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The spin density delocalization and the exchange interaction in N,N′-dioxy-2,6-diazoadamantane
1 November 1977
CHEMICAL PHYSICS LETTERS
Volume 5 1, number 3
THE SPIN DENSITY DELOCALIZATION
AND THE EXCHANGE INTERACTION
IN N,N’-DIOXY-2,6-DIAZOADAMANTANE
R.N. MUSIN and P.V. SCHASTNEV Institute of Chemical Kinetics ant! Combustion. Novosibirsk 630090. USSR Received 3 December 1976 Revised manuscript received 22 June 1977
The contribution to the exchange integral, resulting from a direct overlap of the n-orbitals of >NO fragments and from the spin density deloca!ization to the adamautane core, has been calculated. The delocalization is of primary importante. in the exchange interaction and does not signify in the spin-spin interaction.
in ref. [l] it has been found by the ESR technique that the N,N’-diazoadamantane biradical (see fig. 1) has the triplet state as ground, the exchange integral J = 85 K in the spin hamiltonian H = -2Js,-&, . When the biradical configuration is DZd, the N-O bonds he on the same straight line. The unpaired electrons are located, in general, at the antibonding n-orbitals of the >NO fragments whose planes are mutually orthogonal. According to refs. [2,3], if the unpaired electron orbitals are orthogonal, J is positive and defined only by electron interaction. This simplifies theoretical calculations. The purpose of the present work is to clear up the effect of the direct exchange interaction of >NO radical centers and the role of the “indirect” exchange interaction resulting from partial delocalization of the unpaired eIectrons to the adamantane core. When estimating the direct contribution, account was taken of only the spin densities of the n-orbitah
of >NO fragments. According to ref. [3], for mutua!ly orthogonal radical orbitals the exchange integral may be given as
(1) where the indices p, u, o, r denote the atomic orbitals (AO’s) of the fragments, p (1) * ~~~$~ ::I trix of the first fragment. Gurl ~~e~~ tation is used. The direct exchange (Jo) caIcularions were made for the spin densities obtained for H,NO by the INDO technique in the unrestricted Hartree-Fock (UHF) approximation. The gaussian expansions of the AO’s and the method given in ref. [4] were used to calculate the (~.~rlav) integrals. The value of JO depends significantly on the A0 approximation_ As AO’s we used: (1) HF AO’s with the gaussian 2p - 7(2pG) approximation [5 ] , (2) AO’s with a proper atomic asymptotics, cp(r) N- exp (-w), cr = (201j2, Iis the atomic ionization potential in au, (3) AO’s with asymptote corresponding to the ionization potential I = 6.8 eV of nitrogen oxide radicals [6]. The data obtained for the molecular asymptote should be treated as the upper estimate of Jo. The results of the Jo (in K) calculations for the above cases are: (1) 0.03(0.12),
(2) 0.05(0.22),
(3) 0.57(4.33).
The integrals calculated Fig. 1.
for the unpaired electron orbitals are given in parentheses. The calculated values 487
Volume
51, number
3
CHEhlICAL
PHYSiCS
are much less than the experimental ones, i.e. the direct exchange interaction of the >NO fragments in biradicals is not the principal contribution to the exchange effect observed_ Let us estimate the contribution to J associated with the spin density delocalization to the adamantane core. Among the core atoms, the 4 P-carbon atoms have the greatest spin density (see fig. 1). Therefore, one should expect that the principal contribution to J is made by the intra- and interatomic exchange interaction on the &carbons. When estimating the delocalization contribution, we used pzz obtained for the unpaired electron orbit& calculated by the INDO technique, the Slater functions and semi-empirical values of the intra-atomic integrals [7] _ The values of pti) are perhaps somewhat lowered since the hyperfi~~ isotropic interaction constant with 13C is less than that expected by the factor of 1 S. The intra-atomic contribution calculated is +59.1 K, the interatomic contribution is +0.2 K. For the latter, a considerable compensation of the components associated with integrals of the type (r.~~~~/v~o~)(-S.l K) and (~17~1 u’vl) (+5.3 K) is observed (1,2 - atomic index). Note that the estimate of J using the results of ref. [8] (which takes into account only spin polarization of the bridge groups) gives J = 1 K.
488
LETTERS
I-November
1977
Thus, the delocalization mechanism is of principal importance for the exchange interaction in the biradical considered and, evidently, for other biradicals with the same structure_ It is interesting to note that the delocalization contribution of P-carbons to the spin-spin interaction constant D calculated using the Slater orbitals [9] equals 5.52 G. Since the experimental value of D = 150 G, the delocalization effects are negligible in the spin-spin interaction_
References R-M. Dupeure, A. Rassat and J. Ronzand, J. Am. Chem. Sot. 96 (1974) 6559. I21 P.-O. LEwdin, Rev. Mod. Phys. 34 (1962) 80. [31P.V. Schastnev and KM. Salikhov, Russ. J. Theoret. Exper. Chem. 9 (1973) 291. I41 H. Taketa and S. Huzinaga, J. Phys. Sot. Japan 11 (1966) 2313. 151 C. SaJez and A. Veillard, Theoret. Chim. Acta 11 (1968) 441. 161 0. Kikuchi, Bull. Chem. Sot. Japan 42 (1969) 47. I71 M. Celus, P.M. Vay and G. Berthier, Theoret. Chim_ Acta 9 (1967) 182. VI H-M. McConnell, J. Chem. Phys. 33 (1960) 115. PI M. GeUer and R-IV_ Griffith, J. Chem. Phys. 40 (1964) 2309.
PI
CHEMICAL PHYSICS LETTERS
Volume 5 1, number 3
THE SPIN DENSITY DELOCALIZATION
AND THE EXCHANGE INTERACTION
IN N,N’-DIOXY-2,6-DIAZOADAMANTANE
R.N. MUSIN and P.V. SCHASTNEV Institute of Chemical Kinetics ant! Combustion. Novosibirsk 630090. USSR Received 3 December 1976 Revised manuscript received 22 June 1977
The contribution to the exchange integral, resulting from a direct overlap of the n-orbitals of >NO fragments and from the spin density deloca!ization to the adamautane core, has been calculated. The delocalization is of primary importante. in the exchange interaction and does not signify in the spin-spin interaction.
in ref. [l] it has been found by the ESR technique that the N,N’-diazoadamantane biradical (see fig. 1) has the triplet state as ground, the exchange integral J = 85 K in the spin hamiltonian H = -2Js,-&, . When the biradical configuration is DZd, the N-O bonds he on the same straight line. The unpaired electrons are located, in general, at the antibonding n-orbitals of the >NO fragments whose planes are mutually orthogonal. According to refs. [2,3], if the unpaired electron orbitals are orthogonal, J is positive and defined only by electron interaction. This simplifies theoretical calculations. The purpose of the present work is to clear up the effect of the direct exchange interaction of >NO radical centers and the role of the “indirect” exchange interaction resulting from partial delocalization of the unpaired eIectrons to the adamantane core. When estimating the direct contribution, account was taken of only the spin densities of the n-orbitah
of >NO fragments. According to ref. [3], for mutua!ly orthogonal radical orbitals the exchange integral may be given as
(1) where the indices p, u, o, r denote the atomic orbitals (AO’s) of the fragments, p (1) * ~~~$~ ::I trix of the first fragment. Gurl ~~e~~ tation is used. The direct exchange (Jo) caIcularions were made for the spin densities obtained for H,NO by the INDO technique in the unrestricted Hartree-Fock (UHF) approximation. The gaussian expansions of the AO’s and the method given in ref. [4] were used to calculate the (~.~rlav) integrals. The value of JO depends significantly on the A0 approximation_ As AO’s we used: (1) HF AO’s with the gaussian 2p - 7(2pG) approximation [5 ] , (2) AO’s with a proper atomic asymptotics, cp(r) N- exp (-w), cr = (201j2, Iis the atomic ionization potential in au, (3) AO’s with asymptote corresponding to the ionization potential I = 6.8 eV of nitrogen oxide radicals [6]. The data obtained for the molecular asymptote should be treated as the upper estimate of Jo. The results of the Jo (in K) calculations for the above cases are: (1) 0.03(0.12),
(2) 0.05(0.22),
(3) 0.57(4.33).
The integrals calculated Fig. 1.
for the unpaired electron orbitals are given in parentheses. The calculated values 487
Volume
51, number
3
CHEhlICAL
PHYSiCS
are much less than the experimental ones, i.e. the direct exchange interaction of the >NO fragments in biradicals is not the principal contribution to the exchange effect observed_ Let us estimate the contribution to J associated with the spin density delocalization to the adamantane core. Among the core atoms, the 4 P-carbon atoms have the greatest spin density (see fig. 1). Therefore, one should expect that the principal contribution to J is made by the intra- and interatomic exchange interaction on the &carbons. When estimating the delocalization contribution, we used pzz obtained for the unpaired electron orbit& calculated by the INDO technique, the Slater functions and semi-empirical values of the intra-atomic integrals [7] _ The values of pti) are perhaps somewhat lowered since the hyperfi~~ isotropic interaction constant with 13C is less than that expected by the factor of 1 S. The intra-atomic contribution calculated is +59.1 K, the interatomic contribution is +0.2 K. For the latter, a considerable compensation of the components associated with integrals of the type (r.~~~~/v~o~)(-S.l K) and (~17~1 u’vl) (+5.3 K) is observed (1,2 - atomic index). Note that the estimate of J using the results of ref. [8] (which takes into account only spin polarization of the bridge groups) gives J = 1 K.
488
LETTERS
I-November
1977
Thus, the delocalization mechanism is of principal importance for the exchange interaction in the biradical considered and, evidently, for other biradicals with the same structure_ It is interesting to note that the delocalization contribution of P-carbons to the spin-spin interaction constant D calculated using the Slater orbitals [9] equals 5.52 G. Since the experimental value of D = 150 G, the delocalization effects are negligible in the spin-spin interaction_
References R-M. Dupeure, A. Rassat and J. Ronzand, J. Am. Chem. Sot. 96 (1974) 6559. I21 P.-O. LEwdin, Rev. Mod. Phys. 34 (1962) 80. [31P.V. Schastnev and KM. Salikhov, Russ. J. Theoret. Exper. Chem. 9 (1973) 291. I41 H. Taketa and S. Huzinaga, J. Phys. Sot. Japan 11 (1966) 2313. 151 C. SaJez and A. Veillard, Theoret. Chim. Acta 11 (1968) 441. 161 0. Kikuchi, Bull. Chem. Sot. Japan 42 (1969) 47. I71 M. Celus, P.M. Vay and G. Berthier, Theoret. Chim_ Acta 9 (1967) 182. VI H-M. McConnell, J. Chem. Phys. 33 (1960) 115. PI M. GeUer and R-IV_ Griffith, J. Chem. Phys. 40 (1964) 2309.
PI