Unrestricted Hartree‐Fock calculations of spin densities with orthogonalized atomic orbitals: Proton and ¹³C hyperfine splittings in some pi hydrocarbon radicals

Abstract

AbstractsThe spin density distribution in a few hydrocarbon radicals has been calculated using orthogonalized atomic orbitals in the Unrestricted Hartree-Fock formalism of Amos and Snyder and including certain more important two-electron hybrid and exchange integrals and all the core-resonance integrals. Our calculated spin densities for the cation and anion radicals of alternant hydrocarbons, which are now different due to the breakdown of the pairing theorem, are, in general, of the right relative order so that even the simple McConnell type of relation can account partly for the observed differences in the proton splittings between cations and anions. The proton splittings for position 2 of naphthalene and anthracene radical ions are correctly predicted, thus clearing up the well-known cation-anion anomaly for this position. Comparative calculations have been made to show that the spin density results are worsened with the neglect of the integrals of the type mentioned before. An empirical analysis correlating the observed 13C splittings and the spin density results over a non-orthogonal basis set shows that the available 13C splittings in alternant hydrocarbon radical ions can be explained with a set of sigma-pi parameters which are consistent with the theory. It is shown that even though the spin densities in cations and anions may be different, these can lead to similar 13C splittings.La distribution de la densitt de spin dans quelques radicaux d'hydrocarbures a t t t calculte avec des orbitales atomiques orthogonaliskes dans le formalisme de Hartree-Fock sans restrictions de Amos et Snyder; certaines inttgrales importantes d'hybride et d'tchange et toutes les inttgrales de rtsonance de coeur ont t t t inches. Nos densitts de spin pour les cations et les anions des radicaux des hydrocarbures alternants, qui sont maintenant difftrentes, parce que le "thtortme des paires" n'est plus valable, sont en gtnkral dans I'ordre relatif correct. En constquent meme la relation simple de McConnell peut rendre compte partiellement des differences observtes dans les dtcompositions protoniques entre les cations et les anions. Ces dtcompositions sont prtdites correctement pour la position 2 des ions du n a p h t a h e et de I'anthractne ce qui clarifie l'anomalie bien connue de cette position-la.Des calculs comparatifs ont t t t faits pour montrer que les densitts de spin deviennent pires, si l'on neglige les inttgrales mentionntes. Une analyse empirique, corrtlant les dtcompositions observtes de 13C et les densitts de spin obtenues d'une base non-orthogonale, montre que les dtcompositions connues de 13C dans les ions des radicaux des hydrocarbures alternants peuvent &tre expliqutes avec un nombre de paramttres sigmapi, qui sont conformes A la thtorie. I1 est demontrt que m&me si les densitts de spin peuvent Die Spindichteverteilung in einigen Kohlenwasserstoffradikalen ist mit orthogonalisierten Atomorbitalen im Rahmen der uneingeschrankten Hartree-Fock-Formalismus von Amos und Snyder berechnet worden, wobei gewisse wicht...

Approximate valence‐shell electron unrestricted Hartree‐Fock calculations with orthogonalized atomic orbitals: Proton hyperfine splittings in benzyl and related radicals

“…In order to satisfy the invariance requirements under the rotation of molecular coordinate axes while using Equation (6), the terms Sij(l -Sij) appearing in this equation were first calculated in a local relative coordinate system situated on the two atoms to which the orbitals i a n d j , respectively, belong and were then transformed [36] to the corresponding quantities in the molecular coordinate system. The core elements &'s over the OAO basis were obtained by transformation [13] of Hij's obtained using Equations (4) and (6).…”

“…As mentioned earlier, the spin density matrix p over the completely localized Slater-type AO'S obtained by transformation [13] of over the OAO'S was used in the calculation of proton hyperfine splittings. The expression for the Fermicontact splitting for the nucleus N in terms of the elements of the spin density where Xi(rN) denotes the value of the Slater-type AO xi at the nucleus N .…”

“…While estimating the core attraction integrals involving 3d-orbitals on atom A, yAB was calculated with (Fo(dd) + YBB) replacing (Fotii) + F o b ) ) in Equation (12). Equation ( 5 ) together with the values of kinetic energy integrals Tii (see below) led to the estimate of the one-center quantities V f in Equation (13). I t may be noted that Equation (13) has the correct behaviour at large distances and at R A B = 0.…”