The ground state van der Waals potentials of the strontium dimer and strontium rare-gas complexes

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.

Theoretical Study of Ground-State Barium-Rare Gas Van der Waals Complexes: Combining Rule Modeling and Ab Initio Calculations

The present study aims to generate the potential energy curves (PECs) and spectroscopic constants for barium alkaline earth (AE) atoms interacting with rare gas (RG) atoms (He, Ne, Ar, Kr, and Xe). The study focuses on investigating the van der Waals bonds that characterize the interactions between alkaline-earth metals and RG atoms, with a specific emphasis on employing the Tang and Toennies (TT) potential model, known to accurately describe such interactions. The TT potential model was employed in conjunction with combining rules to calculate its parameters, which include dispersion coefficients C 2n and Born-Mayer constants A and b. Additionally, we have conducted high-level ab initio calculations at the CCSD(T) level for all Ba-RG ground states. Obtained PECs from both methods have been used to evaluate the spectroscopic properties D e, R e, ωe, B e, and ωeχe. Our findings reveal that the derived spectroscopic constants from the TT model exhibit good agreement with the results obtained from CCSD(T) calculations and with other available theoretical studies. Furthermore, to gain insights into the relative differences among AE-RG species, we calculated the κ parameter for AE-RG and AE+-RG (AE = Sr, Ca, Mg, Ba; RG = He-Xe) complexes. It is found that except for the case of Ba-RG and Ba+-RG, the κ values within the same series, AE-RG and AE+-RG, are remarkably close to each other.

Universal Pairwise Interatomic van der Waals Potentials Based on Quantum Drude Oscillators

Repulsive short-range and attractive long-range van der Waals (vdW) forces play an appreciable role in the behavior of extended molecular systems. When using empirical force fields, the most popular computational methods applied to such systems, vdW forces are typically described by Lennard-Jones-like potentials, which unfortunately have a limited predictive power. Here, we present a universal parameterization of a quantum-mechanical vdW potential, which requires only two free-atom properties─the static dipole polarizability α1 and the dipole-dipole C6 dispersion coefficient. This is achieved by deriving the functional form of the potential from the quantum Drude oscillator (QDO) model, employing scaling laws for the equilibrium distance and the binding energy, and applying the microscopic law of corresponding states. The vdW-QDO potential is shown to be accurate for vdW binding energy curves, as demonstrated by comparing to the ab initio binding curves of 21 noble-gas dimers. The functional form of the vdW-QDO potential has the correct asymptotic behavior at both zero and infinite distances. In addition, it is shown that the damped vdW-QDO potential can accurately describe vdW interactions in dimers consisting of group II elements. Finally, we demonstrate the applicability of the atom-in-molecule vdW-QDO model for predicting accurate dispersion energies for molecular systems. The present work makes an important step toward constructing universal vdW potentials, which could benefit (bio)molecular computational studies.

Product-State Distributions of Three-Body Recombination in Zero-Collision-Energy 4He2-Alkaline-Earth-Metal Systems

The distributions of product states after three-body recombination (TBR) of zero-collision-energy 4He2X systems, with X being 9Be, 24Mg, 40Ca, 88Sr, or 138Ba, are investigated in the hyperspherical representation by quantum mechanically solving the Schrödinger equation. It is found that the weakly bound (dimer) product states are preferentially populated for all of these cases, which could be understood from the joint effects of the lowest incident channel and the relatively long-range behavior of the corresponding nonadiabatic couplings among these lowest incident and shallow recombination channels. For the strongly bound products, since the flow is accessible in the small hyperradial region, their distributions are closely related to the behavior of the nonadiabatic couplings among the corresponding deep recombination channels. Particularly, our results indicate that the products are not always formed exclusively in the most weakly bound state when the scattering lengths among the reactants are relatively large and that there may exist a large fluctuation of the strongly bound products versus their binding energies in the universal region. In addition, the total TBR rates of these nonuniversal systems are also accounted for by the joint effects of the main adiabatic potentials and nonadiabatic couplings.

Excited Electronic States of Sr2: Ab Initio Predictions and Experimental Observation of the 21Σu+ State

Despite its apparently simple nature with four valence electrons, the strontium dimer constitutes a challenge for modern electronic structure theory. Here we focus on excited electronic states of Sr₂, which we investigate theoretically up to 25000 cm^-1 above the ground state, to guide and explain new spectroscopic measurements. In particular, we focus on potential energy curves for the 1¹Σ_u⁺, 2¹Σ_u⁺, 1¹Π_u, 2¹Π_u, and 1¹Δ_u states computed using several variants of ab initio coupled-cluster and configuration-interaction methods to benchmark them. In addition, a new experimental study of the excited 2¹Σ_u⁺ state using polarization labeling spectroscopy is presented, which extends knowledge of this state to high vibrational levels, where perturbation by higher electronic states is observed. The available experimental observations are compared with the theoretical predictions and help to assess the accuracy and limitations of employed theoretical models. The present results pave the way for future more accurate theoretical and experimental spectroscopic studies.

Ultracold state-to-state chemistry for three-body recombination in realistic 3He2-alkaline-earth-metal systems

The ultracold state-to-state chemistry for three-body recombination (TBR) in realistic systems recently could be experimentally investigated with full quantum state resolution. However, many detected phenomena remain challenging to be explored and explained from the theoretical viewpoints because this generally requires computational powers beyond the state-of-the-art. Here, the product-state distributions after TBR of 3He2-alkaline-earth-metal systems, i.e. after the processes 3He+3He+X→3HeX+3He with X being 9Be, 24Mg, 40Ca, 88Sr, or 138Ba, in the zero-collision-energy limit are theoretically studied. Two propensity rules for the distribution of the products found in current experiments have been checked, and the mechanism underlying these product-state distributions is explored. Particularly, two main intriguing transition pathways are identified, which may be responsible for the nonlinear distribution of the products versus their rotational quantum number. In addition, the total TBR rates of these systems are also accounted for by the joint effects of major adiabatic potential energies and relevant nonadiabatic couplings.

An accurate potential model for the a3Σu+ state of the lithium dimer

An accurate Tang-Toennies (TT) model potential is introduced to describe the interatomic potential of the lithium dimer in the a³Σ_u⁺ state. With only one well-known parameter, the ionization energy, the new model potential compares favorably with the experimentally fitted Morse/Long-range (MLR) potential of Dattani and Le Roy [J. Mol. Spectrosc., 2011, 268, 199] and is in excellent agreement with the state-of-the-art ab initio potential of Lesiuk et al. [Phys. Rev. A, 2020, 102, 062806]. With the known dispersion coefficients and the ionization energy, the new potential requires only two experimental parameters, namely the depth of the potential well D_e and its location R_e. The new potential can be extended to the region of zero separation by the united atom limit.

Classical threshold law for the formation of van der Waals molecules

We study the role of pairwise long-range interactions in the formation of van der Waals molecules through direct three-body recombination processes A + B + B → AB + B, based on a classical trajectory method in hyperspherical coordinates developed in our earlier works [J. Pérez-Ríos et al., J. Chem. Phys. 140, 044307 (2014); M. Mirahmadi and J. Pérez-Ríos, J. Chem. Phys. 154, 034305 (2021)]. In particular, we find the effective long-range potential in hyperspherical coordinates with an exact expression in terms of dispersion coefficients of pairwise potentials. Exploiting this relation, we derive a classical threshold law for the total cross section and the three-body recombination rate yielding an analytical expression for the three-body recombination rate as a function of the pairwise long-range coefficients of the involved partners.

The development of a full range analytical interatomic potential

A chronological account is given to the development of a full range interatomic potential. Starting with a simple phenomenological model, the terms in the model are gradually modified, so that they can carry some definite physical meaning. To gain insight, a systematic, order by order interaction potential theory is developed. Conversely, this theory suggests the functional form for the potential model. At present, we have a simple interaction model that is capable of describing the van der Waals potentials of many systems from R = 0 to R→∞.

Accommodation of a dimer in an Ar-like lattice: exploring the generic structural motifs

A global optimization strategy is applied to Lennard-Jones models describing the stable trapping sites of a dimer in the face-centered cubic Ar-like lattice. Effective volumes of the trapping sites, quantified as the number of host atoms dislodged from the lattice, are mapped onto the parameter space defined by the strength and range of the dimer interaction potentials. The two models considered differ in the host-guest interaction and give very different maps that reflect the effect of local lattice relaxation. A hierarchical complete-linkage clustering technique is applied to identify generic structural types of the dimer accommodations. The dominant types found and enlisted maintain the symmetry of the isolated dimer and possess high tetrahedral and octahedral symmetry of the host environment with respect to the dimer atoms or center and can be roughly classified as the "whole" or "per atom" dimer accommodations. The results are compared to the analysis of the analogous model for trapped atoms and realistic model for trapped alkaline-earth metal dimers. Implications for matrix isolation spectroscopy are discussed.

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.

An accurate potential model for the a3Σu+ state of the alkali dimers Na2, K2, Rb2, and Cs2

A modified semi-empirical Tang-Toennies potential model is used to describe the a³Σ_u⁺ potentials of the alkali dimers. These potentials are currently of interest in connection with the laser manipulation of the ultracold alkali gases. The fully analytical model is based on three experimental parameters, the well depth D_e, well location R_e, and the harmonic vibrational frequency ω_e of which the latter is only slightly optimized within the range of the literature values. Comparison with the latest spectroscopic data shows good agreement for Na₂, K₂, Rb₂, and Cs₂, comparable to that found with published potential models with up to 55 parameters. The differences between the reduced potential of Li₂ and the conformal reduced potentials of the heavier dimers are analyzed together with why the model describes Li₂ less accurately. The new model potential provides a test of the principle of corresponding states and an excellent first order approximation for further optimization to improve the fits to the spectroscopic data and describe the scattering lengths and Feshbach resonances at ultra-low temperatures.

Absorption spectroscopy of heavy alkaline earth metals Ba and Sr in rare gas matrices--CCSD(T) calculations and atomic site occupancies

Isolation of the heavier alkaline earth metals Ba and Sr in the solid rare gases (RGs) Ar, Kr, and Xe is analysed with absorption spectroscopy and interpreted partly with the assistance of ab initio calculations of the diatomic M ⋅ RG ground state interaction potentials. The y(1)P ← a(1)S resonance transitions in the visible spectral region are used to compare the isolation conditions of these two metal atom systems and calcium. Complex absorption bands were recorded in all three metal atom systems even after extensive sample annealing. Coupled cluster calculations conducted on the ground states of the nine M ⋅ RG diatomics (M = Ca, Sr, and Ba; RG = Ar, Kr, and Xe) at the coupled cluster single, double, and non-iterative triple level of theory revealed long bond lengths (>5 Å) and shallow bound regions (<130 cm(-1)). All of the M ⋅ RG diatomics have bond lengths considerably longer than those of the rare gas dimers, with the consequence that isolation of these metal atoms in a single substitutional site of the solid rare gas is unlikely, with the possible exception of Ca/Xe. The luminescence of metal dimer bands has been recorded for Ba and Sr revealing very different behaviours. Resonance fluorescence with a lifetime of 15 ns is observed for the lowest energy transition of Sr2 while this transition is quenched in Ba2. This behaviour is consistent with the absence of vibrational structure on the dimer absorption band in Ba2 indicating lifetime broadening arising from efficient relaxation to low-lying molecular states. More extensive 2D excitation-emission data recorded for the complex site structures present on the absorption bands of the atomic Ba and Sr systems will be presented in future publications.

Corresponding states principle and van der Waals potentials of Zn2, Cd2, and Hg2

Based on the assumptions that the corresponding states principle is valid for the group 12 dimers and that the interaction potentials of these dimers can be described by the Tang-Toennies potential model, a set of correlation relations between the spectroscopic constants of these dimers are derived. Some recently measured spectroscopic constants satisfy these relations quite well, but older experimental data do not. These recent spectroscopic constants and the newly available dispersion coefficients are used to construct the entire van der Waals potentials of Zn2, Cd2, and Hg2. There are indications that the ground state Hg2 potential predicted by the present study is possibly the most accurate to date. No unequivocal conclusion can be made for Zn2 and Cd2 potentials. Compared with the recent experiments, the present Zn2 bond length is eight percent too small, and the present Cd2 bond length is eight percent too large. However, both Zn2 and Cd2 bond lengths predicted by the present study are in good agreement with the quantum Monte Carlo results.