Long-range potentials and dipole moments of the CO electronic states converging to the ground dissociation limit.

The asymptotic, R → ∞, behavior of the potential-energy and dipole-moment functions (PEFs and DMFs) for all six (1,2)Σ+, (1,2)Π, Σ-, and Δ electronic states converging to the ground C(3P) + O(3P) dissociation limit of the CO molecule are studied in the framework of long-range (LR) perturbation theory. The analytical expressions for the leading coefficients of the LR expansion, C5/R5 for PEF and d4/R4 for DMF, in terms of the atomic quadrupole constants and static dipole polarizabilities are derived. The exact relationships between the LR coefficients for the states of different spatial symmetry are established as well. The analytical results are complemented with the first-principles calculation of the PEFs and DMFs for all the above states at large distances (R = 5-20 Å). The electronic structure calculation is conducted by means of the multi-reference configuration interaction and the averaged-coupled-pair functional methods, which both implemented the aug-cc-pwCVXZ (X = T, Q, and 5) basis sets and finite-field approach. The dispersion coefficients, C5 and C6, extracted from the ab initio PEFs, are found to be very close to their present and previous theoretical counterparts. The analytically estimated d4 = -5 DÅ4 obtained for the ground X1Σ+ state perfectly agrees with the present ab initio DMF but diverges significantly from the literature data.

Ab initio interatomic potentials and transport properties of alkali metal (M = Rb and Cs)-rare gas (Rg = He, Ne, Ar, Kr, and Xe) media.

We performed a first principle systematic calculation on the adiabatic potential energy curves (PECs) of alkali metal (M = Rb and Cs) - rare gas (Rg = He, Ne, Ar, Kr, and Xe) van der Waals molecules over a wide range of interatomic distance R. All electron basis sets of triple and quadruple zeta valence quality were used for the He, Ne, Ar and Kr atoms. Scalar relativistic effects were taken into account for the heavy Rb, Cs and Xe atoms by means of Dirac-Fock effective core potentials. The correlated ground state energies have been obtained within the framework of the spin unrestricted open-shell coupled cluster method, with perturbative treatment of triple excitations. The electronic energies were corrected for the basis set superposition error (BSSE) using the counterpoise method. Energies were extrapolated to the complete basis set (CBS) limit using a two-point scheme. The energy convergence towards the CBS limit was monitored by the saturation of the dummy atom basis set that included bond functions centered at the midpoint of the interatomic distance. The ab initio point-wise PEC was followed to small R to the point where the energy was 0.5 Hartree above the dissociation limit. A Morse long-range (MLR, UM Rg(R)) potential possessing the correct asymptotic behavior at R → ∞ was fitted to the single point energies. The resulting set of fully analytical MLR potentials was then used to evaluate classical collision integrals over a wide range of collision energies. By this means, diffusion coefficients (DM Rg(T)) were predicted as functions of the translation temperature T ≤ 3000 K. The reliability of the present ab initio UM Rg(R) and DM Rg(T) functions was accessed through a comparison with previous theoretical and experimental results.

Intensity anomalies in the rotational and ro-vibrational spectra of diatomic molecules.

We study the anomalies in the distributions of intensities of transitions in the purely rotational bands and the rotational branches of the vibrational bands within the unperturbed ground electronic states in spectra of diatomic molecules. While normally these distributions follow smooth patterns, sudden drops in intensity values are often observed. We analyze the origin of these anomalies in HF, DF, and CO and find that they are predominantly associated with specific forms of the dipole-moment functions (DMFs). The rotational transitions at which these anomalies occur and their severity are very sensitive to these forms, which makes them a promising tool for refining the empirical DMFs.

Peculiarities of high-overtone transition probabilities in carbon monoxide revealed by high-precision calculation.

In the recent work devoted to the calculation of the rovibrational line list of the CO molecule [G. Li et al., Astrophys. J., Suppl. Ser. 216, 15 (2015)], rigorous validation of the calculated parameters including intensities was carried out. In particular, the Normal Intensity Distribution Law (NIDL) [E. S. Medvedev, J. Chem. Phys. 137, 174307 (2012)] was employed for the validation purposes, and it was found that, in the original CO line list calculated for large changes of the vibrational quantum number up to Δn = 41, intensities with Δn > 11 were unphysical. Therefore, very high overtone transitions were removed from the published list in Li et al. Here, we show how this type of validation is carried out and prove that the quadruple precision is indispensably required to predict the reliable intensities using the conventional 32-bit computers. Based on these calculations, the NIDL is shown to hold up for the 0 → n transitions till the dissociation limit around n = 83, covering 45 orders of magnitude in the intensity. The low-intensity 0 → n transition predicted in the work of Medvedev [Determination of a new molecular constant for diatomic systems. Normal intensity distribution law for overtone spectra of diatomic and polyatomic molecules and anomalies in overtone absorption spectra of diatomic molecules, Institute of Chemical Physics, Russian Academy of Sciences, Chernogolovka, 1984] at n = 5 is confirmed, and two additional "abnormal" intensities are found at n = 14 and 23. Criteria for the appearance of such "anomalies" are formulated. The results could be useful to revise the high-overtone molecular transition probabilities provided in spectroscopic databases.

Direct-potential-fit analyses yield improved empirical potentials for the ground X (1)Σ(+)(g) state of Be2.

We have performed new direct-potential-fit (DPF) analyses of the rotationally resolved A (1)Π(u)(ν'=2,3;J' =1,2)→X(1)Σ(+)(g) (ν" ∈[0,11];J" ∈[0,3]) stimulated emission pumping spectra of Be2 [J. M. Merritt, V. E. Bondybey, and M. C. Heaven, Science 324, 1548 (2009)] using two quite different analytical potential energy functions that incorporate the correct theoretically known long-range behaviour in different ways. These functions are: the damped Morse/long-range potential [R. J. Le Roy, C. C. Haugen, J. Tao, and H. Li, Mol. Phys. 109, 435 (2011)], and the Chebyshev polynomial expansion potential [L. Busevica, I. Klincare, O. Nikolayeva, M. Tamanis, R. Ferber, V. V. Meshkov, E. A. Pazyuk, and A. V. Stolyarov, J. Chem. Phys. 134, 104307 (2011)]. In contrast with the expanded Morse oscillator potential determined in the original DPF analysis of Merritt et al. [Science 324, 1548 (2009)], both of these functions unambiguously support the existence of the v″ = 11 last vibrational levels which is bound by only ∼0.5 cm(-1), and they give equivalent, essentially exact predictions for this level when using the original data set which ended at v″ = 10. These empirical potentials predict an equilibrium distance of re = 2.445(5) Å and a well depth of D(e) = 934.9(0.4) cm(-1), values which agree (within the uncertainties) with the best ab initio estimates of 2.444(10) Å and 935(10) cm(-1), respectively [J. Koput, Phys. Chem. Chem. Phys. 13, 20311 (2011)].

Rapid, accurate calculation of the s-wave scattering length.

Transformation of the conventional radial Schrödinger equation defined on the interval r ∈ [0, ∞) into an equivalent form defined on the finite domain y(r) ∈ [a, b] allows the s-wave scattering length a(s) to be exactly expressed in terms of a logarithmic derivative of the transformed wave function φ(y) at the outer boundary point y = b, which corresponds to r = ∞. In particular, for an arbitrary interaction potential that dies off as fast as 1/r(n) for n ≥ 4, the modified wave function φ(y) obtained by using the two-parameter mapping function r(y; ̄r,ß) = ̄r[1 + 1/ß tan(πy/2)] has no singularities, and a(s) = ̄r[1 + 2/πß 1/φ(1) dφ(1)/dy]. For a well bound potential with equilibrium distance r(e), the optimal mapping parameters are ̄r ≈ r(e) and ß ≈ n/2 - 1. An outward integration procedure based on Johnson's log-derivative algorithm [J. Comp. Phys. 13, 445 (1973)] combined with a Richardson extrapolation procedure is shown to readily yield high precision a(s)-values both for model Lennard-Jones (2n, n) potentials and for realistic published potentials for the Xe-e(-), Cs(2)(aΣ(u)(+)(3)), and (3, 4)He(2)(XΣ(g)(+)(1)) systems. Use of this same transformed Schrödinger equation was previously shown [V. V. Meshkov et al., Phys. Rev. A 78, 052510 (2008)] to ensure the efficient calculation of all bound levels supported by a potential, including those lying extremely close to dissociation.

The X2Σ+ state of LiCa studied by Fourier-transform spectroscopy.

The paper reports on a successful observation of high resolution Fourier transform spectra of LiCa. The fine structure of the ground state was observed and attributed to effective spin-rotation interaction. The experimental observations are described by two models using potential energy curves. One of them takes into account the fine structure splitting by means of effective constants, the other by means of a R dependent function γ(R), built in the radial Schrödinger equation. Ab initio calculations were performed for γ(R) which comes close to the experimental function.

Ab initio and quantum-defect calculations for the Rydberg states of ArH.

Potential energy curves were evaluated for the ground and thirteen low-lying excited electronic states of the ArH molecule over a wide range of internuclear distances by the multi-reference averaged quadratic coupled cluster method. The ab initio energy differences and transition dipole moments were used to estimate Einstein emission coefficients, absorption oscillator strengths and radiative lifetimes. Diagonal and off-diagonal quantum defects, as functions of internuclear distance, were extracted from ab initio potentials of the lowest Rydberg states of the neutral ArH molecule by taking account of configuration interaction between Rydberg series converging to the ground and two electronic excited states of the ArH(+) cation. The derived quantum-defect functions were used to generate manifolds of higher excited Rydberg states. The agreement between experimental and calculated energies and radiative transition probabilities was found to be as good as or better than that obtained by earlier calculations.

Theoretical study of the ArH+ electronic states.

Potential energy curves, permanent multipole and transition dipole moments were evaluated for the ground and low-lying excited electronic states of the ArH+ cation over a wide range of internuclear distance by the multireference averaged quadratic coupled cluster method (MR-AQCC). The electric dipole polarisability of the ground X 1sigma state was evaluated by the finite-field method. The permanent multipole moments and dipole polarisabilities corresponding to the ArH+ X 1sigma+ state were used to estimate quantum defect functions of the nonpenetrating d- and f-complex Rydberg states of neutral ArH molecule. The ground state dipole function and potential were tested by a simulation of intensity distributions in the rovibrational deltav = 1 bands, radiative lifetimes and rotational g-factors for the X 1sigma+ state.

Direct deperturbation analysis of the A 2Pi approximately B 2Sigma+ complex of 7,6LiAr isotopomers.

Direct deperturbation analysis of the highly accurate experimental rovibronic term values of the A (2)Pi approximately B (2)Sigma(+) complex of LiAr [R. Bruhl and D. Zimmermann, J. Chem. Phys. 114, 3035 (2001)] has been performed in the framework of inverted close-coupling approach implicitly adjusted to the unified treatment of the overall A approximately B coupling effect without reducing the rovibrational dimensionality. The nonlinear fitting procedure was supported by the ab initio calculations on the spin-orbit and angular coupling matrix elements between the lowest X (2)Sigma(+), A (2)Pi, and B (2)Sigma(+) states. The analytical grid mapping based on the reduced variable representation of the radial coordinate r was used to improve the efficiency of the solution of the close-coupling radial equations near the dissociation limit. The mutual A approximately X perturbation effect on the A (2)Pi term values and spin-rotation splitting of the ground state were evaluated for both (7,6)LiAr isotopomers. The resulting empirical potential-energy curves for the adiabatic A (2)Pi and B (2)Sigma(+) states, along with the refined r-dependent nonadiabatic matrix elements, reproduce the total rovibronic structure of the (7)LiAr complex with the standard deviation of 0.003 cm(-1). The mass invariance of the deperturbed electronic parameters was confirmed by the calculation of the rovibronic term values of the (6)LiAr isotopomer which coincided with their experimental counterparts within 0.004 cm(-1).