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A Study of the Reichardt \(E_{{\text{T}}}^{{\text{N}}} \left( {30} \right)\) Parameter using Solvent Molecular Properties Derived from Computation Chemistry and Consideration of the Kamlet and Taft α Scale of Solvent Hydrogen Bond Donor Acidities

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Abstract

Reichardt’s normalized \(E_{{\text{T}}}^{{\text{N}}} \left( {30} \right)\) parameter for solvent polarity has been analyzed in terms of properties of solvent molecules estimated from quantum–mechanical calculations of isolated solvent molecules. The analyses show that \(E_{{\text{T}}}^{{\text{N}}} \left( {30} \right)\) has a strong dependence on the partial charge on the most positive hydrogen atom in the solvent molecule, reflecting hydrogen bonding at the pendant oxygen atom of the betaine dye used to define the ET(30) scale. There are smaller, and roughly equal, dependences on the dipole moments and quadrupolar amplitudes of the solvent molecules and an inverse dependence on the solvent polarizability. These three dependences reflect the solvent polarity, that is, the ability to stabilize charge through longer-range interactions. The reason for the inverse dependence on the solvent polarizability is unclear, but a similar dependence was found previously in the analysis of the Kamlet, Abboud and Taft π* scale. The resulting equation for \(E_{{\text{T}}}^{{\text{N}}} \left( {30} \right)\) reproduces the experimental values for around 160 solvents, representing most classes of organic solvents, with a standard deviation of around 0.07 {\(E_{{\text{T}}}^{{\text{N}}} \left( {30} \right)\) values range from 0 to 1}. The Kamlet and Taft α scale of hydrogen bond donor acidities, which is, in effect, derived from the differences between the \(E_{{\text{T}}}^{{\text{N}}} \left( {30} \right)\) and π* values for a solvent, is discussed. The results of the present analyses of \(E_{{\text{T}}}^{{\text{N}}} \left( {30} \right)\) and earlier analyses of π* indicate that, while the α values capture the effect of solvent hydrogen bond donor acidity, it also contains residual dependences on other molecular properties. These residual dependences result from the differences in the dependences of the \(E_{{\text{T}}}^{{\text{N}}} \left({30} \right)\) and π* on solvent properties.

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Notes

  1. The quadrupolar amplitude is calculated as \(A = \sqrt {\sum {q_{ij} q_{ij} } } {\text{ with }}i = (x,y,z){\text{ and }}j = (x,y,z),\) where the qij are the components of the traceless quadrupole.

  2. The differences quoted refer to values calculated using density functional theory and charges derived using the CM5 charge model; those from other calculations and charge models are similar. The differences are given as \(E_{{\text{T}}}^{{\text{N}}} \left( {30} \right)_{{{\text{calc}}}} - E_{{\text{T}}}^{{\text{N}}} \left( {30} \right)_{{\exp}}\).

  3. Complex charge distributions, such as those of polyatomic molecules, are commonly represented by a series of superimposed point objects. The first is a point charge (the net charge), which is a scalar quantity, the second is the dipole, which is a vector and the third is the quadrupole, which is a tensor. Just as the dipole has no net charge, the quadrupole has no net moment. The dipole moment and quadrupolar amplitude are used here simply as quantitative measures of the scale of charge centers imbedded in the bulk solvent, the “intensity” of embedded charges. The simplest way to see the necessity for both the dipolar and quadrupolar contributions is to consider CO2, which, despite having partial charges on the O and C atoms, has a zero dipole moment, but a non-zero quadrupolar amplitude.

  4. In reference [2] the derivation is in terms of the energies of the electronic transitions but, as these lead to \(E_{{\text{T}}} \left( {30} \right)\) and π*, Eq. 6 accurately represents the α-scale.

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    W. Earle Waghorne

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Waghorne, W.E. A Study of the Reichardt \(E_{{\text{T}}}^{{\text{N}}} \left( {30} \right)\) Parameter using Solvent Molecular Properties Derived from Computation Chemistry and Consideration of the Kamlet and Taft α Scale of Solvent Hydrogen Bond Donor Acidities. J Solution Chem 49, 1360–1372 (2020). https://doi.org/10.1007/s10953-020-01002-1

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