Polarization differences between isotopic molecules

Abstract

This paper constitutes a brief report on the determination of dipole moment differences by a differential dielectric constant method. The results are sufficiently precise to be compared with the corresponding differences obtained with modern spectroscopic techniques. It is shown that the two sets of results are concordant if-and only if-Van Vleck's equation for electric polarization is used.Over forty years have elapsed since Van Vleck [l, 21 derived the classical Debye equation for electric polarization from quantum mechanical principles. Debye's familiar equation for a dilute polar gas is:The total molar polarization P is conventionally separated into the temperatureindependent "distortion polarization" PE+A and the "orientation polarization" POR, which is linear in the reciprocal temperature. It expresses the inherently macroscopic quantity, P, determined by the bulk dielectric constant E and the molar volume Pin terms of the mean molecular polarizability a and the molecular dipole moment p.Van Vleck confirmed Equation (1) for the quantum-mechanical rotating oscillator, for which ,u is no longer the fixed dipole moment of a rigid rotator but poo, the expectation value for the lowest vibrational level (ui = 0 for all i) of the non-rotating molecule (J = 0). He also showed that, if rotational quantization is taken into account, a third term must be added to Equation (1

The role of electrostatic induction in secondary isotope effects on acidity: theory and computational confirmation

“…The dipole moment derivative of HCl is positive, 18,19 i.e., m increases as the bond is stretched and decreases as it contracts. The charge-dipole interaction is attractive, so the potential energy of the vibrating bond decreases during expansion and increases during compression.…”

“…3.2.2 The effect of hydration. One monohydrate (15) and two dihydrates (16,17) of the acetate ion were optimized, as were one monohydrate (18) and two dihydrates (19,20) of acetic acid. The computation of trihydrates -let alone tetrahydrateswould have been excessively time consuming.…”