Recent Variational Calculations Research Articles

LED based Fourier transform absorption spectroscopy of H217O in the 14900–15600 cm−1 spectral region

The vibration-rotation absorption spectrum of 17O-enriched water vapor in the range 14900–15600 cm−1 was recorded for the first time by a Fourier Transform Spectrometer coupled to a multi-pass White-type cell providing an optical path length of 34.8 m at room temperature with a spectral resolution of 0.05 cm−1 using high luminance LED (light emitting diode) light source. The high signal-to-noise ratio allowed for the accurate determination of 1047 positions of water lines, of which 661 lines were attributed to the H217O water isotopologue. The rovibrational assignment was based on new variational calculations, which allowed retrieving 285 experimental rotational-vibrational energy levels belonging to twelve vibrational states of the H217O molecule: (410), (330), (311), (231), (212), (151), (033), (052), (113), (132), (180), and (081). The 3ν1+ν2+ν3, 2ν1+3ν2+ν3 and 4ν1+ν2 vibrational bands centered, respectively, at 15325.617, 15095.166 and 15322.533 cm−1, dominate the spectrum. A detailed comparison of the H217O line intensities recorded in this study with observed literature data and with recent high-precision variational calculations showed that the calculated intensities for the (231) - (000) band are weaker by 57% than the experimental ones. The data set obtained in this study will help to improve the quality of variational calculations for water vapor.

FTIR spectrum of hydrogen sulfide between 9995 and 10,310 cm−1

Fourier transform absorption spectrum of H2S molecule in the 9995–10,310 cm−1 spectral region from [Bykov A, Naumenko O, Smirnov M, Sinitsa L, Brown L, Crisp J, Crisp D. Can. J. Phys 1994; 72:989] has been theoretically assigned and modeled in the frame of the effective Hamiltonian approach. A set of 205 experimental energy levels has been derived for the (004) and (103) vibrational states at 10,188.303 and 10,194.445 cm−1, respectively. These levels have been reproduced with the root mean square deviation of 0.004 cm−1 by the fitting of 28 parameters of the Watson-type rotational Hamiltonian, as well as resonance parameters accounting for the Coriolis- and Fermi- type resonance interactions between (004) and (103) “bright” states, and (400) “dark” state at 10,292.536 cm−1. Detailed comparison of the experimental line position and intensities with recent variational calculations is presented.

Lamb dip CRDS of highly saturated transitions of water near 1.4 μm.

Doppler-free saturated-absorption Lamb dips were measured at sub-Pa pressures on rovibrational lines of H216O near 7180 cm-1, using optical feedback frequency stabilized cavity ring-down spectroscopy. The saturation of the considered lines is so high that at the early stage of the ring down, the cavity loss rate remains unaffected by the absorption. By referencing the laser source to an optical frequency comb, transition frequencies are determined down to 100 Hz precision and kHz accuracy. The developed setup allows resolving highly K-type blended doublets separated by about 10 MHz (to be compared to a HWHM Doppler width on the order of 300 MHz). A comparison with the most recent spectroscopic databases is discussed. The determined K-type splittings are found to be very well predicted by the most recent variational calculations.

Fourier transform absorption spectrum of [formula omitted] in 7360–8440 cm −1 spectral region

The high-resolution Fourier-transform spectrum of the D 2 16O molecule is recorded and analyzed in the region near 1.27 μ m (7360–8440 cm −1) where the bands of the V=3 ( V= v 1+ v 2/2+ v 3) polyad are located. A total of 2772 transitions have been assigned based on recent variational calculation of Shirin et al. [JQSRT 2008;109:549–58]. A set of 1094 energy levels (564 of which are new) is determined for nine vibrational states including those of newly reported (1 0 2) and (2 2 0) states. Calculations using an effective Hamiltonian are performed to establish reasonable ro-vibrational labeling of the observed energy levels. The latest variational calculation are found to agree well with the experiment for line positions (within 0.026 cm −1 on average); however, the calculated intensities for transitions to upper energy levels which are in close resonance with other states can be distorted.

D 216O: ICLAS between 13 600 and 14 020 cm −1 and normal mode labeling of the vibrational states

The high resolution absorption spectrum of dideuterated water, D 2 16O, has been recorded by Intracavity Laser Absorption Spectroscopy (ICLAS) in the 13 600–14 020 cm −1 spectral region which is the highest energy region reported so far for this water isotopologue. Because the HD 16O absorption is stronger by three orders of magnitude in the region under study, it was necessary to use high deuterium enrichment in order to minimize the HD 16O absorption lines overlapping the D 2 16O spectrum. With the high sensitivity achieved (noise equivalent absorption α min ∼10 −9 cm −1), transitions with line strengths on the order of 5 × 10 −28 cm molecule −1 could be detected. The spectrum analysis, based on recent variational calculations has provided a set of 177 new rovibrational energy levels belonging to six vibrational states. The most complete set of 53 vibrational energy levels of D 2 16O, including the three newly determined band origins, was constructed from an exhaustive review of the literature data. The fitting of the parameters of the vibrational effective Hamiltonian has allowed to reproduce the whole set of vibrational energies with an rms deviation of 0.055 cm −1. This simple model gave consistent vibrational labels of the D 2 16O states up to 18 000 cm −1. Above 15 000 cm −1, Fermi and Darling-Dennison resonance interaction were found to induce strong vibrational mixings of the wave functions in the normal mode basis, leading to ambiguous vibrational labeling.

Intracavity Laser Absorption Spectroscopy of D 2O between 12 850 and 13 380 cm −1

The high resolution absorption spectrum of dideuterated water, D 2O, has been recorded by Intracavity Laser Absorption Spectroscopy (ICLAS) in the 12 850–13 380 cm −1 spectral region which is the higher energy region reported so far for this water isotopologue. Very high deuterium enrichment was necessary to minimize the HDO absorption lines overlapping the D 2O spectrum. The achieved sensitivity (noise equivalent absorption α min ∼ 10 −9 cm −1) allowed detecting transitions with line strengths on the order of 5 × 10 −28 cm/molecule. The spectrum analysis, based on recent variational calculations has provided a set of 422 new rovibrational energy levels belonging to 11 vibrational states, including rotational sublevels for four new vibrational states and one level of the (0 9 1) highly excited bending state. The very weak (1 0 4)–(0 0 0) band at 13 263.902 cm −1, which is the highest D 2 16O band currently observed, could be assigned despite the fact that the HDO absorption in the region is stronger by three orders of magnitude. The list of 996 D 2 16O transitions is provided as Supplementary Material.

Fourier transform measurements of water vapor line parameters in the 4200–6600 cm −1 region

New high-resolution water vapor absorption spectra were obtained at room temperature in the 4200–6600 cm −1 spectral region by combining Fourier transform spectrometers (FTS) with single and multiple reflection cells. With absorption paths from 0.3 to 1800 m in pure and air diluted water vapor, accurate measurements of about 10400 lines in an intensity range from 10 −29 to 10 −19 cm/molecule have been performed. Positions, intensities, self- and air-broadening coefficients and air-induced shifts were determined for the H 2 16O, H 2 17O, H 2 18O and HDO isotopologues. The rovibrational assignment of the observed lines was performed with the use of global variational predictions and allowed the identification of several new energy levels. One major contribution of this work consists of the identification of 3280 new weak lines. A very close agreement between the new measured parameters and those listed in the database is reported as well as between the observations and the most recent variational calculations for the positions and the intensities. The present parameters provide an extended and homogeneous data set for water vapor, which is shown to significantly improve the databases for atmospheric applications, especially in the transmission windows on both sides of the band centered at 5400 cm −1.

Variational calculations using low-momentum potentials with smooth cutoffs

Recent variational calculations of the deuteron and the triton illustrate that simple wave function ansatze become more effective after evolving the nucleon-nucleon potential to lower momentum (``V_lowk''). However, wave function artifacts from the use of sharp cutoffs in relative momentum decrease effectiveness for small cutoffs (< 2 fm^-1) and slow down convergence in harmonic oscillator bases. These sharp cutoff artifacts are eliminated when V_lowk is generated using a sufficiently smooth cutoff regulator.

Probing spin–orbit mixing and the singlet–triplet gap in dichloromethylene via Ka-sorted emission spectra

The magnitude of the singlet-triplet gap in dichloromethylene (CCl(2)) has been a point of controversy in the recent literature. In this study, we report single vibronic level emission spectra of the A(1)B(1)-->X[combining tilde](1)A(1) system of the carbene C(35)Cl(2), which probes the vibrational structure of the X[combining tilde](1)A(1) state up to approximately 10,000 cm(-1) above the vibrationless level. By the careful selection of bands where complete isotope and K(a)' selectivity in excitation was possible, we measured K(a)'-sorted emission spectra in order to test the previously established hypothesis [M.-L. Liu, C.-L. Lee, A. Bezant, G. Tarczay, R. J. Clark, T. A. Miller and B.-C. Chang, Phys. Chem. Chem. Phys., 2003, 5, 1352] that unassigned lines lying above approximately 5,000 cm(-1) belong to levels of the ã(3)B(1) state. The K(a)'-sorting method discriminates between singlet and triplet levels via the (A''-B[combining macron]'') rotational constant, which is significantly larger for pure triplet levels due to the larger equilibrium bond angle. In the region between 3,500 and 9,000 cm(-1) above the vibrationless level of the X[combining tilde](1)A(1) state, we find only a very modest increase in (A''-B[combining macron]''), and approximately 86% of the lines observed between 5,000 and 9,000 cm(-1) can be assigned to X[combining tilde](1)A(1) levels within 3 standard deviations of our Dunham expansion fit, which included more than 140 levels in total. A nearly complete set of Dunham parameters was determined for the C(35)Cl(2) isotopomer, and the X[combining tilde](1)A(1) state term energies up to 4,000 cm(-1) are in excellent agreement with recent variational calculations of Tarczay, et al. [G. Tarczay, T. A. Miller, G, Czakó and A. G. Császár, Phys. Chem. Chem. Phys., 2005, 7, 2881]. Finally, the implication of our results for the singlet-triplet gap in dichloromethylene is discussed.

Single-coil properties and concentration effects forpolyelectrolyte-like wormlike micelles: a Monte Carlo study

Results of an extensive Monte Carlo (MC) study on both single andmany semiflexible charged chains with excluded volume (EV) aresummarized. The model employed has been tailored to mimicwormlike micelles in solution. Simulations have been performedat different ionic strengths of added salt, charge densities,chain lengths and volume fractions Φ, covering the diluteto concentrated regime. At infinite dilution the scatteringfunctions can be fitted by the same fitting functions as foruncharged semiflexible chains with EV, providedthat an electrostatic contribution bel is added to thebare Kuhn length. The scaling of bel is found to be morecomplex than the Odijk-Skolnick-Fixman predictions, andqualitatively compatible with more recent variationalcalculations. Universality in the scaling of the radius ofgyration is found if all lengths are rescaled by the total Kuhnlength. At finite concentrations, the simple model used is ableto reproduce the structural peak in the scattering functionS(q) observed in many experiments, as well as otherproperties of polyelectrolytes (PELs) in solution. Universal behaviourof the forward scattering S(0) is established after arescaling of Φ. MC data are found to be in verygood agreement with experimental scattering measurements withequilibrium PELs, which are giant wormlikemicelles formed in mixtures of nonionic and ionic surfactants indilute aqueous solution, with added salt.

Combination band spectroscopy of H3+

Thirty rovibrational transitions of H3+ have been observed near 1.25 μm using a tunable diode laser and a positive column discharge. In addition to the H3+ transitions, over 200 transitions between Rydberg states of H2 were observed—these could be discriminated against by using a discharge dominated by He, which apparently collisionally quenches the Rydberg states of H2 without affecting H3+. Twenty-eight of the H3+ transitions have been assigned to the ν1+2ν22←0 band, and provide experimentally determined energy levels for most of the levels up to J=4 in the ν1+2ν22 state. The remaining two H3+ transitions have been assigned to the 2ν1+ν2←0 band. These bands represent a crucial test of ab initio calculations, as they reach higher vibrational levels of H3+ than any yet observed. We have compared our experimental results with recent variational calculations by several groups.

00/00434 Nitric oxide formation in dilute hydrogen jet flames: isolation of the effects of radiation and turbulence-chemistry submodels

The high resolution absorption spectrum of dideuterated water, D216O, has been recorded by Intracavity Laser Absorption Spectroscopy (ICLAS) in the 13 600–14 020 cm−1 spectral region which is the highest energy region reported so far for this water isotopologue. Because the HD16O absorption is stronger by three orders of magnitude in the region under study, it was necessary to use high deuterium enrichment in order to minimize the HD16O absorption lines overlapping the D216O spectrum. With the high sensitivity achieved (noise equivalent absorption αmin ∼10−9 cm−1), transitions with line strengths on the order of 5 × 10−28 cm molecule−1 could be detected. The spectrum analysis, based on recent variational calculations has provided a set of 177 new rovibrational energy levels belonging to six vibrational states.The most complete set of 53 vibrational energy levels of D216O, including the three newly determined band origins, was constructed from an exhaustive review of the literature data. The fitting of the parameters of the vibrational effective Hamiltonian has allowed to reproduce the whole set of vibrational energies with an rms deviation of 0.055 cm−1. This simple model gave consistent vibrational labels of the D216O states up to 18 000 cm−1. Above 15 000 cm−1, Fermi and Darling-Dennison resonance interaction were found to induce strong vibrational mixings of the wave functions in the normal mode basis, leading to ambiguous vibrational labeling.

Inclusive and Deep-Inelastic Scattering from a Dressed Structureless Nucleon

Nonperturbative polaron variational methods are used to study inclusive scattering in the context of the scalar Wick-Cutkosky model. We derive the structure functions for a scalar point-like nucleon surrounded by a cloud of strongly interacting mesons from the Compton amplitude that is obtained in a recent variational calculation based on the particle (or worldline) representation. In zeroth variational order, a covariant exponentiated form is obtained, which is identical to the one suggested by Vineyard for scattering of slow neutrons from quantum liquids. In first order, the much richer dependence of the structure function on momentum and energy transfer, which emerges, is evaluated numerically. We study the \(\)-evolution and the perturbative as well as the scaling limit of our variational structure functions. Finally, the momentum sum rule is derived and evaluated in order to determine the momentum fraction carried by the neutral mesons inside the dressed nucleon.

High-precision structural studies of the antiprotonic helium atom p-|Am4He+by observing laser resonances with Δv=Δ(n-l-1)=2

Very weak laser resonances of unfavored transitions (n,l)\ensuremath{\rightarrow}(n+1,l-1) have been observed in metastable p-|${\mathrm{Am}}^{4}$${\mathrm{He}}^{+}$ atoms by using a pulsed antiproton beam. The observed wavelengths (713.578\ifmmode\pm\else\textpm\fi{}0.006 nm for l=34 and 726.095\ifmmode\pm\else\textpm\fi{}0.004 nm for l=35), as well as those of the known favoured transitions, are to a few ppm accounted for by a recent variational calculation of Korobov [Phys. Rev. A 54, R1749 (1996); and (unpublished)] which includes the relativistic correction to the motion of the electron.

Bifurcation in rotational spectra of nonlinear AB2 molecules

A classical microscopic theory of rovibrational motion at high angular momenta in symmetrical nonlinear molecules AB2 is derived within the framework of small oscillations near the stationary states of a rotating molecule. The full-dimensional analysis including stretching vibrations has confirmed the existence of the bifurcation predicted previously by means of the rigid-bender model [see B. I. Zhilinskii and I. M. Pavlichenkov, Opt. Spectrosk. (USSR) 64, 413 (1988)]. The formation of fourfold energy clusters resulting from the bifurcation has been experimentally verified for H2Se and it has been demonstrated in fully-dimensional quantum mechanical calculations carried out with the MORBID computer program. We show in the present work that apart from the level clustering, the bifurcation produces physically important effects including molecular symmetry-breaking and a transition from the normal mode to the local mode limit for the stretching vibrations due to the centrifugal forces. The application of the present theory with realistic molecular potentials to the H2Te, H2Se, and H2S hydrides results in predictions of the bifurcation points very close to those calculated previously. However for the lighter H2O molecule we find that the bifurcation occurs at higher values of the total angular momentum than obtained in previous estimations. The present work shows it to be very unlikely that the bifurcation in H2O will lead to clustering of energy levels. This result is in agreement with recent variational calculations.

Low-energy electron scattering from O2

Absolute differential cross sections for elastic electron scattering from molecular oxygen have been measured at incident electron energies between 1 and 30 eV and over a range of scattering angles between 10 and 130 degrees . These results are compared with other measurements and they highlight a substantial degree of discrepancy between the various experiments at energies below 10 eV. They also indicate some interesting behaviour at low energies and forward angles, which appears to be common to a number of other diatomic molecules. The data are also compared with a recent Schwinger variational calculation, (Ribiero et al., 1994) and total elastic and elastic momentum transfer cross sections, derived from the differential measurements, are also presented and compared with a recent R-matrix calculation.

Laser-induced fluorescence of the A 2πu-X 2πg transition of CS 2+ in solid Ne. Reanalysis of vibronic spectra

Dispersed fluorescence spectra in the spectral range 475–575 nm and fluorescence excitation spectra in the range 410–480 nm were recorded for the A 2 π u-X 2 π g system of CS 2 + and its 13C- and 34S-isotopic species. Based on a comparison of the relative extents of 13C- and 34S-isotopic shifts, new assignments for Fermi polyads of the X 2π g state were derived; they are consistent with recent variational Renner-Teller calculations by Brommer and Rosmus based on three-dimensional potential energy functions derived from ab initio calculations. According to an analogous argument, the vibronic levels of the A 2π u state are assigned based on observed 13C- and 34S-isotopic shifts.

Density dependence of the single particle kinetic energy in 3He [sbnd]4He

We present inelastic neutron scattering measurements of liquid 3He 4He mixtures at 1.5 K and at 3He concentrations of 0,15,40,70 and 100%. There is little apparent concentration dependence of the 3He kinetic energy, in disagreement with recent variational calculations for mixtures. The kinetic energy of the 4He component for the lower concentration mixtures is consistent with theoretical predictions.

Electron collisions with NO: elastic scattering and rovibrational (0 to 1, 2, 3, 4) excitation cross sections

The relative flow technique, utilizing helium as a cross section standard, has been applied to measure absolute elastic differential cross sections for electron scattering from nitric oxide (NO). The present elastic measurements were conducted at nine energies in the range 1.5-40 eV, which represents an important extension to the only previous study of this system by Kubo and co-workers (1981). Furthermore, the uncertainties in the present data are significantly reduced in comparison to those quoted in the earlier work. The current elastic differential cross sections were measured at the Australian National University over an angular range 10 degrees -130 degrees . We also report the first measurements of absolute differential cross sections for rovibrational (0 to 1, 2, 3, 4) excitation of the NO ground electronic state. These were conducted at six energies in the range 7.5-40 eV and were measured at Flinders University over the angular range 10 degrees -90 degrees . The differential cross sections for both the elastic and inelastic processes are compared with the results of the recent Born-closure Schwinger variational method calculation of Mu-Tao Lee and colleagues (1992).

Nonvariational calculation of the relativistic and finite-size corrections for the helium ground state.

Relativistic and finite-size corrections are calculated by using an accurate direct solution of the Schr\"odinger equation [the correlation function hyperspherical harmonic (CFHH) method] for the ground state of the helium atom. In the CFHH method the solution is a product of a correlation function and of a smooth factor expanded into hyperspherical harmonic functions. Given the proper correlation function, chosen from physical considerations, the method generates wave functions, accurate in the whole range of interparticle distances, which leads in turn to precise estimates of the relativistic operators. Our nonvariational results are compared with those obtained in recent variational calculations.