On the proof of the principle of maximum hardness

doi:10.1016/0009-2614(94)01210-5

Chemical Physics Letters

Volume 231, Issue 1, 16 December 1994, Pages 40-42

https://doi.org/10.1016/0009-2614(94)01210-5 Get rights and content

Abstract

It has been suggested that molecules arrange their electronic structure to be such that they have the maximum hardness, this being referred to as the principle of maximum hardness. This principle has been claimed to have been proved rigorously. We show that the proof is in error.

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Correlations between hardness, electronegativity, anomeric effect associated with electron delocalizations and electrostatic interactions in 1,4,5,8-tetraoxadecalin and its analogs containing S and Se atoms
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Citation Excerpt :
Based on the maximum hardness principle, the molecules arrange themselves to be as hard as possible. Although the maximum hardness principle has been successfully applied to the study of some chemical and physical transformations [2–16], there are various exceptions to this principle [17,18]. The concept of absolute electronegativity (χ) has been determined by Parr and co-workers [19,20].
Hybrid density functional theory (B3LYP/6-311++G^∗∗) based method and natural bond orbital (NBO) interpretation were used to investigate the correlations between the global hardness (η), global electronegativity (χ), anomeric effect associated with electron delocalization and electrostatic model associated with dipole–dipole interactions (four important conceptual descriptor in chemistry and physics) in 1,4,5,8-tetraoxadecalin (1), 1,4,5,8-tetrathiadecalin (2) and 1,4,5,8-tetraselenadecalin (3). B3LYP/6-311++G^∗∗ results showed that the calculated Gibbs free energy and corrected electronic energy differences between the cis- and trans-stereoisomers [i.e. ΔG = G_trans − G_cis, ΔE_o = E_o(trans) − E_o(cis)] decrease from compound 1 to compound 3. On the other hand, the global hardness (η) differences between the cis- and trans-stereoisomers (i.e. Δ[η_(cis) − η_(trans)]) decrease from compound 1 to compound 2 but increase from compound 2 to compound 3. Accordingly, the variation of ΔG = G_trans − G_cis, ΔE_o = E_o(trans) − E_o(cis) parameters from compound 1 to compound 3 cannot be justified by the variation of their corresponding global hardness. Therefore, compounds 2 and 3 do not obey the maximum hardness principle. Interestingly, the calculated global electronegativity (χ) differences between the cis- and trans-stereoisomers (i.e. Δ[χ_(cis) − χ_(trans)]) decrease from compound 1 to compound 3. NBO results showed that the anomeric effect associated with the electron delocalization is in favor of the cis stereoisomers. Effectively, with the decrease of the anomeric effect, ΔG = G_trans − G_cis, ΔE_o = E_o(trans) − E_o(cis) parameters decrease from compound 1 to compound 3. Therefore, the variations of the anomeric effect and global electronegativity explain the variations of ΔG = G_trans − G_cis, ΔE_o = E_o(trans) − E_o(cis) parameters from compound 1 to compound 3. It should be noted that the variation of the calculated dipole moment differences between the cis and trans stereoisomers [i.e. Δ(μ_(cis) − μ_(trans)] does not justify the variation of ΔG = G_trans − G_cis, ΔE_o = E_o(trans) − E_o(cis) parameters from compound 1 to compound 3. The total steric exchange energy differences between the cis- and trans-stereoisomers (Δ[TSEE_cis − TSEE_trans]) increase from compound 1 to compound 3 which in the trend observed for the anomeric effect and global electronegativity. The correlations between the global hardness, global electronegativity, anomeric effect, zero point energies, electrostatic model, structural parameters, corrected electronic energies (ΔE_o), and thermodynamic parameters [ΔH, ΔG and ΔS] of compounds 1–3 have been investigated.
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On the proof of the principle of maximum hardness

Abstract

J. Chem. Educ.

J. Am. Chem. Soc.

J. Chem. Phys.

J. Am. Chem. Soc.