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A simple procedure to incorporate one-loop quantum electrodynamic (QED) corrections into the generalized (Gatchina) nonlocal shape-consistent relativistic pseudopotential model is described. The pseudopotentials for Lu, Tl, and Ra replacing only inner core shells (with principal quantum numbers $n\le 3$ for the two former elements and $n\le 4$ for the latter one) are derived from the solutions of reference atomic SCF problems with the Dirac-Coulomb-Breit Hamiltonian to which the model Lamb shift operator added. QED contributions to atomic valence excitation energies evaluated at the SCF level are demonstrated to exceed the errors introduced by the pseudopotential approximation itself by an order of magnitude. Pilot applications of the new model to calculations of excitation energies of two-valence-electron atomic systems using the intermediate-Hamiltonian relativistic Fock space coupled cluster method reformulated here for incomplete main model spaces are reported. Implications for high-accuracy molecular excited state calculations are discussed.

The determination of the matrix elements of single-electron operators for the transitions between electronic states (primarily, the dipole moments of electron transitions) is one of the critical problems in simulating the atomic and molecular spectra. In this study, the efficiency of a simple version of the finite-field method for calculating these values within the Fock-space coupled-cluster theory has been investigated.

Chemical shifts of the Kα1 and Kα2 lines (the 2p3/2 → 1s1/2 and 2p1/2 → 1s1/2 transitions, respectively) of the X-ray emission spectrum of the Yb atom in fluorides have been calculated by ab initio modeling the electronic structure. The valence transition Yb(II) → Yb(III) has been analyzed by examples of YbF2, YbF3, and Yb2F4 molecules and YbF2+ cation. The relativistic pseudopotential and basis sets corresponding to it have been constructed for the ytterbium atom. They were used in calculations by the two-component noncollinear version of the density functional theory (DFT) with the PBE0 exchange-correlation functional. Results for the three-coordinated Yb(II) in the FYbF2YbF dimer demonstrated a very weak dependence of the chemical shift on the coordination number of the Yb atom and on the molecular association of ytterbium difluoride. Chemical shifts of the X-ray emission spectrum for the ytterbium compound are related mainly to the change in the occupation of the 4 f shell.

Chemical shifts of the Kα1 and Kβ1 lines of X-ray-emission spectra of niobium in oxides (Nb2O5)n, n = 1–4, relative to metal Nb have been calculated. Stoichiometric clusters (Nb2O5)n the electronic structure of which was calculated using accurate relativistic pseudopotentials and two-component version of the density functional theory are considered as prototypes for modeling different crystal forms of niobium(V) oxide. The chemical shifts were calculated using the method based on using the property of approximate proportionality of valence spinors in the core region of the heavy atom [11]. Corrections to values of chemical shifts have been determined with allowance for deviations from the abovementioned proportionality. Rapid convergence of results with respect to the size of the niobium oxide cluster has been demonstrated.

The Ti:Saphire laser operated within 13800 - 11800 cm − 1 range was used to excite the c 3 Σ + state of KCs molecule directly from the ground X 1 Σ + state. The laser-induced fluorescence (LIF) spectra of the c 3 Σ + → a 3 Σ + transition were recorded with Fourier-transform spectrometer within 8000 to 10000 cm − 1 range. Overall 673 rovibronic term values belonging to both e / f -components of the c 3 Σ + ( Ω = 1 ± ) state of 39 KCs, covering vibrational levels from v = 0 to about 45, and rotational levels J ∈ [ 11 , 149 ] were determined with the accuracy of about 0.01 cm − 1 ; among them 7 values for 41 KCs. The experimental term values with v ∈ [ 0 , 22 ] were involved in a direct point-wise potential reconstruction for the c 3 Σ + ( Ω = 1 ± ) state, which takes into account the Ω -doubling effect caused by the spin-rotational interaction with the nearby c 3 Σ + ( Ω = 0 − ) state. The analysis and interpretation were facilitated by the fully-relativistic coupled cluster calculation of the potential energy curves for the B 1 Π , c 3 Σ + , and b 3 Π states, as well as of spin-forbidden c − X and spin-allowed c − a transition dipole moments; radiative lifetimes and vibronic branching ratios were calculated. A comparison of relative intensity distributions measured in vibrational c → a LIF progressions with their theoretical counterparts unambiguously confirms the vibrational assignment suggested in [J. Szczepkowski, et al., JQSRT, 204, 133–137 (2018)].

Radium compounds have attracted recently considerable attention due to both development of experimental techniques for high-precision laser spectroscopy of molecules with short-lived nuclei and amenability of certain radium compounds for direct cooling with lasers. Currently, radium monofluoride (RaF) is one of the most studied molecules among the radium compounds, both theoretically and recently also experimentally. Complementary studies of further diatomic radium derivatives are highly desired to assess the influence of chemical substitution on diverse molecular parameters, especially on those connected with laser cooling, such as vibronic transition probabilities, and those related to violations of fundamental symmetries. In this article high-precision \emph{ab initio} studies of electronic and vibronic levels of diatomic radium monochloride (RaCl) are presented. Recently developed approaches for treating electronic correlation with Fock-space coupled cluster methods are applied for this purpose. Theoretical results are compared to an early experimental investigation by Lagerqvist and used to partially reassign the experimentally observed transitions and molecular electronic levels of RaCl. Effective constants of $\mathcal{P}$-odd hyperfine interaction $W_{\rm{a}}$ and $\mathcal{P,T}$-odd scalar-pseudoscalar nucleus-electron interaction $W_{\rm{s}}$ in the ground electronic state of RaCl are estimated within the framework of a quasirelativistic Zeroth-Order Regular Approximation approach and compared to parameters in RaF and RaOH., Comment: 18 pages, 2 figures, 5 tables

The spin-forbidden a 3 Π − X 1 Σ + , a ′ 3 Σ + − X 1 Σ + and spin-allowed A 1 Π − X 1 Σ + electronic transitions dipole moments of carbon monoxide have been ab initio studied in the framework of multi-reference Fock space coupled cluster method combined with the finite-field approach and the generalized relativistic pseudo-potential model for the effective introducing the relativity in all-electron correlation treatment. Radiative lifetimes, τ i ( v ′ , J ′ ) , of the upper i ∈ [ a 3 Π , A 1 Π ] states were evaluated as a function of vibrational, v ′ , and rotational, J ′ , quantum numbers. The τ a -values derived for the triplet a 3 Π 1 ( 0 , 1 ) and a 3 Π 2 ( 0 , 2 ) states at the highest level of computation were found to be 2.59 and 142 ms, which are near perfect agreement with their best experimental counterparts (J. J. Gilijamse, et al., J. Chem. Phys., 127, 221102 (2007)). The intercombination a − X , a ′ − X transition probabilities were numerically proved to be proportional to α 2 , where α = e 2 / ℏ c is the fine structure constant.

We observed the A 1 Σ + ∼ b 3 Π → a 3 Σ + / X 1 Σ + laser-induced fluorescence (LIF) of the RbCs molecule excited from the ground X 1 Σ + state by the Ti:Sapphire laser. The LIF spectra from the common perturbed levels of the singlet-triplet A ∼ b complex was recorded by the Fourier-transform (FT) spectrometer with the instrumental resolution of 0.03 cm − 1 . The relative intensity distribution in the rotationally resolved A ∼ b → a 3 Σ + ( v a ) / X 1 Σ + ( v X ) progressions was measured, and their branching ratio was found to be about of 1 ÷ 5 × 10 − 4 in the bound region of the a 3 Σ + and X 1 Σ + states. The experiment was complemented with the scalar- and full-relativistic calculations of the A / b − X / a transition dipole moments (TDMs) as functions of internuclear distance. The relative systematic error in the resulting ab initio TDM functions evaluated for the strong A − X transition was estimated as few percent in the energy region, where the experimental LIF intensities are relevant. The relative spectral sensitivity of the FT registration system, operated with the InGaAs diode detector and CaF beam-splitter, was calibrated in the range [6 500, 12 000] cm − 1 by a comparison of experimental intensities in the long A ∼ b → X(vX) LIF progressions of the K2 and KCs molecules with their theoretical counterparts evaluated using the ab initio A − X TDMs. Both experimental and theoretical transition probabilities can be employed to improve the stimulated Raman adiabatic passage process, a → A ∼ b → X, which is exploited for a laser assembling of ultracold RbCs molecules.

Actinide compounds are very intriguing objects for the quantum chemistry because, on the one hand, these compounds are of great scientific and technological interest and, on the other hand, quantitative first principle based modeling of their electronic structure is extremely difficult because of strong relativistic effects and complicated electron correlation pattern. The efficiency of high-level all-electron relativistic methods in applications to complex actinide systems of practical interest is questionable and more economical but sufficiently accurate approaches to the studies of such systems are preferable. Recently, generalized relativistic effective core potentials (GRECPs) have been generated for actinides to perform accurate calculations of electronic structure and properties of their compounds with moderate computational cost. The accuracy of different GRECP versions is analyzed in atomic calculations and their applications to molecular and cluster calculations are reviewed. The results are compared with available experimental data and other theoretical studies. © 2015 Wiley Periodicals, Inc.

Molecular properties of the thallium monocyanide (Tl&middot, CN) system in its ground electronic state are studied using high-precision ab initio relativistic two-component pseudopotential replacing 60 inner-core electrons of Tl. A relativistic coupled-cluster method with single, double and perturbative triple amplitudes is employed to account for electronic correlations. Extrapolation of results to the complete basis set limit is used for all studied properties. The global potential energy minimum of Tl&middot, CN corresponds to the linear cyanide (TlCN) isomer, while the non-rigid isocyanide-like (TlNC) structure lies by approximately 11 kJ/mol higher in energy. The procedure of restoration of the wavefunction in the &ldquo, core&rdquo, region of Tl atom was applied to calculate the interaction of the Tl nuclear Schiff moment with electrons. The parameter X of the interaction of the Tl nuclear Schiff moment with electrons in the linear TlCN molecule equals 7150 a.u. The prospects of using the TlCN molecule for the experimental detection of the nuclear Schiff moment are discussed.

The potential curve, dissociation energy, equilibrium internuclear distance, and spectroscopic constants for the ground state of the Ca2 molecule are calculated with the help of the generalized relativistic effective core potential method, which allows one to exclude the inner core electrons from the calculations and to take the relativistic effects into account effectively. Extensive generalized correlation basis sets were constructed and used. The scalar relativistic coupled cluster method with corrections for high-order cluster amplitudes is used for the correlation treatment. The results are analyzed and compared with the experimental data and corresponding all-electron results. © 2013 Wiley Periodicals, Inc.

The ground electronic state of the eka-mercury dimer (E1122) was studied within the model of generalized relativistic effective core potentials. A combined procedure based on describing correlation effects by the scalar relativistic coupled-cluster method and on taking into account spin-dependent interactions by means of density-functional theory was used in the calculations. A high accuracy of this approach was confirmed by the results of similar calculations for the mercury dimer. It was found that the bond length is nearly 0.4 A shorter in E1122 than in Hg2 and that the dissociation energy of the former is approximately twice as high as that of the latter dimer.

Radiative lifetimes for 2≤v′≤44 rovibronic C1Σ+ state levels of NaRb and quenching collision cross-sections with Rb atoms have been directly measured in a thermal cell by detecting time resolved laser induced fluorescence after pulsed excitation. Many body multipartitioning theory was applied to calculate C1Σ+-X1Σ+ and C1Σ+-A1Σ+ transition dipole moments. The relevant ab initio matrix elements were converted to the C1Σ+ state radiative lifetimes. The strong spin-orbit A1Σ+∼ b3Π coupling effect on the total C → A transition probabilities and lifetimes of the C1Σ+ state is discussed. The measured radiative lifetimes show a decrease from 61 to 34 ns as the v′ values increase, the results being in good agreement with calculations. The averaged collisional quenching cross-section value σ=(3±1)×10-14 cm2 was determined for NaRb (C1Σ+) + Rb collisions from the Stern-Volmer plots.

Interactions of Cn (element 112) atom with small Au clusters are studied using accurate ab initio scalar relativistic coupled cluster method for correlation treatment and two-component relativistic density functional theory (RDFT) to take account of spin-dependent relativistic effects. The results demonstrate the failure of RDFT with simple generalized-gradient and hybrid functionals in describing Cn–Au bonds in complex systems. © 2013 Wiley Periodicals, Inc.

The multipartitioning form of the second-order many-body perturbation theory for state-selective effective Hamiltonians is adapted to stabilization calculations of temporary molecular anionic states. We restrict our attention to the simplest case of a system composed of a closed-shell-like molecule and an electron. Pilot applications to the description of the 2Πg state of the nitrogen molecular anion and the 2Π state of CO− are reported.

We present a simple method of ab initio calculations on the systems composed of a closed-shell-like molecule (atom) and a weakly bound electron via constructing a state-specific effective Hamiltonian in a model space generated by placing the extra electron on virtual self-consistent field orbitals of the neutral species in all the possible ways. Correlation contributions are incorporated into the effective Hamiltonian by the second-order multipartitioning many-body perturbation theory. The method prevents the appearance of intruder states without destroying the exact size consistency of results and ensures a proper description of the dynamic correlation effects on the spatial localization of the extra electron and continuous behavior of computed characteristics under variations of molecular geometry. A detailed study of perturbative solutions for a model problem with parameter-dependent Hamiltonian and test calculations of Ca, Sr, and Ba atomic anions are reported. The method is also applied to the description of the hypothetical symmetrical isomer of water dimer anion with the extra electron trapped between the water molecules. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004

A quasirelativistic perturbative method of ab initio calculations on ground and excited molecular electronic states and transition properties within the relativistic effective core potential approximation is presented and discussed. The method is based on the construction of a state-selective many-electron effective Hamiltonian in the model space spanned by an appropriate set of Slater determinants by means of the second-order many-body multireference perturbation theory. The neglect of effective spin–orbit interactions outside of the model space allows the exploitation of relatively high nonrelativistic symmetry during the evaluation of perturbative corrections and therefore dramatic reduction of the cost of computations without any contraction of the model-space functions. One-electron transition properties are evaluated via the perturbative construction of spin-free transition density matrices. Illustrative calculations on the X0+ − A1, B0+, and (ii)1 transitions in the ICl molecule are reported. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002

Recently a number of diatomic and polyatomics molecules has been identified as a prospective systems for Doppler/Sisyphus cooling. Doppler/Sisyphus cooling allows to decrease the kinetic energy of molecules down to microkelvin temperatures with high efficiency and then capture them to molecular traps, including magneto-optical trap. Trapped molecules can be used for creation of molecular fountains and/or performing controlled chemical reactions, high-precision spectra measurements and a multitude of other applications. Polyatomic molecules with heavy nuclei present considerable interest for the search for "new physics" outside of Standard Model and other applications including cold chemistry, photochemistry, quantum informatics etc. Herein we would like to attract attention to radium monohydroxide molecule (RaOH) which is on the one hand an amenable object for laser cooling and on the other hand provides extensive possibilities for searching for P-odd and P,T-odd effects. At the moment RaOH is the heaviest polyatomic molecule proposed for direct cooling with lasers., Comment: 14 pages, 2 figures, 2 tables, figures are changed for better representation of the results, supplementary materials added

The finite-field perturbation theory is applied to the ab initio calculations of electronic transition dipole moments in molecules. The results are less sensitive to the level of electron correlation treatment than the directly computed electric dipole off-diagonal matrix elements. The finite-field approach can provide a substantial gain in accuracy when simple MCSCF electronic wavefunctions are used.

The paper presents \ensuremath{\Lambda} splittings and q factors in the NaK $D{}^{1}\ensuremath{\Pi}$ state, directly measured from the electric radio-frequency-optical double resonance (RF-ODR) in laser-induced fluorescence (LIF) for a number of vibrational states $v=1--22$ with definite rotational levels J between 7 and 46. Permanent electric dipole moment values (d) have been obtained by measuring in LIF spectra the relative intensities of ``forbidden'' lines caused by dc Stark effect induced $e/f$ mixing in the ${}^{1}\ensuremath{\Pi}$ state, with their subsequent processing, which allowed us to obtain the $q/d$ ratio. A possible influence of the hyperfine structure on the RF-ODR signal and relative intensities has been calculated, showing that this influence can be neglected. The $q(v)$ values exhibited a decrease from $q(1)=1.529\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}{\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ to $q(22)=1.171\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}{\mathrm{cm}}^{\mathrm{\ensuremath{-}}1},$ which has been explained by an increase of the difference potential between $D{}^{1}\ensuremath{\Pi}$ and $C{}^{1}{\ensuremath{\Sigma}}^{+}$ states with internuclear distance (R); the respective L-uncoupling matrix element was evaluated as 1.87. It was shown, both by semiempirical treatment and population analysis of ab initio molecular wave functions, that considerable $\ensuremath{\pi}d$ and $\ensuremath{\sigma}d$ configuration admixtures are present in the $D{}^{1}\ensuremath{\Pi}$ and the $C{}^{1}{\ensuremath{\Sigma}}^{+}$ states. For the $B{}^{1}\ensuremath{\Pi}$ state, it was demonstrated that \ensuremath{\Lambda} doubling is caused by two competing perturbers $(A{}^{1}{\ensuremath{\Sigma}}^{+}$ and $C{}^{1}{\ensuremath{\Sigma}}^{+}),$ yielding q factors of $\ensuremath{\sim}\ensuremath{-}2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}{\mathrm{cm}}^{\mathrm{\ensuremath{-}}1},$ in agreement with high-resolution spectroscopy data given in the literature; single-configuration approximation is valid for interacting $B{}^{1}\ensuremath{\Pi}(\ensuremath{\sigma}{3s}_{\mathrm{Na}},\ensuremath{\pi}{4p}_{\mathrm{K}})\ensuremath{\sim}A{}^{1}{\ensuremath{\Sigma}}^{+}(\ensuremath{\sigma}{3s}_{\mathrm{Na}},\ensuremath{\sigma}{4p}_{\mathrm{K}})$ states. The measured $d(v)$ values, which varied from 6.6 to 4.6 D, have been used to obtain the empirical $D{}^{1}\ensuremath{\Pi}$ state $d(R)$ function for $R=6--12\mathrm{a}.\mathrm{u}.$ by means of an improved instability-free inversion procedure exploiting a special functional form. Two independent series of ab initio all-electron calculations of $d(R)$ and $d(v)$ have been performed for the $D{}^{1}\ensuremath{\Pi}$ and $B{}^{1}\ensuremath{\Pi}$ states of NaK. First, d values were computed as expectation values of the electric dipole operator with conventional multireference configuration-interaction wave functions. Second, the finite-field (FF) technique, combined with a multipartitioning perturbation theory (MPPT) treatment of electronic eigenstates, was applied for the calculation of $d(R)$ functions. The FF-MPPT calculations showed excellent agreement with experimental $D{}^{1}\ensuremath{\Pi}d(v)$ values obtained in the present work, as well as the proximity to experimental $B{}^{1}\ensuremath{\Pi}d(v)$ values given in the literature, thus showing that, as distinct from the ground state, it is important to account correctly for effective interactions of valence electrons arising from core-valence correlations, which could not be done properly with previously used pseudopotential techniques. The experimental d and q values dropping out from a smooth $v$ dependence have been considered as perturbed by $D{}^{1}\ensuremath{\Pi}\ensuremath{\sim}d{}^{3}\ensuremath{\Pi}$ interaction and exploited to evaluate respective ${d}_{t}$ and ${c}_{t}$ values for the perturbing $d{}^{3}\ensuremath{\Pi}$ state.

Potential energy and non-adiabatic coupling functions for the two lowest 1 Σ + states of LiF were calculated using the recently proposed perturbative approach, based on the multiple partitioning of the full Hamiltonian, and the difference-dedicated CI method. The results are compared with MRDCI and available full CI data for the same AO basis set. A high accuracy was achieved with a semiempirical perturbative scheme combining the direct calculations at second order with an approximate estimation of higher-order local contributions.

Second-order intermediate Hamiltonian quasi-degenerate perturbation theory is applied to calculate π-electron vertical excitation energies of ethylene and trans-butadiene. The choice of model spaces follows the physical intuition, including the excitations within the π-shell and leaving the σ-orbitals doubly occupied. Model spaces are optimized using the state-average CASSCF procedure. The agreement between calculated and experimental transition energies is better than 0.1 eV. The importance of a decontracted treatment of the model-space projections of wave functions is demonstrated. A simple model study of deviations from size-consistency is reported and implications for calculations on larger molecules are briefly discussed. © 1995 John Wiley & Sons, Inc.

A simple third-order intermediate Hamiltonian method based on the level shift technique is presented and applied to ab initio calculations on low-lying electronic states of CH + , CH 2 + and CH 2 . The method is shown to provide a good approximation to full Cl for both total energies and excitation energies. Numerous intruder states did not give rise to any instability problems. Series resummation using modified operator [2/1] Pade approximants and deviations of solutions by the present method from the strict size consistency are discussed

The level shift technique is applied to derive rigorous order-by-order intermediate Hamiltonian QDPT expansions. The novel approach offers an insight into the relations between different intermediate Hamiltonian theories. The direct comparison with the shifted QDPT expansions for conventional effective Hamiltonian is also presented

A general approach to the construction of Rayleigh-Schrodinger-like perturbative expansions for Hermitian intermediate Hamiltonians using the shift technique is proposed. The shift operator depends on the projector onto the subspace spanned by the 'main' eigenvectors of the intermediate Hamiltonian which should be determined iteratively for a given PT order. The intruder state problem can be completely eliminated by an appropriate choice of an intermediate space and shift parameters without introducing any additional perturbation. Numerical examples are reported in order to demonstrate the convergency properties and approximate size consistency of the novel method.

The radiative lifetimes of the $(3)\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Pi}$ and $D(2)\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Pi}$ states of the NaCs molecule have been directly measured in a thermal cell from fluorescence kinetics after modulated laser excitation. The experimental ${\ensuremath{\tau}}_{(3)\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Pi}}^{\mathrm{rad}}$ values of the $(3)\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Pi}({v}^{\ensuremath{'}}∊[3,25];{J}^{\ensuremath{'}}∊[25,106])$ levels decrease from $29\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}21\phantom{\rule{0.3em}{0ex}}\mathrm{ns}$ as the ${v}^{\ensuremath{'}}$ values increase. The measured ${\ensuremath{\tau}}_{(3)\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Pi}}^{\mathrm{rad}}$ values for two rotational ${J}^{\ensuremath{'}}=45$ and 106 levels of the ${v}^{\ensuremath{'}}=3$ state are 29 and $25\phantom{\rule{0.3em}{0ex}}\mathrm{ns}$, respectively, showing the effect of rotation. The experimental ${\ensuremath{\tau}}_{(2)\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Pi}}^{\mathrm{rad}}$ value of the $D(2)\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Pi}({v}^{\ensuremath{'}}=0;{J}^{\ensuremath{'}}=16)$ level is about $37\phantom{\rule{0.3em}{0ex}}\mathrm{ns}$. The average measured effective quenching collision cross section of excited NaCs molecule with Cs atoms $\ensuremath{\sigma}=(3.5\ifmmode\pm\else\textpm\fi{}1.5)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{2}$. The theoretical radiative lifetimes for the lowest $(1--3)\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Pi}$ states have been evaluated in the framework of a pure $\mathbf{a}$ Hund's coupling case using the approximate sum rule over the lower-lying vibronic states. The required quasirelativistic transition dipole moments were calculated by many-body multipartitioning theory. Propagation of the systematic errors of ab initio transition moments and potential energy curves (PECs) into the ${\ensuremath{\tau}}^{\mathrm{rad}}$ values is discussed. The best lifetime estimates predicted for particular rovibronic levels of the $(3)\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Pi}$ and $D(2)\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Pi}$ states agree with their experimental counterparts within 2--8 % which can be compared with the 1--3 % uncertainties in the measured ${\ensuremath{\tau}}^{\mathrm{expt}}$ values. The lifetimes of the $B(1)\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Pi}$ and $(3)\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Pi}$ states are almost exclusively determined by a single transition to the ground $X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}$ state while a contribution of the $D(2)\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Pi}\ensuremath{\rightarrow}A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}$ transition into the ${\ensuremath{\tau}}_{(2)\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Pi}}^{\mathrm{rad}}$ values reaches up to 10--15 %.

High resolution Fourier transform spectra (FTS) of laser induced fluorescence (LIF) of $C\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+};D\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Pi}\ensuremath{\rightarrow}A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}--b\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}$ and $A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}--b\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}\ensuremath{\rightarrow}X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}$ transitions in ${\mathrm{Na}}^{85}\mathrm{Rb}$ and ${\mathrm{Na}}^{87}\mathrm{Rb}$ were obtained. An analysis of the direct LIF spectra together with the rotational relaxation satellites provided highly accurate rovibronic term values for $(4\ensuremath{\leqslant}J\ensuremath{\leqslant}163)$ of the $A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}--b\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}$ complex, covering about 1950 mostly singlet levels $0\ensuremath{\leqslant}{v}_{A}\ensuremath{\leqslant}49$ and a considerable number $(g360)$ of the predominantly triplet $b\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}_{0,1}$ sublevels. The direct deperturbation analysis of the singlet-triplet $A--b$ complex was performed by means of the inverted channel-coupling approach with Hund's coupling case $\mathbf{a}$ basis functions. The electronic matrix elements of the model $4\ifmmode\times\else\texttimes\fi{}4$ Hamiltonian were defined as piecewise analytical functions of the internuclear distance. Besides the Born-Oppenheimer potential energy curves of the mutually perturbed states and the off-diagonal spin-orbit (SO) $A--b$ coupling function, the SO splitting of the $b\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}$ state was determined due to the pronounced electronic-rotation interaction between the $b\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}_{0}$ and $b\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}_{1}$ components observed for high $J$ levels. Overall, 24 mass-invariant fitting parameters have been required to reproduce about 2300 experimental term values of both isotopomers with a standard deviation of $0.012\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$, which is consistent with the uncertainty of the FTS experiment. An analytical mapping procedure based on a reduced variable representation of the radial coordinate was used to diminish the computational effort for the uniform finite-difference grid solution of the coupled-channel equations. The derived nonadiabatic $A--b$ wave functions were used to evaluate the $A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}--b\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}--D\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Pi}$, $a\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Sigma}^{+}$, $X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}$ rovibronic transition probabilities. The relative intensity distributions predicted for the $D\ensuremath{\rightarrow}A--b$ and $A--b\ensuremath{\rightarrow}X$ LIF progressions agree with their experimental counterparts within the accuracy of the measurements. The calculated $A--b--a$, $X$ transition probabilities were applied for simulation of the stimulated Raman $a\ensuremath{\rightarrow}A--b\ensuremath{\rightarrow}X$ processes, which can lead to efficient formation of ultracold NaRb molecules in the ground level ${v}_{X}=0$; ${J}_{X}=0$.

The article presents first experimental data on the Stark induced $e\text{\ensuremath{-}}f$ mixing in the $(4)\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Pi}$ state of the $^{85}\mathrm{Rb}^{133}\mathrm{Cs}$ molecule, as well as the ab initio calculations of permanent electric dipole moments $(d)$ in the $(1,2,3,4)\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Pi}$ states and $q$ factors in the $(2,4)\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Pi}$ states. The appearance of the ``forbidden'' lines in the laser-induced $(4)\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Pi}\ensuremath{\rightarrow}X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Pi}^{+}$ fluorescence spectrum in the presence of an electric field allowed us to obtain, for the rovibronic ${v}^{\ensuremath{'}}({J}^{\ensuremath{'}})=2(82)$ level of the $(4)\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Pi}$ state correlating to the $\mathrm{Rb}(4d)+\mathrm{Cs}(6s)$ atomic limit, the ratio $q∕d=0.9\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}∕\mathrm{D}$ with 20% experimental error. Electronic structure calculations on the ground and excited states of the RbCs molecule were performed in the framework of the Hund's $a$-coupling scheme by means of the many-body multipartitioning perturbation theory. The ab initio $d(R)$ estimates revealed large values of about $d\ensuremath{\approx}\ensuremath{-}7\phantom{\rule{0.3em}{0ex}}\mathrm{D}$ for the $(4)\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Pi}$ state. The calculated $q$ factor value for the $(2)\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Pi}$ state is in excellent agreement with the literature data. The theoretical estimate of the $q∕d$ ratio for the ${v}^{\ensuremath{'}}({J}^{\ensuremath{'}})=2(82)$ level of the $(4)\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Pi}$ state agrees satisfactory well with the present experimental value.

D 1 P ‐B 1 P transition dipole moments, as well as nonadiabatic L-uncoupling matrix elements between the examined 1 P and four lowest 1 S 1 states for both 23 Na 85 Rb and 23 Na 87 Rb isotopomers. The relevant MPPT ab initio matrix elements and energy curves were converted by means of the approximate sum rule to radiative lifetimes and L-doubling constants ( q factors! for the particular rovibronic levels of the B 1 P and D 1 P states. The theoretical lifetimes agree well with their experimental counterparts for both B 1 P and D 1 P states. The q factor estimates obtained in the singlet-singlet approximation are in good agreement with the experimental ones for the D 1 P(1

A generalization of optimized diatomics-in-molecules method that provides an accurate treatment of overlap integrals is presented. The possibilities of the method to reproduce potential surfaces of the 4B2, 2B2, and 2A1 states of the H3 molecule are investigated. It is shown that satisfactory results can be achieved only for a single state under consideration, but not for the three states simultaneously.