Effective Core Polarization Potentials Research Articles

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.

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.

Theoretical study of the alkaline-earth (LiBe)+ ion: structure, spectroscopy and dipole moments

We study theoretically the structure and spectroscopic properties of the alkali alkaline-earth (LiBe)+ ion. The potential energy curves and their spectroscopic parameters, permanent and transition dipole moments are determined with a quantum chemistry approach. The (LiBe)+ ion is modelled as two valence electron system moving in the field of Be2+ and Li+ cores, which are described by pseudopotentials. In addition, effective core-polarization potentials are included to correct the energy. The molecular calculations are performed using a standard quantum chemistry approach based on the pseudopotential model, Gaussian basis sets, effective core polarization potentials, and full configuration interaction (CI) calculations. The precision of our spectroscopic parameters are discussed by comparison with currently available theoretical results. A rather good agreement is observed for the ground and first excited states. The permanent dipole moments reveal many abrupt changes, which are localized at particular distances corresponding to the positions of the avoided crossings.

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.

Ab initio study of the RbSr electronic structure: potential energy curves, transition dipole moments, and permanent electric dipole moments.

Excited states and the ground state of the diatomic molecule RbSr were calculated by post Hartree-Fock molecular orbital theory up to 22000 cm(-1). We applied a multireference configuration interaction calculation based on multiconfigurational self-consistent field wave functions. Both methods made use of effective core potentials and core polarization potentials. Potential energy curves, transition dipole moments, and permanent electric dipole moments were determined for RbSr and could be compared with other recent calculations. We found a good agreement with experimental spectra, which have been obtained recently by helium nanodroplet isolation spectroscopy. For the lowest two asymptotes (Rb (5s (2)S) + Sr (5s4d (3)P°) and Rb (5p (2)P°) + Sr (5s(2) (1)S)), which exhibit a significant spin-orbit coupling, we included relativistic effects by two approaches, one applying the Breit-Pauli Hamiltonian to the multireference configuration interaction wave functions, the other combining a spin-orbit Hamiltonian and multireference configuration interaction potential energy curves. Using the results for the relativistic potential energy curves that correspond to the Rb (5s (2)S) + Sr (5s4d (3)P°) asymptote, we have simulated dispersed fluorescence spectra as they were recently measured in our lab. The comparison with experimental data allows to benchmark both methods and demonstrate that spin-orbit coupling has to be included for the lowest states of RbSr.

Ab initio calculation of the electronic structure of the strontium hydride ion (SrH+)

The potentials, spectroscopic properties and electric dipole moments of SrH+ are computed for 63 molecular states dissociating up to Sr2+ + H− using an ab initio approach. The ab initio formalism is based on large basis sets, nonempirical atomic pseudopotential for strontium core, correlation treatment for core valence through the effective core polarization potentials and for valence through full valence configuration interaction. Our theoretical molecular constants match published values very well and a large amount of new results is produced. Unusual potential shapes are found in 1Σ+ states often caused by avoided crossing series between them and imprinted by the ionic state Sr2+H−. The high potential energy curves suggest, it is possible to form H− or at least to neutralize H+ in collisions with strontium. © 2014 Wiley Periodicals, Inc.

Structure and spectroscopic properties of the beryllium hydride ion BeH+: potential energy curves, spectroscopic constants, vibrational levels and permanent dipole moments

Ab initio calculations are performed for the beryllium hydride ion BeH+ dissociating into Be+(2s, 2p, 3s, 3p and 3d) + H (1s, 2s and 2p) and Be (2s 2, 2s2p, 2s3s, 2p 2, 2s3p and 2s3d) + H+. We have used a standard quantum chemistry approach based on pseudopotential for atomic core representation Be2+, Gaussian basis sets, effective core polarization potentials, and full configuration interaction calculations. Potential energy curves and their spectroscopic constants for the ground state and the first 44 excited electronic states of 1,3Σ+, 1,3 Π and 1,3 Δ symmetries are determined. Their accuracy is discussed by comparing our well depths and equilibrium positions with the previous experimental and theoretical works. A very good agreement with the theoretical calculations and the few available experimental data is observed. Moreover, we localised and analysed numerous avoided crossings between the electronic states of 1,3Σ+ and 1,3 Π symmetries. Their existence are related to the interaction between electronic states and to the charge transfer process between the two ionic systems Be+H and BeH+. In addition, the vibrational energy level spacings are presented and compared with the available experimental and theoretical results. The permanent dipole moments for several electronic states of 1,3Σ+, 1,3 Π and 1,3 Δ symmetries are determined as function of the internuclear distance.

Adiabatic ab Initio Study of the BaH+ Ion Including High Energy Excited States

An adiabatic study of 1-34 (1,3)Σ(+) electronic states of barium hydride ion (BaH(+)) is presented for all states dissociating below the ionic limit Ba(2+)H(-). The 1-20 (1,3)Π and 1-12 (1,3)Δ states have been also investigated. In our approach, the valence electrons of the Ba(2+) ion described by an effective core potential (ECP) and core polarization potential (CPP) with l-dependent cutoff functions have been used. The ionic molecule BaH(+) has been treated as a two-electron system, and the full valence configuration interaction (CI) is easily achieved. The spectroscopic constants Re, De, Te, ωe, ωexe, and Be are derived. In addition, vibrational level spacing and permanent and transition dipole moments are determined and analyzed. Unusual potential shapes are found and also accidental quasidegeneracy in the vibrational spacing progression for various excited states. The (1)Σ(+) states exhibit ionic charge transfer avoided crossings series which could lead to neutralization or even H(-) formation in collisions of H(+) with Ba.

Ground state of the polar alkali-metal-atom–strontium molecules: Potential energy curve and permanent dipole moment

In this study, we investigate the structure of the polar alkali-metal-atom--strontium diatomic molecules as possible candidates for the realization of samples of ultracold polar molecular species not yet investigated experimentally. Using a quantum chemistry approach based on effective core potentials and core polarization potentials, we model these systems as effective three-valence-electron systems, allowing for calculation of electronic properties with full configuration interaction. The potential curve and the permanent dipole moment of the ${}^{2}{\ensuremath{\Sigma}}^{+}$ ground state are determined as functions of the internuclear distance for LiSr, NaSr, KSr, RbSr, and CsSr molecules. These molecules are found to exhibit a significant permanent dipole moment, though smaller than those of the alkali-metal-atom--Rb molecules.

Electronic structure of the magnesium hydride molecular ion

In this paper, using a standard quantum chemistry approach based on pseudopotentials for atomic core representation, Gaussian basis sets and effective core polarization potentials, we investigate the electronic properties of the MgH+ ion. We first determine potential energy curves for several states using different basis sets and discuss their predicted accuracy by comparing our values of the well depths and position with other available results. We then calculate permanent and transition dipole moments for several transitions. Finally, for the first time, we calculate the static dipole polarizability of MgH+ as a function of the interatomic distance. This study represents the first step towards the modelling of collisions between trapped cold Mg+ ions and H2 molecules.

Systematic trends in electronic properties of alkali hydridesThis article is part of a Special Issue on Spectroscopy at the University of New Brunswick in honour of Colan Linton and Ron Lees.

Obtaining ultracold samples of dipolar molecules is a current challenge, which requires an accurate knowledge of their electronic properties to guide the ongoing experiments. Alkali hydride molecules have permanent dipole moments significantly larger than those of mixed alkali species, and, as pointed out by Taylor-Juarros et al. (Eur. Phys. J. D, 31, 213 (2004)) and by Juarros et al. (Phys. Rev. A, 73, 041403 (2006)), are thus good candidates for cold molecule formation. In this paper, using a standard quantum chemistry approach based on pseudopotentials for atomic core representation, large Gaussian basis sets, and effective core polarization potential, we systematically investigate the electronic properties of the alkali hydrides LiH to CsH, to discuss general trends of their behavior. We computed (for the first time for NaH, KH, RbH, and CsH) the variation of their static polarizability with the internuclear distance. Moreover, in addition to potential curves, we determine accurate values of permanent and transition dipole moments for ground and excited states depending on the internuclear distance. The electronic properties of all alkali hydrides are compared with one another, in the light of the numerous other data available in the literature. Finally, the influence of the quality of the representation of the hydrogen electronic affinity in the approach on the results is discussed.

Electronic properties of francium diatomic compounds and prospects for cold molecule formation

In this work, we investigate the possibility of creating cold Fr2, RbFr and CsFr molecules through the photoassociation of cold atoms. Potential curves, permanent and transition dipole moments for the francium dimer and for the RbFr and RbCs molecules are determined for the first time. The francium atom is modelled as one valence electron moving in the field of the Fr+ core, which is described by a new pseudopotential with averaged relativistic effects, and including effective core-polarization potential. The molecular calculations are performed for both the ionic species Fr+2, RbFr+, CsFr+ and the corresponding neutrals, through the CIPSI quantum chemistry package where we used new extended Gaussian basis sets for Rb, Cs and Fr atoms. As no experimental data are available, we discuss our results by comparison with the Rb2, Cs2 and RbCs systems. The dipole moment of CsFr reveals an electron transfer yielding a Cs+Fr− arrangement, while in all other mixed alkali pairs the electron is transferred towards the lighter species. Finally, the perturbative treatment of the spin–orbit coupling at large distances predicts that in contrast with Rb2 and Cs2 no double-well excited potential should be present in Fr2, probably preventing an efficient formation of cold dimers via the photoassociation of cold francium atoms.

Comment on “Calculation of accurate permanent dipole moments of the lowest Σ+1,3 states of heteronuclear alkali dimers using extended basis sets” [J. Chem. Phys. 122, 204302 (2005)

A few typing errors are corrected in Tables II and III of the quoted paper. In addition, we included an exhaustive list of sets of cut-off radii used by various authors in their effective core polarization potentials. Indeed the final results are very sensitive to the initial adjustment of atomic energies, and such a report should guide the interested readers through the corresponding literature. Moreover, it is emphasized that the values of cut-off parameters strongly depend on the chosen Gaussian basis set.

High-correlation methods for the calculations of the ground (X 1Σ +) and first low-lying excited (A 3Σ + and A 1Σ +) states dipole polarizabilities of NaLi

The dipole polarizability of the ground X 1 Σ + and excited A 3 Σ + , A 1 Σ + states of NaLi has been investigated at the ab initio level with effective core polarization potentials, by using the time-dependent gauge invariant method (TDGI). In the case of X 1 Σ + and A 3 Σ + states, alternative high-correlation methods have been applied for comparison. The accuracy of calculated polarizability components is supported by a careful check of the convergence with respect to the number of the spectroscopic states. The dependence of the polarizability on internuclear separation has also been computed. All the calculated electric properties of A 3 Σ + and A 1 Σ + excited states are new.

Core-valence correlation effects for molecules containing first-row atoms. Accurate results using effective core polarization potentials

The accuracy of employing effective core polarization potentials (CPPs) to account for the effects of core-valence correlation on the spectroscopic constants and dissociation energies of the molecules B2, C2, N2, O2, F2, CO, CN, CH, HF, and C2H2 has been investigated by comparison to accurate all-electron benchmark calculations. The results obtained from the calculations employing CPPs were surprisingly accurate in every case studied, reducing the errors in the calculated valence De values from a maximum of nearly 2.5 kcal/mol to just 0.3 kcal/mol. The effects of enlarging the basis set and using higher-order valence electron correlation treatments were found to have only a small influence on the core-valence correlation effect predicted by the CPPs. Thus, to accurately recover the effects of intershell correlation, effective core polarization potentials such as the ones used in the present work provide an attractive alternative to carrying out computationally demanding calculations where the core electrons are explicitly included in the correlation treatment.

Pseudopotential study of the ground and excited states of Yb 2

The ground state of the van der Waals-type lanthanide dimer Yb2 has been studied by means of relativistic energy-consistent ab initio pseudopotentials using three different core definitions. Electron correlation was treated by coupled-cluster theory, whereby core-valence correlation effects have been accounted for either explicitly by correlating the energetically highest coreorbitals or implicitly by means of an effective core-polarization potential. Results for the first and second atomic ionization potentials, the atomic dipole polarizability, and the spectroscopic constants of the molecular ground state are reported. Low-lying excited states have been investigated with spin-orbit configuration interaction calculations. It is also demonstrated for the whole lanthanide series that correlation effects due to the atomic-like, possibly open 4f-shell in lanthanides can be modeled effectively by adding a core-polarization potential to pseudopotentials attributing the 4f-shell to the core.

The ground state potential of the beryllium dimer

An ab initio X 1Σ g +Be 2 ground state potential is determined from all-electron SCF/valence-shell MR-CI calculations which account for core-valence correlation by an effective core polarization potential. The position of the minimum is found at R e=4.627 bohr in full agreement with experiment and the dissociation energy is obtained to D e=4.068 m E h (893 cm −1, significantly larger than the experimental estimate of D e =790 ± 30 cm −1. ΔG 1 2 is calculated from an analytical form of the potential to be 218.4 cm −1, in slight variance with the observed value of 223.8 cm −1. Discrepancies below 10 cm −1 remain with the observed (less accurate) higher vibrational spacings. The deep inner minimum is shown to be related to chemical binding from interaction with a promoted configuration of spin-paired 3P atoms.

Effective core potentials and accurate energy curves for Cs2 and other alkali diatomics

Energy curves of Cs2 that correlate to the ground (SS) and first excited asymptote (SP) are calculated using compact effective potentials (CEP) and core polarization potentials (CPP) which reduce the alkali atom to a single valence electron. Dissociation energies and equilibrium internuclear separations are in good agreement with experimental values. The long-range properties of the energy curves are analyzed to determine the region where the chemical interactions begin. Analogous energy curves and spectroscopic constants are obtained for the Rb2 molecule. The ground state singlet and triplet energy curves are also determined for K2. For completeness, the ground state spectroscopic constants are also reported for the Li and Na neutral and cation homonuclear diatomic molecules to illustrate the accuracy of the CEP and CPP for all the alkali atoms. Both doublet and quartet energy curves of the homonuclear anions also were examined. The dissociation energies and electron detachment energies of the doublet ground state for Rb−2 and Cs−2 are in good agreement with experiment. An assignment of the photoelectron spectra of Cs−2 is possible from the electronic structure of the ground state and the excitation energies of the neutral states. Quartet excited states of Cs−2 are calculated to be bound relative to the 3Σ+u neutral state but are metastable with respect to the ground 1Σ+g state. The accuracy of the ionic energy curves shows that the CEP and CPP are transferrable to the ionic systems.