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The spin density in an imino nitroxide free radical: A polarized-neutron study
PHYSICA[ Physica B 213&214 11995} 268 271
ELSEVIER
The spin density in an imino nitroxide free radical: A polarized-neutron study A. Zheludev a, M. Bonnet a, D. Luneau b, E. Ressouche ", P. Rey b, J. Schweizer a'* a CEA, CENG. Dbpartement de Recherche Fondamentale sur la Matibre Condens~e, SPSMS, MDN. 17 rue des Martyrs, 38054 Grenoble Cedex 9, France b CEA, CENG, Dbpartement de Recherche Fondamentale sur la Matiere Condensee, SESAM, 17 rue des Martyrs, 38054 Grenoble Cedex 9, France
Abstract
Imino nitroxide free radicals are potential building blocks for molecular-based magnets. They are purely organic and carry a spin ½ which is delocalized over several atoms of the molecule. We have determined the spin density of one of them, the 2-(3-nitrophenyl)-4,4,5,5-tetramethyl-4,5-dihydro-1H-imidazol- 1-oxyl(m-NPl M), by polarized-neutron diffraction on a single crystal. The delocalization of the singly occupied molecular orbital (SOMO) and the spin polarization effects, which give rise to negative spin densities, are observed directly.
1. Introduction
Nitroxide free radicals are spin carriers which are widely used in the design of magnetic molecular compounds. As their unpaired electron is delocalized over the different atoms of the molecule, they are convenient building blocks and ideal magnetic bridges between magnetic metals, to achieve new compounds with particular magnetic properties. To grasp their role as chemical and magnetic ligands, it is essential to understand their electronic properties, and particularly to know how the unpaired-electron wave function is distributed. Among the nitroxide free radicals are the nitronyl nitroxide radicals which include two N - O groups located symmetrically on both sides of a 5-membered ring (Fig. l(a)), and the imino nitroxide radicals with one N O group on one side and one lone N atom on the other side of the same ring (Fig. l(b)t. In the case of
* Corresponding author.
nitronyl nitroxide, the unpaired electron is supposed to be, to a first approximation, equally shared by the four atoms O, N, N and O, and the single occupied molecular orbital (SOMO) is supposed to exhibit a node on the C atom between the two NO's (Fig. l(a)). In the case of imino nitroxide, the unpaired electron is mainly carried by the three atoms N, N and O, but, as the symmetry is broken, no node is expected on the central C atom for the S O M O (Fig. l(b)). Considerable amount of work [1] has already been published on nitronyl nitroxides, including the investigation of the spin density [2, 3]. Much less has been done on the imino nitroxides, probably because of the difficulties in preparing specimens without occupancy disorder between the N and the NO groups. We report here a polarized-neutron diffraction study of the spin density on a single crystal of 2-(3-nitrophenyl)-4, 4, 5, 5-tetramethyl-4,5-dihydro-lH-imidazol-l-oxyl (referred as mN P I M and shown in Fig. 2) and we compare this spin density with that observed previously in a similar radical, the nitronyl nitroxide PNN [2].
0921-4526/95/$09.50 :i 1995 Elsevier Science 13.V. All rights reserved SSDI 0 9 2 1 - 4 5 2 6 ( 9 5 t 0 0 1 2 6 - 3
A. Zheludev et al. /Physica B 213&214 (1995) 268 271 $1
Nitronyl
269
o~
I
node
N2
I
~1~
B)
ol
N :~-,~
~..01
ol
N2 ~,.C3 /02
""'~
(3. I
Imino
A)
no node
C (z
Fig. 1. Nitroxide radicals and their SOMO wave functions: (a) nitronyl nitroxide radical, (b) imino nitroxide radical.
Fig. 3. MaxEnt reconstruction of the spin density of the two molecules A and B of the m-NPIM radical, in projection onto the N C N-O plane. Higher contour steps: 0.05 #B/,A2 (above), lower contour steps: 0.003 #B/,A2 (below). riding a 4.65 T vertical field, and cooled down to 1.6 K. The flipping ratios R = I+/I_ of 248 independent Bragg reflections were measured in these conditions.
02
" " . . . ,.
3. Spin density reconstruction by the MaxEnt method
. f Cl% j
o,
Fig. 2 rn-NPIM radical.
2. Experiment The crystal structure, was determined with X-rays at room temperature [4], and refined with neutrons at 30 K. It belongs to the centrosymmetric monoclinic space group. P2~/c, with the following cell constants a = 13.180 A, b = 7.379 ,~, c = 27.511/~ and fl = 91.02 °. The asymmetric unit cell contains two m - N P I M radicals. Though crystallographically independent, the two molecules (referred to as molecules A and B) are in nearly equivalent positions, closely coinciding with a ¼ translation along the c axis. The polarized-neutron experiment was performed on the DN2 neutron lifting counter diffractometer, at the Siloe reactor. The sample, a crystal of dimensions 5.7 × 5.3 x 1.1 mm 3, was mounted in a cryomagnet pro-
Model-independent methods allow one to reconstruct the spin density without involving any additional knowledge of what the result should look like. In the case of incomplete and noisy data, it is well known that a straightforward application of the inverse Fourier formula gives a rather poor map. On the contrary, the M a x i m u m Entropy (MaxEnt) technique, which selects among all the maps, consistent with the experimental data, the one with the highest intrinsic probability, yields much better results [5]. This method consists in maximizing the entropy functional (1) under the constraint Zz ~< 1: Entropy[S(r)] = -- 1 du n i t s(r)
S(r)
-
Jo
s(r)lns(r)d3r' cell
(1)
S(r) d3r
nit cell
The spin-density map was reconstructed in an asymmetric unit cell on a 32 x 32 x 32 array of pixels using a program based on the MEMSYS subroutine package [6]. The obtained spin distribution is presented in Fig. 3 as a projection onto the O N - C - N planes of each molecule. Several important features, which are observed in both molecules, need to be described here: (i) The majority of the spin resides on the N1, N2 and O1 atoms.
A. Zheludec et al. /Physica B 213&214 (1995) 268 271
270
(ii) On the N1 and Ol sites of both molecules the density is not centered on the nuclei but is slightly shifted away from the center of the N1 O1 bond. The effect is more pronounced on the N1 site. (iii) On the central C1 carbon atoms, the spin density is negative and is off-center, shifted in the N1 N2 direction.
,,:-",!"'
0.001
A2
4. Spin density reconstruction by the multipolar expansion method Another approach to retrieve the spin density is to design a parametrized model of the spin distribution and refine the parameters to best-fit the experimental magnetic structure factors. A flexible and well adapted model is an expansion into a multipolar series around the nuclei [7]: l
S(r) = ~ R'(r) ~ l
m
~,mk,"" (r)
(2)
-1
where y~" are real spherical harmonics, R~(r) are standard Slater radial functions and ~7' are the population coefficients. The model was refined using a modification of the least-squares program MOLLY [8]. In this refinement, the spin populations of corresponding atoms of molecules A and B were constrained to be equal. For atoms N 1 and O1, where large deformations were expected, the expansion was extended up to l = 3. For the other sites the populations were constrained to represent p atomic orbitals. After refinement, the agreement with experimental data was ;(2 = 1.6, which indicates a rather good description of the spin density. The projection of this spin density onto the molecular plane N - C N O is represented in Fig. 4. For comparison, the PNN spin density obtained in the same way is shown in Fig. 5.
5. Discussion Most of the spin density is concentrated on the imino group and is located on the N1, N2 and O1 atoms. This is the spin delocalization (SD) density, that is the one given by the unpaired electron residing on the singly occupied molecular p orbital (SOMO). On the whole, the spin density increases towards the O1 oxygen site, the atomic spin population of the latter being the largest, and the spin residing on the neighboring N1 is greater than that on N2. The O1 :N1 :N2 spin partitioning is approximately 41:34:24. For comparison, in PNN, the spin density is also located on the N, O, O and N atoms of the NO groups, but a more equal partitioning: 25: 25:25 : 25 has been observed.
Fig. 4. Multipolar expansion reconstruction of the spin density of the m-NPIM radical, averaged over molecules A and B and projected onto the N-C-N O plane. Dashed contours denote negative densities.
,U B
0.005 ~
-
, ;.:"
00@? Fig. 5. Multipolar expansion reconstruction of the spin density of the PNN radical, projected onto the O-N C-N O plane. Dashed contours denote negative densities.
The spin density on N1 and O1 is not centered on the nuclei. Instead, it is shifted outwards, towards the periphery, away from the N O bond center. The shifting is what one would expect from the antibonding nature of the SOMO (from the subtraction of two p= atomic orbitals when constructing a LCAO SOMO). This indicates,
A. Zheludev et al. / Physica B 213& 214 (1995) 268-271
that the S O M O has a node on the N1 01 bond. The multipolar expansion of spin density performed in this work only allows one to account for the deformation of spin density crudely. Nevertheless, the model provides a reasonable approximation. It is not the first time that this sort of spin-density deformation has been observed in organic radicals. It was already encountered in our polarized neutron diffraction studies of the tetracyanoethylenide radical-ion [9]. The bridging sp 2 carbon atom CI, unlike the bridging carbon in nitronyl nitroxides, is not necessarily a node of the S O M O and a priori there is no reason for its spin population to be small or negative. Experimentally, a negative C1 spin population is observed. The effect is less pronounced than in nitronyl nitroxides. In the latter, it is exclusively due to the spin polarization (SP) effect. On the contrary, in m-NPIM it is the result of competition between SP and SD. MaxEnt shows an asymmetrical deformation (offcenter, shifting in the N I - N 2 direction) of the negative spin on CI. This is accompanied by a slight shift of the positive spin density on N1 towards the CI atom on the one hand, and, on the other hand, a shifting of the positive spin density on N2 a w a y from C1. On the nitrophenyl group, the spin populations are at the limit of experimental accuracy. However, similarly to our previous study of P N N where alternating • .. + / - / + / . . . . populations of the phenyl-ring carbon atoms were clearly observed, this sign alternation is also present in the m - N P I M radical. The only disagreement with this picture is the relatively large positive population of one of the phenyl C carbon atoms. This
271
may be due to the interaction with the neighboring radical in the crystal (the O1 site of spin the neighbor is only 3.2 A away), but also to the asymmetry of the spin density on the bridging CI site, through which the spin polarization is actually transferred to the nitrophenyl group.
References [1] Recent reviews on molecular magnetism: A. Caneshi, D. Gatteschi and P. Rey, Prog. inorg. Chem. 39 (1991) 331; O Kahn, Molecular Magnetism (VCH Publishers, 1993); J.S. Miller and A.J. Epstein, Angew. Chem. Int. Ed. Engl. 33 (1994) 385. [2] E. Ressouche, J.X. Boucherle, B. Gillon, P. Rey and J. Schweizer, J. Am. Chem. Soc. 115 (1993) 3610. [3] A. Zheludev, V. Barone, M. Bonnet, B. Delley, A. Grand, E. Ressouche, P. Rey, R. Subra and J. Schweizer, J. Am. Chem. Soc. 116 (1994) 2019. [4] F. Lanfranc de Panthou, D. Luneau, J. Laugier and P. Rey, J. Am. Chem. Soc. 115 (1993) 9095. [5] R.J. Papoular and B. Gillon, Europhys. Lett. 13 (1990)429. E6] S.F. Gull and J. Skilling, MEMSYS Users' Manual (Maximum Entropy Data Consultants Ltd, 33 North End, Meldreth, Royston SG8 6NR, England, 1989). [7] B. Gillon and J. Schweizer, in: Molecules in Physics, Chemistry and Biology, ed. Jean Maruani, Vol. II (Kluwer Academic, Dordrecht, 1989) pp. 111 147. [8] N. K. Hansen and P. Coppens, Acta Crystallogr. A 34 11978) 909. [9] A. Zheludev, A. Grand, E. Ressouche, J. Schweizer, B. Morin, A.J. Epstein, D. Dixon and J.S. Miller, Angew. 33 (1994) 1397.
ELSEVIER
The spin density in an imino nitroxide free radical: A polarized-neutron study A. Zheludev a, M. Bonnet a, D. Luneau b, E. Ressouche ", P. Rey b, J. Schweizer a'* a CEA, CENG. Dbpartement de Recherche Fondamentale sur la Matibre Condens~e, SPSMS, MDN. 17 rue des Martyrs, 38054 Grenoble Cedex 9, France b CEA, CENG, Dbpartement de Recherche Fondamentale sur la Matiere Condensee, SESAM, 17 rue des Martyrs, 38054 Grenoble Cedex 9, France
Abstract
Imino nitroxide free radicals are potential building blocks for molecular-based magnets. They are purely organic and carry a spin ½ which is delocalized over several atoms of the molecule. We have determined the spin density of one of them, the 2-(3-nitrophenyl)-4,4,5,5-tetramethyl-4,5-dihydro-1H-imidazol- 1-oxyl(m-NPl M), by polarized-neutron diffraction on a single crystal. The delocalization of the singly occupied molecular orbital (SOMO) and the spin polarization effects, which give rise to negative spin densities, are observed directly.
1. Introduction
Nitroxide free radicals are spin carriers which are widely used in the design of magnetic molecular compounds. As their unpaired electron is delocalized over the different atoms of the molecule, they are convenient building blocks and ideal magnetic bridges between magnetic metals, to achieve new compounds with particular magnetic properties. To grasp their role as chemical and magnetic ligands, it is essential to understand their electronic properties, and particularly to know how the unpaired-electron wave function is distributed. Among the nitroxide free radicals are the nitronyl nitroxide radicals which include two N - O groups located symmetrically on both sides of a 5-membered ring (Fig. l(a)), and the imino nitroxide radicals with one N O group on one side and one lone N atom on the other side of the same ring (Fig. l(b)t. In the case of
* Corresponding author.
nitronyl nitroxide, the unpaired electron is supposed to be, to a first approximation, equally shared by the four atoms O, N, N and O, and the single occupied molecular orbital (SOMO) is supposed to exhibit a node on the C atom between the two NO's (Fig. l(a)). In the case of imino nitroxide, the unpaired electron is mainly carried by the three atoms N, N and O, but, as the symmetry is broken, no node is expected on the central C atom for the S O M O (Fig. l(b)). Considerable amount of work [1] has already been published on nitronyl nitroxides, including the investigation of the spin density [2, 3]. Much less has been done on the imino nitroxides, probably because of the difficulties in preparing specimens without occupancy disorder between the N and the NO groups. We report here a polarized-neutron diffraction study of the spin density on a single crystal of 2-(3-nitrophenyl)-4, 4, 5, 5-tetramethyl-4,5-dihydro-lH-imidazol-l-oxyl (referred as mN P I M and shown in Fig. 2) and we compare this spin density with that observed previously in a similar radical, the nitronyl nitroxide PNN [2].
0921-4526/95/$09.50 :i 1995 Elsevier Science 13.V. All rights reserved SSDI 0 9 2 1 - 4 5 2 6 ( 9 5 t 0 0 1 2 6 - 3
A. Zheludev et al. /Physica B 213&214 (1995) 268 271 $1
Nitronyl
269
o~
I
node
N2
I
~1~
B)
ol
N :~-,~
~..01
ol
N2 ~,.C3 /02
""'~
(3. I
Imino
A)
no node
C (z
Fig. 1. Nitroxide radicals and their SOMO wave functions: (a) nitronyl nitroxide radical, (b) imino nitroxide radical.
Fig. 3. MaxEnt reconstruction of the spin density of the two molecules A and B of the m-NPIM radical, in projection onto the N C N-O plane. Higher contour steps: 0.05 #B/,A2 (above), lower contour steps: 0.003 #B/,A2 (below). riding a 4.65 T vertical field, and cooled down to 1.6 K. The flipping ratios R = I+/I_ of 248 independent Bragg reflections were measured in these conditions.
02
" " . . . ,.
3. Spin density reconstruction by the MaxEnt method
. f Cl% j
o,
Fig. 2 rn-NPIM radical.
2. Experiment The crystal structure, was determined with X-rays at room temperature [4], and refined with neutrons at 30 K. It belongs to the centrosymmetric monoclinic space group. P2~/c, with the following cell constants a = 13.180 A, b = 7.379 ,~, c = 27.511/~ and fl = 91.02 °. The asymmetric unit cell contains two m - N P I M radicals. Though crystallographically independent, the two molecules (referred to as molecules A and B) are in nearly equivalent positions, closely coinciding with a ¼ translation along the c axis. The polarized-neutron experiment was performed on the DN2 neutron lifting counter diffractometer, at the Siloe reactor. The sample, a crystal of dimensions 5.7 × 5.3 x 1.1 mm 3, was mounted in a cryomagnet pro-
Model-independent methods allow one to reconstruct the spin density without involving any additional knowledge of what the result should look like. In the case of incomplete and noisy data, it is well known that a straightforward application of the inverse Fourier formula gives a rather poor map. On the contrary, the M a x i m u m Entropy (MaxEnt) technique, which selects among all the maps, consistent with the experimental data, the one with the highest intrinsic probability, yields much better results [5]. This method consists in maximizing the entropy functional (1) under the constraint Zz ~< 1: Entropy[S(r)] = -- 1 du n i t s(r)
S(r)
-
Jo
s(r)lns(r)d3r' cell
(1)
S(r) d3r
nit cell
The spin-density map was reconstructed in an asymmetric unit cell on a 32 x 32 x 32 array of pixels using a program based on the MEMSYS subroutine package [6]. The obtained spin distribution is presented in Fig. 3 as a projection onto the O N - C - N planes of each molecule. Several important features, which are observed in both molecules, need to be described here: (i) The majority of the spin resides on the N1, N2 and O1 atoms.
A. Zheludec et al. /Physica B 213&214 (1995) 268 271
270
(ii) On the N1 and Ol sites of both molecules the density is not centered on the nuclei but is slightly shifted away from the center of the N1 O1 bond. The effect is more pronounced on the N1 site. (iii) On the central C1 carbon atoms, the spin density is negative and is off-center, shifted in the N1 N2 direction.
,,:-",!"'
0.001
A2
4. Spin density reconstruction by the multipolar expansion method Another approach to retrieve the spin density is to design a parametrized model of the spin distribution and refine the parameters to best-fit the experimental magnetic structure factors. A flexible and well adapted model is an expansion into a multipolar series around the nuclei [7]: l
S(r) = ~ R'(r) ~ l
m
~,mk,"" (r)
(2)
-1
where y~" are real spherical harmonics, R~(r) are standard Slater radial functions and ~7' are the population coefficients. The model was refined using a modification of the least-squares program MOLLY [8]. In this refinement, the spin populations of corresponding atoms of molecules A and B were constrained to be equal. For atoms N 1 and O1, where large deformations were expected, the expansion was extended up to l = 3. For the other sites the populations were constrained to represent p atomic orbitals. After refinement, the agreement with experimental data was ;(2 = 1.6, which indicates a rather good description of the spin density. The projection of this spin density onto the molecular plane N - C N O is represented in Fig. 4. For comparison, the PNN spin density obtained in the same way is shown in Fig. 5.
5. Discussion Most of the spin density is concentrated on the imino group and is located on the N1, N2 and O1 atoms. This is the spin delocalization (SD) density, that is the one given by the unpaired electron residing on the singly occupied molecular p orbital (SOMO). On the whole, the spin density increases towards the O1 oxygen site, the atomic spin population of the latter being the largest, and the spin residing on the neighboring N1 is greater than that on N2. The O1 :N1 :N2 spin partitioning is approximately 41:34:24. For comparison, in PNN, the spin density is also located on the N, O, O and N atoms of the NO groups, but a more equal partitioning: 25: 25:25 : 25 has been observed.
Fig. 4. Multipolar expansion reconstruction of the spin density of the m-NPIM radical, averaged over molecules A and B and projected onto the N-C-N O plane. Dashed contours denote negative densities.
,U B
0.005 ~
-
, ;.:"
00@? Fig. 5. Multipolar expansion reconstruction of the spin density of the PNN radical, projected onto the O-N C-N O plane. Dashed contours denote negative densities.
The spin density on N1 and O1 is not centered on the nuclei. Instead, it is shifted outwards, towards the periphery, away from the N O bond center. The shifting is what one would expect from the antibonding nature of the SOMO (from the subtraction of two p= atomic orbitals when constructing a LCAO SOMO). This indicates,
A. Zheludev et al. / Physica B 213& 214 (1995) 268-271
that the S O M O has a node on the N1 01 bond. The multipolar expansion of spin density performed in this work only allows one to account for the deformation of spin density crudely. Nevertheless, the model provides a reasonable approximation. It is not the first time that this sort of spin-density deformation has been observed in organic radicals. It was already encountered in our polarized neutron diffraction studies of the tetracyanoethylenide radical-ion [9]. The bridging sp 2 carbon atom CI, unlike the bridging carbon in nitronyl nitroxides, is not necessarily a node of the S O M O and a priori there is no reason for its spin population to be small or negative. Experimentally, a negative C1 spin population is observed. The effect is less pronounced than in nitronyl nitroxides. In the latter, it is exclusively due to the spin polarization (SP) effect. On the contrary, in m-NPIM it is the result of competition between SP and SD. MaxEnt shows an asymmetrical deformation (offcenter, shifting in the N I - N 2 direction) of the negative spin on CI. This is accompanied by a slight shift of the positive spin density on N1 towards the CI atom on the one hand, and, on the other hand, a shifting of the positive spin density on N2 a w a y from C1. On the nitrophenyl group, the spin populations are at the limit of experimental accuracy. However, similarly to our previous study of P N N where alternating • .. + / - / + / . . . . populations of the phenyl-ring carbon atoms were clearly observed, this sign alternation is also present in the m - N P I M radical. The only disagreement with this picture is the relatively large positive population of one of the phenyl C carbon atoms. This
271
may be due to the interaction with the neighboring radical in the crystal (the O1 site of spin the neighbor is only 3.2 A away), but also to the asymmetry of the spin density on the bridging CI site, through which the spin polarization is actually transferred to the nitrophenyl group.
References [1] Recent reviews on molecular magnetism: A. Caneshi, D. Gatteschi and P. Rey, Prog. inorg. Chem. 39 (1991) 331; O Kahn, Molecular Magnetism (VCH Publishers, 1993); J.S. Miller and A.J. Epstein, Angew. Chem. Int. Ed. Engl. 33 (1994) 385. [2] E. Ressouche, J.X. Boucherle, B. Gillon, P. Rey and J. Schweizer, J. Am. Chem. Soc. 115 (1993) 3610. [3] A. Zheludev, V. Barone, M. Bonnet, B. Delley, A. Grand, E. Ressouche, P. Rey, R. Subra and J. Schweizer, J. Am. Chem. Soc. 116 (1994) 2019. [4] F. Lanfranc de Panthou, D. Luneau, J. Laugier and P. Rey, J. Am. Chem. Soc. 115 (1993) 9095. [5] R.J. Papoular and B. Gillon, Europhys. Lett. 13 (1990)429. E6] S.F. Gull and J. Skilling, MEMSYS Users' Manual (Maximum Entropy Data Consultants Ltd, 33 North End, Meldreth, Royston SG8 6NR, England, 1989). [7] B. Gillon and J. Schweizer, in: Molecules in Physics, Chemistry and Biology, ed. Jean Maruani, Vol. II (Kluwer Academic, Dordrecht, 1989) pp. 111 147. [8] N. K. Hansen and P. Coppens, Acta Crystallogr. A 34 11978) 909. [9] A. Zheludev, A. Grand, E. Ressouche, J. Schweizer, B. Morin, A.J. Epstein, D. Dixon and J.S. Miller, Angew. 33 (1994) 1397.