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Structure of complexes of radicals with organic ligands 2. CNDO calculations of g-tensors
JOURNAL
OF MAGNETIC
RESONANCE
1!&47-50
(1975)
Structure of Complexesof Radicals with Organic Ligands 2. CNDO Calculations of g-Tensors G.M. ZHIDOMIROV AND A.$. KABANKIN Institute of Organic Chemistry, USSR Academy of Sciences, Moscow, USSR Received October 7,1974 Within the CNDO approximation g-tensors have been calculated for the HzNO radical and three different models of the HzNO *. * HOH system : II model, B model (LN-O a.. H= 120Q), umodel (LN-0 .+. H = 180”). A decrease in the g factor of H,NO upon complexation observed experimentally has been predicted only for the G model of the complex.
Stable nitroxide radicals are able to form hydrogen bonds with various proton donor molecules. There exist two views concerning the structure of such complexes. In the first part of this paper (I) and in (2) the structure has been considered in which the hydrogen bond is formed with the participation of the lone pair electrons on the oxygen atom of the radical (the u model), and arguments confirming that viewpoint have been summarized. An alternative structure has been suggested by Morishima et al. (3-5). In that structure the radical forms a complex with a ligand by virtue of the odd electron orbital so that the proton of a ligand is directly above the oxygen atom of the N-O bond with the X-H bond axis perpendicular to the plane of the radical (the 7rmodel). Upon discussion of that problem so far use was made of the results obtained from quantum chemical calculations of spin densities on atomic orbitals of the radical and ligand. At the same time it is well known that the g factor of the nitroxide radical decreases when complexing with a proton donor molecule (6-8). Qualitative interpretation of this effect with the use of simple Htickel theory was presented by Kawamura et al. (7). The decrease in the g factor upon complexation has been shown to be caused mainly by the decrease in the odd electron density on the oxygen atom of the radical and the increase in the energy difference between the odd electron and oxygen lone pair orbitals. Keller and Aiman (9) have calculated the g factor for the HzNO radical and the 0 model of the H,NO - ** HOH system (LN-0 - * * H = 1SO’). Using the CNDO method with parametrization of Sichel and Whitehead (10) and the Stone expression (II) they found a decrease in the g factor of H,NO upon complexation, however, the calculated absolute magnitudes of the g factor for both the radical and the complex were badly underestimated relative to the experimental values (see Table 1). No systematical calculations of the g factor for different models of the complex of the nitroxide radical with a proton donor molecule have been reported, though it may be expected that such calculations will provide additional information on the structure of the complex. 47 1975 by Academic Press, Inc. %wieht All rights oBreproduction in any form reserved. Printed
in Great Britain
-** 0)=2.5
= 180”
a This work. * For tfte di-t-butyl
r(O*-*0)=2.7ti LNOH=180’
u model
LNOH
r(O*-*0)=2.51(
A
2.5 ii
= 120”
0)=
u model
LNOH
t-(0*-*
u model
40
K model
H2N0. * . HOH
H2N0
System
nitroxide radical.
CNDO
Expt!
INDO CNDO
2.0061
2.0061
2.0062
2.0061
CNDO
CNDO
&bo
Method
2.0023
2.0023
2.0023
2.0023
g11
“Hiickel-type”
2.0071
2.0071
2.0070
2.0070
g11
AE
THE CALCULATEDPRINCI~ALCOMPONENTSOF~-TENSORSFOR
TABLE
2.0088
2.0088
2.0091
2.0090
g33
1
2.00314
2.0053
2.0046
2.0056
2.0059
2.0058 2.0058 2.0062 2.0053 2.00356
giso
HzNO ANDTHE
2.00247
2.0023
2.0023
2.0023
2.0027
2.0023 2.0023 2.0023 2.0023 2.0023
g11
2.00458
2.0035
2.0037
2.0046
2.0061
2.0047 2.0047 2.0050 2.0045 2.00395
g22
AE calculated from Eqs. [5 ]
HzNO **.HOHSYSTEM
2.00237
2.0100
2.0078
2.0099
2.0089
2.0104 2.0104 2.0113 2.0091 2.00442
g33
(9)
=
a
y
(19)
(17) (9)
U8)
&
Reference
z
3
1
5
B s
COMPLEXES
OF RADICALS
WITH
ORGANIC
LIGANDS
49
1n the present work the principal components of the g-gensor for the HzNO radical and three models of the HINO . * . HOH complex (see Table 1) were calculated. The calculations were carried out using the Stone expression (II) and the wave functions determined by the CND0/2 method in the original parametrization (12). The geometry of the HzNO radical was taken from (13). The Stone expression for the components of g tensor may be written in the form
where & is the odd electron MO, cI, is the spin-orbit coupling constant for atom p. Within the framework of this expression two ways are possible while calculating excitation energies AE E E,, - E,,. (1) AE is approximated by the difference in the molecular orbital energies (8) E,, - E. = E, - co,
t31
In this case for correct description of experimental data it is necessary to introduce a semiempirical parameter Iz, gre = g, + 4, &,,I,
141
which was found from comparison with the experimental g-tensor for the phenyl radical. In the CNDO/SP scheme (14) at I, = 4, a satisfactory semiquantitative agreement has been obtained between theoretical and experimental values of g tensors for a number of simple ‘II and 0 electron radicals (IS) evidencing the ability of the CNDO/SP method to reproduce characteristic qualitative trends in g tensors of free radicals. (2) The energy differences AE are calculated from expressions which can be derived by using the effective Hartree-Fock operator for the radical according to LonguetHiggins and Pople (16) (see also (18)).
where tij and Jli are vacant and occupied MO’s, respectively, with orbital energies Edand Ed. Our comparative calculations showed that the use of Eqs. [5] in semiempirical calculations of g-tensors for radicals of various types had no particular advantages over Fqs. [3] and [4], though in some cases they yield results which are in somewhat better agreement with the experimental data. In this paper we examined the two approaches to estimate AE. The results of calculations are presented in table, together with the other investigators’ data available. It can be seen that in the case where the “Hiickel-type” AE is used the theoretical value of the g factor practically does not change upon complexation, whatever the model of the complex, in contrast to the experimental findings. Alternatively the use of Eqs. [5] leads to essentially different g-values for the models concerned. With the R model, the
50
ZHIDOMIROV
AND KABANKIN
calculated value of the g factor changes slightly as compared with the nonhydrogenbonded radical, whereas for the G model an appreciable decrease in the g factor is predicted which in turn depends on the angle of N-O * *. H. The results obtained indicate, therefore, the necessity of the correct calculation of AE in the Stone expression in semiempirical calculations of g tensors for complexes of radicals. On the other hand, they provide additional evidence for the o model of the complex. It is also necessary to note the advantage of the original parametrization of the CND0/2 method (12) over that of Sichel and Whitehead (10) while calculating g tensors of free radicals and their complexes. REFERENCES 1. A. S. KABANKIN, G. M. ZHDOMIROV, AND A. L. BUCMCHENKO, J. Magn. Resonance 9,199 (1973). 2. N. A. SYSOEVA AND A. L. BUCHACHENKO, Zh. Strukt. Khim. 13,42 (1972). 3. I. MORI~HIMA, K. ENDO, AND T. YOMEZAWA, J. Amer. Chem. Sot. 93.2048 (1971). 4. I. MORJSHIMA, K. ENDO, AND T. YONEZAWA, Chem. Phys. Lett. 9,143,203 (1971). 5. I. MORISHIMA, K. ENDO, AND T. YONEZAWA, J. Chem. Phys. Ss, 3146 (1973). 6. A. L. BUCHACHENKO AND 0. P. SUKHANOVA, Zh. Strukt. Khim. 6,32 (1965). 7. T. KAWAMURA, S. MATSUNAMI, T. YONEZAWA, AND K. FUKUJ, Bull. Chem. Sot. Japan 33, 1935 (1965). 8. T. KAWAMURA, S. MATSUNAMI, AND T. YONEZAWA, Bull. Chem. Sot. Japan 40,1111(1967). 9. J. KOLLER AND A. AMMAN, Croat. Chem. Acta 42,583 (1970). 10. J. M. SICHEL AND M. A. W HITEHEAD, 7Xeoret. chim. Acta 11,220 (1968). II. A. J. STONE, Proc. Roy. Sot. A 271,424 (1963). 12. J. A. POPL~ AND G. A. &GAL, J. Chem. Phys. 44,3289 (1966). 13. 0. KIKUCHI, Bull. Chem. Sot. Japan 42,47 (1969). 14. G. M. ZHIDOMIROVAND N. D. CHUVYLKIN, Chem. Phys. Lett. 14,52 (1972). 15. N. D. CHUVYLKIN AND G. M. ZHIDOMIROV, Mol. Phys. 25,1233 (1973). 16. H. C. LONGUET-HIGGINS AND J. A. POPLE, Proc. Phys. Sot. (London) A68,591 (1955). 17. T. MORJKAWA, 0. KIKWHI, AND K. SOMENO, Bull. Chem. Sot. Japan 44,2256 (1971). 18, 0. KIKUCHJ, Bull. Chem. Sot. Japan 42,1187 (1969). 19. 0. H. GRIFFITH, D. W. CORNELL, AND H. M. MCCONNELL, J. Chem. Phys. 43,2909 (1965).
OF MAGNETIC
RESONANCE
1!&47-50
(1975)
Structure of Complexesof Radicals with Organic Ligands 2. CNDO Calculations of g-Tensors G.M. ZHIDOMIROV AND A.$. KABANKIN Institute of Organic Chemistry, USSR Academy of Sciences, Moscow, USSR Received October 7,1974 Within the CNDO approximation g-tensors have been calculated for the HzNO radical and three different models of the HzNO *. * HOH system : II model, B model (LN-O a.. H= 120Q), umodel (LN-0 .+. H = 180”). A decrease in the g factor of H,NO upon complexation observed experimentally has been predicted only for the G model of the complex.
Stable nitroxide radicals are able to form hydrogen bonds with various proton donor molecules. There exist two views concerning the structure of such complexes. In the first part of this paper (I) and in (2) the structure has been considered in which the hydrogen bond is formed with the participation of the lone pair electrons on the oxygen atom of the radical (the u model), and arguments confirming that viewpoint have been summarized. An alternative structure has been suggested by Morishima et al. (3-5). In that structure the radical forms a complex with a ligand by virtue of the odd electron orbital so that the proton of a ligand is directly above the oxygen atom of the N-O bond with the X-H bond axis perpendicular to the plane of the radical (the 7rmodel). Upon discussion of that problem so far use was made of the results obtained from quantum chemical calculations of spin densities on atomic orbitals of the radical and ligand. At the same time it is well known that the g factor of the nitroxide radical decreases when complexing with a proton donor molecule (6-8). Qualitative interpretation of this effect with the use of simple Htickel theory was presented by Kawamura et al. (7). The decrease in the g factor upon complexation has been shown to be caused mainly by the decrease in the odd electron density on the oxygen atom of the radical and the increase in the energy difference between the odd electron and oxygen lone pair orbitals. Keller and Aiman (9) have calculated the g factor for the HzNO radical and the 0 model of the H,NO - ** HOH system (LN-0 - * * H = 1SO’). Using the CNDO method with parametrization of Sichel and Whitehead (10) and the Stone expression (II) they found a decrease in the g factor of H,NO upon complexation, however, the calculated absolute magnitudes of the g factor for both the radical and the complex were badly underestimated relative to the experimental values (see Table 1). No systematical calculations of the g factor for different models of the complex of the nitroxide radical with a proton donor molecule have been reported, though it may be expected that such calculations will provide additional information on the structure of the complex. 47 1975 by Academic Press, Inc. %wieht All rights oBreproduction in any form reserved. Printed
in Great Britain
-** 0)=2.5
= 180”
a This work. * For tfte di-t-butyl
r(O*-*0)=2.7ti LNOH=180’
u model
LNOH
r(O*-*0)=2.51(
A
2.5 ii
= 120”
0)=
u model
LNOH
t-(0*-*
u model
40
K model
H2N0. * . HOH
H2N0
System
nitroxide radical.
CNDO
Expt!
INDO CNDO
2.0061
2.0061
2.0062
2.0061
CNDO
CNDO
&bo
Method
2.0023
2.0023
2.0023
2.0023
g11
“Hiickel-type”
2.0071
2.0071
2.0070
2.0070
g11
AE
THE CALCULATEDPRINCI~ALCOMPONENTSOF~-TENSORSFOR
TABLE
2.0088
2.0088
2.0091
2.0090
g33
1
2.00314
2.0053
2.0046
2.0056
2.0059
2.0058 2.0058 2.0062 2.0053 2.00356
giso
HzNO ANDTHE
2.00247
2.0023
2.0023
2.0023
2.0027
2.0023 2.0023 2.0023 2.0023 2.0023
g11
2.00458
2.0035
2.0037
2.0046
2.0061
2.0047 2.0047 2.0050 2.0045 2.00395
g22
AE calculated from Eqs. [5 ]
HzNO **.HOHSYSTEM
2.00237
2.0100
2.0078
2.0099
2.0089
2.0104 2.0104 2.0113 2.0091 2.00442
g33
(9)
=
a
y
(19)
(17) (9)
U8)
&
Reference
z
3
1
5
B s
COMPLEXES
OF RADICALS
WITH
ORGANIC
LIGANDS
49
1n the present work the principal components of the g-gensor for the HzNO radical and three models of the HINO . * . HOH complex (see Table 1) were calculated. The calculations were carried out using the Stone expression (II) and the wave functions determined by the CND0/2 method in the original parametrization (12). The geometry of the HzNO radical was taken from (13). The Stone expression for the components of g tensor may be written in the form
where & is the odd electron MO, cI, is the spin-orbit coupling constant for atom p. Within the framework of this expression two ways are possible while calculating excitation energies AE E E,, - E,,. (1) AE is approximated by the difference in the molecular orbital energies (8) E,, - E. = E, - co,
t31
In this case for correct description of experimental data it is necessary to introduce a semiempirical parameter Iz, gre = g, + 4, &,,I,
141
which was found from comparison with the experimental g-tensor for the phenyl radical. In the CNDO/SP scheme (14) at I, = 4, a satisfactory semiquantitative agreement has been obtained between theoretical and experimental values of g tensors for a number of simple ‘II and 0 electron radicals (IS) evidencing the ability of the CNDO/SP method to reproduce characteristic qualitative trends in g tensors of free radicals. (2) The energy differences AE are calculated from expressions which can be derived by using the effective Hartree-Fock operator for the radical according to LonguetHiggins and Pople (16) (see also (18)).
where tij and Jli are vacant and occupied MO’s, respectively, with orbital energies Edand Ed. Our comparative calculations showed that the use of Eqs. [5] in semiempirical calculations of g-tensors for radicals of various types had no particular advantages over Fqs. [3] and [4], though in some cases they yield results which are in somewhat better agreement with the experimental data. In this paper we examined the two approaches to estimate AE. The results of calculations are presented in table, together with the other investigators’ data available. It can be seen that in the case where the “Hiickel-type” AE is used the theoretical value of the g factor practically does not change upon complexation, whatever the model of the complex, in contrast to the experimental findings. Alternatively the use of Eqs. [5] leads to essentially different g-values for the models concerned. With the R model, the
50
ZHIDOMIROV
AND KABANKIN
calculated value of the g factor changes slightly as compared with the nonhydrogenbonded radical, whereas for the G model an appreciable decrease in the g factor is predicted which in turn depends on the angle of N-O * *. H. The results obtained indicate, therefore, the necessity of the correct calculation of AE in the Stone expression in semiempirical calculations of g tensors for complexes of radicals. On the other hand, they provide additional evidence for the o model of the complex. It is also necessary to note the advantage of the original parametrization of the CND0/2 method (12) over that of Sichel and Whitehead (10) while calculating g tensors of free radicals and their complexes. REFERENCES 1. A. S. KABANKIN, G. M. ZHDOMIROV, AND A. L. BUCMCHENKO, J. Magn. Resonance 9,199 (1973). 2. N. A. SYSOEVA AND A. L. BUCHACHENKO, Zh. Strukt. Khim. 13,42 (1972). 3. I. MORI~HIMA, K. ENDO, AND T. YOMEZAWA, J. Amer. Chem. Sot. 93.2048 (1971). 4. I. MORJSHIMA, K. ENDO, AND T. YONEZAWA, Chem. Phys. Lett. 9,143,203 (1971). 5. I. MORISHIMA, K. ENDO, AND T. YONEZAWA, J. Chem. Phys. Ss, 3146 (1973). 6. A. L. BUCHACHENKO AND 0. P. SUKHANOVA, Zh. Strukt. Khim. 6,32 (1965). 7. T. KAWAMURA, S. MATSUNAMI, T. YONEZAWA, AND K. FUKUJ, Bull. Chem. Sot. Japan 33, 1935 (1965). 8. T. KAWAMURA, S. MATSUNAMI, AND T. YONEZAWA, Bull. Chem. Sot. Japan 40,1111(1967). 9. J. KOLLER AND A. AMMAN, Croat. Chem. Acta 42,583 (1970). 10. J. M. SICHEL AND M. A. W HITEHEAD, 7Xeoret. chim. Acta 11,220 (1968). II. A. J. STONE, Proc. Roy. Sot. A 271,424 (1963). 12. J. A. POPL~ AND G. A. &GAL, J. Chem. Phys. 44,3289 (1966). 13. 0. KIKUCHI, Bull. Chem. Sot. Japan 42,47 (1969). 14. G. M. ZHIDOMIROVAND N. D. CHUVYLKIN, Chem. Phys. Lett. 14,52 (1972). 15. N. D. CHUVYLKIN AND G. M. ZHIDOMIROV, Mol. Phys. 25,1233 (1973). 16. H. C. LONGUET-HIGGINS AND J. A. POPLE, Proc. Phys. Sot. (London) A68,591 (1955). 17. T. MORJKAWA, 0. KIKWHI, AND K. SOMENO, Bull. Chem. Sot. Japan 44,2256 (1971). 18, 0. KIKUCHJ, Bull. Chem. Sot. Japan 42,1187 (1969). 19. 0. H. GRIFFITH, D. W. CORNELL, AND H. M. MCCONNELL, J. Chem. Phys. 43,2909 (1965).