## THE SPACING AND SEQUENCE OF THE LOWEST $\eta-\pi$ ELECTRONIC LEVELS IN N-HETEROCYCLICS

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Ohio State University##### Abstract:

``Naive''} LCAO-MO theory applied to the $\eta-\pi$ transitions in pyridine predicts that the allowed transition is at a longer wavelength than the forbidden one. This prediction, which is rigorous within the framework of the naive method, not depending upon parameter values, has placed a dilemma in the way of theoretical interpretation of $\eta-\pi$ transitions, for the observed transitions are in the reverse order. ASMO theory shows however that excitation energies are given by an orbital energy difference plus a set of electron interaction terms between the vacated and excited orbitals. \Delta{E}^{1,3}=\epsilon_{\pi^{*}}-\epsilon_{\eta}-({J}_{\eta\pi^{*}}-{K}_{\eta\pi^{*}})\pm{K}_{\eta\pi^{*}} Here $\epsilon_{\pi^{*}}-\epsilon_{\eta}$ is the orbital energy difference, ${J}_{\eta\pi^{*}}$ and ${K}_{\eta\pi^{*}}$ are coulomb and exchange integrals taken over the excited $\pi$ MO and the $\sigma$ type AO, $\eta$. In the forbidden case, $\pi^{*}$ has ${A}_{2}$ symmetry (possessing a node through the nitrogen), and in the allowed case, ${B}_{2}$ symmetry (no node through the nitrogen). Use of the inequality, (\eta{N}:\eta{N})>>(\eta{K}:\eta{K}^{\prime}), where N refers to the nitrogen $2\rho\pi$AO, and K to any of the carbon $\pi$ AO’s, provides the following inequality: ({J}_{\eta\pi}{^{*}_{{A}_{2}}}-2{K}_{\eta\pi}{^{*}_{{A}_{2}}})>({J}_{\eta\pi}{^{*}_{{B}_{2}}}-2{K}_{\eta\pi}{^{*}_{{B}_{2}}}) This latter relation then opposes the corresponding orbital energy inequality, making theory consistent with the observed transition order. The split in the $\eta-\pi$ singlet and triplet levels may be approximated by $2{a}_{\pi}^{2}*_{\eta}(\eta{N}:\eta {N})$ predicting a very small split in the forbidden transition, but an appreciable one in the allowed transition. These considerations have been extended to the diazines. This work was prompted by a valuable discussion with Dr. Michael Kasha.

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$^{*}$Work done under a contract between the Office of Scientific Research, Air Research and Development Command, and the Florida State University.

Author Institution: Department of Chemistry, Florida State University; Department of Chemistry, Iowa State College

Author Institution: Department of Chemistry, Florida State University; Department of Chemistry, Iowa State College

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