Improved Partition Functions and Related Thermochemical Quantities for the 16O2 and H216O Molecules

Accurate temperature-dependent ideal-gas internal partition functions, Qint(T), and several derived thermochemical functions are reported for heavy water, with an oxygen content corresponding to the isotopic composition of Vienna Standard Mean Ocean Water (VSMOW), and its constituent isotopologues, D216O, D217O, and D218O, for temperatures between 0 and 6000 K. The nuclear-spin-dependent partition functions are obtained by the direct summation technique, involving altogether about 16 000 measured and more than nine million computed bound rovibrational energy levels for the three molecules. Reliable standard uncertainties, as a function of temperature, are estimated for each thermochemical quantity determined, including the enthalpy, the entropy, and the isobaric heat capacity of the individual nuclear-spin-equilibrated isotopologues and of heavy water. The accuracy of the heavy-water ideal-gas Cp(T) is unprecedented, below 0.01% up to 1800 K. All the thermochemical functions are reported, in 1 K increments, in the supplementary material.

A much improved temperature-dependent ideal-gas internal partition function, Qint(T), of the H216O molecule is reported for temperatures between 0 and 6000 K. Determination of Qint(T) is principally based on the direct summation technique involving all accurate experimental energy levels known for H216O (almost 20 000 rovibrational energies including an almost complete list up to a relative energy of 7500 cm−1), augmented with a less accurate but complete list of first-principles computed rovibrational energy levels up to the first dissociation limit, about 41 000 cm−1 (the latter list includes close to one million bound rovibrational energy levels up to J = 69, where J is the rotational quantum number). Partition functions are developed for ortho- and para-H216O as well as for their equilibrium mixture. Unbound rovibrational states of H216O above the first dissociation limit are considered using an approximate model treatment. The effect of the excited electronic states on the thermochemical functions is neglected, as their contribution to the thermochemical functions is negligible even at the highest temperatures considered. Based on the high-accuracy Qint(T) and its first two moments, definitive results, in 1 K increments, are obtained for the following thermochemical functions: Gibbs energy, enthalpy, entropy, and isobaric heat capacity. Reliable uncertainties (approximately two standard deviations) are estimated as a function of temperature for each quantity determined. These uncertainties emphasize that the present results are the most accurate ideal-gas thermochemical functions ever produced for H216O. It is recommended that the new value determined for the standard molar enthalpy increment at 298.15 K, 9.904 04 ± 0.000 01 kJ mol−1, should replace the old CODATA datum, 9.905 ± 0.005 kJ mol−1.

The W2020 database of validated experimental transitions and accurate empirical energy levels of water isotopologues, introduced in the work of Furtenbacher et al. [J. Phys. Chem. Ref. Data 49, 033101 (2020)], is updated for H216O and newly populated with data for H217O and H218O. The H217O/H218O spectroscopic data utilized in this study are collected from 65/87 sources, with the sources arranged into 76/99 segments, and the data in these segments yield 27 045/66 166 (mostly measured) rovibrational transitions and 5278/6865 empirical energy levels with appropriate uncertainties. Treatment and validation of the collated transitions of H216O, H217O, and H218O utilized the latest, XML-based version of the MARVEL (Measured Active Rotational-Vibrational Energy Levels) protocol and code, called xMARVEL. The empirical rovibrational energy levels of H217O and H218O form a complete set through 3204 cm−1 and 4031 cm−1, respectively. Vibrational band origins are reported for 37 and 52 states of H217O and H218O, respectively. The spectroscopic data of this study extend and improve the data collated by an International Union of Pure and Applied Chemistry Task Group in 2010 [J. Tennyson et al., J. Quant. Spectrosc. Radiat. Transfer 110, 2160 (2010)] as well as those reported in the HITRAN2016 information system. Following a minor but significant update to the W2020-H216O dataset, the joint analysis of the rovibrational levels for the series H216O, H217O, and H218O facilitated development of a consistent set of labels among these three water isotopologues and the provision of accurate predictions of yet to be observed energy levels for the minor isotopologues using the combination of xMARVEL results and accurate variational nuclear-motion calculations. To this end, 9925/8409 pseudo-experimental levels have been derived for H217O/H218O, significantly improving the coverage of accurate lines for these two minor water isotopologues up to the visible region. The W2020 database now contains almost all of the transitions, apart from those of HD16O, required for a successful spectroscopic modeling of atmospheric water vapor.

Accurate, empirical rovibronic energy levels, with associated uncertainties, are determined for the lowest seven electronic states of the 16O2 molecule using the MARVEL (Measured Active Rotational-Vibrational Energy Levels) algorithm. After careful analysis and validation of 30 671 rovibronic transitions (including 24 376 measured and 6295 artificial transitions), collected from 91 publications, 4279 empirical rovibronic energy levels are determined. The highly accurate empirical (MARVEL) energy database is then augmented with rovibronic energies obtained from accurate effective Hamiltonians for the lowest six electronic states, establishing a hybrid database containing 15 946 rovibronic energy levels. Based on this hybrid database, complete up to the first dissociation limit, 41 260 cm−1, an accurate temperature-dependent ideal-gas partition function, Qint(T), and some related thermochemical functions [isobaric heat capacity, Cpo(T), entropy, So(T), and (absolute) enthalpy, Ho(T)] are derived for 16O2 employing the direct-summation technique. All thermochemical functions are reported, in 1 K increments up to 5000 K, in the supplementary material to this paper.

The far infrared absorption spectra of D216O, D217O, and D218O are analyzed with improved accuracy and sensitivity in the 50–720 cm−1 range corresponding to the rotational band. Four room-temperature absorption spectra of highly deuterated water vapor were recorded at the SOLEIL synchrotron by high-resolution Fourier transform spectroscopy. Line centers are reported with a typical accuracy of 5 × 10−5 cm−1 for well isolated lines. The combined line list of about 9700 water lines was assigned to about 10 400 transitions of the nine stable water isotopologues (H2XO, HDXO, D2XO, with X = 16, 17, and 18). A total of 2885 transitions of eight bands involving the first five vibrational states were assigned to D216O. Among them, 2057 are newly reported. The obtained set of transition frequencies was merged with literature data to generate a new set of empirical energy levels for the first five vibrational states of D216O. A total of 1089 transitions of the (000)–(000) and (010)–(010) bands were measured for D217O. They were merged with literature sources to derive 724 empirical term values of seven vibrational states, up to 8088 cm−1. 348 D217O levels are newly determined. A set of 1150 transitions belonging to the (000)–(000) and (010)–(010) bands was measured for D218O. 3451 empirical energies of rotation–vibration levels up to 9222 cm−1 were retrieved using our observations and literature sources. The extension and accuracy of the derived empirical energy levels allow us to recommend new line lists with empirically corrected line positions for D216O, D217O, and D218O.

The far-infrared spectrum of 18O enriched water vapour (40–700 cm−1)

Validation tests of the W2020 energy levels of water vapor

The accepted values of the fundamental atomic constants are largely based on indirect measurements rather than those of the constants themselves. Certain relations lead to quantities which can be evaluated with high precision and the use of selected measurements of this sort gives the values of the constants as we know them today.

Fundamental physical constants govern key effects in high-energy particle physics and astrophysics, including the stability of particles, nuclear reactions, formation and evolution of stars, synthesis of heavy nuclei and emergence of stable molecular structures. Here, we show that fundamental constants also set an upper bound for the frequency of phonons in condensed matter phases, or how rapidly an atom can vibrate in these phases. This bound is in agreement withab initiosimulations of atomic hydrogen and high-temperature hydride superconductors, and implies an upper limit to the superconducting transition temperatureTcin condensed matter. Fundamental constants set this limit to the order of 102-103K. This range is consistent with our calculations ofTcfrom optimal Eliashberg functions. As a corollary, we observe that the very existence of the current research of findingTcat and above 300 K is due to the observed values of fundamental constants. We finally discuss how fundamental constants affect the observability and operation of other effects and phenomena including phase transitions.

Every four years, the CODATA Task Group on Fundamental Constants presents tables of recommended values of the fundamental physical constants. Recently, 2010 CODATA recommended values (Mohr P J, Taylor B N, and Newell D B “CODATA recommended values of the fundamental physical constants: 2010” Rev. Mod. Phys. 84 1527 (2012)), based on global data up to 31 December 2010, were published. In the present review, we briefly analyze the new recommended values, as well as new original data, on which the determination is based. To facilitate the consideration, the data are subdivided into several groups. New original theoretical and experimental results are discussed for each group separately. Special attention is paid to experimental and theoretical progress in the determination of the Rydberg constant , the electron–proton mass ratio , the fine-structure constant , the Planck constant , the Boltzmann constant , the Newtonian constant of gravitation , and the anomalous magnetic moment of the muon . In conclusion, the prospects of redefining units of the International System (SI) in terms of fundamental physical constants, which is currently under active discussion by the metrological community, are considered. The very possibility and efficiency of a practical realization of such a scenario with the redefinition directly depends on the status of the determination of the fundamental constants.

Precision experiments and fundamental physics at low energies – Part I

Hot line lists for two isotopologues of water, \octo\ and \heto, are presented. The calculations employ newly constructed potential energy surfaces (PES) which take advantage of a novel method for using the large set of experimental energy levels for \hato\ to give high quality predictions for \octo\ and \heto. This procedure greatly extends the energy range for which a PES can be accurately determined, allowing accurate prediction of higher-lying energy levels than are currently known from direct laboratory measurements. This PES is combined with a high-accuracy, {\it ab initio} dipole moment surface of water in the computation of all energy levels, transition frequencies and associated Einstein A coefficients for states with rotational excitation up to $J=50$ and energies up to 30~000 \cm. The resulting HotWat78 line lists complement the well-used BT2 \hato\ line list (Barber et.al, 2006, MNRAS, {\bf 368}, 1087). Full line lists are made available in the electronic form as supplementary data to this article and at \url{www.exomol.com}.

In July 1976, some thirty young scientists and their lecturers were privileged to participate in a conference on "Metrology and the Fundamental Constants" at Varenna, this being the 68th course in the "Enrico Fermi International School of Physics". Now, at last, we are all privileged to share in that experience—to a large degree—with the appearance of the Proceedings, published last summer under the auspices of the Italian Physical Society.This rather massive volume (800 pages) places in one's hands a summary of the "state of the art" in the greater part of physical metrology. It is not, however, a metrology handbook, designed to assist the unskilled in making trustworthy measurements. It summarizes, via the lectures of internationally-recognized experts, the most recent attempts to realize with enhanced accuracy the basic units of measurement and, in so doing, it presents the subject of measurement science as the central (or all-pervasive) topic in physics itself. Clearly demonstrated is the progress from discovery to "understanding" of physical phenomena which is made possible through the historical alternation of observation and measurement.The volume includes informative reviews of the fundamentals of this fundamental science, namely, the concepts of quantities and units (Allisy); systems of units and the Système International, SI. (Terrien); international aspects of metrology and standards (Terrien); practical considerations in a hierarchy of standards (Terrien); materials problems affecting metrology (Ferro Milone and Sourdo) and statistical methods (Allisy). These discussions alone, being brought together in one place, are of particular usefulness.The remaining, and major, part of the book is taken up by authoritative and generally very readable discussions of measurement topics, for the most part separately focused on one of the base units. For these one cannot help noticing nor refrain from recording a measure of imbalance: some quantities (for example, time and frequency) are accorded several lectures and lecturers, while most receive only one each. That choice by the conference's organizers is not explained in the Foreword. But it is not a very serious drawback; nor—for the anglophone reader, at least—is the appearance here and there of quaint inventions in English which, in fact, add to the charm.There are short articles on the Determination of Atomic Masses of Nuclides (Wapstra), some Problems in Photometry (Korte); two by A Bray on Force Standards, one dealing with Dissemination and the other with Measurement of "g"; Time Scales (Leschiutta); determining the Volume of a Sphere (Terrien); and two by Giacomo, one commenting on Mass Measurements and one discussing the Speed of Light. Of intermediate length are reviews of the Determination of Best Values of the Fundamental Physical Constants (Cohen); Length Measurement Standards (Giacomo), and Topics in Quantum Electrodynamics (Combley and Picasso).The extended treatment of time and frequency metrology includes three major articles by Audoin: a general (largely analytical) one on Frequency Metrology, followed by detailed discussions of Cesium Beam and Hydrogen Maser technology. There are, in addition, specialized treatments of Optically-Pumped Microwave Devices (Arditi) and of Optical Frequency Standards (i.e., lasers) by Chebotayev; finally, a brief note by De Marchi on Problems in Frequency Synthesis in the far Infrared Region. A long article by Petley covers the many-faceted subject of Electrical Metrology and the Fundamental Constants. Equally variegated, although belied by its simple title, is a discussion of Thermometry by Quinn. And last, but not least, is a detailed account by Deslattes of his determination of Avogadro's Constant which ranges over the topics of Infrared to Gamma-ray Reference Wavelengths, Mass and Density.In summarizing it is difficult to avoid the assertion, however hackneyed, that no physicist can afford to be without—or, at least, do without reading—a copy of these Proceedings.

A full lattice dynamical method has been applied to the calculation of the oxygen isotopic partition function ratio for α-quartz in order to examine the result of the Debye-Einstein model calculation. The modified Urey-Bradley force field was used as a force field model of α-quartz. The phonon dispersion curves and elastic constants of α-quartz have also been calculated. These calculated values are in fairly good agreement with the available experimental data. The agreement gives additional grounds for the use of the modified Urey-Bradley force field. The wave vector-dependence of Infqtz(q) has been examined along the x, y, and z directions in the Brillouin zone. It has been found that the Infqtz(q) little changes with the wave vector. The changes of the Infqtz(q) along the three directions are only less than 0.5% at 0°C, although the value of Infqtz(q) becomes a minimum at the Brillouin zone center. By virtue of the small wave-vector dependence of Inqtz(q), the reduced partition function ratio for α-quartz given by the direct summation technique converges very rapidly. The reduced partition function ratio for α-quartz has been evaluated in the temperature range between 0 and 550°C by means of the direct summation technique combined with the perturbation method. The obtained values of the oxygen isotope fractionation factor between α-quartz and liquid water below 100°C can be expressed as 103Inαqtz-H2O(1) = -17.287+8.6913(103/T) + 1.8459(103/T)2. This temperature scale gives only 1-1.5 ‰ higher fractionations than that of the earlier Debye-Einstein model calculation. When the small differences of the fractionations between the present and earlier calculations and the error associated with the theoretical calculation are taken into consideration, the Debye-Einstein approximation in evaluating the isotopic partition function ratio for α-quartz can be concluded not to bias seriously the result.

Quantum Metrology and Fundamental Physical Constants