Theoretical calculation of the excited states of the KCs molecule including the spin-orbit interaction

Accurate semiempirical potential energy curves for the a3Σ+-state of NaCs, KCs, and RbCs

A five parameter semiempirical Tang-Toennies type model is used to describe the potential curves of the a³Σ⁺-state of the heteronuclear polar molecules NaCs, KCs, and RbCs. These molecules are of current interest in experiments at ultra-cold conditions to explore the effects of the strong dipole-dipole forces on the collective many-body quantum behavior. New quantum phenomena are also anticipated in systems consisting of atomic species with different fermion/boson statistics. The model parameters are obtained by simultaneously fitting all five of the parameters to the extensive LIF-Fourier transform spectroscopy published by Tiemann and collaborators [e.g., Docenko et al. J. Phys. B: At., Mol. Opt. Phys. 39, S929-S943 (2006)], who also report best fit potential curves. Although the new potentials are in good agreement with the earlier potentials, they have the advantage that they are continuous over the entire range of internuclear distances and have the correct long-range behavior. The scattering lengths for all isotope combinations show good agreement with dedicated experiments where available. The new potentials are also in excellent agreement with combining rules based on the potentials of the homonuclear systems.

Fourier-transform spectroscopy and potential construction of the (2)(1)Π state in KCs

The paper presents an empirical pointwise potential energy curve (PEC) of the (2)(1)Π state of the KCs molecule constructed by applying the Inverted Perturbation Approach routine. The experimental term values in the energy range E(v', J') ∈ [15 407; 16 579] cm(-1) involved in the fit were based on Fourier-Transform spectroscopy data obtained with 0.01 cm(-1) accuracy from the laser-induced (2)(1)Π → X(1)Σ(+) fluorescence spectra. Buffer gas Ar was used to facilitate the appearance of rotation relaxation lines in the spectra, thus enlarging the (2)(1)Π data set and allowing determination of the Λ-splitting constants. The data set included vibrational v' ∈ [0, 28] and rotational J' ∈ [7, 274] quantum numbers covering about 67% of the potential well. The present PEC reproduces the overall set of data included in the fit with a standard deviation of 0.5 cm(-1). The obtained value of the Λ-doubling constant q = + 1.8 × 10(-6) cm(-1) for J' > 50 and v' ∈ [0, 6] is in an excellent agreement with q = + 1.84 × 10(-6) cm(-1) reported in Kim, Lee, and Stolyarov [J. Mol. Spectrosc. 256, 57-67 (2009)].

Fourier-transform spectroscopy of (4)1Σ+ → A1Σ+ - b3Π, A1Σ+ - b3Π → X1Σ+, and (1)3Δ1→b3Π(0±) transitions in KCs and deperturbation treatment of A1Σ+ and b3Π states

High resolution Fourier-transform spectroscopy data of term values in the spin-orbit (SO) coupled first excited A(1)Σ(+) and b(3)Π states in KCs were obtained from (4)(1)Σ(+) → A(1)Σ(+) - b(3)Π, A(1)Σ(+) - b(3)Π → X(1)Σ(+), and (1)(3)Δ1→b(3)Π(0(±)) spectra of laser-induced fluorescence (LIF). About 3000 new rovibronic term values of the A(1)Σ(+) and b(3)Π(Ω) states were obtained with an uncertainty about 0.01 cm(-1) and added to the previously obtained 3439 term values in Kruzins et al. [Phys. Rev. A 81, 042509 (2010)] and 30 term values of the b(3)Π(0(+)) state levels below the A(1)Σ(+) state in Tamanis et al. [Phys. Rev. A 82, 032506 (2010)]. The data field was extended considerably, going down to vibrational level v(b) = 0 and up in energy to 13,814 cm(-1), as compared to previously achieved v(b) = 14 and E = 13,250 cm(-1). Overall 6431 e-symmetry term values of (39)K(133)Cs were included in 4 × 4 coupled-channel deperturbation analysis. The analytical Morse-Long-Range (MLR) function yielded empirical diabatic potentials for the A(1)Σ(+) and b(3)Π(0(+)) states while the morphing of the SO ab initio points [J. T. Kim et al., J. Mol. Spectrosc. 256, 57 (2009)] provided the empirical diagonal and off-diagonal SO functions. Overall 98.5% of the fitted term values were reproduced with a rms (root mean square) uncertainty of 0.004 cm(-1). The reliability of the model is proved by a good agreement of predicted and measured term values of the (41)K(133)Cs isotopologue, as well as of measured and calculated intensities of (4)(1)Σ(+) → A(1)Σ(+) - b(3)Π LIF progressions. Direct-potential-fit of low-lying v(b) levels of the b(3)Π(0(-)) component yielded the MLR potential which represents the 204 f-symmetry experimental term values with a rms uncertainty of 0.002 cm(-1). The Ω-doubling of the b(3)Π0 sub-state demonstrates a pronounced vb-dependent increase.

Relations between harmonic frequencies of diatomic molecules

The relations between the harmonic frequencies of different molecules are revealed with the aid of the spring constants of atoms in molecules. Using the atomic spring constants in the related molecules, the force constants for a new molecule can be estimated. The simplest scheme to obtain the force constant of a given molecule is similar to a simple chemical reaction formula, such as A(2) + B(2) → AB, and the corresponding relation between the molecular force constants is k(AB)(-1) = (2k(A(2)))(-1) + (2k(B(2)))(-1). For a given molecule, one can design numerous schemes to obtain its force constant from the atomic spring constants in other molecules. A high degree of periodical regularity appears in the application of different kinds of schemes to the ground states. The reliable schemes for the ground electronic states can be adopted for the excited states. Over two hundred molecules with experimental data available for comparison have been tested. The discrepancies between the calculated and the experimental harmonic frequencies can reach 1% and better; the results show that the present approach is simple in theory and handy to use. The harmonic frequencies for dozens of hetero-nuclear molecules of the transition-metal elements are also predicted.

Ab initio calculation of the low-lying electronic states of the ZrN molecule

An ab initio calculation of the low-lying electronic states of zirconium nitride (ZrN) were performed by using a complete active space self-consistent field with multireference single and double excitation configuration interaction (MRSDCI). The potential energy curves of 21 low-lying electronic states of the ZrN molecule with different spin and spatial symmetries, in the representation 2s+1Λ(+/−) and below 30 000 cm–1, were identified. The harmonic frequency (ωe), the equilibrium internuclear distance (Re), the rotational constants (Be), the electronic energy with respect to the ground state (Te), and the permanent dipole moment (µ) were calculated for the considered electronic states. The comparison of these values with those available in the literature shows a very good agreement with either theoretical or experimental data. Fifteen new electronic states were studied here for the first time.

B1(1)Π state of KCs: high-resolution spectroscopy and description of low-lying energy levels

The diode laser induced B(1)(1)Π → X(1)Σ(+) fluorescence spectra of the KCs molecule were recorded by Fourier-transform spectrometer with resolution of 0.03 cm(-1). Buffer gas Ar was used to facilitate appearance of rotation relaxation lines in the spectra, thus enlarging the B(1)(1)Π dataset, allowing one to determine the Λ-splitting constants and to reveal numerous local perturbations. A dataset was systematically obtained for B(1)(1)Π vibrational levels ν(') ∈ [0; 5] nonuniformly covering rotational levels with J(') ∈ [7; 233]. For ν(') ∈ [0; 3], the less-perturbed data of f-components were included in the fit. A pointwise potential energy curve (PEC) based on the inverted perturbation approach, as well as the Dunham coefficients, was obtained and compared with ab initio calculations; in particular, the energy of the PEC's minimum T(e) = 14,044.918(6) cm(-1) was determined. Both approaches allowed us to reproduce the vast majority of data used in the fit with accuracy of 0.02 cm(-1). Tentative molecular constants for several vibrational levels of the near lying C(3)(1)Σ(+) state were estimated.

Ab initio and long-range investigation of the Ω((+∕-)) states of NaK dissociating adiabatically up to Na(3s 2S(1/2)) + K(3d 2D(3/2))

A theoretical investigation of the electronic structure of the NaK molecule including spin-orbit effects has been performed for the 34 Ω((+∕-)) states dissociating adiabatically into the limits up to Na(3s(2)S(1/2)) + K(3d(2)D(3/2)) from both an ab initio approach and a long-range model. Equilibrium distances, transition energies, harmonic frequencies as well as depths of wells and heights of humps are reported for all the states. Formulas for calculating the long-range energies for all the 0(+∕-), 1, 2, and 3 states under investigation are also displayed. They are expressed in terms of the C(n) (n = 6,8, ...) long-range coefficients and exchange integrals for the (2S+1)Λ((+)) parent states, available from literature. As present data could help experimentalists we make available extensive tables of energy values versus internuclear distances in our database at the web address: http://www-lasim.univ-lyon1.fr/spip.php?rubrique99.

Unravelling complex spectra of a simple molecule: REMPI study of the 420 nm band system of KRb

Complex spectra of the KRb 420 nm system are analyzed by mass-resolved resonance enhanced two-photon ionization in a cold molecular beam. Vibronic structures of three singlet-singlet (4(1)Π, 7(1)Σ(+), and 5(1)Π←X(1)Σ(+)) transitions were identified for the first time. By comparing with highly accurate ab initio calculations, we assigned the singlet excited electronic states, and determined their electronic term values and vibrational constants. Weak singlet-triplet transitions were observed and identified as the 5(3)Π(0(+))←X(1)Σ(+) transitions by the homogeneous perturbation selection rule.