Theoretical investigation of theX2Σ+,A2Π, andB2Σ+ states of LiAr and LiKr

Isotope study of the nonlinear pressure shifts of 85Rb and 87Rb hyperfine resonances in Ar, Kr, and Xe buffer gases

Measurements of the 0-0 hyperfine resonant frequencies of ground-state ⁸⁵Rb atoms show a nonlinear dependence on the pressure of the buffer gases Ar, Kr, and Xe. The nonlinearities are similar to those previously observed with ⁸⁷Rb and ¹³³Cs and presumed to come from alkali-metal-noble-gas van der Waals molecules. However, the shape of the nonlinearity observed for Xe conflicts with previous theory, and the nonlinearities for Ar and Kr disagree with the expected isotopic scaling of previous ⁸⁷Rb results. Improving the modeling alleviates most of these discrepancies by treating rotation quantum mechanically and considering additional spin interactions in the molecules. Including the dipolar-hyperfine interaction allows simultaneous fitting of the linear and nonlinear shifts of both ⁸⁵Rb and ⁸⁷Rb in either Ar, Kr, or Xe buffer gases with a minimal set of shared, isotope-independent parameters. To the limit of experimental accuracy, the shifts in He and N₂ were linear with pressure. The results are of practical interest to vapor-cell atomic clocks and related devices.

Elastic and glancing-angle rate coefficients for heating of ultracold Li and Rb atoms by collisions with room-temperature noble gases, H2, and N2

Trapped ultracold alkali-metal atoms can be used to measure pressure in the ultra-high-vacuum and XHV pressure regimes, those with p < 10^-6 Pa. This application for ultracold atoms relies on precise knowledge of collision rate coefficients of alkali-metal atoms with residual room-temperature atoms and molecules in the ambient vacuum or with deliberately introduced gasses. Here, we determine combined elastic and inelastic rate coefficients as well as glancing-angle rate coefficients for ultracold ⁷Li and ⁸⁷Rb with room-temperature noble gas atoms as well as H₂ and ¹⁴N₂ molecules. Glancing collisions are those processes where only little momentum is transferred to the alkali-metal atom and this atom is not ejected from its trap. Rate coefficients are found by performing quantum close-coupling scattering calculations using ab initio ground-state electronic Born-Oppenheimer potential energy surfaces. The potentials for Li and Rb with noble gas atoms and also for Rb(²S)-H₂(XΣ_g ⁺) and Rb(²S)-N₂(X¹Σ_g ⁺) systems are based on the non-relativistic spin-restricted coupled-cluster method with single, double, and noniterative triple excitations [RCCSD(T)]. For Li(²S)-N₂(X¹Σ_g ⁺), the potential is computed at the explicitly correlated spin-restricted RCCSD(T)-F12 level. For Rb, Kr, and Xe atoms, scalar relativistic corrections to the core electrons have been included, while second-order spin-orbit corrections from the valence electrons have been estimated. Data for Li-H₂ and Li-He were taken from the existing literature. We estimate standard uncertainties of the rate coefficients by comparing rate coefficients calculated using potentials found with electronic basis sets of increasing size, including estimates of relativistic spin-orbit corrections and the uncertainty of the van der Waals coefficients. The relative uncertainties of rate coefficients are 1%-2% with the exception of ⁷Li or ⁸⁷Rb colliding with ²⁰Ne. Those have relative uncertainties of 9% and 8%, respectively. We also show that a commonly used semiclassical approximation for the total elastic rate coefficient agrees with the quantum calculations to 10% with the exception of ⁷Li and ⁸⁷Rb collisions with H₂, where the semiclassical value underestimates the quantum value by 20%.

Accurate ab initio structural parameters of the diatomic and triatomic van der Waals molecules (11)BNg (X(2)Π, A(2)Σ(+)) and (11)BNg2 (X̃(2)B1), Ng = (4)He, (20)Ne, (40)Ar, (84)Kr, and (132)Xe

The weakly interacting BNg and BNg2 molecular systems, Ng = He, Ne, Ar, Kr, and Xe, have been thoroughly studied through coupled-cluster RCCSD(T) calculations and large correlation consistent basis sets. For the BNg diatomics, the states examined are the X(2)Π and A(2)Σ(+), and the X̃(2)B1 state for the C2v BNg2 triatomics. A series of corrections render our final results reliable, judging as well from the (limited) experimental numbers available. Both BHe and BHe2 are marginally unbound, whereas the attractive interactions of the BNg X(2)Π states, where Ng = Ne, Ar, Kr, and Xe, are D0 = 19.8, 98.2, 141.9, and 209.1 cm(-1), respectively. For the BRn (Rn = radon) species, an estimated value of interaction energy D0 ≈ 280 cm(-1) is obtained by a D0 versus static polarizability (α) extrapolation. Corresponding atomization energies of the BNg2 (X̃(2)B1) molecules are AE0 = 52.0 (BNe2), 263.4 (BAr2), 384.6 (BKr2), and 576.9 (BXe2) cm(-1).

Potential energy curves and spin-orbit coupling of light alkali-heavy rare gas molecules

The potential energy curves of the X, A, and B states of alkali-rare gas diatomic molecules, MKr and MXe, are investigated for M = Li, Na, K. The molecular spin-orbit coefficients a(R)=<(2)Π(½)|Ĥ(SO)|(2)Π(½)> and b(R)=<(2)Π(-½)|Ĥ(SO)|(2)Σ(½)> are calculated as a function the interatomic distance R. We show that a(R) increases and b(R) decreases as R decreases. This effect becomes less and less important as the mass of the alkali increases. A comparison of the rovibrational properties deduced from our calculations with experimental measurements recorded for NaKr and NaXe shows the quality of the calculations.

Electronic structure and spectra of the RbAr van der Waals system including spin-orbit interaction

The potential energy curves and spectroscopic constants of the ground and excited states of the RbAr van der Waals system have been determined using a one-electron pseudopotential approach. This technique is used to replace the effect of the Rb(+) core and the electron-Ar interactions by effective potentials. The core-core interaction for Rb(+)Ar was incorporated using the accurate CCSD(T) potential of Hickling et al. [Hickling, H. L.; Viehland, L. A.; Shepherd, D. T.; Soldán, P.; Lee, E. P. F.; Wright, T. G. Phys. Chem. Chem. Phys. 2004, 6, 4233-4239]. This model reduces the number of active electrons of the RbAr van der Waals systems to just the single valence electron, permitting the use of very large basis sets for the Rb and Ar atoms. Using this approach, the potential energy curves of the ground and excited states dissociating into Rb(5s, 5p, 4d, 6s, 6p, 6d, and 7s) + Ar are calculated at the SCF level. Spin-orbit interaction was also considered within a semiempirical scheme for the states dissociating into Rb(5p) and Rb(6p). Spectroscopic constants are derived and compared with the available theoretical and experimental data. Such comparisons for RbAr show very good agreement for the ground and the first excited states. Furthermore, we have predicted the B(2)Σ(+)(1/2) ← X(2)Σ(+), A(2)Π(1/2) ← X(2)Σ(+), A(2)Π(3/2) ← X(2)Σ(+), A(2)Π(3/2) ← X(2)Σ(+), 5(2)Σ(+) ← X(2)Σ(+), 3(2)Π(1/2) ← X(2)Σ(+), and 3(2)Π(3/2) ← X(2)Σ(+) absorption spectra.

One-electron pseudopotential investigation of CsAr van der Waals system including the spin-orbit interaction

The potential energy curves of the ground state and many excited states of the CsAr van der Waals system have been determined using [Cs(+)] and [Ar] core pseudopotentials and by considering core polarization operators on both atoms. This has permitted to reduce the number of active electrons of the CsAr system to only one electron, i.e., the valence electron, which led to use of large basis sets for Cs and Ar atoms. In this context, the potential energy curves of the ground state and many excited states are performed at the self consistent field (SCF) level. Spin-orbit interaction is also considered within a semiempirical scheme for the states dissociating into Cs(6p) and Cs(5d). The core-core interactions for Cs(+)Ar is included using the coupled cluster simple and double excitation (CCSD) accurate potential of Hickling et al. (Hickling, H.; Viehland, L.; Shepherd, D.; Soldan, P.; Lee, E.; Wright, T. Phys. Chem. Chem. Phys. 2004, 6, 4233). In addition, the spectroscopic constants of these states are derived and compared with the available theoretical and experimental works. Such comparison has shown a very good agreement for the ground and the first excited states. However, the spectroscopic data for the higher excited states are presented for the first time.

Direct deperturbation analysis of the AΠ2∼BΣ+2 complex of LiAr7,6 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).

On the nature of bonding in HCOOH...Ar and HCOOH...Kr complexes

The chemical interaction in HCOOH...Ng (Ng=Ar, Kr) complex was analyzed by topological analysis of the electron density based on Atoms-In-Molecules theory. For all computationally stable equilibrium structures of 1:1 HCOOH...Ng complexes, an intermolecular bond path with a "bond" critical point was found and perturbation of formic acid (FA) atomic basins and electron density was observed. The intermolecular interaction between the two complex subunits can be classified, according to its nature, as a closed-shell van der Waals type of interaction. However, one of the computed structures (complex II), pictures a noble gas atom attached linearly to the acidic O-H tail of FA. In this particular case, the electron density at the intermolecular bond critical point was found to resemble a hydrogen-bonded system and thus, may be termed a hydrogen-bond-like interaction. This change in the nature of the interaction is also shown by large perturbations of the FA properties found for this complex structure. The structural and vibrational perturbations are larger than for the other three structures and they increase for the Kr complexes compared to the Ar complex. [Figure: see text]. Electron density analysis of HCOOH...Ng (Ng=Ar,Kr) complex.