Abstract Generated abstract
This letter corrects several formulas and conclusions in the author’s earlier article on the molecular orbital theory of diamagnetism in cyclic molecules and the magnetic anisotropy of cyclopropane. It states that specified paramagnetic tensor terms should be zero, invalidating the previous argument concerning the paramagnetism of interatomic contributions, and provides corrected expressions for the relevant diamagnetic contributions. Using a semiempirical evaluation of the Hamiltonian matrix elements with stated carbon orbital parameters, the corrected interatomic contribution to the anisotropy of the cyclopropane ring is reported as negative, with a value of minus 23.5 times 10 to the minus 6 cubic centimeters per mole.
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LETTER TO THE EDITOR
In my article (R. M. Aminova, “On the molecular-orbital theory of the diamagnetism of cyclic molecules. Calculation of the magnetic anisotropy of cyclopropane”), published in DAN, vol. 157, no. 6, 1964, the following corrections must be made.
In formulas (14), (16), and (19) one should read \((\chi_p)_{\alpha\beta} = 0\); in formula (21) one should read \(\Delta\chi_p^{\mathrm{C_3H_6}} = 0\), in connection with which the arguments concerning the paramagnetism of interatomic contributions should be regarded as invalid. Formula (12) should read:
\[ L_{\mu\nu}^{2} = (e^{2}/4\hbar^{2}c^{2})\, H_{\alpha}H_{\beta}(\mathbf{R}_{\mu}\times\mathbf{R}_{\nu})_{\alpha}(\mathbf{R}_{\mu}\times\mathbf{R}_{\nu})_{\beta}. \tag{12} \]
Then formulas (15), (18), (20) should read:
\[ (\chi_d)_{\alpha\beta} = (Ne^{2}/2\hbar^{2}c^{2}) \sum_{\mu<\nu} P_{\mu\nu} (\mathbf{R}_{\mu}\times\mathbf{R}_{\nu})_{\alpha} (\mathbf{R}_{\mu}\times\mathbf{R}_{\nu})_{\beta} \mathcal{H}_{\mu\nu}^{(0)}; \tag{15} \]
\[ (\chi_d^{A-B})_{\alpha\beta} = (Ne^{2}/2\hbar^{2}c^{2}) \sum_{\mu<\nu}^{A-B} P_{\mu A\nu B} (\mathbf{R}_{A}\times\mathbf{R}_{B})_{\alpha} (\mathbf{R}_{A}\times\mathbf{R}_{B})_{\beta} \mathcal{H}_{\mu A\nu B}^{(0)}; \tag{18} \]
\[ \Delta\chi_d^{\mathrm{C_3H_6}} = \chi_{\parallel}-\chi_{\perp} = \chi_{zz} = \frac{2Ne^{2}}{\hbar^{2}c^{2}} \sum_{\text{bonds}} \sum_{\mu<\nu}^{A-B} S_{AB}^{2}P_{\mu A\nu B}\mathcal{H}_{\mu A\nu B}^{(0)}. \tag{20} \]
If \(\mathcal{H}_{\mu A\nu B}^{(0)}\) is found semiempirically, taking \(\mathcal{H}_{ij}=0.5K(\mathcal{H}_{ii}+\mathcal{H}_{jj})S_{ij}'^{(1)}\) (\(S_{ij}'\) is the overlap integral), and adopting \(\mathcal{H}_{ii}(C\cdot 2p\sigma)=-11.17\) eV, \(\mathcal{H}_{ii}(C\cdot 2p\pi)=-9.44\) eV, \(\mathcal{H}_{ii}(C\cdot 2s)=-21.4\) eV\({}^{(2)}\), then the interatomic contribution to the anisotropy of the cyclopropane ring will be equal to
\[ \Delta\chi_d^{\mathrm{C_3H_6}}=-23.5\cdot 10^{-6}\ \mathrm{cm^3/mol}. \]
R. M. Aminova
CITED LITERATURE
\({}^{1}\) R. Hoffmann, J. Chem. Phys., 39, no. 6, 1397 (1963). \({}^{2}\) R. Mulliken, J. Chem. Phys., 2, no. 11, 782 (1934).