Abstract
The Kamlet and Taft solvent basicity parameter, β, and solvent polarity/polarizability parameter, π*, were analyzed in terms of properties of the solvent molecules derived from computational chemistry. The analysis of β, using a larger data set, confirms earlier conclusions that, for aprotic solvents, the basicity is determined by the partial charge on the most negative atom of the solvent molecule and by the energy of the highest energy molecular orbital associated with the donor site. For alcohols and nitrogen bases containing N–H moieties, the β values deviate systematically from those for the non-hydrogen bonding solvents. Analysis of the polarity/polarizability parameter, π*, shows that it depends directly on the dipole moment, and quadrupolar amplitude of the solvent and on the energy of the highest occupied molecular orbital, but decreases linearly with increasing solvent polarizability.
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Notes
Generally this was the highest occupied molecular orbital, except for aromatic compounds where the two, high energy, ring π-orbitals were excluded.
The standard deviations were recalculated from the data in Table III in [3] and differ from the precisions reported there.
In the case where both solvents i and j respond to hydrogen bonding there will be a deviation from Eq. 3 provided that the ratio of their spectroscopic responses to hydrogen bonding differs from s.
The quadrupolar amplitude is calculated as \(A = \sqrt {\sum {q_{ij} q_{ij} } };\, i = x,y,z \, j = x,y,z\) where the qij are the components of the traceless quadrupole.
Statistical parameters such as the p-value or correlation coefficient involve the assumption that the scatter of the data can be represented by the normal distribution function. The values of solvent parameters and molecular descriptors tend to cluster, those of ketones being similar, for example, and so the scatter of the data is not random and may not be described by the normal distribution.
The alkanes were an exception to this and for these the total charge on the most negative CHn group was found to correlate far better than that on the C atom.
This depends on the method used to derive the partial charges. The discussion relates to the density functional based properties and CM5 derived charges. For density functional based properties these are around 0.2 lower if Hirshfeld charges are used and 0.1 lower with NBO derived charges.
In comparing the experimental and calculated β values, the values recovered from the density functional calculations and the CM5 derived charges are used throughout, as these show the best agreement with the experimental data. Qualitatively the other values show similar trends.
The simplest example of the importance of the quadrupolar contribution is to consider CO2, which has a zero dipole moment since it is linear, but considerable separation of charges, which is reflected in the quadrupolar amplitude.
While not identical to the Lorenz–Lorentz term \({{\left( {n^{2} - 1} \right)} \mathord{\left/ {\vphantom {{\left( {n^{2} - 1} \right)} {\left( {n^{2} + 2} \right)}}} \right. \kern-\nulldelimiterspace} {\left( {n^{2} + 2} \right)}}\), this term increases similarly with increasing n and so provides a measure of the polarizability. (For an interesting history of the parallel developments of Lorenz and Lorentz, leading to their equation, see [17].
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Waghorne, W.E. A Study of Kamlet–Taft β and π* Scales of Solvent Basicity and Polarity/Polarizability Using Computationally Derived Molecular Properties. J Solution Chem 49, 466–485 (2020). https://doi.org/10.1007/s10953-020-00979-z
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DOI: https://doi.org/10.1007/s10953-020-00979-z