The van der Waals potential of the magnesium dimer

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.

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.

Quantum Chemistry Study on the Structures and Electronic Properties of Bimetallic Ca2-Doped Magnesium Ca2Mgn (n = 1–15) Clusters

Here, by utilizing crystal structure analysis through the particle swarm optimization (CALYPSO) structural searching method with density functional theory (DFT), we investigate the systemic structures and electronic properties of Ca₂Mg_n (n = 1–15) clusters. Structural searches found that two Ca atoms prefer to occupy the external position of magnesium-doped systems at n = 2–14. Afterward, one Ca atom begins to move from the surface into the internal of the caged skeleton at n = 15. Calculations of the average binding energy, second-order difference of energies, and HOMO–LUMO gaps indicated that the pagoda construction Ca₂Mg₈ (as the magic cluster) has higher stability. In addition, the simulated IR and Raman spectra can provide theoretical guidance for future experimental and theoretical investigation. Last, further electronic properties were determined, including the charge transfer, density of states (DOS) and bonding characteristics. We hope that our work will provide theoretical and experimental guidance for developing magnesium-based nanomaterials in the future.

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→∞.

Probing the structural evolution and electronic properties of divalent metal Be2Mgn clusters from small to medium-size

Bimetallic clusters have aroused increased attention because of the ability to tune their own properties by changing size, shape, and doping. In present work, a structural search of the global minimum for divalent bimetal Be₂Mg_n (n = 1-20) clusters are performed by utilizing CALYPSO structural searching method with subsequent DFT optimization. We investigate the evolution of geometries, electronic properties, and nature of bonding from small to medium-sized clusters. It is found that the structural transition from hollow 3D structures to filled cage-like frameworks emerges at n = 10 for Be₂Mg_n clusters, which is obviously earlier than that of Mg_n clusters. The Be atoms prefer the surface sites in small cluster size, then one Be atom tend to embed itself inside the magnesium motif. At the number of Mg larger than eighteen, two Be atoms have been completely encapsulated by caged magnesium frameworks. In all Be₂Mg_n clusters, the partial charge transfer from Mg to Be takes place. An increase in the occupations of the Be-2p and Mg-3p orbitals reveals the increasing metallic behavior of Be₂Mg_n clusters. The analysis of stability shows that the cluster stability can be enhanced by Be atoms doping and the Be₂Mg₈ cluster possesses robust stability across the cluster size range of n = 1-20. There is s-p hybridization between the Be and Mg atoms leading to stronger Be-Mg bonds in Be₂Mg₈ cluster. This finding is supported by the multi-center bonds and Mayer bond order analysis.

Convergent energies and anharmonic vibrational spectra of Ca2H2 and Ca2H4 constitutional isomers

Three constitutional isomers of both Ca₂H₂ and Ca₂H₄ have been characterized with molecular electronic structure theory. Correlation methods as complete as CCSDT(Q) and basis sets as large as cc-pwCV5Z have been used to converge the relative energies within chemical accuracy (≤1 kcal mol^-1). Anharmonic vibrational frequencies were computed using second-order vibrational perturbation theory employing CCSD(T)/cc-pwCVTZ cubic and quartic force-fields and a CCSD(T)/cc-pwCVQZ quadratic force field. The monobridged [Ca(μ₂-H)CaH] and dibridged [Ca(μ₂-H)₂Ca] isomers of Ca₂H₂ were predicted to lie 6.5 and 12.9 kcal mol^-1 below the energy of the classical HCaCaH linear isomer, respectively. Despite the energetic favorability of the bridged Ca₂H₂ isomers, we conclude (surprisingly) that only the higher energy linear structure has been observed in the laboratory. At 0 K, the tribridged [Ca(μ₂-H)₃CaH] isomer of Ca₂H₄ is predicted to be enthalpically favored by 0.9 kcal mol^-1 in comparison to the enthalpy of the dibridged [HCa(μ₂-H)₂CaH] structure. Comparison of experiment with our computed frequencies suggests that the observed vibrational features arise from both the dibridged and the tribridged Ca₂H₄ structures.

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 ab initio investigation on the low-lying electronic states of NaMg

Theoretical investigations for NaMg have been performed on the icMRCI + Q level employing basis set of quintuple-ζ quality with corrections of core-valence correlation and scalar relativistic effect. The geometrical parameters, potential energy curves, vibrational energy levels, spectroscopic constants for the eight Λ-S states, with respect to the lowest four dissociation limits, are investigated. Through the spin-orbit coupling effect, these states split into fourteen Ω states. The permanent dipole moments, transition dipole moments, Einstein emission coefficients, radiative lifetimes and Franck-Condon factors for all Ω states are studied. The feasibility of performing laser cooling of NaMg has also been discussed. Our predictive results are anticipated to serve as guidelines for further researches on NaMg.

Photoinduced Molecule Formation of Spatially Separated Atoms on Helium Nanodroplets

Besides the use as cold matrix for spectroscopic studies, superfluid helium droplets have served as a cold environment for the synthesis of molecules and clusters. Since vibrational frequencies of molecules in helium droplets exhibit almost no shift compared to the free molecule values, one could assume the solvated particles move frictionless and undergo a reaction as soon as their paths cross. There have been a few unexplained observations that seemed to indicate cases of two species on one droplet not forming bonds but remaining isolated. In this work, we performed a systematic study of helium droplets doped with one rubidium and one strontium atom showing that besides a reaction to RbSr, there is a probability of finding separated Rb and Sr atoms on one droplet that only react after electronic excitation. Our results further indicate that ground-state Sr atoms can reside at the surface as well as inside the droplet.

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.

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.

A Density Functional with Spherical Atom Dispersion Terms

A new hybrid density functional, APF, is introduced, which avoids the spurious long-range attractive or repulsive interactions that are found in most density functional theory (DFT) models. It therefore provides a sound baseline for the addition of an empirical dispersion correction term, which is developed from a spherical atom model (SAM). The APF-D empirical dispersion model contains nine adjustable parameters that were selected based on a very small training set (15 noble gas dimers and 4 small hydrocarbon dimers), along with two computed atomic properties (ionization potential and effective atomic polarizability) for each element. APF-D accurately describes a large portion of the potential energy surfaces of complexes of noble gas atoms with various diatomic molecules involving a wide range of elements and of dimers of small hydrocarbons, and it reproduces the relative conformational energies of organic molecules. The accuracy for these weak interactions is comparable to that of CCSD(T)/aug-cc-pVTZ calculations. The accuracy in predicting the geometry of hydrogen bond complexes is competitive with other models involving DFT and empirical dispersion.

Mg2H2: new insight on the Mg-Mg bonding and spectroscopic study

The six dimensional potential energy surface of the electronic ground state X̃(1)Σ(g)(+) of Mg(2)H(2) has been generated by the coupled-cluster approach with single, double and perturbative triple excitations [CCSD(T)] combined with the aug-cc-pCVTZ basis set for Mg atoms and the aug-cc-pVTZ basis set for the H atoms. The analytical representation of this surface was used in variational calculations of the rovibrational energies of Mg(2)H(2), Mg(2)D(2), and HMg(2)D for J = 0 and 1. For Mg(2)H(2), the rotational constant B(0) is computed to be 0.1438 cm(-1), and the fundamental anharmonic wavenumbers are calculated to be ν(1) = 1527.3 cm(-1) (Σ(g)(+)), ν(2) = 275.3 cm(-1) (Σ(g)(+)), ν(3) = 1503.6 cm(-1) (Σ(u)(+)), ν(4) = 312.9 cm(-1) (Π(g)), and ν(5) = 256.5 cm(-1) (Π(u)). In addition, the electronic ground states of Mg(2)H, MgH(2), Mg(2), and MgH have been investigated in order to compute the bonding energies of Mg(2)H(2) and to explain the strength of the Mg-Mg bond in this tetra-atomic molecule. The nature of the low-lying excited states of Mg(2)H(2) is also studied.