Calculated Term Values Research Articles

The new investigation of the [formula omitted] system of AlH

The b3Σ−–a3Π visible system of AlH was observed at high resolution by using a high accuracy, dispersive optical spectroscopy technique. The emission spectrum was excited in an aluminum hollow-cathode lamp with two anodes, filled with a static Ne/NH3 gas mixture. In the 25,900–26,500cm−1 spectral region, the rotational structure of the two overlapped 0–0 and 1–1 bands was clearly observed and precisely measured. In total, 260 transition wavenumbers have been assigned with an estimated accuracy of about 0.005cm−1. The open rotational structure of the Q branches in both bands has been measured for the first time, and the Λ-doubling in the a3Π,v=0,1 levels has been described by o,p and q parameters. For example, the values for the v=0 level are p0=1.754(14)×10−2cm−1, q0=3.264(28)×10−3cm−1 and o0=9.34(20)×10−2cm−1. Moreover, the spin–orbit interaction constants for the a3Π state have been obtained experimentally as follows: A0=40.6040(42)cm−1 and A1=40.419(59)cm−1. The a3Π,v=0,1 levels are considered as regular, while for the b3Σ−,v=0,1 levels considerable perturbations in the rotational structure have been observed. Consequently, these states have been represented in a different way in our least-squares treatment: a3Π state by molecular constants and b3Σ− state by term values. The observed irregularities in the b3Σ− state have been graphically described by plotting experimental minus calculated term values versus quantum number N for the v=0 level, as well as by plotting reduced term values versusN(N+1) for the v=1 level.

An ab initio study of SbH2 and BiH2: The Renner effect, spin–orbit coupling, local mode vibrations and rovibronic energy level clustering in SbH2

We present the results of ab initio calculations for the lower electronic states of the Group 15 (pnictogen) dihydrides, SbH2 and BiH2. For each of these molecules the two lowest electronic states become degenerate at linearity and are therefore subject to the Renner effect. Spin–orbit coupling is also strong in these two heavy-element containing molecules. For the lowest two electronic states of SbH2, we construct the three dimensional potential energy surfaces and corresponding dipole moment and transition moment surfaces by multi-reference configuration interaction techniques. Including both the Renner effect and spin–orbit coupling, we calculate term values and simulate the rovibrational and rovibronic spectra of SbH2. Excellent agreement is obtained with the results of matrix isolation infrared spectroscopic studies and with gas phase electronic spectroscopic studies in absorption. For the heavier dihydride BiH2 we calculate bending potential curves and the spin–orbit coupling constant for comparison. For SbH2 we further study the local mode vibrational behavior and the formation of rovibronic energy level clusters in high angular momentum states.

Fourier transform emission spectroscopy of the A2Π–X2Σ+ (red) system of 13C14N (II)

High resolution emission spectra of the A2Π–X2Σ+ transition of 13C14N have been measured in the 15000–24000cm−1 region. Molecules were produced by the reaction of 13CH4 and 14N2 in an active nitrogen afterglow discharge. The spectra were recorded using the Fourier transform spectrometer associated with the McMath-Pierce Solar Telescope of the National Solar Observatory. A rotational analysis of 27 bands involving the excited state vibrational levels v′=9–22 and the ground state vibrational levels up to v″=12 has been obtained. An improved set of spectroscopic constants has been determined for the v=0–22 levels of the A2Π state by combining the present measurements with those reported previously for the v=0–8 vibrational levels of the A2Π state [Ram et al., Astrophys. J. Suppl. Ser. 188 (2010) 500] and existing infrared and millimeter-wave measurements of 13C14N. The 6–3, 7–4, 8–5 and 9–6 bands of the B2Σ+–A2Π transition were also identified in the 23300–24000cm−1 region and were included in the final analysis. An experimental line list and calculated term values are provided.

FOURIER TRANSFORM EMISSION SPECTROSCOPY OF THE B 2 Σ + - X 2 Σ + (VIOLET) SYSTEM OF 13 C 14 N

Emission spectra of the B {sup 2}{Sigma}{sup +}-X {sup 2}{Sigma}{sup +} transition of {sup 13}C{sup 14}N have been observed at high resolution using the Fourier transform spectrometer associated with the McMath-Pierce Solar Telescope of the National Solar Observatory. The spectra have been measured in the 21000-30000 cm{sup -1} region and a total of 52 vibrational bands involving vibrational levels up to v = 15 of the ground and excited states have been rotationally analyzed to provide a much improved set of spectroscopic constants. An experimental line list and calculated term values are provided. The results of the present analysis should prove useful in the identification of additional {sup 13}C{sup 14}N lines in comets and cool stars, and will help in the determination of the {sup 12}C/{sup 13}C abundance ratio.

FOURIER TRANSFORM EMISSION SPECTROSCOPY OF THE A 2 Π- X 2 Σ + (RED) SYSTEM OF 13 C 14 N

Emission spectra of the A2Π–X2Σ+ transition (red system) of 13C14N have been measured in the 4000–15,000 cm−1 region using the Fourier transform spectrometer associated with the McMath–Pierce Solar Telescope of the National Solar Observatory. The 13C14N free radical was produced in microwave discharge of a mixture of 13CH4 and 14N2. Rotational analysis of 22 vibrational bands involving vibrational levels up to v' = 8 and v'' = 5 of the excited and ground states has been obtained and much improved spectroscopic constants have been determined. An experimental line list and calculated term values are provided. The results of the present analysis are useful for the identification of 13C14N lines in late-type stars in the red and near-infrared spectral regions.

New spectroscopic data, spin-orbit functions, and global analysis of data on the AΣu+1 and bΠu3 states of Na2

The lowest electronically excited states of Na2 are of interest as intermediaries in the excitation of higher states and in the development of methods for producing cold molecules. We have compiled previously obtained spectroscopic data on the A 1Sigmau+ and b 3Piu states of Na2 from about 20 sources, both published and unpublished, together with new sub-Doppler linewidth measurements of about 15,000 A<--X transitions using polarization spectroscopy. We also present new ab initio results for the diagonal and off-diagonal spin-orbit functions. The discrete variable representation is used in conjunction with Hund's case a potentials plus spin-orbit effects to model data extending from v=0 to very close to the 3 2S+3 2P12 limit. Empirical estimates of the spin-orbit functions agree well with the ab initio functions for the accessible values of R. The potential function for the A state includes an exchange potential for S+P atoms, with a fitted coefficient somewhat larger than the predicted value. Observed and calculated term values are presented in an auxiliary (EPAPS) file as a database for future studies on Na2.

New potential energy surfaces for the and states of CH

We report new ab initio calculations of the three-dimensional potential energy surfaces for the Renner-effect coupled ground electronic state and first excited electronic state of the CH molecule. We also make an ab initio calculation of the spin–orbit coupling surface between these states. Using these ab initio surfaces in our computer program RENNER, we calculate term values and absorption line intensities, and compare with recently observed high resolution spectra. Adjusting two parameters in the potential surfaces we are able to achieve satisfactory agreement with the experimental results except for those that involve the state (, l = 1) vibronic level. The implication of this disagreement is discussed.

Perturbed 5snd 1,3D2 Rydberg series of Sr.

The energy levels of the Sr 5snd${\mathrm{}}^{1,3}$${\mathit{D}}_{2}$ Rydberg series have been measured using an autoionization scheme, which provides an excellent opportunity for the application of the multichannel quantum-defect theory (MQDT) to their spectra. MQDT parametrizations of the $^{1,3}$${\mathit{D}}_{2}$ bound-state Rydberg series are presented, including calculated term values for these series. Furthermore, it is found that MQDT wave functions that are derived from experimentally determined level energies are capable of predicting such wave-function-sensitive properties as natural radiative lifetimes of Sr 5snd${\mathrm{}}^{1,3}$${\mathit{D}}_{2}$ Rydberg states.

Precise Rovibronic Term Values of Some Vibrational Levels of the A1Π, B1Σ+, C1Σ+, and E1Π States of 12C18O and 13C18O

Term values of the A1Π, v = 1 and 2 levels of 12C18O and v = 1 level of 13C18O from the experimental data of the A1Π-X1Σ+ system (Haridass et al., J. Mel, Spectrosc. 167, 334-352, 1994) were calculated. Term values of the Rydberg states B1Σ+, v = 0 and 1, C1Σ+, v = 0, and E1Π, v = 0 of these two isotopomers were calculated by combining the data of the A1Π-X1Σ+ system and those of the B1Σ+-A1Π, C1Σ+-A1Π, and E1Π-A1Π systems taken from the literature. The interaction between the C and E states was taken into account in determining their molecular parameters. Finally, the molecular constants of the B, C, and E states of 12C18O and 13C18O were determined from the calculated term values.

A Computer-Assisted Assignment Procedure for Complex Emission Spectra Applied to the GK1Σ+g State of T2

Using Dieke′s unpublished table of T2 emission wavenumbers, we search for transitions involving the well-known B1Σ+u vibration-rotation levels as lower states. To make new assignments, we exploit the availability of ab initio predictions of the higher singlet gerade states of T2. Since, however, the calculated term values are generally saddled with systematic deviations from the "true" ones up to a few cm−1, a new computer-assisted procedure is used to assign spectral lines and to estimate new upper term values. The procedure can handle gaps in the set of measurements adequately. In addition, a rule for flagging any batch of dubious assignments is introduced. It is based on a statistical argument. Results on the GK1Σ+g state of T2 serve to illustrate the method. Since the B1Σ+u term values have never been published, we have determined them from the known EF1Σ+g → B1Σ+u bands.

The Visible Absorption Spectrum of Matrix-Isolated NH 2 and Its Deuterides - Comparison with Calculated Spectroscopic Properties

Absorption spectra of matrix-isolated NH 2 and its deuterides were measured in the range 370- 880 nm. Comparison with calculated term values, transition moments, spin-orbit splittings, and with gas-phase data rendered possible the nearly complete assignment of the spectra. At 5 K the à 2 A 1, X̃ 2 B 1 ( v 1, v 2, 0) ← X̃ 2 B 1 (0, 0, 0) system consists of Π-bands, and of very weak Σ* ← Σ and Δ* ← Σ bands which are induced by a local translational mode of ca. 70 cm −1. At elevated temperatures regular Σ and Δ bands have also been identified. This fact as well as the temperature dependence of the band shapes confirms that the radicals undergo (nearly) free rotation in therare gas cage. Term values and intensity distributions are well reproduced by the calculations, ifallowance is made for intensity borrowing by assigned and some unassigned Fermi resonances.

Energy levels for S, P, and D states in He through precision variational calculations.

Nonrelativistic variational calculations with the relativistic correction to order ${\ensuremath{\alpha}}^{2}$ have been carried out to obtain the energy levels for the n $^{1}$,3S, n $^{1}$,3P, and ${n}^{1}$,3D series in He up to n=8. The calculated term values have converged generally to within an uncertainty of \ensuremath{\sim}${10}^{\mathrm{\ensuremath{-}}4}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$, a value matching the accuracy of recent high-precision wavelength measurements. The results are combined with theoretical Lamb shifts and systematically compared with currently available high-precision experimental data. The consistency between theory and experiment is good, although for some low-lying (n=3--6) S and P states there exist small discrepancies, presumably caused by the estimated Lamb shifts. The calculated term values for high-lying excited states have better accuracies than existing experimental data. Addition of the theoretical term values to the corresponding experimental excitation energies suggests a value of 198 310.7725(5) ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ for the ground-state ionization energy on the energy scale fixed by the ${2}^{1}$P value of 171 135.0000 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$.

New values for someHe4I1snlenergy levels, ionization energies, and Lamb shifts

Recent experimental determinations of energy separations within the $1snl$ term system ($n=2\ensuremath{-}6$) have been used to reevaluate 35 levels. Most of the levels have estimated errors less than 0.001 ${\mathrm{cm}}^{\ensuremath{-}1}$ relative to the $2 ^{3}P$ levels. Addition of accurate theoretical term values (ionization energies) available for several $1snl$ levels to the corresponding experimental level values gives generally consistent values for the principal ionization energy (${E}_{I}$). The theoretical energies are further confirmed by the agreement of the weighted average of seven of these ${E}_{I}$ values with a value obtained by fitting Ritz formulas to three accurately determined $1snl$ series; the suggested new ${E}_{I}$ is 198 310.7745(40) ${\mathrm{cm}}^{\ensuremath{-}1}$ on an energy scale fixed by the value 171 135.0000 ${\mathrm{cm}}^{\ensuremath{-}1}$ for $2 ^{1}P$. Lamb shifts are derived for the $2$, $3$, $4 ^{3}S_{1}$, $2 ^{1}S_{0}$, $2 ^{3}P_{1}$, and $2 ^{1}P_{1}$ levels as differences between experimental term values obtained with the new ${E}_{I}$ and corresponding calculated term values not including Lamb shifts. The experimental and calculated values for the ${1s}^{2} ^{1}S_{0}$ ground level relative to the present $1snl$ excited-level system are 0.00\ifmmode\pm\else\textpm\fi{}0.15 and 0.073\ifmmode\pm\else\textpm\fi{}0.009 ${\mathrm{cm}}^{\ensuremath{-}1}$, respectively, so that a \ensuremath{\sim}20-fold increase in the experimental accuracy would be required to test the calculated ground-level Lamb shift.

Simplified methods for ab initio calculations. The valence states of CH2 and CH

AbstractThree simplifying methodds are discussed and applied to the four lowest valence states of CH2(3B1, 1A1, 1B1 and 1Σ(1A)) and to the two lowest of CH(2A1 and 2∏u(2B1)). These methods concern: (1) the development of polarization functions for Gaussian‐lobe basis sets by least‐square fitting of numebrical multiconfigurational atomic fuinctions (this approach is tested also on (C2H2, (2) the use of intermediate Hamiltonians to calculate avoided crossings between potential hypersurfaces, and (3) thecalculation of correlation energies using an atoms‐in‐molecule approach.The calculated equilibrium geometries of the CH2 States are within 0.02 Å and 5° of available experimental data. The calculated term values and ionization potentials, Te(1A1 = 0.35 eV, Te (1B1) = 1.22 eV, Te (1Σ(1A)) 2.48 eV, I.P. (2A1) = 10.39 eV and I. P. (2∏u(2B1)) = 10.58 eV, are in agreement with some recent theoretical studies, and are very close to existing experimental information.

Bound, even-parityJ=0andJ=2spectra of Sr

Extensive new data on the even-parity, $J=0$ and $J=2$ states of Sr have been obtained using multiphoton ionization spectroscopy. Revised term values for previously observed $5s9d^{1}D_{2}$ and $^{3}D_{2}$, and $5s13d$ to $5s16d^{3}D_{2}$ states are presented in addition to term values for newly observed $^{1}S_{0}$ states up to $5s21s$, $^{1}D_{2}$ states up to $5s60d$, and $^{3}D_{2}$ states up to $5s37d$. The new data clearly show an avoided crossing between the $^{1}D_{2}$ and $^{3}D_{2}$ series near the $5s16d$ levels. A strong $J=2$ autoionizing resonance is also observed, \ensuremath{\sim}450 ${\mathrm{cm}}^{\ensuremath{-}1}$ above the first ionization limit. Multichannel quantum-defect theory (MQDT) parametrizations of the $^{1}S_{0}$, $^{1}P_{1}^{o}$, $^{1}D_{2}$, and $^{3}D_{2}$ bound-state Rydberg series are also presented, including calculated term values for these series. The MQDT analysis of the $J=2$ series in Sr differs from the earlier analysis of Ca in that both configuration interactions and recoupling between $^{1}D_{2}$ and $^{3}D_{2}$ series must be treated simultaneously. Further, it is found that all of the major perturbations of the $J=2$ bound states can be reproduced without including any interactions due to a $4{d}^{2}^{1}D_{2}$, even though $3{d}^{2}^{1}D_{2}$ is a major perturber of the $^{1}D_{2}$ series in Ca.

Rotational Analysis of the A-X and B-X Band Systems of CaH

The absorption spectrum of CaH in the region 6 130-7 125 Å has been generated using a King furnace. The spectrum was recorded photographically in a 10.685 m concave grating spectrograph. Ten bands belonging to the A2Π-X2Σ and B2Σ-X2Σ systems have been rotationally analyzed. Perturbations between the two excited states have been observed. Computer methods have been used to calculate term values and to evaluate molecular constants.

Rotational Analysis of the A-X Band System of CoD

The absorption spectrum of CoD has been produced by using a King furnace. The spectrum in the region 3 500-7 500 Å was recorded photographically in a 10.685 metre concave grating spectrograph. Six perturbed bands belonging to the A3Φ4-X3Φ4 sub-system have been analysed. Computer methods have been used to calculate term values and to evaluate molecular constants, some of which are (in cm-1).

Use of Model Potentials in the Study of Molecular Rydberg States

In this paper we investigate the applicability of simple model potentials containing adjustable parameters to the description of molecular Rydberg states. Qualitative criteria for the selection of appropriate potentials are discussed and the results of numerical calculations relevant to the Πu3 states of H2, the Σu1(2Σgcore) states of N2, and some Rydberg states of benzene are presented. It is found that the model potentials proposed adequately describe the effective potential of the positively charged core in the Rydberg states. In the case of benzene, a unique assignment of the experimentally observed Rydberg series is impossible because of the ambiguity of the calculated term values arising from the adjustable parameters in the potential. We also discuss the limitations of semiempirical potentials and suggest the use of model potentials that contain no adjustable parameters.