Collision-induced dipole polarizability of helium dimer from explicitly correlated calculations

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.

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.

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.

DFT and spatial confinement: a benchmark study on the structural and electrical properties of hydrogen bonded complexes

An extended set of 37 exchange correlation functionals, representing different DFT approximations, has been evaluated on a difficult playground represented by the dipole moment (μ_z), polarizability (α_zz), first hyperpolarizability (β_zzz), and the corresponding interaction-induced electrical properties (Δμ_z, Δα_zz, Δβ_zzz) of spatially confined hydrogen bonded (HB) dimers. A two-dimensional harmonic oscillator potential was used to exert the effect of spatial restriction. The performance of DFT methods in predicting hydrogen bond lengths in the studied molecular complexes upon confinement has also been examined. The data determined using a high-level CCSD(T) method serve as a reference. The conducted analyses allow us to conclude that methods rooted in DFT constitute a precise tool for the calculation of μ_z and α_zz as well as Δμ_z and Δα_zz, as most of the tested functionals provide results affected by rather small relative errors. On the other hand, an accurate description of the nonlinear optical response of the studied HB systems remains a great challenge for most of the analyzed DFT functionals, both in vacuum and in the presence of an analytical confining potential. Some of the tested DFT methods are found to be prone to catastrophic failure in the prediction of β_zzz as well as Δβ_zzz. The obtained results indicate that there is no great chasm in performance between functionals belonging to different DFT approximations or functionals including different amount of Hartree-Fock exchange when the values of dipole moment and first hyperpolarizability as well as the corresponding interaction-induced electrical properties are considered. However, a higher fraction of Hartree-Fock exchange improves the quality of predictions of α_zz and Δα_zz. Additionally, it has been shown that only three functionals from the examined set, namely B2PLYP, B3LYP and ωB97X-D, provide highly accurate structural parameters for the investigated systems. Of significant importance is the conclusion that the ωB97X-D functional, representing a modern and highly parametrized range-separated hybrid, demonstrates the most coherent behavior, showing rather small deviations from the reference data in the case of μ_z, α_zz, Δμ_z and Δα_zz as well as the structural parameters of the studied HB dimers. Moreover, our results indicate that the presence of spatial confinement has a rather small effect on the performance of DFT methods.

Highly-accurate density-virial-coefficient values for helium, neon, and argon at 0.01 ○C determined by dielectric-constant gas thermometry

The dielectric-constant gas thermometer of Physikalisch-Technische Bundesanstalt (PTB) developed for measuring the Boltzmann constant with a relative uncertainty of 1.9 parts per million was used for determining the virial coefficients of the three noble gases, helium, neon, and argon, at the triple point of water (0.01 ^○C). For this purpose, isotherms were measured up to a maximum pressure of 7 MPa. The evaluation of the highly accurate data by fitting is required to derive an extended working equation for the dependence of the gas pressure on the dielectric constant. The following values have been obtained for the second B and third C virial coefficients, with the standard uncertainties given in parentheses as a multiple of the last digit, considering literature data for the dielectric virial coefficients: helium: B_DCGT ^He0.01 ^○C=11.925715 cm³/mol, C_DCGT ^He0.01 ^○C=113.4958 cm⁶/mol²; neon: B_DCGT ^Ne0.01 ^○C=10.994528 cm³/mol, C_DCGT ^Ne0.01 ^○C=215.815 cm⁶/mol²; argon: B_DCGT ^Ar0.01 ^○C=-21.233144 cm³/mol, C_DCGT ^Ar0.01 ^○C=1143.339 cm⁶/mol². These values are compared with the results of the latest ab initio calculations of the second and third virial coefficients.

Refractive-index gas thermometry

The principles and techniques of primary refractive-index gas thermometry (RIGT) are reviewed. Absolute primary RIGT using microwave measurements of helium-filled quasispherical resonators has been implemented at the temperatures of the triple points of neon, oxygen, argon and water, with relative standard uncertainties ranging from 9.1 × 10-6 to 3.5 × 10-5. Researchers are now also using argon-filled cylindrical microwave resonators for RIGT near ambient temperature, with relative standard uncertainties between 3.8 × 10-5 and 4.6 × 10-5, and conducting relative RIGT measurements on isobars at low temperatures. RIGT at optical frequencies is progressing, and has been used to perform a Boltzmann constant measurement at room temperature with a relative standard uncertainty of 1.2 × 10-5. Uncertainty budgets from implementations of absolute primary microwave RIGT, relative primary microwave RIGT and absolute primary optical RIGT are provided.

Accurate High-Pressure Measurements of Carbon Monoxide's Electrical Properties

Accurate measurements of carbon monoxide's electrical properties were carried out at high pressure for the first time enabling stringent comparisons with theoretical values calculated ab initio. Dielectric permittivity measurements were conducted utilising a microwave re-entrant cavity resonator over the temperature range from (255 to 313) K and at pressures up to 8 MPa with a relative combined expanded uncertainty (k=2) less than or equal to 52 ppm. The new data enable carbon monoxide's molar polarizability to be correlated within 0.5 %, significantly improving upon existing literature data, which have a relative scatter of about 10 %. The measured molecular polarizability and electric dipole moment of carbon monoxide were determined to be 2.176×10^-40  C²  m²  J^-1 and 0.107 D. Literature values from ab initio calculations for these properties are within 0.28 % and 3.9 %, respectively, of the measured quantities. Moreover, our measurement of the electric dipole moment at finite temperature agrees within 2.2 % with the value derived from accurate spectroscopic measurements for the ground rovibrational state. The second dielectric virial coefficient of carbon monoxide was determined experimentally for the first time to be b_ϵ =(1.015±0.044) cm³  mol^-1 , which compares reasonably with ab initio estimates.

Accurate virial coefficients of gaseous krypton from state-of-the-art ab initio potential and polarizability of the krypton dimer

We have developed a new krypton-krypton interaction-induced isotropic dipole polarizability curve based on high-level ab initio methods. The determination was carried out using the coupled-cluster singles and doubles plus perturbative triples method with very large basis sets up to augmented correlation-consistent sextuple zeta as well as the corrections for core-core and core-valence correlation and relativistic effects. The analytical function of polarizability and our recently constructed reference interatomic potential [J. M. Waldrop et al., J. Chem. Phys. 142, 204307 (2015)] were used to predict the thermophysical and electromagnetic properties of krypton gas. The second pressure, acoustic, and dielectric virial coefficients were computed for the temperature range of 116 K-5000 K using classical statistical mechanics supplemented with high-order quantum corrections. The virial coefficients calculated were compared with the generally less precise available experimental data as well as with values computed from other potentials in the literature {in particular, the recent highly accurate potential of Jäger et al. [J. Chem. Phys. 144, 114304 (2016)]}. The detailed examination in this work suggests that the present theoretical prediction can be applied as reference values in disciplines involving thermophysical and electromagnetic properties of krypton gas.

Two-photon absorption of the spatially confined LiH molecule

In the present contribution we study the influence of spatial restriction on the two-photon dipole transitions between the X¹Σ⁺ and A¹Σ⁺ states of lithium hydride. The bond-length dependence of the two-photon absorption strength is also analyzed for the first time in the literature. The highly accurate multiconfiguration self-consistent field (MCSCF) method and response theory are used to characterize the electronic structure of the studied molecule. In order to render the effect of orbital compression we apply a two-dimensional harmonic oscillator potential, mimicking the topology of cylindrical confining environments (e.g. carbon nanotubes, quantum wires). Among others, the obtained results provide evidence that at large internuclear distances the TPA response of lithium hydride may be significantly enhanced and this effect is much more pronounced upon embedding of the LiH molecule in an external confining potential. To understand the origin of the observed variation in the two-photon absorption response a two-level approximation is employed.

Frequency-dependent polarizability of helium including relativistic effects with nuclear recoil terms

Future metrology standards will be partly based on physical quantities computed from first principles rather than measured. In particular, a new pressure standard can be established if the dynamic polarizability of helium can be determined from theory with an uncertainty smaller than 0.2 ppm. We present calculations of the frequency-dependent part of this quantity including relativistic effects with full account of leading nuclear recoil terms and using highly optimized explicitly correlated basis sets. A particular emphasis is put on uncertainty estimates. At the He-Ne laser wavelength of 632.9908 nm, the computed polarizability value of 1.39181141 a.u. has uncertainty of 0.1 ppm that is 2 orders of magnitude smaller than those of the most accurate polarizability measurements. We also obtained an accurate expansion of the helium refractive index in powers of density.