Spin-orbit splitting in the X2Π, a4Π, B2Π and H2Π electronic states of the NS radical

A model calculating the laser fields at a flat structureless surface taking into account the surface photoelectric effect is presented. The photon is p or transverse magnetic linearly polarized, continuous and its wave length is long, i.e. λ _vac  ≥ 12.4 nm. The sharp rise of the electron density at the interface generates an atomic scale spatial dependence of the laser field. In real space and in the temporal gauge, the vector potential A of the laser is obtained as a solution of the classical Ampère-Maxwell and the material equations. The susceptibility is a product of the electron density of the material system with the surface and of the bulk tensor and non-local isotropic (TNLI) polarizability. The electron density is obtained quantum mechanically by solving the Schrödinger equation. The bulk TNLI polarizability including dispersion is calculated from a Drude-Lindhard-Kliewer model. In one dimension perpendicular to the surface the components \hbox{$\mathcal{A}_x(z,\omega)$} ?? _x (z,ω) and \hbox{$\mathcal{A}_z(z,\omega)$}?? _z (z,ω) of the vector potential are solutions of the Ampère-Maxwell system of two coupled integro-differential equations. The model, called vector potential from the electron density-coupled integro-differential equations (VPED-CIDE), is used here to obtain the electron escape probability from the power density absorption, the reflectance, the electron density induced by the laser and Feibelman’s parameters d _∥ and d _⊥. Some preliminary results on aluminium surfaces are given here and in a companion paper the photoelectron spectra are calculated with results in agreement with the experiment.     

Characterization of the [Xtilde] 1Σ+ à 3Π and à 1Π electronic states of BBO

The three lowest-lying electronic states, [Xtilde] ¹Σ⁺, à ³II and à ¹II, of the linear BBO molecule have been systematically investigated using ab initio electronic structure theory. The equilibrium structures and physical properties including dipole moments, vibrational frequencies and associated infrared intensities, Renner parameters and energetics for the three states of BBO have been determined employing SCF, CISD, CCSD and CCSD(T) levels of theory and a wide range of basis sets. The ground state of BBO presents a degenerate real bending frequency, while the à ³II and à ¹II states show two distinct real bending frequencies due to the Renner-Teller interaction. The bending motion of the à ¹II state was analysed using the equation-of-motion (EOM)-CCSD and EOM-CC3 techniques in order to avoid possible variational collapse to a lower-lying state. The [Xtilde] ¹Σ⁺-à ³II separation was predicted to be T ₀ = 16.6 kcal mol^?1 (5800 cm^?1, 0.719 eV) at the cc-pVQZ CCSD(T) level of theory. With the cc-pVQZ EOM-CC3 method the [Xtilde] ¹Σ⁺-à ¹II splitting was predicted to be T ₀ = 48.0 kcal mol^?1 (16 800 cm^?1, 2.08 eV), which is in good agreement with the experimental value of T ⁰ = 46.6 kcal mol^?1 (16 300 cm^?1, 2.02 eV). The Renner parameters and averaged harmonic frequencies of the bending mode were determined to be ? = 0.184 and ω₂ = 363 cm^?1 for the à ³II state, and ? = 0.246 and ω₂ = 383cm^?1 for the à ¹II state. The theoretical [Xtilde] ¹Σ⁺ state harmonic B-B stretching frequency ω₃ = 636 cm^?1 is somewhat higher than the experimental estimate of 582 cm^?1 and the predicted à ¹II state harmonic B-B stretching frequency ω₃ = 861 cm^?1 is significantly higher than the experimental estimate of 440 cm^?1     

Hypervirial treatment of centrifugal distortion of 2Π energy levels

An analytical perturbation has been carried out, using a hypervirial scheme, of the wave equation with Morse potential and additional perturbations involving powers of [1-exp(-aq)]. The centrifugal distortion contributions to rovibrational energies are derived for diatomic molecules and compact formulae are obtained for successive radial derivatives of the spin-orbit function. Numerical applications are described to the X²Π states of several molecules.     

Radiative lifetime measurements of vibrational levels of Cl2 + A 2Π u

The radiative lifetimes of several vibrational levels of Cl₂ ⁺ A ²Π _u are measured by a novel technique. A uniform electric field extracts the ions from the observation region of a spectrometer, and the decrease of fluorescence signal as a function of the electric field strength is measured to obtain the radiative lifetime. Measurements are made on 20 different vibronic bands of the Cl₂ ⁺ A ²Π _u -X ²Π _g system, and the results are compared with other methods. An attempt is made to correlate the results with the highly perturbed spectroscopic nature of the A ²Π _u electronic state.     

Revised molecular constants and term values for the XΣ and AΠ states of NH

The vibration–rotation spectra of NH have been reinvestigated using laboratory spectra and infrared solar spectra recorded from orbit by the ACE and ATMOS instruments. In addition to identifying the previously unobserved 6–5 vibration–rotation band in the laboratory spectra, many additional high N rotational lines have been observed. By combining the new observations with the previously published data and recent far infrared data, an improved set of molecular constants and term values have been derived for the X³Σ⁻ and A³Π states.     

The X2Π and A2Σ+ states of FH+, ClH+ and BrH+: theoretical study of their g -factors and fine/hyperfine structures

Theoretical calculations on the fine, hyperfine and Zeeman (g-factor) parameters are reported for the X²Π and A²Σ⁺ states of FH⁺, ClH⁺ and BrH⁺. The fine-structure constants [spin–orbit (A), Λ-doubling (p, q) and spin–rotation constants (γ _Π, γ _Σ)] are evaluated up to second order (via SO/L couplings with several excited states) using a multireference configuration interaction (MRCI) method, a Breit–Pauli Hamiltonian and 6-311++(2d,2pd) basis sets. Hyperfine constants of magnetic and electric type [Frosch–Foley (a, b, c, d) and nuclear quadrupole (eQq ₀, eQq ₂)] are studied with density functional methods and various basis sets. Magnetic dipole moments (parameterized via g-factors) are calculated in second order like the fine structure constants. The situation is somewhat complex for X²Π since no less than five different g’s have to be evaluated in second order. In general, our results are in good agreement with those reported in the literature, mostly limited to the ground state. Our calculations confirm that, at equilibrium, all second-order properties are dominated by the couplings between the electronic states X and A.     

Is there a stable B2Π state for the CNO molecule?

We report MRD-CI calculations on the ground state X²Π and the excited states A²Σ⁺ and B²Π of the CNO molecule in linear geometry. The surfaces for oxygen and carbon extraction are calculated using a limited CI expansion of 47 configuration state functions; in the vicinity of the minima obtained with this procedure large-scale CI calculations are carried out including deter-mination of the spin-orbit splitting of the ²Π states of the minima. We find that the B²Π state will be difficult to detect spectroscopically due to an avoided crossing just at the equilibrium geometry of the ground state at R_CN = 2.25 a.u., R_NO = 2.30 a.u. Accordingly we find two shallow minima for B²Π at R_CN = 2.33 a.u., R_NO = 2.91 a.u. and R_CN = 2.78 a.u., R_NO = 2.28 a.u., respectively.     

Calculs numériques de facteurs de Franck-Condon et effets isotopiques: perturbation de H2 C 1Π u et prédissociation de H2 D 1Π u

On utilise l'opérateur de couplage entre le mouvement rotationnel et le mouvement électronique sous une forme condensée, plus explicite que celle donnée par van Vleck en 1951. On calcule numériquement les facteurs de Franck-Condon appropriés, et, pour obtenir les éléments de matrice en valeur absolue, on utilise l'hypothèse de précession pure. L'accord obtenu avec les mesures expérimentales de déplacement de niveaux est très bon. En ce qui concerne la prédissociation, pour laquelle les informations expérimentales sont fragmentaires, on prédit l'effet de J, l'effet de v et les effets isotopiques.     

Rotational analysis of a 2Δ-2Π system of NiF

A ²Δ-²Π system of NiF has been obtained in emission from a “composite wall hollow cathode” in the blue region. High-dispersion rotational analysis has led to the following constants (in cm^?1):

     

16.

Rovibrational transition properties of the X1Σ+ and A1Π states of carbon monosulfide     

Wei Xing  Jinfeng Sun 《Molecular physics》2020,118(18)

Carbon monosulfide was detected in outer space by rovibrational spectroscopy of the X ¹Σ⁺ state and A ¹Π – X ¹Σ⁺ system. This work calculated the potential energy curves and dipole moment functions of the X ¹Σ⁺ ₀₊ and A ¹Π₁ states, and computed the transition dipole moments between the two states employing the CASSCF method, followed by the valence icMRCI approach. Core-valence correlation and scalar relativistic corrections were included. The extrapolation of potential energies to the complete basis set limit was performed. The spin-orbit coupling effect was included. The Einstein A coefficients, band origins, and oscillator strengths were calculated for the rovibrational transitions when J?≤?150. The rovibrational transitions of the X ¹Σ⁺ ₀₊ and A ¹Π₁ states became very weak when Δυ?≥?6. The Einstein A coefficients of vibronic emissions of the A ¹Π₁ – X ¹Σ⁺ ₀₊ system were large, indicating that the emissions were able to be measured easily through spectroscopy. Several rovibrational transitions of the A ¹Π₁ – X ¹Σ⁺ ₀₊ system were analysed in detail. The distribution of radiative lifetime varying as rotational quantum number was calculated. The results obtained in this work agree well with the available experimental values.     

17.

Reinvestigation of the CO A1Π state and its perturbations: The v = 0 level     

《Journal of Molecular Spectroscopy》1987,121(2):337-379

     

18.

Fock space coupled cluster study of the 11Π g state of the Li2 molecule     

Monika Musiał  Łukasz Lupa  Stanisław A. Kucharski 《Molecular physics》2017,115(5):579-586

     

19.

A Theoretical Study of AtildeΠ MgCN     

Tina Erica OdakaTsuneo Hirano  Per Jensen 《Journal of Molecular Spectroscopy》2002,216(2):379-396

We use the RENNER program system (see, for example, P. Jensen, G. Osmann, and P. R. Bunker, in “Computational Molecular Spectroscopy” (P. Jensen and P. R. Bunker, Eds.), Wiley, Chichester, 2000, and references therein) to make a detailed calculation of the rovibronic energies in the first excited electronic state, òΠ, of the MgCN radical. This calculation is based on ab initio data computed at the MR-SDCI(+Q)/[TZ3P+f (Mg), aug-cc-pVQZ (N and C)] level of theory. We have also obtained the standard spectroscopic constants and have used these to calculate vibronic energies from perturbation expressions (J. T. Hougen and J. P. Jesson, J. Chem. Phys.38, 1524-1525 (1963)); these results are compared to those computed with RENNER. It is shown that for MgCN, the perturbation theory is dilapidated due to Fermi resonances. No spectra involving the Ã²Π electronic state of MgCN have been observed. To assist such observations, we have calculated Franck-Condon factors for some of the vibronic bands in the òΠ←Xtilde;²Σ⁺ electronic transition.     

20.

Optical-optical double-resonance spectroscopy of BaF: The E²Σ⁺ and F²Π states     

Precila C.F Ip  Peter F Bernath  Robert W Field 《Journal of Molecular Spectroscopy》1981,89(1):53-61

Sub-Doppler optical-optical double-resonance excitation spectra of BaF were recorded using two single-mode cw dye lasers. In the 30 000-cm^?1 region, the electronic states observed were E²Σ⁺ and F²Π. The latter had been previously assigned as the “F²Σ⁺” state by Fowler [Phys. Rev.59, 645–652 (1941)]. The (3, 0) and (4, 0) bands of the E²Σ⁺-B²Σ⁺ transition and the (1, 0) and (2, 0) bands of the F²Π-B²Σ⁺ transition were rotationally analyzed. The molecular constants suggest inferences about the dominant atomic orbital character of the Rydberg molecular orbitals responsible for the E²Σ⁺ and F²Π electronic states. A new electronic state, the $\text{E′}{}^2\text{Π}$, is predicted. The molecular parameters obtained (in cm^?1, 1σ uncertainty in parentheses) are

	2Π1/2	2Π3/2	2Δ3/2	2Δ5/2
B	0.3861	0.3886	0.3772	0.3792
D × 106	0.46	0.35	0.40	0.37
p	0.154
pj	?3.8 × 10-6

     

	$\text{v′}{}_{\mathrm{E}}$	$\text{E}{}^2\text{Σ}{}^{\mathrm{+}}$	$\text{v′}{}_{\mathrm{F}}$	$\text{F}{}^2\text{Π}$
$\text{T}{}_{\mathrm{v\prime 0}}$	3	29 767.32(1)	1	29 997.29(1)
$\text{Δ}\text{G}{}_{\mathrm{<mtext>v\prime \; +\; </mtext><mtext>1</mtext><mtext>2</mtext>}}$	3	522.841(27)	1	522.553(2)
$\text{B}{}_{\mathrm{e}}$		0.22990(22)		0.22931(8)
$\text{α}{}_{\mathrm{e}}$		0.00113(14)		0.00108(2)
$\text{A}{}_{\mathrm{v\prime }}$			1	56.9840(12)
$\text{p}{}_{\mathrm{v\prime }}$			1	?0.02426(6)
$\text{γ}{}_{\mathrm{v\prime }}$	3	?0.17367(46)

Rovibrational transition properties of the X1Σ+ and A1Π states of carbon monosulfide

Carbon monosulfide was detected in outer space by rovibrational spectroscopy of the X ¹Σ⁺ state and A ¹Π – X ¹Σ⁺ system. This work calculated the potential energy curves and dipole moment functions of the X ¹Σ⁺ ₀₊ and A ¹Π₁ states, and computed the transition dipole moments between the two states employing the CASSCF method, followed by the valence icMRCI approach. Core-valence correlation and scalar relativistic corrections were included. The extrapolation of potential energies to the complete basis set limit was performed. The spin-orbit coupling effect was included. The Einstein A coefficients, band origins, and oscillator strengths were calculated for the rovibrational transitions when J?≤?150. The rovibrational transitions of the X ¹Σ⁺ ₀₊ and A ¹Π₁ states became very weak when Δυ?≥?6. The Einstein A coefficients of vibronic emissions of the A ¹Π₁ – X ¹Σ⁺ ₀₊ system were large, indicating that the emissions were able to be measured easily through spectroscopy. Several rovibrational transitions of the A ¹Π₁ – X ¹Σ⁺ ₀₊ system were analysed in detail. The distribution of radiative lifetime varying as rotational quantum number was calculated. The results obtained in this work agree well with the available experimental values.     

A Theoretical Study of AtildeΠ MgCN

We use the RENNER program system (see, for example, P. Jensen, G. Osmann, and P. R. Bunker, in “Computational Molecular Spectroscopy” (P. Jensen and P. R. Bunker, Eds.), Wiley, Chichester, 2000, and references therein) to make a detailed calculation of the rovibronic energies in the first excited electronic state, òΠ, of the MgCN radical. This calculation is based on ab initio data computed at the MR-SDCI(+Q)/[TZ3P+f (Mg), aug-cc-pVQZ (N and C)] level of theory. We have also obtained the standard spectroscopic constants and have used these to calculate vibronic energies from perturbation expressions (J. T. Hougen and J. P. Jesson, J. Chem. Phys.38, 1524-1525 (1963)); these results are compared to those computed with RENNER. It is shown that for MgCN, the perturbation theory is dilapidated due to Fermi resonances. No spectra involving the Ã²Π electronic state of MgCN have been observed. To assist such observations, we have calculated Franck-Condon factors for some of the vibronic bands in the òΠ←Xtilde;²Σ⁺ electronic transition.     

Optical-optical double-resonance spectroscopy of BaF: The E2Σ+ and F2Π states

Sub-Doppler optical-optical double-resonance excitation spectra of BaF were recorded using two single-mode cw dye lasers. In the 30 000-cm^?1 region, the electronic states observed were E²Σ⁺ and F²Π. The latter had been previously assigned as the “F²Σ⁺” state by Fowler [Phys. Rev.59, 645–652 (1941)]. The (3, 0) and (4, 0) bands of the E²Σ⁺-B²Σ⁺ transition and the (1, 0) and (2, 0) bands of the F²Π-B²Σ⁺ transition were rotationally analyzed. The molecular constants suggest inferences about the dominant atomic orbital character of the Rydberg molecular orbitals responsible for the E²Σ⁺ and F²Π electronic states. A new electronic state, the $\text{E′}{}^2\text{Π}$, is predicted. The molecular parameters obtained (in cm^?1, 1σ uncertainty in parentheses) are