Accurate Ab Initio Investigation of Electronic and Radiative Properties, and Cross Sections for Charged Diatomic Systems FrLi+ and FrNa. ACS Omega 2023;8:44977-44987. [PMID: 38046336 PMCID: PMC10688152 DOI: 10.1021/acsomega.3c06338] [Citation(s) in RCA: 0] [Impact Index Per Article: 0]

This paper presents an extensive ab initio investigation of the electronic properties and elastic collisions of charged diatomic systems FrLi+ and FrNa+. We employ an accurate ab initio approach using nonempirical pseudopotentials for Li+, Na+, and Fr+ cores. We calculate the potential energy curves of the ground state and low-lying excited states of 2Σ+, 2Π, and 2Δ symmetries, identifying and interpreting avoided crossings between higher 2Σ+ and 2Π states. The spectroscopic parameters, transition dipole moments, and vibrational energies associated with 1-32Σ+ states are calculated, along with the radiative lifetimes of the vibrational states trapped in the 22Σ+ state. Using accurate potential energy data, we evaluate partial and total cross sections across a wide range of energies. At low energies (<1 mK), the elastic cross section follows the Wigner law threshold comportment, while at high energies, it scales as E-1/3. To the best of our knowledge, no theoretical or experimental data have been collected on these charged diatomic systems until now. Hence, we proceeded to analyze our findings by comparing them with data acquired from comparable systems. The information pertaining to electronic structures, spectroscopic parameters, transition properties, and collision data provided in this work is expected to serve as a valuable guideline for future theoretical and experimental research on each considered system.

Potential Energy Surface and Bound States of Ne-Li2+(X2Σg+) van der Waals Complex Based on Ab Initio Calculations

Theoretical studies of the potential energy surface and vibrational bound states calculations were performed for the ground state of the Ne-Li2+(X2Σg+) van der Waals (vdW) complex. The intermolecular interactions were investigated by using an accurate monoconfigurational RCCSD(T) method and large basis sets (aug-cc-pVnZ, n = T, Q, 5), extrapolated to the complete basis set (CBS) limit. In turn, the obtained raw data from RCCSD(T)/CBS(Q5) calculations were numerically interpolated using the Morse + vdW model and the Reproducing Kernel Hilbert Space (RKHS) polynomial method to generate analytic expressions for the 2D-PES. The RKHS interpolated PES was then used to assess the bound states of the Ne-Li2+(X2Σg+) system through nuclear quantum calculations. By studying the aspect of the potential energy surface, the analysis sheds light on the behavior of the Ne-Li2+(X2Σg+) complex and its interactions between repulsive and attractive forces with other particles. By examining the vibrational states and wave functions of the system, the researchers were able to gain a better understanding of the behavior of the Ne-Li2+(X2Σg+) complex. The calculated radial and angular distributions for all even and odd symmetries are discussed in detail. We observe that the radial distributions exhibit a more complicated nodal structure, representing stretching vibrational behavior in the neon atom along its radial coordinate. For the highest bound states, the situation is very different, and the energies surpass the angular barrier.

Pairwise Model Potential and DFT Study of Li+Nen Clusters (n = 1-20): The Structural, Electronic, and Thermodynamic Properties

The structural properties, relative stabilities, electronic, and thermodynamic properties, of Li+Nen (n = 1-20) clusters have been studied based on a pairwise model and density functional theory (DFT) methods. In the pairwise method, the potential energy surface considered interactions between Li+Ne, Ne - Ne, and many-body term. For the DFT calculations, the B3LYP functional combined with the 6-311 + + G (2d,2p) basis sets has been employed. In both methods, the Li+Ne6 cluster demonstrated high stability with an octahedral structure, where the Li+ cation was surrounded by Ne atoms. Thus, the octahedral Li+Ne6 structure was considered to be the core for larger cluster sizes. Relative stabilities were assessed based on binding energies, second-order differences of energies, transition dipole moment, and HOMO-LUMO energy gaps. Furthermore, thermodynamic properties were calculated, revealing that the formation process of Li+Nen clusters is endothermic and nonspontaneous.

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.

Structural, Spectroscopic, and Dynamic Properties of Li2+(X2∑g+) in Interaction with Krypton Atom

We report a computational study of the potential energy surface (PES) and vibrational bound states for the ground electronic state of Li2+Kr. The PES was calculated in Jacobi coordinates at the Restricted Coupled Cluster method RCCSD(T) level of calculation and using aug-cc-pVnZ (n = 4 and 5) basis sets. Afterward, this PES is extrapolated to the complete basis set (CBS) limit for correction. The obtained interaction energies were, then, interpolated numerically using the reproducing kernel Hilbert space polynomial (RKHS) approach to produce analytic expressions for the 2D-PES. The analytical PES is used to solve the nuclear Schrodinger equation to determine the bound states' eigenvalues of Li2+Kr for a J = 0 total angular momentum configuration and to understand the effects of orientational anisotropy of the forces and the interplay between the repulsive and attractive interaction within the potential surface. In addition, the radial and angular distributions of some selected bound state levels, which lie below, around, and above the T-shaped 90° barrier well, are calculated and discussed. We note that the radial distributions clearly acquire a more complicated nodal structure and correspond to bending and stretching vibrational motions "mode" of the Kr atom along the radial coordinate, and the situation becomes very different at the highest bound states levels with energies higher than the T-shaped 90° barrier well. The shape of the distributions becomes even more complicated, with extended angular distributions and prominent differences between even and odd states.

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.

Structure, energetics, and spectroscopy of the K2+(X2Σ+g) interacting with the noble gas atoms Ar, Kr and Xe

The structure, energetic, and spectroscopy properties of the ionic system K₂⁺(X²Σ⁺_g) interacting with the noble gas atoms Argon, Krypton and Xenon are studied. The computations are done by an accurate ab initio approach based on the pseudo-potential technique, Gaussian basis sets, parameterized l-dependent polarization potentials and an analytic potential form for the K⁺Ar, K⁺Kr and K⁺Xe interactions. These interactions are added via the CCSD(T) potential taken from literature and fitted applying the analytical expression of Tang and Toennies. The application of the pseudo-potential approach reduces the number of active electrons of each complex to only one electron. The potential energy surfaces are analyzed on a large range of the Jacobi coordinates, R and θ. By the general interpolation outline based on the RKHS (Reproducing Kernel Hilbert Space) procedure, we have reproduced for each complex from our ab initio results the two-dimensional contour plots of an analytical potential. To evaluate the stability of each complex, we have determined from the potential energy surfaces the equilibrium distance (R_e), the well depth (D_e), the quantum energy (D₀), the zero-point-energy (ZPE) and the ZPE%. The results showed that the linear configurations, where the noble gas atom connected to the K₂⁺(X²Σ⁺_g) system, are the more stable.

Electronic structure, cold ion-atom elastic collision properties and possibility of laser cooling of BeCs+ molecular ion

The BeCs⁺ system represents a possible future candidate for the realization of samples of cold or ultra-cold molecular ion species that have not yet been investigated experimentally or theoretically. With the aim of highlighting the spectroscopic and electronic structure of the cesium and beryllium cation BeCs⁺, we theoretically investigate ground and low lying excited states of ^1,3Σ⁺, ^1,3Π and ^1,3Δ symmetries below the first nine asymptotic limits dissociating into Be⁺(2s) + Cs(6s, 6p, 5d) and Be(2s², 2s2p, 2s3s, 2p²) + Cs⁺. We used a quantum chemistry approach based on a semi-empirical pseudo potential for Be²⁺ and Cs⁺ cores, core polarization potentials (CPP), large Gaussian basis sets and full configuration interaction (FCI) method for the valence electrons. Additional calculations have been performed for the ground state using CCSD(T)/CI methods with different basis sets. Adiabatic potential energy curves, spectroscopic constants, vibrational levels, and permanent and transition dipole moments are reported in this work. Furthermore, the elastic scattering properties at low energy for both ground 1¹Σ⁺ and second excited states 3¹Σ⁺, of BeCs⁺ are theoretically investigated, and isotopic effects on cold and ultra-cold energy collisions are also detected. Vibrational lifetimes of the ground state 1¹Σ⁺ are calculated taking into account both spontaneous and stimulated emissions and also the absorption induced by black body radiation at room temperature (T = 300 K). Vibrational radiative lifetimes for the first 2¹Σ⁺ and second 3¹Σ⁺ excited states are also calculated and extensively analyzed. We found that the radiative lifetimes of the lower vibrational levels of the 1¹Σ⁺ state have an order of magnitude of seconds (s), while those of 2¹Σ⁺ and 3¹Σ⁺ states have an order of nanoseconds (ns). The Franck-Condon factors are also calculated for transitions from the low lying excited 2¹Σ⁺, 3¹Σ⁺, 1¹Π states to the ground state 1¹Σ⁺. We found that the favourite vibrational transition to the 1¹Σ⁺(v = 0) ground state is obtained for 1¹Π (v''' = 0)-1¹Σ⁺(v = 0) with a diagonal structure and a large Franck-Condon factor value of 0.94. This Franck-Condon factor value is sufficiently large to make the BeCs⁺ system a favorable candidate for direct laser cooling.

Electronic Structures and Transition Properties of BeSe and BeTe Molecules

The electronic structure of BeSe and BeTe molecules has been investigated using the ab initio CASSCF/(MRCI + Q) method at the spin-free and spin-orbit level. The potential energy curves, the permanent dipole moment, the spectroscopic constants T e, R e, ωe, and B e, and the dissociation energy D e are determined in addition to the vertical transition energy Tv. The molecules' percentages of ionic character are deduced, and the trends of the spectroscopic constants of the two molecules are compared and justified. A ro-vibrational study is performed using the canonical function approach to calculate the constants E v, B v, and D v and the turning points R min and R max. All the ground-state vibrational levels have also been investigated. The radiative lifetimes of vibrational transitions among the electronic ground states are also discussed. The results for BeSe have been compared with the previously published data while those for BeTe molecules are presented here for the first time.

Theoretical Study of Cationic Alkali Dimers Interacting with He: Li2+-He and Na2+-He van der Waals Complexes

We present a theoretical study on the potential energy surface and bound states of He-A₂⁺ complexes, where A is one of the alkali Li or Na atoms. The intermolecular interactions were systematically investigated by high-level ab initio electronic structure computations, and the corresponding raw data were then employed to reproduce accurate analytical expressions of the potential surfaces. In turn, we used these potentials to evaluate bound configurations of the trimers from nuclear quantum calculations and to extract information on the effect of orientational anisotropy of the forces and the interplay between repulsive and attractive interaction within the potential surfaces. The spatial features of the bound states are analyzed and discussed in detail. We found that both systems are going under large amplitude stretching and bending motions with high zero-point energies. Despite the large differences in the potential well-depths, the correct treatment of nuclear quantum effects provides insights on the effect of different strength of the ionic interaction on the spectral structure of such cationic alkali van der Waals complexes, related to the mobility of ions and the formation of cold-molecules in He-controlled environments.

Theoretical Investigation of the Electronic Structure and Spectra of Mg(2+)He and Mg(+)He

The ground and many excited states of the Mg(+)He van der Waals molecular system have been explored using a one-electron pseudopotential approach. In this approach, effective potentials are used to consider the Mg(2+) core and the electron-He effects. Furthermore, a core-core interaction is included. This has reduced the number of active electrons of the Mg(+)He, to be considered in the calculation, to a single valence electron. This has permitted to use extended Gaussian basis sets for Mg and He. Therefore, the potentianl energy and dipole moments calculations are carried out at the Hartree-Fock level of theory, and the spin-orbit effect is included using a semiclassical approach. The core-core interaction for the Mg(2+)He ground state is included using accurate CCSD(T) calculations. The spectroscopic constants of the Mg(+)He electronic states are extracted and compared with the existing theoretical works, where very good agreement is observed. Moreover, the transition dipole function has been determined for a large and dense grid of internuclear distances including the spin-orbit effect.

Theoretical study of the CsNa molecule: adiabatic and diabatic potential energy and dipole moment

The adiabatic and diabatic potential energy curves of the low-lying electronic states of the NaCs molecule dissociating into Na (3s, 3p) + Cs (6s, 6p, 5d, 7s, 7p, 6d, 8s, 4f) have been investigated. The molecular calculations are performed using an ab initio approach based on nonempirical pseudopotential, parametrized l-dependent polarization potentials and full configuration interaction calculations through the CIPCI quantum chemistry package. The derived spectroscopic constants (Re, De, Te, ωe, ωexe, and Be) of the ground state and lower excited states are compared with the available theoretical and experimental works. Moreover, accurate permanent and transition dipole moment have been determined as a function of the internuclear distance. The adiabatic permanent dipole moment for the first nine (1)Σ(+) electronic states have shown both ionic characters associated with electron transfer related to Cs(+)Na(-) and Cs(-)Na(+) arrangements. By a simple rotation, the diabatic permanent dipole moment is determined and has revealed a linear behavior, particularly at intermediate and large distances. Many peaks around the avoided crossing locations have been observed for the transition dipole moment between neighbor electronic states.

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.

Rydberg states of small NaArn* clusters

The 4s and 5s Rydberg excited states of NaAr(n)* clusters are investigated using a pseudopotential quantum-classical method. While NaAr(n) clusters in their ground state are known to be weakly bound van der Waals complexes with Na lying at the surface of the argon cluster, isomers in 4s or 5s electronically excited states of small NaAr(n)* clusters (n< or =10) are found to be stable versus dissociation. The relationship between electronic excitation and cluster geometry is analyzed as a function of cluster size. For both 4s and 5s states, the stable exciplex isomers essentially appear as sodium-centered structures with similar topologies, converging towards those of the related NaAr(n)+ positive ions when the excitation level is increased. This is consistent with a Rydberg-type picture for the electronically excited cluster, described by a central sodium ion solvated by an argon shell, and an outer diffuse electron orbiting around this NaAr(n)+ cluster core.