during the Raman scattering process. We also show some preliminary measurements of the process for Raman conversion in hydrogen. This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

Insights on the CN B 2Σ+ + Ar potential from ultraviolet fluorescence excitation and infrared depletion studies of the CN–Ar complex

UV laser-induced fluorescence and IR-UV fluorescence depletion studies have been used to characterize the intermolecular levels of the CN-Ar complex in the excited state correlating with CN B (2)Σ(+) + Ar. Additional CN-Ar features are identified to lower wavenumber than reported previously. Fluorescence depletion spectra are recorded to confirm that these CN-Ar features and other higher energy features in the B-X spectrum originate from a common ground state level. The UV depletion is induced by IR excitation of CN-Ar from the ground state zero-point level to a hindered internal rotor state (n(K) = 1(1)) in the CN overtone region. The lowest energy feature in the B-X spectrum at 25,714.1 cm(-1) is assigned as a transition to the zero-point level of the B state and also yields its binding energy, D(0) = 186(2) cm(-1), which is in excellent accord with theoretical predictions. The next feature approximately 40 cm(-1) higher is attributed to overlapping transitions to intermolecular levels with bend (v(b)(K)=1(1)) or stretch (v(s) = 1) excitation. Yet higher features (previously reported) are also assigned, based on their transition type and wavenumber, which are consistent with the intermolecular energy level pattern computed theoretically. Finally, the intensity profile of the lowest energy features in the B-X spectrum reflects the predicted change in the CN (B (2)Σ(+), X (2)Σ(+)) + Ar potentials upon electronic excitation from a weakly anisotropic potential about the linear N≡C-Ar configuration in the ground state to a more strongly bound linear C≡N-Ar structure in the excited B electronic state.

Modeling of photoacoustic Raman spectroscopy.

Photoacoustic Raman spectroscopy (PARS) is a technique used to identify chemical species mixed in a gas or liquid based on their pattern of vibrational energy levels. Raman spectroscopy differs from the more familiar absorption spectroscopy by using a nonlinear two-photon process that can be more sensitive to small differences in vibrational energy levels. Thus, it can detect defect sites in solid-state optical materials or low concentrations of chemical species in gases. The Raman scattering process generates acoustic pulses that can be detected with a microphone. In this talk, we present an overview of PARS and present a model of the production of these acoustic pulses from the energy deposited in the medium during the Raman scattering process. We will discuss the different types of PARS (cw, pulsed, and resonant) and their relative advantages. Finally, we describe an experimental platform that we plan to use for validating the model. [This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract No. DE-AC52-07NA27344.]

Torsion–rotation coupling and the determination of the torsional potential energy function of HSOH

Hindered torsional motion in a molecule such as HSOH leads to tunnelling splittings. Lying between the simpler limiting cases of strongly hindered torsion (the "we can simply neglect the tunnelling" limit) and that of free internal rotation (the "tunnelling pair of levels are just different vibrational states" limit) HSOH is particularly challenging due to strong and inherent torsion-rotation coupling. The low symmetry due to the different terminal moieties, SH and OH, further enriches the energy level pattern by allowing a systematic mixing within each quadruplet of torsion- and asymmetry-doubled levels. This mixing, which varies in a systematic manner with angular momentum quantum numbers, can reach 50% and is in addition to the mass-dependent and quasicyclic variation of the tunnelling splittings. We show that a carefully implemented reduced-dimension model, the Generalised SemiRigid Bender (GSRB), combined with a few modest ab initio calculations, is sufficient to account for the bulk of these physical effects. We also point out the reversal of energy pairing of torsional levels with increased energy. That is, at low torsional energy the lowest of the torsional level pair is the symmetric level while at high torsional energy it is the antisymmetric level which is the lowest. Finally, we present a purely empirical determination of the tunnelling splittings for K = 0, 1, 3, 4, and 5.

Analysis of the FASSST rotational spectrum of NCNCS in view of quantum monodromy

Quantum monodromy has a strong impact on the ro-vibrational energy levels of chain molecules whose bending potential energy function has the form of the bottom of a champagne bottle (i.e. with a hump or punt) around the linear configuration. NCNCS, cyanogen iso-thiocyanate, is a particularly good example of such a molecule and clearly exhibits a distinctive monodromy-induced dislocation of the energy level pattern at the bending-rotation energy at the top of the potential energy hump. Indeed, NCNCS [B. P. Winnewisser et al., Phys. Rev. Lett. 2005, 95, 243002] and the water molecule [N. F. Zobov et al., Chem. Phys. Lett. 2005, 414, 193-197] were the first two molecules for which experimental confirmation of quantum monodromy was obtained. We used the fast scan sub-millimetre spectroscopic technique (FASSST) to extend the measurements and spectral analysis to pure rotational transitions (end-over-end) in bending vibrational states lying well above the monodromy point. The analysis of 9204 lines assigned to 7 vibrational states, presented here, shows that the topological properties of the bending potential function are mapped onto every aspect of the ro-vibrational energy levels involving excitation of the quasi-linear bending vibration. In order to model the large amplitude dynamics of such a molecular system, and also to achieve some insight beyond satisfactory parameters for reproducing the spectrum, we used the generalized semi-rigid bender (GSRB) Hamiltonian, which is described in some detail. This Hamiltonian provides a good description of the energy levels over the seven bending states observed, coming close to experimental accuracy. Due to high J values of the measured rotational transitions (J</= 116), the least squares fitting procedure was applied not directly to the measured frequencies, but to effective constants derived from fitting the transition frequencies to a set of polynomials in J(J + 1) yielding effective B(eff) and D(eff) constants. The GSRB wave functions are used to show that the expectation values of any quantity which varies with the large amplitude bending coordinate will also have monodromy-induced dislocations. This includes the electric dipole moment components. High level ab initio calculations not only provided the molecular equilibrium structure of NCNCS, but also the electric dipole moment components mu(a) and mu(b) as functions of the large-amplitude bending coordinate. Calculated expectation values of these quantities for individual ro-vibrational levels show the now recognizable monodromy pattern. Finally, a generalization of the quasi-linear parameter gamma(0) is suggested.

Ab initio potential energy surface and intermolecular vibrational frequency of C3-He complex

The intermolecular potential energy surface for C3–He complex has been constructed using supermolecular CCSD(T) and MP4 methods. The potential surfaces have been calculated for 27 values of R ranging from 2.8 to 8.0 Å and 19 values of θ equally spaced between 0° and 180°. Both CCSD(T) and MP4 potentials have similar global behaviors. The global minimum in each of the potentials corresponds to the slightly distorted T-shaped geometry. On the basis of these two potentials, the intermolecular vibrational energies and wavefunctions were calculated. The energy level pattern of the vdW vibrational states was predicted for C3–He complex. The zero point bending motion of this complex has a range of 180°. The calculated fundamental frequency of vdW bending is 3.16 cm−1 at CCSD(T) level, and 5.38 cm−1 at the MP4 level. In addition, we have also constructed the intermolecular potential energy surface with C3 bending coordinate of 160° by using supermolecular CCSD(T) method. Two local minima including arrow-shaped and Y-shaped configurations were determined. The rotational constants of three C3–He structures including T-shaped, arrow-shaped and Y-shaped configurations at CCSD(T) level were also reported.

Vibrational energy levels of CH5+

We present a parallelized contracted basis-iterative method for calculating numerically exact vibrational energy levels of CH(5)(+) (a 12-dimensional calculation). We use Radau polyspherical coordinates and basis functions that are products of eigenfunctions of bend and stretch Hamiltonians. The bend eigenfunctions are computed in a nondirect product basis with more than 200x10(6) functions and the stretch functions are computed in a product potential optimized discrete variable basis. The basis functions have amplitude in all of the 120 equivalent minima. Many low-lying levels are well converged. We find that the energy level pattern is determined in part by the curvature and width of the valley connecting the minima and in part by the slope of the walls of this valley but does not depend on the height or shape of the barriers separating the minima.

Ab initio potential energy surface and intermolecular vibrational frequencies of C3–Ar complex

The intermolecular potential energy surfaces for C3–Ar have been calculated by supermolecular CCSD(T) and MP4 methods. The MP4 and CCSD(T) potentials have similar global behaviours. Their global minima all correspond to the slightly distorted T-shaped geometries. From these two potentials, the intermolecular vibrational energies and wavefunctions were calculated. The energy level patterns of the vdW vibrational states were predicted for the C3–Ar complex. The zero point bending motion of this complex has a range of approximately 60°. The calculated transition frequencies of vdW bending agree well with available experimental data.

Large-amplitude quantum mechanics in polyatomic hydrides. II. A particle-on-a-sphere model for XHn (n=4,5)

This paper describes the application of a relatively simple, but computationally tractable, "particle-on-a-sphere" (POS) model for quantum-mechanical calculation of large-amplitude, H atom dynamics in polyatomic hydrides (XH(n)), based on radially relaxed, two-dimensional angular motion of H atoms on the surface of a sphere. This work focuses on systems with many degrees of freedom, i.e., XH(4) (eight dimensional) and XH(5) (ten dimensional), with corresponding molecular analogs of CH(4) and CH(5) (+) and is applicable to rovibrationally excited states with J> or =0. A pairwise-additive potential fit for CH(5) (+), which yields remarkable agreement with geometries, energies, and barrier heights on the full-dimensional surface of Brown et al. [J. Chem. Phys. 121, 4105 (2004)] is presented. Comparisons with experimental data and diffusion quantum Monte Carlo (DMC) methods test convergence for the POS model and provide insight into multidimensional quantum rovibrational dynamics. In particular, POS energy-level patterns for a series of scaled CH(5) (+) potentials indicate an absence of strong tunneling behavior, consistent with the highly delocalized wave functions, large zero-point energies, and small interconversion barriers noted in previous DMC studies of Brown et al.

Individual differences in energy-tension cycle and self-regulation of mood

The theory of mood proposed by Thayer is examined in a sample of Spanish psychology students (N = 176). Results showed the existence of a circadian pattern of energy and tension levels, individual differences, such as gender, circadian type (morningness or eveningness), and some possible cross-cultural differences, though energy levels in American and Spanish samples were similar. Data also indicated differences in the assessment and interpretation of personal problems in relation to mood: according to energy level and mood, everyday problems and stress situations are interpreted in different ways. Finally, the results showed different manners in which people regulate mood. Implications for intervention and future research are discussed.

Electronic structure, absorption spectra, and hyperpolarisabilities of some novel push–pull zinc porphyrins. A DFT/TDDFT study

DFT/TDDFT calculations have been performed on some novel push–pull zinc porphyrins (denoted ZnPor 1, ZnPor 2, and ZnPor 3). This theoretical work aims to investigate the electronic structure, absorption spectra, and hyperpolarisabilities of these molecules. To examine the effects of the peripheral substituents on the molecular properties, zinc porphine (ZnP) and zinc tetraphenylporphine (ZnTPP) were also included in the study. The orbital energy level patterns of the substituted zinc porphyrins are indeed rather different from those of ZnP and ZnTPP. The peripheral substitution breaks the molecular D4h symmetry of the porphyrin, thereby leading to the splitting of the absorption Q band. On the other hand, the B band in the spectra may not arise only from a single excited state; instead, it could be made up of several states that are close in energy. The calculated hyperpolarisabilities (β vec) increase strongly from ZnPor 1 to ZnPor 2 to ZnPor3. The latter two molecules were predicted to have a large β vec value and thus may have potential application in the development of nonlinear optical (NLO) materials.

Site‐selective spectroscopy of erbium in wide band gap semiconductors

AbstractIn this paper results of site‐selective spectroscopy of Er3+ ions in wide band gap semiconductors, such as cubic and hexagonal GaN, and 6H SiC are presented. Photoluminescence excitation (PLE) spectroscopy was applied to find the Stark splitting pattern of energy levels in the 4I9/2 manifolds. It is shown that in cubic and hexagonal GaN only one center dominates. In the case of wurtzite GaN it is most probably due to Er occupying a Ga site, whereas in the cubic phase point‐charge model calculations suggest a slightly distorted, Td interstitial site. In 6H SiC three different centers were distinguished. The energy level schemes for the 4I9/2 and the ground 4I15/2 states were determined for all three centers, basing on the results of photoluminescence and PLE measurements. (© 2008 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Rotation–vibration energy level clustering in the [formula omitted] ground electronic state of PH 2

We use previously determined potential energy surfaces for the Renner-coupled X ∼ 2 B 1 and A ∼ 2 A 1 electronic states of the phosphino (PH 2) free radical in a calculation of the energies and wavefunctions of highly excited rotational and vibrational energy levels of the X ∼ state. We show how spin–orbit coupling, the Renner effect, rotational excitation, and vibrational excitation affect the clustered energy level patterns that occur. We consider both 4-fold rotational energy level clustering caused by centrifugal distortion, and vibrational energy level pairing caused by local mode behaviour. We also calculate ab initio dipole moment surfaces for the X ∼ and A ∼ states, and the X ∼ – A ∼ transition moment surface, in order to obtain spectral intensities.

Anisotropic magnetic susceptibility and crystal field analysis in the Van Vleck paramagnetPrF3

The magnetic susceptibility of PrF3 was measured in an external magnetic field of 0.01 T directed across and along the crystallographicc-axisat temperatures in the range 2–300 K. The maximum values of the measured susceptibilities (less than1.2 × 10−4 emu g−1) are consistent with the expected pattern of non-degenerate energy levels of the electronic4f2 configuration in the low-symmetry crystal field. The longitudinal susceptibility decreasesmonotonically with the temperature increase while the transversal susceptibility has abroad maximum at 60 K. A crystal field analysis based on the magnetic susceptibility dataand calculations in the framework of the exchange charge model was carried out. The set ofcrystal field parameters related to the crystallographic system of coordinates has beenobtained and used to reproduce successfully the temperature dependences of thelongitudinal and transversal components of the susceptibility tensor and the crystalfield energies, as well as the parameters of the effective spin Hamiltonian of the141Pr nuclei.

The forbidden rotational Q branch of CH 3SiF 3: A study in internal rotation

The pure rotational spectrum driven by the small dipole moment produced perpendicular to the symmetry axis by centrifugal distortion has been investigated for CH 3SiF 3 in the ground vibrational state using a Fourier transform waveguide spectrometer. Between 10.9 and 17.0 GHz, four ( k + 3 ← k) series in the Q branch have been measured in the lowest torsional state v 6 = 0 for k = 4, 5, 6, and 7 with 54 ⩽ J ⩽ 65. In each transition, the quantum number σ = 0, +1, −1 labelling the different torsional sub-levels is conserved. For given ( J, k), splittings from ∼10 to ∼45 MHz have been observed between lines with different values of σ. The global data set includes the anticrossing molecular beam energy differences of [W.L. Meerts, I. Ozier, Chem. Phys. 71 (1982) 401–415] as well as the mm-wave R branch frequencies and ( A 1 − A 2) splittings of [P. Dréan, J.-M. Colmont, J. Demaison, L. Dore, C. Degli Esposti, J. Mol. Spectrosc. 176 (1996) 23–27]). A good fit was obtained by varying 15 molecular parameters characterizing the torsion–rotation Hamiltonian H TR for the vibrational ground state. Because of the strong correlation between two of the quartic torsion–distortion parameters ( F 0,3 K and D 0, Km ) and a redundancy connecting the centrifugal distortion constants, four models were obtained yielding comparable fits. In each case, effective values were determined for the A-rotational constant and the height of the potential hindering the internal rotation. A high precision determination of the structural parameter ρ was made that is the same in all four models. For the off-diagonal quartic centrifugal distortion constant ε 0 and the sextic constants H 0, J , H 0, JK , H 0, KJ , and h 0,3, the differences in the values obtained in the two different reductions used have been explained in terms of the redundancy connecting these parameters. For σ = 0, +1, −1, the energy level pattern for (| k| = 3) is discussed for the case where the pure torsional energy splitting and the matrix elements off-diagonal in k are of comparable magnitude. A method is described of using an R branch study of the resulting σ-splittings for (| k| = 3) to probe the zeroth-order torsional Hamiltonian.

Case 1: The long and short of it

A 13-and-a-half-year-old girl presented to the family physician with poor growth. She was first noticed to be short at around 10 years of age (height less than the third percentile). The problem had recently become more noticeable when the mother saw the younger sister overtake the patient in growth. The weight gain was also inadequate and she fell from the third percentile to less than the third percentile. The patient had no other symptoms. Specifically, there was no abdominal pain, nausea, vomiting, constipation, diarrhea, fever, rash or arthralgia. The patient’s appetite, energy level and sleep pattern were normal. The patient’s history was generally unremarkable. Her general development had been normal. She had not started menstruating. The family history was negative for any gastrointestinal diseases. The older sister had a goiter. The mother also had problems with her thyroid gland. Both parents and other family members were of average height. Physical examination revealed a well-looking, noticeably short adolescent. Her height was 135 cm (well below the third percentile for age) and her weight was 33.8 kg (less than the third percentile). Her vital signs were normal. There was no pallor, digital clubbing or thyromegaly. Pubertal development was early Tanner stage III breast development. There was no axillary or pubic hair. The rest of the examination was unremarkable. A laboratory investigation revealed a normal complete blood count (hemoglobin 134 g/L). Serum electrolytes, calcium, glucose, urea, creatinine, liver enzymes, ferritin, immunoglobulins, albumin, thyroid-stimulating hormone and free thyroxine were all normal. A paediatric endocrinology referral had been done. Several investigations, including growth hormone tests, an adrenocorticotropic hormone stimulation test and a luteinizing hormone-releasing hormone stimulation test, were all normal. A diagnostic test was performed.

Optical Analysis of the Light Emission from Porous Silicon: A Hybrid Polyatom Surface-Coupled Fluorophor

The most extensive data set yet generated correlating photoluminescence excitation (PLE) and photoluminescence (PL) spectra is presented for aged (equilibrated) porous silicon (PS) samples. The observed features, which are temperature independent over the range 10-300 K, show a detailed correlation with the results of photoacoustic spectroscopy (PAS) and with molecular electronic structure calculations. The observed energy level patterns are reproduced in the photoabsorption (PA) of PS films released after the etching of a silicon wafer. It is concluded that the energy level pattern found for the photoluminescing surface of PS results from a structure which is neither uniquely molecule- or bulk-like but represents a hybrid form for which the density of states associated with a polyatomic vibrationally excited surface-bound fluorophor dominates the nature of the observed features which are not those of a semiconductor. These fluorophor features are broadened and shifted to lower excitation energy as a result of the intimate presence of the silicon surface to which the fluorophor is bound. The dominance of the surface-bound fluorophor accounts for the temperature-independent PLE and PL features. The observed spectral features are thus suggested to be the result of a strong synergistic interaction in which the silicon surface influences the location of surface-bound fluorophor excited states whereas the nature of the vibrationally excited surface-bound fluorophor coupling to the silicon surface provides the mechanism for an enhanced vibronic structure dominated interaction and energy transfer. The observed PLE, PL, PAS, and PA measurements are found to be consistent with previous photovoltaic and photoconductivity measurements, correlating well with a surface-bound oxyhydride-like emitter. This study suggests the important role that the overtone structure of a molecule bound to a surface can play as one forms a hybrid system.

Spectroscopic signatures of nonrigidity: Algebraic analyses of infrared and Raman transitions in nonrigid species

An algebraic scheme is proposed to explore the influence of nonrigidity upon spectroscopic (infrared/Raman) transitions. Application of this approach to large amplitude bending motion relies upon a Hamiltonian that embodies both rigidly-linear and rigidly-bent behavior, with the attendant U(3) dynamical algebra uniformly describing all pertinent operators. The bending mode supported by the quasilinear carbon trimer (C 3) is investigated, yielding algebraic predictions for vibrational energy level patterns and infrared transition matrix elements that are in reasonable accord with their ab initio counterparts. A coherent state formalism is employed to extract dependence of potential energy and dipole moment functions on C 3 bending coordinate.

Electronic spectra of molecules with two C3 v internal rotors: Torsional analysis of the [formula omitted] LIF spectrum of biacetyl

The laser-induced fluorescence excitation spectrum of the biacetyl A 1 A u ( S 1)– X 1 A g ( S 0) transition in the region from 22 182 to 22 800 cm −1 shows a complicated absorption line spectrum, which is believed to arise from a long progression in the torsional vibrations of the two equivalent methyl tops in this molecule. In this paper, we discuss three topics: (i) a numerical calculation of these energy levels using a kinetic and potential energy formalism and constants from the literature [M.L. Senent, D.C. Moule, Y.G. Smeyers, A. Toro-Labbé, F.J. Peqalver, J. Mol. Spectrosc. 164 (1994) 66], (ii) a qualitative description of the calculated energy level pattern using local-mode ideas applied to the two equivalent methyl rotors together with G 36 permutation-inversion group symmetry species, and (iii) a least-squares refinement of the torsional potential parameters based on results of some of our high-resolution rotational analyses, followed by a comparison of energy levels calculated from the refined parameters with a low-resolution spectrum taken in the region from 0 to 500 cm −1 above the A– X band origin. Concerning (ii), we find that the two vibrational levels with one quantum of torsional excitation are best described by a normal mode formulation, but that many levels with more than one quantum of torsional excitation are better described by a local-mode formulation. Concerning (iii), we obtain low-order molecular constants quite similar to those reported by Senent et al., but higher-order constants which are quite different. Our calculated spectrum agrees well with the low-resolution spectrum, but full confirmation of the present interpretation for levels with three or more quanta of torsion excited will require high-resolution studies of additional bands.