Alkaline-earth Dimers Research Articles

Relativistic treatment of alkaline earth dimers in the presence of non-central molecular potential in N-dimensions

Abstract Within the framework of relativistic theory, N-dimensional non-central Morse potential as anharmonic model is considered thoroughly to describe the internuclear motion of alkaline earth dimers in the different electronic states. We illustrate the surface plots of alkaline earth dimers to examine the effect of angular potential, due to existence of molecular systems in which spherical symmetry disappears. Also, the contribution of angle dependent interaction to the relativistic energy spectra has been investigated in N-dimensions. We determine the relativistic vibrational transition frequencies in the lower vibrational states for the X 1 Σ g + ground state of 24 Mg 2 , 40 Ca 2 , 24 Mg 40 Ca and A 1 Σ u + excited state of 88 Sr 2 alkaline earth diatomic molecules. The theoretical results have been compared with Rydberg-Klein-Rees (RKR) and the inverted perturbation approach (IPA) experimental data. We also discussed the validity of Pekeris approximation around the equilibrium distance as well as the repulsive and attractive regions for alkaline earth dimers.

Prospects for laser cooling of polyatomic molecules with increasing complexity

Optical cycling transitions and direct laser cooling have recently been demonstrated for a number of alkaline-earth dimers and trimer molecules. This is made possible by diagonal Franck-Condon factors between the vibrational modes of the optical transition. Achieving a similar degree of cooling to micro-Kelvin equivalent kinetic energy for larger polyatomic molecules, however, remains challenging. Since polyatomic molecules are characterized by multiple degrees of freedom and have a correspondingly more complex structure, it is far from obvious whether there exist polyatomic molecules that can repeatedly scatter photons. Here, we propose chemical substitution approaches to engineer large polyatomic molecules with optical cycling centers (OCCs) containing alkaline-earth oxide dimers or acetylenic alkaline-earth trimers (i.e. M--C$\equiv$C) connected to CH$_n$ chains or fullerenes. To validate the OCC-character of the selected molecules we performed electronic structure calculations of the equilibrium configuration of both ground and excited potential energy surfaces, evaluated their vibrational and bending modes, and corresponding Franck-Condon factors for all but the most complex molecules. For fullerenes, we have shown that OCCs based on M--C$\equiv$C can perform better than those based on alkaline-earth oxide dimers. In addition, for heavier polyatomic molecules it might be advantageous to attach two OCCs, thereby potentially doubling the photon scattering rate and thus speeding up cooling rates.

Selective control of photoassociation of alkaline earth dimers: A theoretical study

AbstractThe laser synthesis of alkaline earth dimers (Be2, Mg2, Ca2, Sr2, and Ba2) is investigated by theoretical calculation. Photoassociation based on ab initio calculations is rationalized by Franck‐Condon filtering. The optimal target states of photoassociations have been obtained, which are A1∑+u state for Be2, Mg2, and Ca2, and are B1∑+u state for Sr2 and Ba2, corresponding to vibrational transition bands from X1∑+g to excited state are 0‐1, 0‐7, 0‐10, 0‐13, and 0‐3, respectively. The proposed laser drive transitions to target states are also investigated that range from 350 to 740 nm. By using quantum wave‐packet dynamic methods, we calculated the absorption cross sections of photon energy and yields for the selected states of photoassociation. It show that the most sensitive molecules for quantum selective control of photoassociation are Be2 and Ba2 for alkaline earth dimers. These important parameters will provide a feasible scheme for further experimental researches.

Weak Interactions in Alkaline Earth Metal Dimers by Pair-Density Functional Theory

Alkaline earth dimers have small bond energies (less than 5 kcal/mol) that provide a difficult challenge for electronic structure calculations. They are especially challenging for Kohn-Sham density functional theory (KS-DFT) using generalized gradient approximations (GGAs) as the exchange-correlation density functional because GGAs often do not provide accurate results for weak interactions. Here we treat alkaline earth dimers from six different rows of the periodic table. We show that the dominant correlating configurations are the same in all six dimers. We also show that multiconfiguration pair-density functional theory (MC-PDFT) using a fully translated GGA as the on-top density functional not only performs much better than KS-DFT with GGAs in predicting equilibrium distances and dissociation energies but also performs better than the more computationally demanding complete active space second-order perturbation theory (CASPT2) with large basis sets and performs even better than CASPT2 with smaller basis sets.

The vibrational index at dissociation: An extended treatment

The simple empirical expression recently proposed Hajigeorgiou (2013) [1] for estimating the effective non-integer vibrational index at dissociation in a diatomic molecule, has been revised by considering information for 22 ground electronic states of a variety of diatomic molecules. In addition, analogous expressions have been derived for molecules that form exceptions to the general expression, indicating that families of chemically related molecules can display regularity and predictability as far as the vibrational index at dissociation is concerned. In particular, the alkaline-earth dimers and inert-gas dimers have been considered.

The alkaline earth dimer cations (Be2 +, Mg2 +, Ca2 +, Sr2 +, and Ba2 +). Coupled cluster and full configuration interaction studies†

Although all of the neutral alkaline earth dimers have been studied experimentally, only for the beryllium and strontium systems have the diatomic radical cations been subjected to modern spectroscopic techniques. In the present research, both coupled cluster and full configuration interaction methods were used to describe the M2 + systems. Basis sets as large as aug-cc-pCV5Z were chosen. For both Be2 + and Sr2 + agreement with the experiments is outstanding. Final predictions for the unknown dissociation energies are 10,651 (Mg2 +), 9605 (Ca2 +), and 8980 cm−1 (Ba2 +). The M2 + dissociation energies decrease monotonically going down the periodic except for the Sr2 + - Ba2 + pair. The unknown bond distances re are 3.015 (Mg2 +), 3.814 (Ca2 +), 4.194 (Sr2 +), and 4.587 Å (Ba2 +).

Theoretical investigation for spectroscopic constants of ground-state alkaline-earth dimers with high accuracy

In this work, we provide highly accurate theoretical estimates for spectroscopic constants of the ground-state alkaline-earth dimers (Ca2, Sr2, and Ba2). Electron correlation energies are calculated with coupled-cluster method at the single, double, and noniterative triple excitations [CCSD(T)] level, and the effects of full triples as well as quadruple excitations are also taken into account at the CCSDT and the CCSDT(Q) level. Our results demonstrate that high-order electron correlation is important to achieve results with high accuracy. We also find that results for Ca2 with counterpoise corrections, which are designed to eliminate the basis set superposition error, deviate further away from those at the complete basis set limit than the uncorrected ones. The calculated binding energies and equilibrium bond lengths for Ca2 and Sr2 are in excellent agreement with recent experimental data. On the other hand, our results for Ba2 are quite different from previous theoretical data, and there is no available experimental equilibrium bond length and binding energy for calibration. Based on the performance of the adopted approach for Ca2 and Sr2, our results should be more reliable and could be helpful for future investigations.

Single reference coupled cluster calculations for weakly bound alkaline-earth metal dimers in the ground state: a useful perturbative scheme for an iterative triples correction

We apply here a new iterative triples correction for the single reference coupled-cluster method with singles and doubles scheme (termed as CCSDT-1a+d). All diagonal terms in have been included in the T 3 determining equation, in addition to . This minor change in the CCSDT-1a approximation (includes the primary effects of connected triples excitations iteratively) shows a dramatic change in the study of correlation of weakly bonded systems as discussed here. To achieve a general assessment of the potentiality of the CCSDT-1a + d calculations, the ground state potential energy surfaces (PESs) of alkaline-earth dimers, including Mg2, Ca2 and the challenging Be2 are considered. The systems considered here are treated as four-electron systems, keeping other electrons frozen in the correlation calculations. Generation of PESs for these dimers is very sensitive to the level of theory employed for the electron correlation. Basic spectroscopic constants including dissociation energy extracted from the calculated ground state PES are also reported. For all systems under study, the overall performance of CCSDT-1a+d is very competitive with that of the CCSD(T)/CCSDT method, and better than that of CCSDT-1a indicating that the former approach is more effective in handling dynamic correlation effects in comparison to the latter one in the presence of quasi-degeneracy to different extents. To calibrate our results we also report frozen-core FCI calculations.

Corresponding States Principle for the Alkaline Earth Dimers and the van der Waals Potential of Ba2

A simple method based on the corresponding states principle and the Tang-Toennies potential model is used for the determination of the ground state van der Waals potential of barium dimer. The potential energy curve calculated from the theoretical dispersion coefficients and the experimental vibrational frequency is comparable to other quantum chemical calculations. To assess its validity, the same method is used to calculate the potential of the strontium dimer, for which there are many theoretical and experimental determinations. A comparison with experimental measurements suggests that the present method is highly accurate. The potentials of five alkaline earth dimers are compared. The potentials of Mg(2), Ca(2), Sr(2), and Ba(2) are shown to be nearly conformal with each other. The potential of Be(2) has a different shape.

A first-principles study of weakly bound molecules using exact exchange and the random phase approximation

We present a study of the binding energy (BE) curves of rare gas and alkaline-earth dimers using an energy functional that includes exact exchange (EXX) and correlation energies within the random phase approximation (RPA). Our results for the equilibrium positions and long range behavior of the potential energy curves show great improvements over those obtained at the density functional theory level, within local and semilocal approximations. BEs are improved as well in the case of rare gas dimers. For Ar and Kr, the accuracy of our results is comparable to that of so-called van der Waals density functionals, although EXX/RPA yields BE curves that agree better with experiment for large separation distances, as expected. We also discuss shortcomings of the EXX/RPA perturbative approach and analyze possible sources of error in the description of the potential energy curve of alkaline-earth dimers, in particular, Be(2), exhibiting an unphysical maximum at large separations. We suggest that the lack of self-consistency in current EXX/RPA approaches might be largely responsible for most of the observed shortcomings. Finally, we present a tight-binding approach to obtain the eigenvalues of the dielectric matrix entering the calculation of the RPA correlation energy that greatly improves the efficiency of EXX/RPA calculations.

High-accuracy calculations of dipole, quadrupole, and octupole electric dynamic polarizabilities and van der Waals coefficients C 6, C 8, and C 10 for alkaline-earth dimers

The static and dynamic electric dipole, quadrupole, and octupole polarizabilities of the alkaline- earth atoms (beryllium, magnesium, calcium, strontium, and barium) in the ground state were calculated. The dynamic polarizabilities obtained were used to calculate the van der Waals coefficients C 6 , C 8 , and C 10 of alka- line-earth metal dimers for the interaction of two like atoms in the ground state. The results are compared with other theoretical and experimental data.

Potential curves for alkaline-earth dimers by density functional theory with long-range correlation corrections

Potential curves of alkaline-earth dimers, Be 2, Mg 2 and Ca 2, bound by London dispersion forces, are determined with the recently developed range separated hybrid method with perturbational long-range correlation corrections (RSH + MP2), and are compared to wave function approaches (MP2), to conventional density functional (LDA, PBE, BLYP, BPW91) and hybrid functional (PBE0, B3LYP) results. In contrast to rare gas dimers, functionals involving Becke’s exchange are not repulsive, but yield a relatively profound potential well. The RSH + MP2 approach outperforms the MP2 method considerably and reduces the basis set superposition error. It represents a promising alternative for the study of larger alkaline-earth clusters.

Relativistic atomic natural orbital type basis sets for the alkaline and alkaline-earth atoms applied to the ground-state potentials for the corresponding dimers

New basis sets of the atomic natural orbital (ANO) type have been developed for the atoms Li–Fr and Be–Ra. The ANOs have been obtained from the average density matrix of the ground states and the lowest excited states of the atom, the positive ion, and the dimer at its equilibirium geometry. Scalar realtivisitc effects are included through the use of a Douglas–Kroll Hamiltonian. Multiconfigurational wave functions have been used with dynamic correlation included using second-order perturbation theory (CASSCF/CASPT2). The basis sets are applied in calculations of the ground-state potentials for the dimers. Computed bond energies are accurate to within 0.05 eV for the alkaline dimers and 0.02 eV for the alkaline-earth dimers (except for Be2).

Nature of binding in the alkaline–earth clusters: Be3, Mg3, and Ca3

The study of the interaction energy and its many-body decomposition in a broad distance interval for the Ben, Mgn, and Can (n=2,3) clusters at the SCF and MP4 levels are performed. A comparative analysis of the obtained results allows one to conclude that the only stabilization factor in the dimers is the dispersion forces. So, the alkaline–earth dimers can be attributed to the van der Waals molecules. The trimers are stabilized by the two-body localized dispersion forces and three-body delocalized exchange forces. The binding in the alkaline–earth trimers has a mixed physical (van der Waals) and chemical (nonadditive exchange) nature. An NBO population analysis reveals a relatively large p-population in all clusters. A surprisingly large p-population at the MP4 level is also obtained for the isolated atoms.

Absorption and Laser-Excited Fluorescence Spectra of Matrix-Isolated Metal van der Waals Dimers

75 references are cited in this review which deals only with the metal dimers of Group IIA and IIB. Applications to the study of these dimers of the low-temperature matrix-isolation technique in which a stream of metal atoms is allowed to condense on a cryogenic surface with a large excess of an inert gas, usually Ne or Ar, are a focus point of the review. The electronic structure and bonding of the alkaline earth dimers in general are discussed. This discussion is followed by a somewhat detailed consideration of the dimers, Be/sub 2/, Mg/sub 2/, Ca/sub 2/, Sr/sub 2/, Ba/sub 2/, CaMg, SrMg, BaMg, and SrCa. (BLM)