Our Initial Issues, Revisited

In addition to giving summary answers to the two issues singled out in Chapter 1—concerning (1) what Perrin established about Brownian motion itself and (2) how the standing of molecular theory changed between 1905 and 1913—the chapter answers three further questions raised by the intervening chapters: (3) What did Perrin and Brownian motion contribute to the new standing? (4) Given that Ostwald had already come to accept molecules before he encountered Perrin’s work, what led him to do so and what did the new standing amount to in his eyes? (5) How did the success in determining values for the interlinked principal molecular constants during the period of 1905 to 1913 contribute to the reliance on evidence from complementary theory-mediated measurements of interlinked “fundamental constants” that has been at the center of research in microphysics ever since?

Converging Values for Avogadro’s Number

Perrin’s values for Avogadro’s numbers presuppose that the mean kinetic energies in Brownian motion match those of molecules in the surrounding liquid. In support of these values and the presupposition, Perrin turns to values of Avogadro’s number and mean kinetic energies of molecules obtained by means of theory-mediated measurements by Planck (from blackbody radiation), Rutherford and his colleagues (from α‎-particle radiation), and Millikan (from ionization). While Perrin’s values differed from these others, they all collectively yielded values for the molecular constants within a theretofore unachievable window of ±5 percent. This chapter assesses first the evidence for Perrin’s values from his appeals to each of these “agreeing” complementary determinations, and then the evidence that molecules exist from all of them taken together. The conclusion is that the latter warranted taking molecules to exist in ongoing research into microphysics even though the referent of the word “molecule” remained seriously underspecified.

Franck – Condon Factors And r- Centroids of D – A and D – B band systems of AlO molecule

Franck–Condon factors and r-centroids were computed for the D2S+ - A2Πi and D2S+ - B2S+ band systems of the aluminium oxide (AlO) molecule for the v' = 10; v" = 10 matrix using the method developed by Jarmain and Nicholls. The latest Fourier-transform Spectrometer molecular constants of ground and excited state are used. The intensities of these bands are discussed and the Franck–Condon factors and r-centroids obey the established relationships

Internal methyl rotation and molecular structure of trifluorotoluenes: microwave rotational spectra of 2,3,4- and 2,4,5-trifluorotoluene

The microwave rotational spectra of 2,3,4- and 2,4,5-trifluorotoluenes, along with all 13C isotopic species in natural abundance, have been recorded in the frequency range 8–27 GHz employing pulsed-jet Fourier transform microwave spectroscopy. The analysis of the spectra in the lowest torsional state has yielded the rotational constants, centrifugal distortion constants, three-fold barrier to methyl rotation, and the direction of the internal rotation axis in the moment of inertia principal axes systems of these trifluorotoluenes. For both molecules, the molecular constants of their eight isotopologues have been used to obtain the substitution rs structures of the ring and the methyl-carbon. The potential barriers hindering the internal rotation of the methyl top in 2,3,4- and 2,4,5-trifluorotluene are 2.5878(80) and 2.2809(23) kJ/mol, respectively.

SPECTROSCOPIC AND THERMOCHEMICAL PROPERTIES OF ACTINIDE-CONTAINING SPECIES FROM FIRST PRINCIPLES: THORIUM AND AMERICIUM MONOXIDE MOLECULES

A relativistic version of a composite ab initio treatment of molecular spectroscopy and thermochemistry is developed, focusing on high-accuracy description of the properties of actinide (An) containing species. It is based on combining the calculation results at levels of theory with sufficiently full account of electron correlation, e.g., at the CCSDT(Q) level, but tackling only scalar relativity, with those obtained from more rigorous four-component relativistic calculations with the Dirac–Coulomb Hamiltonian. High accuracy achievable via this approach is revealed taking the examples of thorium and americium monoxide molecules. The errors in ab initio values for the bond length re, vibrational frequency ωe, and atomization energy D0 of the ThO molecule did not exceed 0.001 Å, 2.5 cm–1, and 0.5 kcal/mol, respectively. The composite numerical values for the first ionization potentials of the AmO molecule and the Am atom deviate from the experimental data just by 0.03 eV and 1 cm–1, respectively. For the first time, the proposed approach enabled high-accuracy evaluation of the molecular constants re, ωe and D0 for AmO and AmO+, as well as the second and third ionization potentials of the Am atom. The calculation results are indicative of a minor actinide contraction of the An–O bonds on going through the molecular series ThO → UO → AmO: the bond length in AmO is by 0.0073 Å shorter than that in ThO. The re(An–O) value is shown to be linearly dependent on the actinide atomic number in the periodic table. The results obtained may be used as benchmarks for parametrizing and calibrating the DFT functionals designed for treating An-containing molecules.