Analysis of the long range potentials of the X 1Σ+ and a 3Σ+ states of NaK

The difference in energy between the singlet and triplet states of NaK dissociating to Na(3s) and K(4s) is found from experimental data and from pseudopotential calculations. The contributions of various one- and two-electron integrals are evaluated, illustrating the present ambiguity over the exchange integral and the exchange interaction terms.     

Nodal surfaces of the wave functions of the hydrogen molecule in the triplet state 3Σu +

For molecular hydrogen in the triplet state ³Σ_u ⁺, the nodal surfaces of the wave function corresponding to the minimum basis set of Slater orbitals in the Hartree—Fock approximation and those of the wave function used in calculations by the diffusion quantum Monte Carlo method were plotted and analyzed. Taking account of the condition for antisymmetrical wave function of the triplet state ³ S of He atom, the Hartree-Fock approximation in the minimum basis set of one-electron orbitals is inappropriate for a priori determination of the nodal surfaces of many-electron wave functions (MWF). An MWF quantum chemical method developed by the authors is outlined. The alternative nodal surfaces for H₂ (³Σ_u ⁺) a priori specified in this method are presented.     

Electric dipole moments of the MgO B1Σ+ and X1Σ+ states

The electric dipole moment of the excited B¹∑⁺ (υ′ = 0) state of MgO produced in a gas-phase reaction of Mg(¹S) atoms and N₂O is measured using the technique of Stark quantum-beat spectroscopy. It is shown to be |μ_υ′=0| = 5.94(24) D. The lifetime of the excited B¹∑⁺ (υ′ = 0) state is determined as τ = 22.5(1.5) ns. Using laser excitation spectroscopy and by direct observation of the P(1) line splitting at high electric field strengths in the B¹∑⁺−X¹∑⁺ (0,0) system the ground state electric dipole moment is measured yielding |μ_υ=0| = 6.2(6) D. Furthermore an electric-field-induced Q branch is observed.     

Adiabatic calculations of the 2Σ+g excited states of He+2

The first six ²Σ⁺_g adiabatic potential energy curves of He⁺₂ are calculated with the MRD CI method employing configuration selection (T = 10 μ hartree) and perturbative energy corrections and using two basis sets differing in the number of diffuse functions. The non-adiabatic matrix elements at the numerous avoided crossings are also calculated and approximate diabatic curves are constructed. Various aspects of the results are discussed.     

The A1Σ+-X1Σ+ band system of the KH and KD molecules

The molecular constants of the A¹Σ⁺ and X¹Σ⁺ states of the KH and KD molecules have been determined using mass relations correspondent to a normal isotope shift. For the calculation we have used data of the laser-induced fluorescence spectrum by the Ar⁺ 4881 Å exciting line photographed in our laboratory, as well as previous data presented by other authors. From the spectroscopic terms, quantum-mechanical PMO-RKR-van der Waals hybrid potentials have been generated. Numerical calculations for the A¹Σ⁺ and X¹Σ⁺ states of the KH and KD species are comapred with quantum-mechanical values obtained by numerical solution of the radial Schrödinger equation. Vibrational wavefunctions appropriate to the potential curves yield values of E_υ and B_υ which are in close agreement with the experimental results. The probability distribution functions and Franck-Condon factors for the A¹Σ⁺ ↔ X¹Σ⁺ band system have also been determined. It is observed that the anomalous behaviour of the A state is clearly revealed with a changed anharmonicity for the lowest vibrational levels.     

New self-consistent potentials for the X1Σ+ and A1Σ+ states of KH

The vibrational and rotational molecular constants have been determined for the A¹Σ⁺  X¹Σ⁺ system of the isotopic potassium hydrides: KH and KD. From these experimental term values, isotopically combined PMO-RKR-van der Waals potentials are constructed, which are checked by direct integration of radial Schrödinger equation. As an additional check on the accuracy of the potentials, the wavefunctions were used to compute B_ν, D_ν, H_ν and L_ν values. The agreement between the calculated and experimental results is quite satisfactory. Franck-Condon overlap integrals and probability density distributions have been calculated. The anomalous behaviour of the A¹Σ⁺ state may be observed in the probability density functions of the lowest vibrational levels.     

A CAS SCF CI study of the 1Σ+g and 3IIu states of the C2 molecule and the 4Σ−g and 2IIu states of the C+2 ion

Ab initio calculations of the X ¹Σ⁺_g and a ³II_u states of C₂ and the X⁴Σ⁻_g and a²II_u states of the C⁻₂ molecular ion are performed to determine the corresponding potential curves around the potential minima and at the dissociation limits. A large Gaussian basis set augmented by three d-type polarization functions on each carbon center is used to approximate the molecular orbits. The calculations are done at the complete-active-space SCF and multi-reference configuration interactions level. Spectroscopic constants and rotation—vibration energies are derived from the ab initio calculated potentials. Good agreement between theory and experiment is obtained for the X¹Σ⁺_g and a ³II_u states of C₂. In the earlier tentative assignment of the observed electronic transition around 2490 Å to the ²Σ⁻_g ← ²II_u system in C⁺₂, the lower state is confirmed by the present calculations to be C⁺ ₂ (²II_u).     

Rotational analysis and deperturbation of the A2Π → X2Σ+ and B'2Σ+ → X2Σ+ emission spectra of MgH

Deperturbation analysis of the A(2)Π → X(2)Σ(+) and B(')(2)Σ(+) → X(2)Σ(+) emission spectra of (24)MgH is reported. Spectroscopic data for the v = 0 to 3 levels of the A (2)Π state and the v = 0 to 4 levels of the B'(2)Σ(+) state were fitted together using a single Hamiltonian matrix that includes (2)Π and (2)Σ(+) matrix elements, as well as off-diagonal elements coupling several vibrational levels of the two states. A Dunham-type fit was performed and the resulting Y(l,0) and Y(l,1) coefficients were used to generate Rydberg-Klein-Rees (RKR) potential curves for the A (2)Π and the B'(2)Σ(+) states. Vibrational overlap integrals were computed from the RKR potentials, and the off-diagonal matrix elements coupling the electronic wavefunctions (a(+) and b) were determined. Zero point dissociation energies (D(0)) of the A(2)Π and B'(2)Σ(+) states of (24)MgH were determined to be 12,957.5 ± 0.5 and 10,133.6 ± 0.5 cm(-1), respectively. Using the Y(0,1) coefficients, the equilibrium internuclear distances (r(e)) of the A(2)Π and B'(2)Σ(+) states were determined to be 1.67827(1) ? and 2.59404(4) A?, respectively.     

Bound vibrational levels of the two lowest 1Σ+ states of LiF

The energies of the vibrational levels of the two lowest ¹Σ⁺ states of LiF corresponding to adiabatic and to diabatic potential energy curves are calculated and compared. The high-lying levels of the ionic adiabatic and diabatic states separating to Li⁺ + F^- are represented by quantum defect formulas.     

The potential energy curves and probability density distributions of the X1Σ+ and A1Σ+ states of RBH

The potential energy curves PMO—RKR—van der Waals of the electronic A¹Σ⁺ and X₁Σ⁺ states of RbH have been determined. The potentials obtained are self-consistent with the experimental data because they have been tested by direct numerical solution of the radial Schrödinger equation. From exact vibrational eigenfunctions probability density distributions and Franck—Condon factors have been calculated over the range of vibrational levels observed. It is observed that the anomalous behaviour of the A¹Σ⁺ state arises in the υ′ = 1, 2 and 3 levels with probability density functions similar to those of a harmonic oscillator.     

A study of the perturbations between the A1Σ+u and b3Πu states of Na2

The interaction between the A¹Σ⁺_u and b³Π_Ωu states of Na₂ is explored by resonantly exciting A states via A-X transitions and, after an adjustable delay time, photoionizing them. For long delays signals arise only from states with significant fractions of both A and b state character. Thus the regions where the interaction is important stand out clearly in the spectrum. Using this technique we have investigated perturbations of the A v' = 3, 7 and 8 states by the b v' = 10, 13 and 14 states.     

Rotationally resolved (3 + 1) rempi of H 2 via the B1Σ+u state

In the paper, we compare the results of our ab initio calculations for the ro-vibrational branching ratios resulting from a (3+1) REMPI of H₂ via the B¹Σ⁺_u state with the experimental data of Pratt, Poliakoff, Dehmer and Dehmer. These results indicate that non-Franck-Condon effects are less important here than in the (3+1) REMPI of H₂ via the C¹Π_u state. We observe that the ΔJ = ±3 peaks in the photoelectron spectrum are of negligible strength and that the ratio of ΔJ = +1 to ΔJ = −1 peak is independent of the ionic vibrational state. A detailed analysis indicates that these features arise as a result of a dynamic interference between the do and dμ ionization channels and do not imply either the smallness of the d-wave or the smallness of the j_t = 3 angular momentum coupling terms.     

Self-consistent potential energy curves for the A1Σ+ and X1Σ+ states of isotopic cesium hydrides

From the spectroscopic experimental data available in the literature we have determined the mass-reduced Dunham coefficients for the A¹Σ⁺ ↔ X¹Σ⁺ system of the isotopic species CsH and CsD. Based upon these results, for both ground and excited states of cesium hydride and deuteride we report new hybrid rotationless potential energy curves (PMO-RKR-van der Waals) up to the dissociation. As a consistency check on the accuracy of the potentials the eigenvalues were calculated by direct numerical integration of the radial Schrödinger equation and found to agree within the rms error 0.39 cm⁻¹ (X¹Σ⁺) and 0.41 cm⁻¹ (A¹Σ⁺) with the experimental vibrational energies. From the wavefunctions, the rotational constants B_υ, centrifugal distortion terms D_υ, H_υ and L_υ, Franck—Condon factors, and probability density distributions were obtained. The probability density distributions for the lowest vibrational levels of the A¹Σ⁺ show an anharmonicity associated with the anomalous behavior of that state.     

Decay of the A2Σ+ and B2II quasibound states of HeH

The X²Σ⁺, A²Σ⁺ and B²II wavefunctions of the HeH molecule are calculated as single configurations state functions built from molecular orbitals generated by the Fock operator of the HeH⁺ ion. Dipole transition moments and non-adiabatic coupling matrix elements are evaluated in order to study the competition between dissociative photoemission and predissociation of the A and B states. Particular attention is paid to the X-A (2σ–3σ) avoided crossing and comparisons are made between its characteristics and those of the corresponding 2¹Σ⁺–3¹Σ⁺ (2σ–3σ) avoided crossing in the HeH⁺ ion. The predissociation lifetime of the A state is found to be of the order of 10⁻¹³ s which precludes its decay via dissociative photoemission in agreement with the analysis of recent translational spectroscopy experiments. The predissociation lifetime of the B state is found to be of the same order of magnitude as its radiative lifetime (i.e. of the order of a few 10⁻⁸ s). It is still not understood why this state would radiate rather than predissociate as has been inferred from experiment.     

Experimental studies of the NaCs 5(3)Π0 and 1(a)3Σ+ states

We report high resolution measurements of 372 NaCs 5(3)Π(0)(v, J) ro-vibrational level energies in the range 0 ≤ v ≤ 22. The data have been used to construct NaCs 5(3)Π(0) potential energy curves using the Rydberg-Klein-Rees and inverted perturbation approximation methods. Bound-free 5(3)Π(0)(v, J) → 1(a)(3)Σ(+) emission has also been measured, and is used to determine the repulsive wall of the 1(a)(3)Σ(+) state and the 5(3)Π(0) → 1(a)(3)Σ(+) relative transition dipole moment function. Hyperfine structure in the 5(3)Π(0) state has not been observed in this experiment. This null result is explained using a simple vector coupling model.     

The X1Σ+ ground state of kh near the dissociation limit

Fluorescence excited in the A¹Σ⁺ -X¹Σ⁺ system of ³⁹KH by the 4880 Å argon-ion laser line gives information about the ground state as far as the last bound rovibrational level. This is identified as J = 6 in v = 23, and, assuming a limit midway between J = 6 and J = 7, D_e(KH) = 14776 ± 4 cm⁻¹.