Non-empirical Pseudopotentials Research Articles

Electronic structure of ground and low-lying excited states of BaLi+ molecular ion: spin-orbit effect, radiative lifetimes and Franck-Condon factor

The study of BaLi+ and its reactivity plays a crucial role in advancing our understanding of chemical bonding or reaction mechanisms. The aim of this work is to represent a complete and extended theoretical study of BaLi+ molecular ion including ground and highly excited electronic states of 1,3Σ, 1,3Π and 1,3Δ symmetries, dissociated to the first seven dissociation limits. The corresponding potential energy curves (PECs), permanent and transition dipole moments have been investigated. These calculations were performed using the multireference configuration interaction (MRCI) method in combination with optimized basis sets and non-empirical pseudopotentials (ECP) for both Ba and Li atoms. Afterwards, the spin–orbit (SO) operator is incorporated in valence MRCI calculation using optimized relativistic spin–orbit pseudopotentials and 16 Ω states are generated and splitted into Λ-S states. The SO effect gives rise to a more complicated structure of electronic states presented in PEC and permanent and transition dipole moments. Nonadiabatic coupling matrix elements between the five lowest 1Σ+ states are also presented for the nonrelativistic results. Based on the vibrational radiative lifetime and Franck–Condon calculation, the possibilities of laser cooling of this system have been also discussed.

Accurate Ab Initio Investigation of Electronic and Radiative Properties, and Cross Sections for Charged Diatomic Systems FrLi+ and FrNa.

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.

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 electronic structure and prospects for the formation of ultracold calcium–alkali-metal-atom molecular ions

Experiments with cold ion–atom mixtures have recently opened the way for the production and application of ultracold molecular ions. Here, in a comparative study, we theoretically investigate ground and several excited electronic states and prospects for the formation of molecular ions composed of a calcium ion and an alkali-metal atom: CaAlk+ (Alk = Li, Na, K, Rb, Cs). We use a quantum chemistry approach based on non-empirical pseudopotentials, operatorial core-valence correlation, large Gaussian basis sets, and full configuration interaction method for valence electrons. Adiabatic potential energy curves, spectroscopic constants, and transition and permanent electric dipole moments are determined and analyzed for the ground and excited electronic states. We examine the prospects for ion-neutral reactive processes and the production of molecular ions via spontaneous radiative association and laser-induced photoassociation. After that, spontaneous and stimulated blackbody radiation transition rates are calculated and used to obtain radiative lifetimes of vibrational states of the ground and first-excited electronic states. The present results pave the way for the formation and spectroscopy of calcium–alkali-metal-atom molecular ions in modern experiments with cold ion–atom mixtures.

Theoretical study of the LiNa molecule beyond the Born–Oppenheimer approximation: adiabatic and diabatic potential energy curves, radial coupling, adiabatic correction, dipole moments and vibrational levels

ABSTRACTThe adiabatic potential energy curves for ground and many excited states of 1, 3Σ+, 1,3Π, 1,3Δ symmetries of the LiNa molecule have been performed. We have used an ab initio approach based on non-empirical pseudopotentials, parameterised l-dependent polarisation potentials and full configuration interaction calculations. In addition, the adiabatic potential energy curves determined in our previous work [Mabrouk and Berriche, J. Phys. B: At. Mol. Opt. Phys. 41, 155101 (2008).] are corrected by using a diabatisation procedure, based on the effective Hamiltonian theory and an effective metric. The diabatic permanent moments for first 10 1Σ+ electronic states show linear behaviours, especially at intermediate and large distance. The transition dipole moment between neighbour states has revealed many peaks located around the avoided crossing positions. The radial coupling between the adiabatic states was calculated using the Hellmann-Feynman formula and numerical differentiation of the rotation matrix. The first and the second derivatives revealed many peaks, associated to neutral-neutral and ionic-neutral crossings. Furthermore, the radial coupling is used to evaluate the adiabatic correction, which is found to be of an order of tens and hundreds of cm−1, especially of higher excited states. In addition, we have determined the vibrational level spacing for all studied states.

Theoretical evaluation of the radiative lifetimes of LiCs and NaCs in the A1Σ+ state

Calculations of the adiabatic potential energy curves and the transition dipole moments between the ground (A1Σ+) and the first excited (A1Σ+) states have been determined for the LiCs and NaCs molecules. The calculations are performed using an ab initio approach based on non-empirical pseudopotentials for Cs+, Li+ and Na+ cores, parameterized l-dependent polarization potentials and full configuration interaction calculations. The potential energy curves and the transition dipole moment are used to estimate the radiative lifetimes of the vibrational levels of the A+Σ+ state using the Franck–Condon (FC) approximation and the approximate sum rule method. The radiative lifetimes associated with the A+Σ+ state are presented here for the first time. These data can help experimentalists to optimize photoassociative formation of ultracold molecules and their longevity in a trap or in an optical lattice.

Electronic Structure and Spectra of the MgLi(+) Ionic Molecule.

Using an ab initio approach based on nonempirical pseudopotentials for the Mg(2+) and Li(+) cores, Gaussian basis sets, effective core polarization potentials and full configuration interaction calculations, the adiabatic potential energy curves, the spectroscopic constants, the permanent and transition electric dipole moments of the several lowest electronic states of the alkali-alkaline earth ion MgLi(+) have been performed. These states dissociate into Mg(+)(3s and 3p) + Li (2s, 2p, 3s, 3p, 3d, 4s, 4p, and 4d) and Mg (3s(2), 3s3p, 3s4s, 3s3d, 3s4p, 3s5s, and 3s4d) + Li(+). The spectroscopic constants (Re, De, Te, ωe, ωexe, and Be) of the ground state and nearly 53 excited states of (1,3)Σ(+), (1,3)Π, and (1,3)Δ symmetries are derived. Most of them are computed for the first time. Moreover, several avoided crossings between the electronic states of (1,3)Σ(+), (1,3)Π symmetries are localized and analyzed. Their existence is related to the interaction between the potential energy curves and to the charge transfer process between the two ionic systems Mg(+)Li and MgLi(+). Furthermore, accurate adiabatic permanent and transition dipole moments for several transitions have been calculated for a large and dense grid of internuclear distances for the first 15 (1)Σ(+) electronic states. A linear behavior is observed in the permanent dipole moments for several electronic states. Additionally, the transition electric dipole moments between neighbor states have shown many peaks situated around the avoided crossing positions.

Structure and electronic properties of the doubly charged diatomic dications BeX2+ (X = Na, K)

The structural and electronic properties of the doubly charged diatomic dications BeX2+ (X = Na, K) have been systematically investigated. The ab initio calculations method is based on the use of non-empirical pseudopotentials for the Be2+, Na+, and K+ cores, Gaussian basis sets, and parameterized l-dependent polarization potentials. The potential energy curves and their spectroscopic properties for the low-lying electronic states of 2Σ+, 2Π, and 2Δ symmetries have been determined for the species BeNa2+ and BeK2+ for the first time. Results show, for each diatomic dication, that the ground and the first excited electronic states are repulsive. For both systems, for which no experimental and theoretical data are available, we discuss our results by comparing their potential energies with similar systems. Numerous avoided crossings between electronic states of 2Σ+ and 2Π symmetries have been localized and analyzed. Their existence is related to the interaction between the electronic states and to the charge transfer process between the two ionic structures Be(2+)X and Be(+)X(+). Furthermore, the transition dipole functions from the ground state to the 2-102Σ+ and between neighbor electronic states of 2Σ+ symmetry, revealed many abrupt changes, which are localized at particular distances corresponding to the positions of the avoided crossings.

Ab initio study of Ba+Arn (n = 1–4) clusters: spectroscopic constants and vibrational energy levels

ABSTRACTThis study is interested in the illustration of ab initio potential energy curves for Ba+Arn (n = 1–4) clusters. The electronic structures of these molecules are calculated using [Ba2+] and [Ar] non-empirical core pseudo-potentials complemented by the core polarisation operators for both atoms, which allow the consideration of core valence correlation effects. The structure and stabilities of Ba+Arn (n = 1–4) clusters are investigated. These molecules are treated as one-electron active system. Spectroscopic constants and vibrational energy levels have been derived from their potentials. The analysis of the geometric forms, basing on the potential energy curves and the spectroscopic constants, clearly shows the importance of rare gas induced dipole. We also show that the dipolar interactions can influence the coupling between atoms.

Ab Initio Investigation of Electronic Properties of the Magnesium Hydride Molecular Ion

In this work, adiabatic potential energy curves, spectroscopic constants, dipole moments, and vibrational levels for numerous electronic states of magnesium hydride molecular ion (MgH(+)) are computed. These properties are determined by the use of an ab initio method involving a nonempirical pseudopotential for the magnesium core (Mg), the core polarization potential (CPP), the l-dependent cutoff functions and the full valence configuration interaction (FCI). The molecular ion is thus treated as a two-electron system. Our calculations on the MgH(+) molecular ion extend previous theoretical works to numerous electronic excited states in the various symmetries. A good agreement with the available theoretical and experimental works is obtained for the spectroscopic constants, the adiabatic potential energy curves, and the dipole moments for the lowest states of MgH(+).

Potential energy and dipole moment of the Na2+ ionic molecule

The potential energy curves of 26 electronic states of 2Σ+g, u, 2Πg, u, and 2Δg, u symmetries of the alkali dimer Na2+, dissociating up to Na(4d) + Na+, are investigated using an ab initio approach involving a nonempirical pseudopotential for the Na+(1s22s22p6) core and core‐valence correlation corrections. Furthermore, the transition dipole functions between many electronic states and vibrational energy spacings are presented. The spectroscopic constants of these electronic states are extracted and compared with the available theoretical and experimental results. A very good agreement is observed, especially, for the ground and the first excited states. However, the comparison between our study and the model potential (MP) calculations (Magnier and Masnnou‐Seeuws Mol. Phys. 1996, 89, 711) for several states has shown a clear disagreement. The MP well depths of the 3‐42Σ+g, 12Πg, 3‐42Πg, and 22Πu electronic states are largely underestimated. In addition, the 5‐72Σ+g, 3‐72Σ+u, 22Πg, 42Πg, and 1‐22Δu MP electronic states are repulsive, although in this work, they are attractive with potential well depths of some hundreds of cm−1. The data presented in this study are very useful for studies on ion–atom interaction and cold collision in the presence of electromagnetic fields. © 2013 Wiley Periodicals, Inc.

Theoretical investigation of the low-lying electronic states of the alkaline hydride BeH2+ ion: Potential energy curves, spectroscopic constants, vibrational levels, and transition dipole functions

The structure and spectroscopic properties of the alkaline hydride BeH2+ ion have been investigated using an ab initio approach based on nonempirical pseudopotentials and parameterized l-dependent polarization potentials. The adiabatic potential energy curves and their spectroscopic constants for the ground and seventeen excited electronic states, dissociating into Be+(2s, 2p, 3s, 3p, 3d, 4s, 4p, and 4d) + H+ and Be2+ + H(1s and n = 2), of 2Σ+, 2Π, and 2Δ symmetries have been determined. As no experimental data are available, our results are discussed and compared with the few existing theoretical calculations. A very good agreement has been found with the previous theoretical data for the ground state; however many potential energy curves for the higher excited states are presented here, for the first time. Numerous avoided crossings between electronic states for 2Σ+ and 2Π symmetries have been localized and analyzed. Their existence is related to the interaction between the electronic states and to the charge transfer process between the two ionic systems Be2+H and Be+H+. In addition, we have calculated the vibrational energy level spacings of the bound electronic states. Furthermore, the adiabatic transition dipole functions from the X2Σ+ and 22Σ+ states to the higher excited states of 2Σ+ and 2Π symmetries have been evaluated and compared with the available theoretical work. This study represents the necessary initial step towards the investigation of the charge transfer processes in collision between Be+-H+ and Be2+-H.

One‐electron pseudopotential study of the alkali hydride cation NaH+: Structure, spectroscopy, transition dipole moments, and radiative lifetimes

AbstractThe structure and spectroscopic properties of the ground and the lowest excited electronic states of the alkali hydride cation NaH+ have been investigated using an ab initio approach. In this approach, a nonempirical pseudopotential for the Na+ core has been used and a core–core and a core‐valence correlation corrections have been added. The adiabatic potential energy curves and the molecular spectroscopic constants for numerous electronic states of 2Σ+, 2Π, and 2Δ symmetries, dissociating up to Na (4d) + H+ and Na+ + H (3d), have been calculated. As no experimental data are available, we discuss our results by comparing with the available theoretical calculations. A satisfying agreement has been found for the ground state with previous works. However, a clear disagreement between this study and the model potential work of Magnier (Magnier, J. Phys. Chem. A 2005, 109, 5411) has been observed for several excited states. Numerous avoided crossings between electronic states of 2Σ+ and 2Π symmetries have been found and analysed. They are related to the interaction between the potential energy curves and to the charge transfer process between the two ionic systems Na+H and NaH+. Furthermore, we provide an extensive set of data concerning the transition dipole moments from X2Σ+ and the 22Σ+ states to higher excited states of 2Σ+ and 2Π symmetries. Finally, the adiabatic potential energy curves of the ground (X2Σ+) and the first (22Σ+) excited states and the transition dipole moments between these states are used to evaluate the radiative lifetimes for the vibrational levels of the 22∑+ state for the first time. In addition to the bound–bound contribution, the bound‐free term has been evaluated and added to the total radiative lifetime. © 2012 Wiley Periodicals, Inc.

Structural and Spectroscopic Study of the LiRb Molecule beyond the Born–Oppenheimer Approximation

Adiabatic and diabatic potential energy curves and the permanent and transition dipole moments of the low-lying electronic states of the LiRb molecule dissociating into Rb(5s, 5p, 4d, 6s, 6p, 5d, 7s, 6d) + Li(2s, 2p) have been investigated. The molecular calculations are performed with an ab initio approach based on nonempirical pseudopotentials for Rb(+) and Li(+) cores, parametrized l-dependent core polarization potentials and full configuration interaction calculations. The derived spectroscopic constants (R(e), D(e), T(e), ω(e), ω(e)x(e), and B(e)) of the ground state and lower excited states are in good agreement with the available theoretical works. However, the 8-10(1)Σ(+), 8-10(3)Σ(+), 6(1,3)Π, and 3(1,3)Δ excited states are studied for the first time. In addition, to the potential energy, accurate permanent and transition dipole moments have been determined for a wide interval of internuclear distances. The permanent dipole moment of LiRb has revealed ionic characters both relating to electron transfer and yielding Li(-)Rb(+) and Li(+)Rb(-) arrangements. The diabatic potential energy for the (1,3)Σ(+), (1,3)Π, and (1,3)Δ symmetries has been performed for this molecule for the first time. The diabatization method is based on variational effective Hamiltonian theory and effective metric, where the adiabatic and diabatic states are connected by an appropriate unitary transformation.

Ab Initio Adiabatic and Diabatic Energies and Dipole Moments of the CaH+ Molecular Ion

The diabatic and adiabatic potential-energy curves and permanent and transition dipole moments of the highly excited states of the CaH(+) molecular ion have been computed as a function of the internuclear distance R for a large and dense grid varying from 2.5 to 240 au. The adiabatic results are determined by an ab initio approach involving a nonempirical pseudopotential for the Ca core, operatorial core-valence correlation, and full valence configuration interaction. The molecule is thus treated as a two-electron system. The diabatic potential energy curves have been calculated using an effective metric combined to the effective Hamiltonian theory. The diabatic potential-energy curves and their permanent dipole moments for the (1)∑(+) symmetry are examined and corroborate the high imprint of the ionic state in the adiabatic representation. Taking the benefit of the diabatization approach, correction of hydrogen electron affinity was taken into account leading to improved results for the adiabatic potentials but also the permanent and transition electric dipole moments.

Electronic states of CsLi and CsLi+ molecules

Configuration interaction calculations have been carried out on electronic states of the CsLi molecule and the CsLi+ cation. Adiabatic potential energy, spectroscopic constants, dipole moments, and vibrational levels are presented for the lowest states of 1,3Σ+, 1,3Π, and 1,3Δ symmetries of the alkali dimer CsLi molecule dissociating into Cs (6s, 6p, 5d, 7s, and 7p) + Li (2s, 2p, 3s, 3p, and 3d) as well as for the lowest 2Σ+, 2Π, and 2Δ electronic states of the CsLi+ cation dissociating into Li (2s, 2p, 3s, 3p, and 3d) + Cs+ and Li+ + Cs (6s, 6p, 5d, 7s, and 7p). The results of the present many-electron configuration interaction calculations on the cation support the previous core-polarization effective potential calculations. The present calculations on the CsLi molecule are complementary to previous theoretical work on this system, including recently observed electronic states that had not been calculated previously. We have used an ab initio approach involving a nonempirical pseudopotential for the Li (1s2) and Cs cores and a core-valence correlation correction. A very good agreement of data from spectroscopic constants for some of the lowest states of the CsLi and CsLi+ molecules with those available in recent theoretical works has been obtained. The existence of numerous avoided crossings between electronic states of 2Σ+ and 2Π symmetries is related to a charge transfer process between the two ionic CsLi+ and LiCs+ systems.

Theoretical Study of the LiCs Molecule: Adiabatic and Diabatic Potential Energy and Dipole Moment

For nearly all the states dissociating into Cs (6s, 6p, 5d, 7s, 7p, 6d, 8s) and Li (2s, 2p, 3s), we present an extensive adiabatic study for (1,3)Sigma(+), (1,3)Pi, and (1,3)Delta symmetries of the LiCs molecule. We have used an ab initio approach based on nonempirical pseudopotentials, parametrized l-dependent polarization potentials, and full configuration interaction calculations. A diabatisation procedure based on the effective Hamiltonian theory and an effective metric is used to produce the quasi-diabatic potential energy for all studied states. The spectroscopic constants (R(e), D(e), T(e), omega(e), omega(e)x(e), and B(e)) of these states are derived and compared with the available theoretical and experimental works. In addition to the potential energies, accurate permanent and transition dipole moment have been determined for a wide range of internuclear distances. The adiabatic permanent dipole moment for the first 10 (1)Sigma(+) electronic states has revealed ionic characters relating to electron transfer and yielding both Li(-)Cs(+) and Li(+)Cs(-) arrangements. The quasi-diabatic permanent moments show linear behaviors, especially at intermediate and large distance. The transition dipole moment between neighbor states has revealed many peaks located around the avoided crossing positions.

Theoretical calculation of the low lying electronic states of the molecular ion KH + with spin–orbit effects

The potential energy has been calculated for the 36 lowest electronic states of symmetries Ω = 1/2, 3/2, 5/2 for the molecular ion KH +. Using an ab initio method the calculation is based on non-empirical pseudo-potentials and parameterized ℓ-dependent polarization potentials. Gaussian basis sets have been used for both atoms and spin–orbit effects have been taken into account. The spectroscopic constants for 18 electronic sates have been calculated by fitting the calculated energy values to a polynomial in terms of the internuclear distance R. In order to have a good accuracy of this spin–orbit study the calculation has been done with a given number of significant figures for these constants. The transition dipole moments have been calculated for the considered Ω-states. The comparison of the present results with those available in literature shows a very good agreement.

Theoretical calculation of the low laying electronic states of the molecular ion RbH+

AbstractUsing an ab initio method, the potential energy has been calculated for the 29 lowest molecular states of symmetries 2Σ+, 2Π, 2Δ for the molecular ion RbH+. The calculation is based on nonempirical pseudopotentials and parameterized ℓ‐dependent polarization potentials. Gaussian basis sets have been used for both atoms. The spectroscopic constants for 18 electronic sates have been calculated by fitting the calculated energy values to a polynomial in terms of the internuclear distance R. Through the canonical functions approach the eigenvalue Ev, the abscissas of the corresponding turning points (Rmin and Rmax) and the rotational constants Bv have been calculated up to 24 vibrational levels for the considered bound states. The comparison of the present results with those available in literature shows a very good agreement. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010

Theoretical calculation of the low lying electronic states of the molecular ion RbH+ with spin-orbit effects

The potential energy has been calculated for the 42 lowest electronic states of symmetries Omega=12,32,52, for the molecular ion RbH(+). Using an ab initio method, the calculation is based on nonempirical pseudopotentials and parametrized [script-l]-dependent polarization potentials. Gaussian basis sets have been used for both atoms, and spin-orbit effects have been taken into account. The spectroscopic constants for 19 electronic states have been calculated by fitting the calculated energy values to a polynomial in terms of the internuclear distance r. The permanent dipole moment and the transition dipole moments have been calculated for the considered Omega states. Through the canonical functions approach the eigenvalue E(v), the abscissas of the corresponding turning points (r(min) and r(max)) and the rotational constants B(v) have been calculated. The comparison of the present results with those available in literature shows a very good agreement.