Argon pair potential at basis set and excitation limits

A Simple Model for the Pauli Repulsion with Possible Utility in QM, MM and Chemical Education

The Pauli repulsion is the intermolecular force responsible for the volume and low compressibility of condensed-phase matter at normal conditions. A simple model for this force is presented, wherein per-atom electron densities are represented as spherical charge distributions that are prevented from significantly overlapping. In the example of two noble gas atoms approaching one another beyond their van der Waals radii, the distance between the centers of the electronic charge distributions becomes larger than the distance between the nuclei, giving rise to an unfavorable electrostatic interaction. For the purpose of calculating this interaction, the model is further simplified by representing the per-atom electron density as a negative point charge, loosely inspired by the classical Drude oscillator. The dispersion interaction is simplified to an R-6 term, centered on the aforementioned point charges. Despite the gross simplicity of the resulting formalism, near-quantitative agreement with high-level QM interaction energies of noble gas dimers is achieved. Accordingly, the present model is thought to have utility in force fields, in post-HF and post-DFT dispersion corrections, and in chemical education.

100 Years of the Lennard-Jones Potential

It is now 100 years since Lennard-Jones published his first paper introducing the now famous potential that bears his name. It is therefore timely to reflect on the many achievements, as well as the limitations, of this potential in the theory of atomic and molecular interactions, where applications range from descriptions of intermolecular forces to molecules, clusters, and condensed matter.

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.

Collision-induced three-body polarizability of helium

We present the first-principles determination of the three-body polarizability and the third dielectric virial coefficient of helium. Coupled-cluster and full configuration interaction methods were used to perform electronic structure calculations. The mean absolute relative uncertainty of the trace of the polarizability tensor, resulting from the incompleteness of the orbital basis set, was found to be 4.7%. Additional uncertainty due to the approximate treatment of triple and the neglect of higher excitations was estimated at 5.7%. An analytic function was developed to describe the short-range behavior of the polarizability and its asymptotics in all fragmentation channels. We calculated the third dielectric virial coefficient and its uncertainty using the classical and semiclassical Feynman-Hibbs approaches. The results of our calculations were compared with experimental data and with recent Path-Integral Monte Carlo (PIMC) calculations [Garberoglio et al., J. Chem. Phys. 155, 234103 (2021)] employing the so-called superposition approximation of the three-body polarizability. For temperatures above 200 K, we observed a significant discrepancy between the classical results obtained using superposition approximation and the ab initio computed polarizability. For temperatures from 10 K up to 200 K, the differences between PIMC and semiclassical calculations are several times smaller than the uncertainties of our results. Except at low temperatures, our results agree very well with the available experimental data but have much smaller uncertainties. The data reported in this work eliminate the main accuracy bottleneck in the optical pressure standard [Gaiser et al., Ann. Phys. 534, 2200336 (2022)] and facilitate further progress in the field of quantum metrology.

The ab initio potential energy curves of atom pairs and transport properties of high-temperature vapors of Cu and Si and their mixtures with He, Ar, and Xe gases

The potential energy curves (PECs) for the homonuclear He-He, Ar-Ar, Cu-Cu, and Si-Si dimers, as well as heteronuclear Cu-He, Cu-Ar, Cu-Xe, Si-He, Si-Ar, and Si-Xe dimers, are obtained in quantum Monte Carlo (QMC) calculations. It is shown that the QMC method provides the PECs with an accuracy comparable with that of the state-of-the-art coupled cluster singles and doubles with perturbative triples corrections [CCSD(T)] calculations. The QMC data are approximated by the Morse long range (MLR) and (12-6) Lennard-Jones (LJ) potentials. The MLR and LJ potentials are used to calculate the deflection angles in binary collisions of corresponding atom pairs and transport coefficients of Cu and Si vapors and their mixtures with He, Ar, and Xe gases in the range of temperature from 100 K to 10 000 K. It is shown that the use of the LJ potentials introduces significant errors in the transport coefficients of high-temperature vapors and gas mixtures. The mixtures with heavy noble gases demonstrate anomalous behavior when the viscosity and thermal conductivity can be larger than that of the corresponding pure substances. In the mixtures with helium, the thermal diffusion factor is found to be unusually large. The calculated viscosity and diffusivity are used to determine parameters of the variable hard sphere and variable soft sphere molecular models as well as parameters of the power-law approximations for the transport coefficients. The results obtained in the present work include all information required for kinetic or continuum simulations of dilute Cu and Si vapors and their mixtures with He, Ar, and Xe gases.

Transferable Force Fields from Experimental Scattering Data with Machine Learning Assisted Structure Refinement

Deriving transferable pair potentials from experimental neutron and X-ray scattering measurements has been a longstanding challenge in condensed matter physics. State-of-the-art scattering analysis techniques estimate real-space microstructure from reciprocal-space total scattering data by refining pair potentials to obtain agreement between simulated and experimental results. Prior attempts to apply these potentials with molecular simulations have revealed inaccurate predictions of thermodynamic fluid properties. In this Letter, a machine learning assisted structure-inversion method applied to neutron scattering patterns of the noble gases (Ne, Ar, Kr, and Xe) is shown to recover transferable pair potentials that accurately reproduce both microstructure and vapor-liquid equilibria from the triple to critical point. Therefore, it is concluded that a single neutron scattering measurement is sufficient to predict macroscopic thermodynamic properties over a wide range of states and provide novel insight into local atomic forces in dense monatomic systems.

Machine learning for non-additive intermolecular potentials: quantum chemistry to first-principles predictions

Prediction of thermophysical properties from molecular principles requires accurate potential energy surfaces (PES). We present a widely-applicable method to produce first-principles PES from quantum chemistry calculations. Our approach accurately interpolates three-body non-additive interaction data, using the machine learning technique, Gaussian Processes (GP). The GP approach needs no bespoke modification when the number or type of molecules is changed. Our method produces highly accurate interpolation from significantly fewer training points than typical approaches, meaning ab initio calculations can be performed at higher accuracy. As an exemplar we compute the PES for all three-body cross interactions for CO₂-Ar mixtures. From these we calculate the CO₂-Ar virial coefficients up to 5th order. The resulting virial equation of state (EoS) is convergent for densities up to the critical density. Where convergent, the EoS makes accurate first-principles predictions for a range of thermophysical properties for CO₂-Ar mixtures, including the compressibility factor, speed of sound and Joule-Thomson coefficient. Our method has great potential to make wide-ranging first-principles predictions for mixtures of comparably sized molecules. Such predictions can replace the need for expensive, laborious and repetitive experiments and inform the continuum models required for applications.

Rotational spectroscopy of the argon dimer by time-resolved Coulomb explosion imaging of rotational wave packets

We report time-domain rotational spectroscopy of the argon dimer, Ar₂, by implementing time-resolved Coulomb explosion imaging of rotational wave packets. The rotational wave packets are created in Ar₂ with a linearly polarized, nonresonant, ultrashort laser pulse, and their spatiotemporal evolution is fully characterized by measuring angular distribution of the fragmented Ar⁺ promptly ejected from Ar₂²⁺ generated by the more intense probe pulse. The pump-probe measurements have been carried out up to a delay time of 16 ns. The alignment parameters, derived from the observed images, exhibit periodic oscillation lasting for more than 15 ns. The pure rotational spectrum of Ar₂ is obtained by Fourier transformation of the time traces of the alignment parameters. The frequency resolution in the spectrum is about 90 MHz, the highest ever achieved for Ar₂. The rotational constant and the centrifugal distortion constant are determined with much improved precision than the previous experimental results: B₀ = 1.72713 ± 0.00009 GHz and D₀ = 0.0310 ± 0.0005 MHz. The present B₀ value does not match within the quoted experimental uncertainty with that from the VUV spectroscopy, so far accepted as an experimental reference to assess theories. The present improved constants would stand as new references to calibrate state-of-the-art theoretical investigations and an indispensable experimental source for the construction of an accurate empirical intermolecular potential.

First-principles determination of the solid-liquid-vapor triple point: The noble gases

We report first-principles calculations of the triple point that allow us to predict the triple point temperature of atomic fluids to an accuracy that has not been previously possible. This is achieved by proposing a molecular simulation technique that can be used for solid-liquid equilibria at arbitrarily low pressures. It is demonstrated that the triple point is significantly influenced by the choice of two-body, three-body and quantum interactions. An improved theoretical understanding of triple points is important for both science in general, and metrology in particular, as it links the Boltzmann constant and the Kelvin temperature scale to fundamental constants.

Bulk viscosity of gaseous argon from molecular dynamics simulations

The bulk viscosity of dilute argon gas is calculated using molecular dynamics simulations in the temperature range 150-500 K and is found to be proportional to density squared in the investigated range of densities 0.001-1 kg m^{-3}. A comparison of the results obtained using Lennard-Jones and Tang-Toennies models of pair interaction potential reveals that the value of the bulk viscosity coefficient is sensitive to the choice of the pair interaction model. The inclusion of the Axilrod-Teller-Muto three-body interaction in the model does not noticeably affect the values of the bulk viscosity in dilute states, contrary to the previously investigated case of dense fluids.

Theoretical modeling of molecules in weakly interacting environments: trifluoride anions in argon

The properties of molecules can be affected by the presence of a host environment. Even in inert rare gas matrices such effects are observable, as for instance in matrix isolation spectroscopy. In this work we study the trifluoride anion in cryogenic argon environments. To investigate the structure and vibrational properties of the guest-host systems, a potential energy surface of compound F-3-argon structures is determined from ab initio calculations with the CCSD(T)-F12b approach. Argon environments are probed with minima hopping optimizations of extended trifluoride-argon clusters. The vibrations of F-3 within the optimized environments are examined with anharmonic vibrational analyses. Among the three identified structural surroundings for the trifluoride, two are characterized by relatively favorable guest-host and host-host interactions as well as vibrational zero-point energies. A striking dependence of the trifluoride properties on the particular argon environment reveals the delicate influence of the host atoms on the guest molecule. Very good agreement with measured data suggests that in experiment F-3 occupies a double-vacancy site.

Path-integral calculation of the third dielectric virial coefficient of noble gases

We present a rigorous framework for fully quantum calculation of the third dielectric virial coefficient C_ɛ(T) of noble gases, including exchange effects. The quantum effects are taken into account with the path-integral Monte Carlo method. Calculations employing state-of-the-art pair and three-body potentials and pair polarizabilities yield results generally consistent with the few scattered experimental data available for helium, neon, and argon, but rigorous calculations with well-described uncertainties will require the development of surfaces for the three-body nonadditive polarizability and the three-body dipole moment. The framework, developed here for the first time, will enable new approaches to primary temperature and pressure metrology based on first-principles calculations of gas properties.

Solvation of Isoelectronic Halide and Alkali Metal Ions by Argon Atoms

This work systematically examines the interactions of alkali metal cations and their isoelectronic halide counterparts with up to six solvating Ar atoms (M⁺Ar_n and X^-Ar_n, where M = Li, Na, K, and Rb; X = H, F, Cl, and Br; and n = 1-6) via full geometry optimizations with the MP2 method and robust, correlation-consistent quadruple-ζ (QZ) basis sets. 116 unique M⁺Ar_n and X^-Ar_n stationary points have been characterized on the MP2/QZ potential energy surface. To the best of our knowledge, approximately two dozen of these stationary points have been reported here for the first time. Some of these new structures are either the lowest-energy stationary point for a particular cluster or energetically competitive with it. The CCSD(T) method was employed to perform additional single-point energy computations upon all MP2/QZ-optimized structures using the same basis set. CCSD(T)/QZ results indicate that internally solvated structures with the ion at/near the geometric center of the cluster have appreciably higher energies than those placing the ion on the periphery. While this study extends the prior investigations of M⁺Ar_n clusters found within the literature, it notably provides one of the first thorough characterizations of and comparisons to the corresponding negatively charged X^-Ar_n clusters.

Transport coefficients of isotopic mixtures of noble gases based on ab initio potentials

The transport coefficients such as viscosity, thermal conductivity, diffusion and thermal diffusion of neon, argon, krypton, and xenon are computed for a wide range of temperatures taking into consideration their real isotopic compositions. A new concept of isotopic thermal diffusion factor is introduced and calculated. The Chapman-Enskog method based on the 10th order approximation with respect to the Sonine polynomial expansion is applied. Ab initio potentials of interatomic interactions are employed to compute the transport cross-sections as they are part of the coefficient expressions. To study the influence of the isotopic composition, the same transport coefficients have been calculated for the single gases having an average atomic mass. The estimated numerical error of the present results is a function of the temperature and is different for each coefficient. At the room temperature, the relative numerical error of viscosity, thermal conductivity and diffusion coefficient is on the order of 10-6. The numerical error of the thermal diffusion factor affects the fifth decimal digit. The influence of the isotopic composition on viscosity and thermal conductivity depends on the gas species. It is negligible for argon and significant (about 0.02%) for xenon, while neon and krypton are weakly affected by the isotopic composition. The diffusion coefficient for each pair of isotopes differs from the corresponding self-diffusion coefficient by about 3%. The thermal diffusion factor of each isotope differs from the thermal self-diffusion factor in the third decimal digit.

Thermophysical properties of low-density neon gas from highly accurate first-principles calculations and dielectric-constant gas thermometry measurements

New interatomic potential energy and interaction-induced polarizability curves for two ground-state neon atoms were developed and used to predict the second density, acoustic, and dielectric virial coefficients and the dilute gas shear viscosity and thermal conductivity of neon at temperatures up to 5000 K. The potential energy curve is based on supermolecular coupled-cluster (CC) calculations at very high levels up to CC with single, double, triple, quadruple, and perturbative pentuple excitations [CCSDTQ(P)]. Scalar and spin-orbit relativistic effects, the diagonal Born-Oppenheimer correction, and retardation of the dispersion interactions were taken into account. The interaction-induced polarizability curve, which in this work is only needed for the calculation of the second dielectric virial coefficient, is based on supermolecular calculations at levels up to CCSDT and includes a correction for scalar relativistic effects. In addition to these first-principles calculations, highly accurate dielectric-constant gas thermometry (DCGT) datasets measured at temperatures from 24.5 to 200 K were analyzed to obtain the difference between the second density and dielectric virial coefficients with previously unattained accuracy. The agreement of the DCGT values with the ones resulting from the first-principles calculations is, despite some small systematic deviations, very satisfactory. Apart from this combination of two virial coefficients, the calculated thermophysical property values of this work are significantly more accurate than any available experimental data.

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→∞.

The Lennard-Jones Potential Revisited: Analytical Expressions for Vibrational Effects in Cubic and Hexagonal Close-Packed Lattices

Analytical formulas are derived for the zero-point vibrational energy and anharmonicity corrections of the cohesive energy and the mode Grüneisen parameter within the Einstein model for the cubic lattices (sc, bcc, and fcc) and for the hexagonal close-packed structure. This extends the work done by Lennard-Jones and Ingham in 1924, Corner in 1939, and Wallace in 1965. The formulas are based on the description of two-body energy contributions by an inverse power expansion (extended Lennard-Jones potential). These make use of three-dimensional lattice sums, which can be transformed to fast converging series and accurately determined by various expansion techniques. We apply these new lattice sum expressions to the rare gas solids and discuss associated critical points. The derived formulas give qualitative but nevertheless deep insight into vibrational effects in solids from the lightest (helium) to the heaviest rare gas element (oganesson), both presenting special cases because of strong quantum effects for the former and strong relativistic effects for the latter.

Conformal Analytical Potential for All the Rare Gas Dimers over the Full Range of Internuclear Distances

An analytical model for the potential between two rare gas atoms at distances between R=0 to R→∞ is assumed to be conformal with the previously published potential for He_{2} [J. Chem. Phys. 142, 131102 (2015)JCPSA60021-960610.1063/1.4916740]. The potential curves of the rare gas dimers all have the same shape and only depend on the well parameters D_{e} and R_{e}. The potentials and the vibrational levels for the 11 homonuclear and heteronuclear dimers for which recent ab initio calculations are available agree, within several percent, with the ab initio results. For the other rare gas dimers, the new potential provides the first realistic estimates for the potentials.

Vapor-liquid equilibria and cohesive r-4 interactions

The role of cohesive r^-4 interactions on the existence of a vapor phase and the formation of vapor-liquid equilibria is investigated by performing molecular simulations for the n-4 potential. The cohesive r^-4 interactions delay the emergence of a vapor phase until very high temperatures. The critical temperature is up to 5 times higher than normal fluids, as represented by the Lennard-Jones potential. The greatest overall influence on vapor-liquid equilibria is observed for the 5-4 potential, which is the lowest repulsive limit of the potential. Increasing n initially mitigates the influence of r^-4 interactions, but the moderating influence declines for n > 12. A relationship is reported between the critical temperature and the Boyle temperature, which allows the critical temperature to be determined for a given n value. The n-4 potential could provide valuable insight into the behavior of non-conventional materials with both very low vapor pressures at elevated temperatures and highly dipolar interactions.

Path-Integral Calculation of the Second Dielectric and Refractivity Virial Coefficients of Helium, Neon, and Argon

We present a method to calculate dielectric and refractivity virial coefficients using the path-integral Monte Carlo formulation of quantum statistical mechanics and validate it by comparing our results with equivalent calculations in the literature and with more traditional quantum calculations based on wavefunctions. We use state-of-the-art pair potentials and polarizabilities to calculate the second dielectric and refractivity virial coefficients of helium (both 3He and 4He), neon (both 20Ne and 22Ne), and argon. Our calculations extend to temperatures as low as 1 K for helium, 4 K for neon, and 50 K for argon. We estimate the contributions to the uncertainty of the calculated dielectric virial coefficients for helium and argon, finding that the uncertainty of the pair polarizability is by far the greatest contribution. Agreement with the limited experimental data available is generally good, but our results have smaller uncertainties, especially for helium. Our approach can be generalized in a straightforward manner to higher-order coefficients.

Exact solutions for shock waves in dilute gases

In 1922 Becker found an exact solution for shock waves in gases using the Navier-Stokes-Fourier constitutive equations for a Prandtl number of value 3/4 with constant transport coefficients. His analysis has been extended to study some cases where an implicit solution can be found in an exact way. In this work we consider this problem for the so-called soft-spheres model in which the viscosity and thermal conductivity are proportional to a power of the temperature η,κ∝T^{σ}. In particular, we give implicit exact solutions for the Maxwell model (σ=1), hard spheres (σ=1/2), and when σ (the viscosity index) is a natural number.

Molecular simulation of orthobaric isochoric heat capacities near the critical point

A molecular simulation strategy is investigated for detecting the divergence of the isochoric heat capacity (C_{V}) on the vapor and liquid coexistence branches of a fluid near the critical point. The procedure is applied to the empirical Lennard-Jones potential and accurate state-of-the-art ab initio two-body and two-body + three-body potentials for argon. Simulations with the Lennard-Jones potential predict the divergence of C_{V}, and the phenomenon is also observed for both two-body and two-body + three body potentials. The potentials also correctly predict the crossover between vapor and liquid C_{V} values and the subcritical liquid C_{V} minimum, which marks the commencement C_{V} divergence. The effect of three-body interactions is to delay the onset of divergence to higher subcritical temperatures.

Do Semilocal Density-Functional Approximations Recover Dispersion Energies at Small Intermonomer Separations?

The methods that add dispersion energies to interaction energies computed using density-functional theory (DFT), known as DFT+D methods, taper off the dispersion energies at distances near van der Waals minima and smaller based on an assumption that DFT starts to reproduce the dispersion energies there. We show that this assumption is not correct as the alleged contribution behaves unphysically and originates to a large extent from nonexchange-correlation terms. Thus, dispersion functions correct DFT in this region for deficiencies unrelated to dispersion interactions.

Predicting vapor liquid equilibria using density functional theory: A case study of argon

Predicting vapor liquid equilibria (VLE) of molecules governed by weak van der Waals (vdW) interactions using the first principles approach is a significant challenge. Due to the poor scaling of the post Hartree-Fock wave function theory with system size/basis functions, the Kohn-Sham density functional theory (DFT) is preferred for systems with a large number of molecules. However, traditional DFT cannot adequately account for medium to long range correlations which are necessary for modeling vdW interactions. Recent developments in DFT such as dispersion corrected models and nonlocal van der Waals functionals have attempted to address this weakness with a varying degree of success. In this work, we predict the VLE of argon and assess the performance of several density functionals and the second order Møller-Plesset perturbation theory (MP2) by determining critical and structural properties via first principles Monte Carlo simulations. PBE-D3, BLYP-D3, and rVV10 functionals were used to compute vapor liquid coexistence curves, while PBE0-D3, M06-2X-D3, and MP2 were used for computing liquid density at a single state point. The performance of the PBE-D3 functional for VLE is superior to other functionals (BLYP-D3 and rVV10). At T = 85 K and P = 1 bar, MP2 performs well for the density and structural features of the first solvation shell in the liquid phase.

State-of-the-art ab initio potential energy curve for the xenon atom pair and related spectroscopic and thermophysical properties

A new ab initio interatomic potential energy curve for two ground-state xenon atoms is presented. It is based on supermolecular calculations at the coupled-cluster level with single, double, and perturbative triple excitations [CCSD(T)] employing basis sets up to sextuple-zeta quality, which were developed as part of this work. In addition, corrections were determined for higher coupled-cluster levels up to CCSDTQ as well as for scalar and spin-orbit relativistic effects at the CCSD(T) level. A physically motivated analytical function was fitted to the calculated interaction energies and used to compute the vibrational spectrum of the dimer, the second virial coefficient, and the dilute gas transport properties. The agreement with the best available experimental data for the investigated properties is excellent; the new potential function is superior not only to previous ab initio potentials but also to the most popular empirical ones.

Thermophysical properties of krypton-helium gas mixtures from ab initio pair potentials

A new potential energy curve for the krypton-helium atom pair was developed using supermolecular ab initio computations for 34 interatomic distances. Values for the interaction energies at the complete basis set limit were obtained from calculations with the coupled-cluster method with single, double, and perturbative triple excitations and correlation consistent basis sets up to sextuple-zeta quality augmented with mid-bond functions. Higher-order coupled-cluster excitations up to the full quadruple level were accounted for in a scheme of successive correction terms. Core-core and core-valence correlation effects were included. Relativistic corrections were considered not only at the scalar relativistic level but also using full four-component Dirac-Coulomb and Dirac-Coulomb-Gaunt calculations. The fitted analytical pair potential function is characterized by a well depth of 31.42 K with an estimated standard uncertainty of 0.08 K. Statistical thermodynamics was applied to compute the krypton-helium cross second virial coefficients. The results show a very good agreement with the best experimental data. Kinetic theory calculations based on classical and quantum-mechanical approaches for the underlying collision dynamics were utilized to compute the transport properties of krypton-helium mixtures in the dilute-gas limit for a large temperature range. The results were analyzed with respect to the orders of approximation of kinetic theory and compared with experimental data. Especially the data for the binary diffusion coefficient confirm the predictive quality of the new potential. Furthermore, inconsistencies between two empirical pair potential functions for the krypton-helium system from the literature could be resolved.

Modeling of Manganese Atom and Dimer Isolated in Solid Rare Gases: Structure, Stability, and Effect on Spin Coupling

Structures and energies of the trapping sites of manganese atom and dimer in solid Ar, Kr, and Xe are investigated within the classical model, which balances local distortion and long-range crystal order of the host and provides a means to estimate the relative site stabilities. The model is implemented with the additive pairwise potential field based on the ab initio and best empirical interatomic potential functions. In agreement with experiment, Mn single substitution (SS) and tetrahedral vacancy (TV) occupation are identified as stable for Ar and Kr, whereas the SS site is only found for Xe. Stable trapping sites of the weakly bound Mn₂ dimer are shown to be the mergers of SS and/or TV atomic sites. For Ar, (SS + SS) and (TV + TV) sites are close in energy, whereas (SS + TV) site lies higher. The (SS + SS) accommodation is identified as the only stable site in Kr and Xe at low energies. The results are compared with the resonance Raman, electron spin resonance, and absorption spectroscopy data. Reproducing the numbers of stable sites, the calculations tend to underestimate the matrix effect on the dimer vibrational frequency and spin-spin coupling constant. Nonetheless, the level of agreement is found to be informative for tentative assignments of the complex features seen in Mn₂ matrix isolation spectroscopy.

Towards J/mol Accuracy for the Cohesive Energy of Solid Argon

The cohesive energies of argon in its cubic and hexagonal closed packed structures are computed with an unprecedented accuracy of about 5 J mol(-1) (corresponding to 0.05 % of the total cohesive energy). The same relative accuracy with respect to experimental data is also found for the face-centered cubic lattice constant deviating by ca. 0.003 Å. This level of accuracy was enabled by using high-level theoretical, wave-function-based methods within a many-body decomposition of the interaction energy. Static contributions of two-, three-, and four-body fragments of the crystal are all individually converged to sub-J mol(-1) accuracy and complemented by harmonic and anharmonic vibrational corrections. Computational chemistry is thus achieving or even surpassing experimental accuracy for the solid-state rare gases.