Core Polarization Potential Research Articles

Theoretical Modeling of Sr(q+) He (q = 0, 1, 2) van der Waals Systems Including Spin-Orbit Coupling.

Using an ab initio methodology that incorporates pseudopotential technique in conjunction with pair potential approaches, core polarization potentials (CPP), large basis sets of Gaussian type, and full configuration interaction calculations, we investigate interaction of neutral and charged Srq+(q = 0,1,2) with helium atom. In this context, the core-core interaction of Sr2+-He is included using an accurately performed potential for the ground state at CCSD(T) level of calculation. Also, the potential energy curves and permanent and transition dipole moments of the ground state and numerous excited states have been performed respectively for Sr+He and SrHe systems. Subsequently, the spin-orbit effect is considered by utilizing a semiempirical method for states dissociating into Sr+(5p) + He, Sr+(6p) + He, Sr+(4d) + He, Sr+(5d) + He, Sr(5s5p) + He, and Sr(5s4d) + He. The spectroscopic constants of the Srq+(q = 0, 1, 2) He states, with and without spin-orbit interaction, are derived and assessed in comparison to the existing theoretical and experimental studies. Such comparison has revealed good agreement, especially, for the Sr+He ionic system. Additionally, the spin-orbit effect is considered for the X2Σ+ → 22Π1/2,3/2 and X2Σ+ → 32Σ1/2 + transition dipole moments for Sr+He.

UNDULATING POTENTIALS OF RYDBERG Σ+-STATES OF ME-RG MOLECULES: NON-EMPIRICAL TREATMENT OF NA-HE EXCIPLEX

The multi-reference con guration interaction method based on single and double excitations (MR-CISD), l-independent core polarization potential (CPP) and diffuse function-saturated cc-pVQZ and aug-cc-pV5Z basis sets for Na and He atoms, respectively, have been used to perform non-relativistic calculations of potential energy curves and permanent dipole moment functions for the ground and excited electronic states of the exciplex Na-He molecule up to the Na(62S) state. The ab initio results obtained in a wide range of internuclear distances R [1.7, 20.0] (Å) have quantitatively claimed the undulating behavior of interatomic potentials, predicted within the framework of the inelastic scattering theory. It has been established that at large R the interatomic potentials and dipole moments of highly excited (3,6,10)2Σ+ states, converging to Na (n = 4, 5, 62S)+He(22S) atomic limits, are modulated by the nodal structure of the radial Rydberg wave function (n > 3) s-electron of Na atom during its scattering on the remote He atom.

Electron Collisions with Multielectron Atoms and Fullerene Molecules: Strong Polarisation Effects

Regge pole-calculated low-energy electron elastic total cross sections for multielectron atoms/fullerenes are characterised by ground, metastable and excited negative-ion formation, shape resonances and Ramsauer-Townsend minima. In this article, we demonstrate through the total cross sections for Eu, Au and At atoms and C60 fullerene the sensitivity of stable negative-ion formation to the crucial core-polarisation potential. The energy positions of the dramatically sharp resonances corresponding to the binding energies of the formed anions during the collisions agree excellently with the measured electron affinities of the atoms and C60. The sensitivity of Ramsauer-Townsend minima and shape resonances to the electronic structure and dynamics of Bk and Cf permits their first ever use as novel validation of the experimental observation that Cf is indeed a transitional element in the actinide series. Their electron affinities are also calculated.

Potential Energy Surfaces and Arrangement Effects of RbNa2 Complex.

Ab initio calculations of alkaline diatomic molecule interactions with alkaline atoms provide detailed information about their electronic structure, vibrational frequencies, and spectroscopic properties, which are difficult to measure experimentally. This knowledge can aid in designing and interpreting experiments and guide the development of computational models and advanced dynamical calculation. Using the quantum chemistry ab initio methods based on multi-reference configuration interaction with Davidson correction (MCSCF/MRCI + Q), atomic effective core potentials, core-polarization potentials, and the interactions between the sodium atom and the NaRb diatomic molecule are investigated. To describe the potential energy surfaces of the RbNa2 system, we introduce two geometries described in the Z-matrix coordinates (Re, R, θ). Potential energy surfaces of the ground state 12A' and the first excited state 22A' were calculated for different approach directions of the sodium atom to the NaRb molecule and two geometries were considered. The first geometry is where the Na atom approaches the Rb atom of the RbNa dimer, and the second one is when it approaches the Na atom of the RbNa dimer. Global minima of the ground and first excited states and conical intersections between these states are determined for both geometries. The RbNa dimer in interaction with the sodium atom is found to be strongly attractive in its first excited state, which may be important for the experimenters particularly in the field of cold alkali polar dimers. Thereafter, the potential energy curves correlated to the lowest-lying dissociation limits are calculated in the linear form for the two geometrical cases (angle θ at 180°) and the atomic arrangement effect is observed.

Spectroscopic Properties of the Alkali-Krypton Diatomic M-Kr (M = Rb, Cs, and Fr) van der Waals Systems Including the Spin-Orbit Coupling.

Using an ab initio approach based on pseudopotential technique, pair potential approach, core polarization potentials, and large Gaussian basis sets, we investigate interaction of heavy alkali-krypton diatomic M-Kr (M = Rb, Cs, and Fr) van der Waals dimers. In this context, the core-core interactions for M+-Kr (M = Rb, Cs, and Fr) are calculated at coupled-cluster single and double excitation (CCSD) level and included in the total potential energy. Therefore, the potential energy curves are performed for 14 electronic states: eight of 2Σ+ symmetry, four of 2Π symmetry, and two of 2Δ symmetry. Furthermore, for each M-Kr dimer, the spin-orbit coupling has been considered for the B2Σ+, A2Π, 32Σ+, 22Π, 52Σ+, 32Π, and 12Δ states. In addition, the transition dipole moment has been determined, including the spin-orbit effect using the rotational matrix issued from the spin-orbit potential energy calculations.

Correlation Consistent Basis Sets and Core Polarization Potentials for Al-Ar with ccECP Pseudopotentials.

New correlation consistent basis sets for the second-row atoms (Al–Ar) to be used with the neon-core correlation consistent effective core potentials (ccECPs) have been developed. The basis sets, denoted cc-pV(n+d)Z-ccECP (n = D, T, Q), include the “tight”-d functions that are known to be important for second-row elements. Sets augmented with additional diffuse functions are also reported. Effective core polarization potentials (CPPs) to account for the effect of core–valence correlation have been adjusted for the same elements, and two different forms of the CPP cutoff function have been analyzed. The accuracy of both the basis sets and the CPPs is assessed through benchmark calculations at the coupled-cluster level of theory for atomic and molecular properties. Agreement with all-electron results is much improved relative to the basis sets that originally accompanied the ccECPs; moreover, the combination of cc-pV(n+d)Z-ccECP and CPPs is found to be a computationally efficient and accurate alternative to including core electrons in the correlation treatment.

Adiabatic investigation of the electronic and dipolar properties of the LiNe system in ground state and numerous excited states

Using ab-initio adiabatic calculation, we studied the electronic properties of the LiNe molecule. In our calculation, we investigate the adiabatic potential energy curves (PECs) of numerous 2Σ+, Π and Δ electronic states. Then, we derive spectroscopic constants, as well as their vibrational levels spacing. For the 2Σ+ states, we determined the permanent and transition dipole moment (PDM and TDM). Our approach is based on the full configuration interaction (FCI), an effective core potential (ECP) which describes the valence electron of the molecule, and the core polarization potential (CPP). Using a large Gaussian basis set, a full configuration interaction is easily carried out.

Calculations of dynamic multipolar polarizabilities of the Cd clock transition levels* *Project supported by the National Key Research and Development Program of China (Grant No. 2017YFA0304402), the Strategic Priority Research Program of the Chinese Academy of Sciences (Grants No. XDB21030300), and the Hubei Province Science Fund for Distinguished Young Scholars, China (Grant No. 2019CFA058).

The pursuit of a systematic frequency uncertainty beyond 10−18 clock has triggered a multitude of investigations on the multipolar and higher-order lattice light shifts. The Cd atom has been proposed as a new candidate for the development of a lattice clock because of its smaller blackbody radiation shift at room temperature. Here, we apply an improved combined method of the Dirac–Fock plus core polarization and relativistic configuration interaction methods to calculate the dynamic multipolar polarizabilities of the Cd clock states. The effects of the high-order core-polarization potentials on the energies, reduced matrix elements, and multipolar polarizabilities have been evaluated systematically. The detailed comparison with available literature demonstrates that taking into account of the high-order core-polarization potentials is a simple and effective approach to improve the results of atomic properties for heavy atoms.

Towards photoassociation processes of ultracold rubidium trimers

We theoretically investigate the prospects for photoassociation (PA) of Rb$_3$, in particular at close range. We provide an overview of accessible states and possible transitions. The major focus is placed on the calculation of equilibrium structures, the survey of spin-orbit effects and the investigation of transition dipole moments. Furthermore we discuss Franck-Condon overlaps and special aspects of trimers including the (pseudo) Jahn-Teller effect and the resulting topology of adiabatic potential-energy surfaces. With this we identify concrete and suitable PA transitions to potentially produce long-lived trimer bound states. Calculations are performed using the multireference configuration-interaction method together with a large-core effective core potential and a core-polarization potential with a large uncontracted even-tempered basis set.

Electronic states of NaLi molecule: Benchmark results with Fock space coupled cluster approach.

Accurate potential energy curves (PECs) are obtained for 20 lowest lying electronic states of the NaLi molecule. The computational scheme used here is based on the multireference coupled cluster theory formulated in the (2,0) sector of the Fock space. The latter sector provides the description of states obtained by attachment of two electrons to the reference system. This makes it possible to adopt the doubly ionized NaLi+2 molecule as a Fermi vacuum. The latter has a very concrete advantage in calculations of the PECs since it dissociates into closed shell fragments (NaLi+2 → Na+ + Li+); hence, the restricted Hartree-Fock method can be used within the whole range of interatomic distances. Computed PECs and spectroscopic constants stay very close to the experimental values (if the latter are available) with the accuracy exceeding the other theoretical approaches including those based on the effective core polarization potentials. Relativistic corrections included at the infinite-order two-component level have a non-negligible effect on the accuracy of computed excitation and dissociation energies with contributions up to 50 cm-1.

Theoretical study of the Coriolis effect in LiNa, LiK, and LiRb molecules.

The non-adiabatic electronic matrix elements, LΠΣ(R), that arise from the spin-conserving electron-rotational interactions between all mΣ+ and mΠ states, where multiplicity m = 1, 3, converging to the lowest three dissociation limits of Li-containing alkali diatomics, LiM (M = Na, K, Rb), were calculated ab initio up to large internuclear distances, R. The required electronic wavefunctions were obtained within the framework of the multi-reference configuration interaction treatment of the two-valence-electron problem constructed using small-core scalar-relativistic effective core potentials and l-independent core-polarization potentials. A least squares analysis of the ab initio functions at large internuclear distances in conjunction with long-range perturbation theory (LRPT) revealed three different asymptotic behaviors of the LΠΣ(R → +∞)-functions: const. + β[n]/Rn, characterized by n = -1, 3 and 6. The asymptotic coefficients β[n], extracted from the point-wise ab initio data, were found to be in agreement with their LRPT counterparts, which were evaluated analytically using the relevant atomic parameters. The mass dependence of the LΠΣ matrix elements was investigated analytically and numerically. To confirm the reliability of the LΠΣ(R)-functions and interatomic potentials at small and intermediate distances, the empirical q-factors available for the D1Π-states of all LiM molecules studied were compared with their theoretical counterparts derived from the present ab initio data.

One and two electrons pseudo-potential investigation of the (FrCs)+ and FrCs systems

In this study, the potential energy curves (PECs) and dipole moments for 1,3Σ+, 1,3Π and 1,3Δ states of the molecule FrCs and for 2Σ+, 2Π and 2Δ of (FrCs)+ have been computed using a quantum chemistry procedure. This method is based on pseudo-potentials for the representation of atomic core, effective core polarization potential, and large Gaussian basis sets. Besides, we have been deduced from these curves the vibrational levels and the spacing's for all symmetries. The (FrCs)+ and FrCs are modeled as one and two valence electrons, respectively and the Fr+ and Cs+ core are indicated by a pseudo-potential with middle relativistic effects together with the potential of effective core polarization. Since, no experimental results are available for these systems, we have compared our result with the theoretical result found by Aymar et al. and found a good agreement.

Spectroscopic proprieties of the ground and the higher excited states of the KCs

Potential energy curves, spectroscopic parameters, electric dipole moments (PEDM and TEDM) and vibrational levels’ spacing for 141Σ+, 133Σ+, 81,3Π, and 31,3Δ electronic states, including the ionic limit K−Cs+, are highly computed and presented in adiabatic representation. These properties are determined by the use of an ab initio method involving non-empirical pseudo-potentials, the core polarization potentials, the l-dependent cut-off functions, and the full valence configuration interaction. An important shape where an ionic state behaving as (−1/R), has been clearly pointed out in the 1Σ+ symmetry. This irregularity has been made due to the ionic charge transfer state (K−Cs+), which induces a series of avoided crossings at intermediate and long internuclear ranges. It is interesting to note that the ionic character linked to the ionic charge transfer K−Cs+ state has been clearly illustrated in the PEDM. The current calculations on the KCs molecule are complementary to the published theoretical works, including recently observed electronic states that had not been calculated previously. For the low-lying electric states, spectroscopic constants, PEDM, as well as TEDM are in good agreement with the available experimental data. The relevant data of the KCs molecule are meaningful and useful in several prospective experiments such as photo-association experiments or the manipulation of ultra-cold molecules.

Ab-initio study of the ground and low-lying excited states including the spin-orbit effect of RbBa molecule and laser cooling feasibility

In this work, we present a thorough theoretical structure and spectroscopic study of the ground and low lying excited states of RbBa molecule. High-level ab-initio calculations are performed, using MCSCF/MRCI+Q level of method, based on the effective core potential (ECP) and core-polarization potential (CPP) approach. The potential energy curves, spectroscopic parameters, vibrationnel energy levels of the 16(2,4Σ+,2,4Π,2,4Δ) first electronic states, with respect to the lowest five dissociation limits were calculated. The comparison of the spectroscopic constants of the ground state X2Σ+ with the available theoretical work, are in good agreement. The study of all the excited states is performed in this work for the first time. Afterwards, the spin-orbit operator is incorporated in valence MRCI calculation using optimized relativistic spin-orbit pseudo-potentials and 33 Ω states are generated and split into Λ-S states. In addition, both relativistic and non relativistic calculations of permanent and transition dipole moments are presented and discussed. Stimulated black body (T= 300 K) and spontaneous transition rates of vibrational states of X2Σ+ state were evaluated. The related vibrational lifetimes for RbBa are found to be in order of 103 s which is sufficiently large for ultracold experiments. Moreover, the vibrational life-time for the A2Σ+(v’) and A2П (v”) states are measured and the possibility of Laser Cooling for the RbBa molecule is discussed based on Franck–Condon factors calculation of A2Σ+ (v’)→ X2Σ+(v) and A2П(v”) → X2Σ+(v) transition. This work represents a significant contribution for experimentalists as it provides efficient information in order to form cold alkali and alkaline-earth RbBa molecules.

Ab initio calculations of electronic structure of the BaCs molecule: adiabatic potential energy curves, spectroscopic constants, spin–orbit effect and permanent and transition electric dipole moments

An ab initio approach based on effective core potentials (ECPs), core polarization potentials (CPPs) with three valence electrons and multireference configuration interaction (MRCI) level of calculation is used to determine the adiabatic potential energy curves, the spectroscopic constants and the permanent and transition electric dipole moments of the lowest doublet and quartet electronic states of BaCs. These sates are dissociating into the first six asymptotic limits of the alkali–alkaline earth molecule, BaCs. Only the ground state has been studied in the literature, and the comparison with the available results has shown a very good agreement. The spin–orbit interaction has been included in the next step of our calculation, and its effect on the potential energy curves and spectroscopic parameters on the Ω representation states has been thoroughly studied. Both relativistic and nonrelativistic calculations of permanent and transition dipole moments are also presented, which allows us to determine the influence of relativistic effects on the dipole moment.

Non-relativistic and relativistic investigation of the low lying electronic states of Sr2+Xe, Sr+Xe and SrXe systems

The potential energy curves and permanent and transition dipole moments of the neutral SrXe and the ionic Sr+Xe systems are calculated with an ab initio approach using pseudopotential techniques, core polarization potentials, large Gaussian basis sets and full configuration interaction for two electron calculations. The spectroscopic constants of the ground state and lower excited states are in good agreement with the available experimental and theoretical works. The spin–orbit coupling is also included for the ionic system Sr+Xe and the neutral one SrXe. Its effect is significant on the potential energy curves, dipole moments and energy level spacing. For SrXe, the spin–orbit splitting has been considered for the states (2)3Σ0,1, (1,2)3Π0,1,2 and (1)3Δ0,1,2,3.

Spectroscopic, vibrational and structural properties analysis of CaXen (n = 1–4) clusters

A systematic ab initio calculations based on a complete Configuration Interaction (CI) including the pseudo-potential model where the core valence correlation was presented by the Core Polarization Potential (CPP), were employed to determine the geometric structures of CaXen (n = 1–4) neutral clusters. For the diatomic (CaXe) and tri-atomic (CaXe2) systems, the potential energy curves for the ground and several excited states are determined and the different spectroscopic constants are illustrated. Interested structures were seen in the PECs which their effects in the vibrational levels' spacing and the electric dipole moments variations were shown. The agreement with the experimental and the theoretical constants for n = 1 was excellent. Accordingly, for the higher clusters the predicted geometries should be reliable. The bent geometry of CaXe2 ground state with (C2v) symmetry was performed and hence was concluded to be the most adaptable with a bond angle of 54.84° and bond distance dXe-Xe of 8.08 a0. As well as, the bent isomer for the excited states was also studied to illustrate the most compact geometry for each state. For the ground state of CaXe3, the most stable geometry was trigonal-pyramidal with (C3v) symmetry with dXe-Xe = 8.13 a0. And concerned n = 4, four configurations were treated; the tetrahedral structure, the square pyramid structure, the trigonal bipyramid structure with (C3v) symmetry and the trigonal bipyramid structure with (C2v) symmetry. The comparison between their minimal energies showed that the most compact geometry for CaXe4 is the trigonal bipyramid with (C3v) symmetry with dXe-Xe = 8.17 a0. Consequently, this work illustrates that the mechanism of cluster forming is consistent with the calcium location on the xenon clusters' surface model.

Electronic structure and photoassociation scheme of ultracold (MgK+) molecular ions

The adiabatic potential energy curves, permanent and transition dipole moments (TDMs) of the highly-excited states of the MgK+ molecular ion have been computed as a function of the inter-nuclear distance R. The results are obtained by an ab initio approach involving a non-empirical pseudo-potential for the Mg and K cores, correlation treatment for core valence through an effective core polarisation potential, and full valence configuration interaction. The molecule is thus treated as a two electron system. Ab initio electronic TDM functions are calculated for all dipole-allowed transitions among the 42 states of MgK+. Many of these moment functions exhibit interesting behaviour due to charge transfer or ion-atom pair correlations. The positions of a number of satellite bands are predicted from the potential energy difference curves. We verified our results by performing complete active space self-consistent field calculations followed by a multireference configuration interaction and including Davidson correction. We observe a rather good agreement for most of them especially for the ground and lower excited states. We investigate ion-atom cold collisions at quantum regime. Furthermore, we explore ion-atom elastic collisions at low temperatures, predicting the formation of translationally and rotationally cold molecular ion MgK+ in the ground state electronic potential by stimulated Raman type process. Our results are important in the perspective of upcoming experiments aiming at merging cold alkali atom and alkaline-earth ion in a hybrid trap for the creation of cold molecular ions by photoassociation.

Ab initioand analytical studies of the spin-orbit coupling in heteronuclear alkali-metal dimersAB(A, B= Li, Na, K, Rb) at long ranges

The spin-orbit (SO) coupling matrix elements between the excited states of the lightest heteronuclear alkali metal dimers AB(A, B = Li, Na, K, Rb) converging to the first three dissociation limits were evaluated by employing the quasirelativistic electronic wave functions in a wide range of interatomic distances, $R$. The inner-shell electrons of alkali atoms were described using nonempirical shape-consistent effective core potentials. To take the core-valence correlation effects into account, core polarization potentials for each atom were implemented. Dynamical correlation was introduced through the multireference configuration interaction method, which was applied to two valence electrons keeping all subvalence electrons frozen. The reliability of the derived SO functions is accessed through comparison, wherever possible, with their preceding theoretical and experimental counterparts. The ab initio SO matrix elements were approximated beyond the LeRoy radius using the formula: ${\ensuremath{\xi}}_{if}^{\text{SO}}(R)=\ensuremath{\alpha}+{\ensuremath{\beta}}_{if}^{[k]}/{R}^{k}$, where (1) $k=6$ and $\ensuremath{\alpha}={\ensuremath{\xi}}_{n^{2}\mathrm{P}}^{\text{SO}}$ is the SO splitting of the atom $\mathrm{A}(n^{2}\mathrm{P}$) for the states of the AB molecule converging to the same $\mathrm{A}({n}_{\mathrm{A}}^{2}\mathrm{P}$) + $\mathrm{B}({n}_{\mathrm{B}}^{2}\mathrm{S}$) dissociation limit, and (2) $k=3$ and $\ensuremath{\alpha}=0$ for the molecular $i$ and $f$ states converging to the $\mathrm{A}({n}_{\mathrm{A}}^{2}\mathrm{P})+\mathrm{B}({n}_{\mathrm{B}}^{2}\mathrm{S})$ and $\mathrm{A}({n}_{\mathrm{A}}^{2}\mathrm{S})+\mathrm{B}({n}_{\mathrm{B}}^{2}\mathrm{P}$) atomic thresholds, respectively. A theoretical justification of these formulas was derived from the multipole expansion of the molecular SO operator in terms of the inverse powers of the internuclear distance and of products of operators acting on the electronic coordinates of the atoms A and B.

Spectroscopic and electric dipole properties of the Van der Waals interaction between barium and krypton atoms

ABSTRACTVan der Waals interactions between the valence electrons of the barium atom and the closed-shell cores have been studied using ab initio methods with a combination of pseudopotentials and core polarisation potential. We have reported the potential energy curves, the spectroscopic constants, the vibrational levels as well as the electric dipole moments for the ground and several excited states of Ba+Kr and BaKr complexes. Interesting behaviour has been observed in the potential energy curves, particularly for Σ+ states. This can show the strong repulsive interactions between Rydberg electrons and the Krypton atom.