J. Phys. Chem. 1990, 94, 105-113
105
Orbital Symmetry Control and g-Factor Anisotropy in a Low-Spin Macrocyclic Cobalt( I I ) Complex A. Ceulemans,*,t R. Debuyst,t F. Dejehet,* G . S. D. King,$ M. Vanhecke: and L. G . Vanquickenborne? Quantum Chemistry and Crystallography Laboratories, University of Leuven, Celestijnenlaan 200 F & C, B-3030 Leuven, Belgium, and Laboratoire de Chimie Inorganique et NuclPaire, UniversitP de Louvain 2, Chemin du Cyclotron, B- 1348 Louvain-la-Neuve, Belgium (Received: February 6, 1989; In Final Form: June 26, 1989)
The single-crystal EPR spectrum of the tetraimine macrocyclic Co( 11) complex [ C O ( C , ~ H ~ ~ N ~diluted ) ] C I ~in, the analogous Ni(I1) complex, and the crystal structure of the host have been determined. [Ni(CloH20N8)]C12 crystallizes in the space group Pi,with n = 7.523 (2) A, b = 9.502 (2) A, c = 11.447 (4) A, (Y = 95.82 (2)O, fl = 108.01 (2)O, y = 98.62 (3)O, and Z = 2. The EPR spectrum is anisotropic with g, = 2.217, gu = 2.681, g, = 1.966 and A, = 44, A, = 105, A, = 115 G. Superhyperfine interactions with one axial chlorine nucleus are observed along the z-direction. The spatial orientation of the molecular g tensor in this complex is controlled by orbital symmetry. The observed orientational selectivity is reminiscent of the stereochemical selection rules for carbocyclic reactions.
Introduction Macrocyclic Co( 11) complexes provide suitable examples for investigating the specific electronic effects of double bonding in chelated metal complexes, first described by Orgel.' The compound chosen for the present study has a tetraimine macrocycle containing two conjugated a-diimine groups. This type of double bonding constitutes a missing link in the existing theoretical and experimental ~ t u d i e s ~of- ~the Orgel effect.
I. Molecular Orbital Treatment At issue is a study of symmetry-controlled interactions between the d orbitals of a transition-metal ion and the a orbitals of a conjugated macrocyclic ligand. In this opening section, a simplified molecular orbital description of this interaction will be developed, from Fukui's frontier orbital t h e ~ r y . ~As a starting point, we consider the bonding of a a-conjugated bidentate ligand. The next step involves the fusion of two such bidentates to form a quadridentate macrocycle. A . Coordination of a a-Conjugated Bidentate Ligand. A a-conjugated bidentate ligand consists of a r-conjugated linear chain with ligating atoms at both ends. Typical examples2 are the a-diimines, such as glyoxal bis(methy1imine) (gmi), and the P-diketonates, such as acetylacetonate (acac-). In their planar cis conformation, these chains are excellent chelating agents for transition-metal ions. H
H
I
H
9"
acac-
The subsequent description of the bonding in a monochelate M(L-L) will make use of a Cartesian coordinate frame on M, with the ligator atoms in the xy-plane, and the y-axis along the bisector of the chelate bridge. A symmetrical bidentate has C2, symmetry; more specifically, this point group will be denoted as C$'" to indicate that its e2axis coincides with the y-direction.
'K.U. Leuven, Laboratorium voor Quantumchemie. * U.C.L., Laboratoire de Chimie Inorganique et NucEaire. I K.U. Leuven, Laboratorium voor Kristallografie.
0022-3654/90/2094-0105$02.50/0
Some relevant symmetry labels for this and other point groups of interest are defined in Table I. In the Cartesian coordinate frame, the bonding may be resolved into its in-plane ( x y ) and out-of-plane (z) components. The in-plane component comprises the usual u and r bonds between M and L. These bonds also occur in the molecular plane of a saturated bidentate ligand. Of more interest in the present case are the out-of-plane or "perpendicular" aLbonds, since these may interact with the r-conjugated network of the unsaturated bridge. The essential features of these aL interactions have been described by Orgel' and by Lin and Orgel.6 A detailed ligand field formulation of the problem is given in ref 2. Here, we present a simplified analysis, using the frontier molecular orbital theory of F ~ k u i This . ~ method allows identification of the principal orbital interactions given the participating fragment orbitals and their relative energies. As far as the metal center is concerned, the important fragment orbitals are the d,, and d,,, orbitals, which are the only d r orbitals capable of perpendicular ?r interactions. These orbitals are assumed to lie between the highest occupied (HOMO) and lowest unoccupied (LUMO) aL molecular orbitals of the ligand chain. The approximate LCAO structure of the frontier ligand MO's may be inferred from Huckel-type calculations, taking into account the orbital basis set of the atomic pz orbitals on the backbone atoms (1) Orgel, L. E. J . Chem. SOC.1961, 3683. (2) Ceulemans, A,; Dendooven, M.; Vanquickenborne, L. G. Inorg. Chem. 1985. 24. 1153. (3) Ceulemans, A,; Dendooven, M.; Vanquickenborne, L. G. Inorg. Chem. 1985. - - - ,24. - , 1159. ~~(4) Dad, C.; Schlapfer, C. W.; von Zelewsky, A. Struct. Bonding (Berlin) 1979, 36, 129. ( 5 ) Fukui, K. Fortschr. Chem. Forsch. 1970, I S , 1. (6) Lin, W. C.; Orgel, L. E. Mol. Phys. 1963, 7, 131.
0 1990 American Chemical Society
106
The Journal of Physical Chemistry, Vol. 94, No, 1, 1990
Ceulemans et al.
TABLE I: Characterization of Relevant Symmetry Labels for CI,,Dlh, and tbe Double Croup DZh*
e
a.
e;
e
e;
i
-ilE’+ 1/2) i1.E’- 1 / 2 )
/E’- 1/2) -IE’+ 1/2)
-iJE’- 1 / 2 ) -iJE’+ 1 / 2 )
/ E ’ + 1/2) IE’- 1/2)
D2h*
E,’
IE’+ 1 / 2 ) JE’- 1 / 2 )
dvz)
O,,(XY)
CY
spin
p spin
b2 i
L b21 L U M O I
I
Figure 1. Orbital energy diagram showing the interaction between the d a orbitals and the HOMO and LUMO of a four-membered (left) and five-membered (right) double-bonded bidentate chain. Symmetry labels a2 and b2 refer to the Cv,point group and are defined in Table I.
of the chain. For simple a- and @-disubstitutedchains, such as gmi and acac-, the symmetry characteristics of the frontier M O s are found to be the same as for the respective parent hydrocarbons, butadiene and the pentadienyl Knowing the frontier orbitals on the metal and the ligand we may now consider the symmetry-allowed interactions. These interactions are depicted in the orbital energy diagram of Figure 1. The ligand orbitals span either the a2 or the b2 representation, as shown in the figure. In the b2 orbitals, the p, functions on the ligator atoms appear with the same sign. Therefore, these combinations may also be referred to as in-phase coupled combinations. In turn, the a2 orbitals have outer functions with opposite signs and may therefore be characterized as out-of-phase coupled combinations. The d,, and d,, orbitals transform, respectively, as a2 and b2. Since only interactions between orbitals of the same symmetry type are allowed, the d,, orbital will interact only with the out-of-phase combination while the d,, orbital will interact (7) Ito, T.; Tanaka, N.; Hanazaki, I.: Nagakura, S. Bull. Chem. SOC.Jpn. 1968, 41, 365.
(8) Hanazaki. 1.; Hanazaki, F.; Nagakura, S. J. Chem. Phys. 1969, 50, 265.
only with the in-phase coupled combination. Schematically these interactions may be represented as follows.
a2 - d x z
b2
- dyz
In the case of a four-membered chelate chain (left-hand side of Figure l ) , the d,, level is raised as a result of A donation from the a2 HOMO, while the d, level is stabilized through A backbonding with the b2 LUMO. The result is a measurable splitting of the d r level with d,, clearly above dyz. Either of these interactions, taken separately, will place d, well above d,:. Hence, this orbital order is unequivocal for simple a-disubstituted conjugated bidentates, regardless of whether donor
Orbital Symmetry and g Factors in a Co(I1) Complex b
39
blu
1I
The Journal of Physical Chemistry, Vol. 94, No. 1, 1990 107
\
/ /
i
I
-M-
I/
/I
b3g' b l u
I W
I
I
I
I
t2
It
sf3
bischelate
monochelate
Dzh
CZ"
X
Figure 2. Orbital energy diagram for the coordination of a macrocycle with two butadiene parts, trans to each other. The frontier orbitals of the bischelate are g and u combinations of the HOMO and LUMO of the monochelate.
or acceptor interactions predominate. If the number of links in the chain is increased by one to yield a j3-disubstituted chain, the a2 and b2 symmetries of HOMO and LUMO will simply be switched (right-hand side of Figure 1). This leads to a reversal of the d r orbital order. In conclusion, the influence of ligand A conjugation on the d n orbitals of the metal may be summarized as follows: (i) There will be a measurable splitting of the d r orbitals. (ii) The sign of the splitting alternates with chain length. B. Coordination of a *-Conjugated Macrocycle. As we have previously demonstrated,2 the treatment of section LA may be generalized to describe the bonding of two or more ?r-conjugated bidentate ligands in different coordination geometries. The geometry that yields the largest splitting of the d r levels is the square-planar arrangement of two bidentate ligands. Such complexes should thus constitute the most sensitive probes for measuring the influence of ligand conjugation on the d-orbital energies. Stable compounds of this type can be formed by fusing two conjugated bidentates via one or two saturated bridges. These bridges do not interfere with the A conjugation of the ligands, but their primary role is to keep the four ligator atoms in one plane. Suitable examples are the macrocyclic ligands,*12 listed in Table 11. The symmetry aspects of the coordination of a macrocycle with two butadiene-type parts, trans to each other, are illustrated in the orbital diagram of Figure 2. The diagram was constructed using the D2hpoint group of a symmetrical dimeric chelate. The out-of-phase a2 H O M O of the monomer is seen to give rise to a b2, and an a, dimer combination. Likewise, the in-phase b2 LUMO of the monomer induces b3, and b,, dimer orbitals. In turn, the d x orbitals, d,, and dy,, transform as b2$ and b3,, respectively. Hence, the b2, H O M O will interact with d,,, while (9) Peng, S.-M.; Gordon, G.C.; Goedken, V. L. Inorg. Chem. 1978, 17, 119. (IO) von Zelewsky, A.; Fierz, H.Helv. Chim. Acra 1973, 94, 2436. ( I 1 ) Zobrist, M. Dissertation No. 732, University of Freiburg, Switzerland, 1974. (12) von Zelewsky, A.; Zobrist, M. Helv. Chim.Acra 1981, 64, 2154.
the b3gLUMO will interact with dyz. Clearly, the two MO's of odd parity are unable to form A bonds with the even-parity d orbitals. The symmetry-allowed interactions may thus be represented schematically as follows.
b z q - dxz
As in the case of the monomer, the out-of-phase coupled combination forms a A donor bond with d,,, while the in-phase coupled combination forms a A acceptor bond with dy,. Thus, the d,, orbital is again predicted to have a higher energy than dy,, but the magnitude of the splitting for the bischelate amounts to about twice that for the monochelate. As before, the orbital ordering will simply be reversed when the chain length of the conjugated parts is changed by one atomic link. Strictly speaking, the above treatment applies only to symmetrical macrocycles with approximate DZhsymmetry. Nonetheless, even in lower symmetry cases such as the N202Schiff base complexe~,~ unequivocal predictions along similar lines are usually possible on the basis of simple overlap considerations. The basic feature that relates these overlap considerations to the rigorous symmetry treatment for symmetrical macrocycles appears to be the phase relationship between the frontier p, orbitals on the ligator atoms.2 In summary, (i) in square-planar bischelates the splitting of the d?r orbitals will be about twice as large as in the corresponding monochelate, and (ii) the orbital phase relationship in the con-
108 The Journal ofPhysica1 Chemistry, Vol. 94, No. I , 1990
Ceulemans et al.
TABLE 11: d r Orbital Ordering and g-Factor Anisotropy in Square-Planar Cobalt(I1) Complexes of Quadridentate Schiff Bases" orbital ordering
structure
g
anisotropy
ref
Bis(a-diimine) Chelate dxz > d,,
N"
[CO(CIOH~ONS)IC~~
gy
>> gx. g,
9, this work
hvN Bis(P-keto imine) Chelate i ? d,, > dxz gx >> gy>gz
Co(sa1en)
'
\
4, I O
Co(amben)
Ligand abbreviations: salen, N,N'-ethylenebis(sa1icylaldiminate); amben, N,N'-ethylenebis(0-aminobenzylideniminate),
jugated chains controls the ordering of d,, and dy?. A convenient experimental technique for determining the absolute d-orbital ordering is single-crystal EPR spectroscopy, using divalent cobalt as the central metal This method has so far only been applied to square-planar Co(I1) complexes of pdisubstituted Schiff bases. For both P-keto imines,I0 such as Co(salen), and P-diimines,"J2 such as Co(amben), dyzis found to be higher in energy than d,,, in agreement with the prediction from MO theory (see Table 11). Clearly,for a complete proof of the theory, one must also verifv whether there is a reversal of this orbital ordering, when the @-disubstitutedchains are replaced by a-disubstituted ones. We have therefore carried out similar single-crystal EPR measurements on the Co(I1) complex of the tetraimine macrocycle CloH20N8, which has the desired type of A conjugation9 (see Table 11). The results of this experiment are discussed in the following sections. 11. Experimental Section A. Synthesis. Single crystals of [Ni(C,oHzoN8)]C12, doped with Co(I1) for the EPR measurements, were prepared following the method of Peng, Gordon, and Goedken? The starting material was a host-guest mixture of 95% by weight NiClZ.6H20and 5% by weight CoCI2.6H20. Synthesis and crystallization were carried out under a nitrogen atmosphere. The reaction solution was left standing overnight, and then the precipitate was filtered off. From the remaining solution, small crystals could be grown in a few days. The same procedure can also be used to obtain single crystals of the pure Ni and Co complexes. These complexes were characterized by UV-vis and IR spectroscopy. The absorption spectrum of the [Ni(C,oHzoN8)]C12complex in aqueous solution was consistent with the results of Goedken et aL9 B. Structure Determination. X-ray diffraction data for the Ni( 11) host complex were collected from a single crystal (0.17 X 0.15 X 0.05 mm) by the w - 28 scan technique on a Syntex P21 diffractometer using graphite-monochromatized Cu K a radiation ( A = 1.541 78 A). Cell parameters were obtained by a leastsquares analysis of the 20 values of 24 reflections. The crystal data are as follows: Ni(CloHmN8)]C1,M = 381.92, space group Pi, a = 7.523 (2) b = 9.502 (2) c = 11.447 (4) A, a = 95.82 (2)', p = 108.01 (2)', y = 98.62 (3)", Z = 2, ~ ( C K Ua ) = 52.2 cm-I, d,,,, = 1.669 g . ~ m - ~ .
1,
i,
Figure 3. Crystal habit of the Co(I1)-doped [Ni(CIOH20N8)]C12 single crystal used for the EPR measurements. The (100) faces are seen to predominate.
Intensities were collected for a complete reciprocal sphere of radius (2 sin @ / A = 1.05 A-I and were corrected empirically for absorption.13 Values for symmetry-equivalent reflections were averaged to give 1841 unique structure factors of which 1784 had intensities greater than 2 standard deviations and were considered as observed. The structure was solved by Patterson and Fourier methods; hydrogen atoms were located in difference electron density maps. They were placed at calculated positions such that N-H = 0.85 8, and C-H = 1.05 A. They were all in regions of positive difference electron density. The atomic coordinates with anisotropic displacement parameters for the non-hydrogen atoms were refined by full matrix least-squares methods to R = 0.06 for all 1841 reflections and 0.059 for the 1784 observed reflections. All calculations were carried out with the XTAL 2.2 system.14 Drawings were made with the PLUTO 78 routines. C. EPR Spectrometry. A single crystal of [Ni(C,oH20N8)]C1z, doped with Co(I1) and of dimensions 0.5 X 1.5 X 2 mm was glued inside a U-shaped perspex support, mounted on a quartz rod that was itself inserted in a goniometer. The sample was rotated about three perpendicular axes, and for each rotation, EPR spectra were recorded at 20-deg intervals, from 0' to 220'. All measurements were performed at 135 K. A Bruker X-band ER 200tt spectrometer was used. The magnetic field was measured with a Bruker B-NM 12 N M R oscillator; the measurement of t h e klystron frequency was performed with a 12.5 MHz 5216 A Hewlett-Packard frequency counter and a 1/ IO00 5260 A Hew-
-
(13) Syntex XTL User's Manual, Cupertino, California, 1975. (14) Hall, S. R., Stewart, J. M., Eds. XTAL 2.2 User's Manual, Universities of Western Australia and Maryland, 1987.
Orbital Symmetry and g Factors in a Co(I1) Complex
The Journal of Physical Chemistry, Vof. 94, No. 1 , 1990 109
TABLE 111: Atomic Coordinates and Isotropic Displacement Parameters for the Non-Hydrogen Atoms in [Ni(Cl&ImN8)lCl,“ X
Ni CI 1 c12 NI N2 c3 N4 N5 C6 c7 C8 c9 N10 NI I c12 N13 N14 CIS C16 C17 C18
0.6588 ( I ) 0.3007 (2) 0.0512 (2) 0.7352 (7) 0.7639 (7) 0.6522 (9) 0.7221 (7) 0.7097 (7) 0.7511 (8) 0.7243 (8) 0.8138 (9) 0.7506 ( I O ) 0.6663 (6) 0.6335 (7) 0.5442 (8) 0.6524 (7) 0.6827 (6) 0.7401 (8) 0.7673 (8) 0.7791 ( I O ) 0.8238 (9)
ux
z
Y 0.3488 ( I ) 0.3185 (2) 0.9252 (2) 0.3986 (5) 0.5406 (5) 0.6291 (6) 0.6611 (5) 0.5398 (5) 0.5534 (6) 0.4123 (6) 0.6955 (7) 0.3966 (7) 0.3035 (5) 0.1663 (5) 0.0561 (6) 0.0401 (5) 0.1642 (5) 0.1556 (6) 0.2939 (6) 0.0241 (7) 0.3048 (7)
0.2619 ( I ) 0.1435 (1) 0.3361 (1) 0.1260 (4) 0. IO70 (4) 0.1568 (5) 0.2918 (4) 0.3473 (4) 0.4676 (5) 0.5100 (5) 0.5512 (5) 0.6425 (5) 0.4198 (4) 0.4450 (4) 0.3357 (5) 0.2511 (4) 0.1988 (4) 0.1023 (5) 0.0581 (5) 0.0437 (5) -0.0558 (5)
100 (A*) 2.46 (4) 3.12 (6) 4.00 (7) 2.45 (19) 3.25 (21) 3.23 (25) 3.02 (19) 2.43 (18) 2.54 (23) 2.43 (22) 3.68 (26) 3.65 (26) 2.23 (18) 3.05 (20) 2.96 (24) 2.87 (20) 2.30 (18) 2.47 (22) 2.45 (22) 3.79 (27) 3.51 (25)
“Standard deviations for the last digit are given in parentheses. TABLE IV: Selected Bond Lengths INi(CIPmNdlCI,
N11 31-
c9
17
18
CB
^^ w
oal N11 A
N
1
3
(A) and Angles (deg) for
Bond Lengths Ni-CI1 2.571 (5) Ni-N I 1.896 (5) Ni-N5 1.897 (5) Ni-N I O 1.886 (5) Ni-N14 1.884 (5) NI-C16 1.298 (8) N5-C6 1.302 (7) N10-C7 1.301 (7)
N14-CI5 NI-N2 N4-N5 NIO-NII N13-NI4 C3-N2 C3-N4 C12-Nll
1.304 (8) 1.384 (7) 1.376 (7) 1.367 (7) 1.396 (7) 1.466 (9) 1.453 (7) 1.455 (6)
C12-NI3 C6-C7 C6-C8 C7-C9 C15-CI6 C15-CI7 C16-CI8
1.455 (9) 1.479 (9) 1.493 (8) 1.493 (8) 1.464 (8) 1.499 (9) 1.499 (9)
18
w Figure 4. Drawings of the Ni(C,oH20NB)CI+ cation. The symmetry is nearly C,. Bond distances and angles are given in Table IV.
Bond Angles N I -Ni-N 5 N5-Ni-N I O N10-Ni-N14 N 14-Ni-N 1 Ni-N I-N2 Ni-N5-N4 Ni-NIO-N11 Ni-N 14-N I3
96.0 (2) 82.0 (2) 95.1 (2) 81.8 (2) 120.6 (4) 124.1 (3) 124.2 (3) 124.8 (4)
Ni-NI-C16 Ni-N5-C6 Ni-NIO-C7 Ni-N 14-C 15 CI-Ni-NI CI-Ni-N5 CI-Ni-N10 CI-Ni-N I4
116.1 (4) 116.0 (4) 115.6 (4) 116.3 (4) 94.6 (2) 100.3 ( I ) 103.4 (2) 95.8 (2)
lett-Packard frequency divider. The crystallographic axes were determined by Weissenberg techniques and are shown on Figure 3. As can be seen from the figure, the (100)faces predominate. A spectrum of a powdered sample was taken at 77 K . 111. Results A. Description of the Crystal Structure. The final atomic coordinates and equivalent isotropic displacement parameters for the Ni(I1) host complex are given in Table I11 and selected bond lengths and angles in Table IV. An overview of the molecular geometry is represented in Figure 4. Seen along the Ni-CI bond, the molecule exhibits nearly C,, symmetry. The side view in Figure 4 illustrates that the macrocyclic ligand plane is slightly domed. The Ni(I1) ion is displaced 0.28 A from the plane of the four ligator atoms. One of the chloride counterions forms a weak axial bond. The coordination geometry thus resembles a square pyramid. The two outer carbon atoms, C3 and C12, are also elevated above the macrocycle, which thus adopts a boatlike conformation. Figure 5 shows a drawing of the unit cell contents. Furthermore, the crystal structure of the analogous Cu( 11) complex has been shown to be isomorphous with the Ni(I1) host c0mp1ex.l~ A detailed comparison of the corresponding coordination geometries is deferred to a forthcoming publication. ~
~~
~~~
(15) King, G.S. D.; Vanhecke, M. Unpublished results.
-
Figure 5. Unit cell of the [Ni(CI,H2,NB)]C12 host crystal. The cell contains two molecules, related by an inversion center.
B. EPR Spectroscopy. The EPR spectrum exhibits the eight hyperfine lines of a single magnetic species (S = l / 2 , I,, = the two molecules of the unit cell being related by an inversion center (see Figure 5 ) . The spacings between neighboring hyperfine lines mainly increase with magnetic field, indicating that second-order corrections are operative. Spectra close to the direction of the Ni-CI bond reveal the presence of four superhyperfine lines due to the CI nucleus (Icl = 3/2). Some low-intensity lines appear among the normal ones; these could be due to “forbidden” transitions. The EPR spectra were analyzed with the spin Hamiltonian 7f = PB-gS + I.Ac,.S, where the superhyperfine and the quadrupole
’12),
Ceulemans et al.
110 The Journal of Physical Chemistry, Vol. 94, No. 1 1990 ~
G;BZ"
Ip=-bo
2Od8 IlnWI 100 k H I v 9379 8 M H i Gal" i 105 Modul i I I 10 Tpp
N5 AX
I
Figure 7. Schematic view of the directions of the g and A tensors, in comparison with the coordination bonds (see also Table V ) .
Figure 6 shows three spectra taken near the three eigenvectors. Table V gives the final principal values and directions with respect to a molecular xyz-system. These molecular axes are defined in accordance with the conventions in Figure 2. The xy-plane is the best plane passing through the tetraimine nitrogens. The positive z-axis points to the axial chloride ligand, while the y-axis bisects the conjugated chains, as indicated below: t C
Figure 6. Three single-crystal EPR spectra of Co(I1)-doped [Ni(CIoH2,,N8)]Cl2taken near the three eigenvector directions. Experimental parameters and &o values are specified in the figure. A comparison is made between the observed hyperfine splittings and the calculated values, including second-order terms. TABLE V: Principal Values and Axes for the g, Co Hyperfine, and CI Superhyperfine Tensors X
g
g , = 2.217 gv = 2.681 g, = 1.966 A, = 44 G (46.104 cm-I) A, = 105 G (131.104 cm-I) A, = 115 G (1 06.1O4 cm-') A, = 19 G (17.104 a")
Y
z
0.992 0.081 -0.094 -0.056 0.998 -0.020 0.079 -0.032 0.996 0.997 0.041 -0.061
4
coupling terms are omitted. The procedure followed for the estimation of the 2 and $A2 tensor elements and their diagonalization is described in ref 16. A first-order analysis of the data, based on the center of the positions of the outer hyperfine lines, provides approximate g eigenvalues (g, = 2.230, gv = 2.688, g, = 1.970) and eigenvectors from which the values of the spherical coordinates (8,q) of the magnetic field in the g-coordinate system are calculated. The hyperfine coupling is estimated from the positions of lines with the same m: values. The resulting values and directions are used to compute the second-order correction terms for each orientation, according to eq 2-4 of ref 17. These in turn yield refined g values and directions. The cycle is repeated twice in order to give a satisfactory agreement between calculated and experimental line positions.
Figure 7 shows a schematic view of the eigenvectors in comparison with the molecular bonds. The g and hyperfine principal axis systems are not quite collinear, since the angles between gi and Ai ( i = x,y,z) are 3 O , 8", and 8 O , respectively. This small misalignment, which is perhaps not significant, was not taken into account when analyzing the data and the expressions used from ref 17 suppose coincident principal axes. Figure 7 shows that the eigenvectors do not lie along the molecular bonds but in between them. From Table V, it is clear that the largest g value is along the y-axis, in contrast to the anisotropy in @-disubstitutedmacrocycles (cf. Table 11). The g, and A, eigenvectors, the normal to the best plane through the tetraimine nitrogens (N,,N5,Nlo,N14),and the Ni-Cl bond lie within 7' of each other, which is of the order of the experimental error (-So). Finally, Figure 8 shows a powder spectrum taken at 77 K. We have also measured the powder spectrum of [Co(CIOH2ON&](C104)2,diluted in the analogous Ni(I1) salt. This spectrum is similar to that in Figure 8, except that the superhyperfine structure due to the axial chloride ion is lacking. The g factors of the perchlorate complex (gl = 2.768, g2 = 2.263, g3 = 1.999) are in line with the results for the chloride complex, given in Table V. However, there is a large difference from the results reported by Nishida et al.Is A direct determination of the orientation of the
(16) Schifflers, E.;Debuyst, R.J . Magn. Reson. 1974, 14, 85. (17) Atherton, N. M.; Winscom, C. J . Inorg. Chem. 1973, 12, 383.
(18) Nishida, Y . ; Hayashida, K.; Sumita, A,; Kida, S . Bull. Chem. SOC. Jpn. 1980, 53, 2498.
hyperfine Co
superhyperfine CI
0.993
0.115
0.042 -0.172
0.984
0.039 -0.026
0.999
-0.003
The Journal of Physical Chemistry, Vol. 94, No. I, 1990 111 TABLE VI: Symmetry-Adapted Kramers Components for the Three Possible Ground States of a d7 Ion in a Tetraimine Complex with Dzh Symmetry"
IE'+ 1/2) 12B3pP) = ~ ~ ( x z ) ~ ( z-~Y')~QZP)I )~(x~ J2A,z2a)= I ( x z ) ~ ( z ~ ~ ) ( x ' - y 2 ) 2 ~ ~ ) 2 1 I2B2, 4 )= I ( x ~ B ) ( z * ) ~-( x ~ IE'- 1/2) ( 2 B 3 p c r )= il(xz)2(z2)2(x2- y 2 ) 2 ~ z a ) I I2A,z2p)= I ( x z ) ~ ( z ~ P ) ( xv~ ~ ) ~ Q z ) ~ ~ IZB2,xza) = - I ( X Z C X ) ( E ~ ) ~ ( X ~ - y 2 ) 2 Q ~ ) 2 1
"Notice the minus sign in front of 12B2,xza). This sign arises when Figure 8. Powder spectrum of Co(I1)-doped [Ni(C,oH20N8)]C12, taken at 77 K. Note the superhyperfine structure in the z-direction, due to the
axial chloride ion. g tensor in the perchlorate complex could not be carried out, since all attempts to prepare doped single crystals of sufficient size were unsuccessful.
IV. Interpretation of the EPR Results We shall avoid elaborate calculations and give preference to a simple transparent model. Such an approach is more appropriate for explaining qualitatively the connection between the d?r orbital order and the anisotropy of g and A tensors. A. "Three-State" Model. The macrocyclic ligands listed in Table 11 provide a strong equatorial ligand field that highly destabilizes the d, orbitaL3s4 Accordingly, in the ground state of a stable low-spin Co(I1) complex with a d7 configuration, the d, orbital will remain unoccupied. This leaves seven electrons for four orbitals, as shown below. d
__+_
dZ2. d x 2 - y Z ' d X Z d Y
Depending on which of the four low-lying d orbitals is singly occupied, four different ground state configurations are conceivable. However, the configuration with the unpaired electron in dX2+ is highly repulsive, since it has the three holes (one from dx19 and two from d,) localized in a single plane. This reduces the number of possible ground states to three, with the unpaired electron in dyz,d t , or d,. The DZhsymmetry labels of these states are 2B3,bz), 2Ag(z2),and 2 B 2 g ( ~ zfollowing ), the definitions of Table 1. The corresponding symmetry-adapted Kramers components are given in Table VI. Since the three states span the same two-valued E' representation of the D2hdouble group, they can interact via spin-orbit coupling. The corresponding 3 X 3 interaction matrix H is
I
e{ to 12B2,xz@).
The partner of the Kramers doublet may be generated from this equation by applying the e{ symmetry operation, both on the spatial functions and on the spins. IE'- 7 2 ) = u ~ ~ B ~ ~+zbI2A,z2p) cY) c ~ ~ B ~ , x z c(2b) Y)
+
We thus obtain a "three-state" or "three-parameter" model of the electronic ground state. The associated ground-state energy may of course be expressed as a function of the three parameters. ( E ' & f/,l%lE'& 1 / 2 ) = a2Haa4- b2Hbb 4- C2Hcc4- {(3'l2ab UC 3II2bc) (3)
+ +
Likewise, one may obtain simple expressions for the g tensor of the Zeeman splitting as a function of the three parameters a, b, and c. g, = 2.0023(a2 bZ - )'c - 4(3'l2)ab
+
g, = 2.0023(-a2
+ b2 + )'c
g, = 2.0023(-a2
XY
-+p-]
applying
I
In eq 1, Hal, Hbb, and H, denote the energies of the unperturbed 2B3,, ZAk,and 2B2gstates. The parameter {, which appears in the interaction terms, is the one-electron spin-orbit coupling constant of the Co(l1) ion ({ = 400 cm-I). Clearly, the most general solution of the energy matrix will be an eigenvector involving all three unperturbed states. As we have shown previ~usly,~ such an eigenvector may be expressed with the aid of three real normalized coefficients a, b, and c. IE'+ y2) = a12B3pvzp)+ bI2A,zZa) + C ~ ~ B ~ , X Z(2a) P)
- 4(31/2)b~
+ b2 - c2) +
(4) These expressions are similar to the published results of von Zelewsky et a1.4 The squared terms denote the spin contributions while the cross products refer to the orbital contributions. The latter terms should in principle be attenuated by orbital reduction factors.19 However, since we are only interested in qualitative trends, we shall not take these factors into account explicitly. Finally, expressions for the hyperfine tensor may also be derived, by standard procedures. A , = P[-4(3'l2)Ub (77 - K ) x (a2 + b2 - )'c + 2/7(c2- 4a2 - 3b2 - ~ U -C 3'/'bc)] ~ U C
+
+ (77 - X + b2 + c2) + 2/7(a2- 4c2 - 3b2 - ~ U -C 3 ' / 2 ~ b ) ]
A, = P[-4(31/2)b~
(-a2 A, = P[4ac 4-
(-a2
(77 -
K)
K)
X
+ b2 - )'c + '/7(a2+ 'C + 3 1 / 2 ~+b 3 1 / 2 b ~ )(]5 )
The symbols in this equation have their usual significance. For Co(I1) Schiff base complexes, von Zelewsky and co-workers4report a P value of 220 X lo4 cm-l. The parameter K , which describes the isotropic Fermi contact term, usually has a value near 0.3. However, anomalous K values are possible for a ground state with the unpaired electron mainly in dzz. In a square-planar complex, such a ground state may acquire substantial 4s character as a result of 4s-3d22 orbital interaction.2*22 This implies an increase of the spin density at the origin, yielding K values of zero or even -0.1. Before comparing the abc model with experimental results, it is well to keep in mind that the three parameters involved are not independent but obey a normalization condition: a2 b2 c2 = 1 (6)
+ +
A further constraint stems from the fact that the abc parameters (19) Hitchman, M. A. Inorg. Chem. 1977, 16, 1985. (20) McGarvey, B. R. Can. J. Chem. 1975, 53, 2498. (21) Dad, C.; Weber, J. Helu. Chim. Acta 1982, 65, 2486. (22) Ceulemans, A,; Beyens, D.; Vanquickenborne, L. G. Inorg. Chim. Acra 1982, 61, 199.
112 The Journal of Physical Chemistry, Vol. 94, No. 1, 1990
a=O
b=O
Ceulemans et al.
c
:o
CO [ a c a c e n ) Co ( a m b e n J
Figure 9. Three different orbital ordering of the d,,, dyz,and d,z orbitals in square-planar cobalt(I1) complexes of a quadridentate macrocycle. Each orbital ordering gives rise to a different anisotropy pattern (see also eq IO).
are eigenvector coefficients of a ground-state function. According to the variation principle, the associated energy, given in eq 3, must be below that of the lowest unperturbed state. This can only be realized if the spin-orbit contributions in eq 3 are negative. Hence, in addition to the normalization condition, the model parameters must also obey the following inequality:
the largest g value from the x to the y direction is seen to correspond to a reversal of d,, and dyz! This exchange of d,, and d,, is precisely what was predicted on the basis of the MO treatment in section I and Figure 2. All that was required to establish these results was the experimental determination of the orientation of the largest g component. However, the two-state approximation is insufficient for a 3‘I2ab + ac 3Il2bc < 0 (7) further examination of the g tensor of [ C O ( C , ~ H ~ ~ N since ~)]C~~, it does not explain the difference between g, and g,. Furthermore B. Analysis of the g Tensor. A convenient starting point for it is impossible to decide whether the unpaired electron resides the analysis of the g tensor is the limiting situation, where the mainly in dZ2(b2 > c2) or in d,, (b2 < c2),unless the signs of g, ground state is essentially a mixture of only two states instead and g, are known. These shortcomings of the two-state model of three. In terms of orbital energies, this “two-state” limit is may be remedied by resorting to the full three-parameter model4 reached if one of the three participating d orbitals is well below and allowing for a small admixture of the 2B3,(yz) state with the the Fermi level, so that only two magnetic orbitals remain, as eigenvector coefficient a. indicated in Figure 9. The characteristic g-tensor anisotropy of As can be seen from the master equation (eq 4), such a small the two-state limit can immediately be obtained from the master perturbation will indeed give rise to a divergence of g, and g,. equation (eq 4) by setting one of the three parameters to zero. With g, the larger of the two, the secondary anisotropy of the As an example, for a = 0, the unpaired electron is confined to xz-plane appears to be closer to the c = 0 two-state system than d,z and d,,. The corresponding expressions for the g components to the b = 0 two-state system. This clearly favors the 2A,(d,z) read: state as the dominant ground-state component. An almost perfect g, = g, = 2.0023(b2 - c’) fit of the g tensor is in fact obtained with b = 0.9944, c = -0.0994, a = -0.0369. gy = 2.0023 - 4(3’I2)bc (8) The very large value of b indicates that the ground state almost Likewise the sign condition of eq 7 reduces to coincides with the unperturbed 2A (ds) state. This is not unexpected for square-planar compounjs with weak axial l i g a t i ~ n . ~ , ~ ~ bc < 0 (9) From simple perturbation theory, the 2B2,(d,,) and 2B3,(d,,) excited states may be positioned at about 3500 and 9500 cm-l, In view of this sign condition, the orbital term -4(3’I2)bc in eq respectively. These energy estimates are highly uncertain, not 8 will be of the same sign as the spin contribution, giving rise to only because the orbital reduction factors were not taken into a value of g, that is large compared to g, and g,. Similar conconsideration but also because large changes of the energies of clusions apply to the b = 0 and c = 0 limits. For each case, one such remote states produce only minor modifications of the obtains one larger g value due to parallel orbital and spin conground-state eigenvector. tributions, together with two small and degenerate g components. Nonetheless, as we have shown, a qualitative analysis of the The resulting anisotropy patterns are summarized in eq 10. )]CI~ anisotropy of the g tensor in [ C O ( C ~ ~ H ~ ~ Nis~perfectly a = 0: gy >> g,,g, capable of assigning the orbital ordering d,z > d,, > d,, in an unequivocal way. b = 0: g, >> gx,gy C. Analysis ofthe A Tensor. Inserting the parameter values c = 0: g, >> g,,g, (10) from the g-tensor analysis in the general expressions for the A tensor (eq 5) and putting P = 220.104 cm-’ and K = 0, one obtains In this scheme, the Co(acacen) and Co(amben) complexesi0J2 A, = 3.10-4 cm-l, A, = 90.104 cm-’, and A, = 112.10-4 cm-l. clearly fall in the c = 0 group in view of their very large g, values. In view of the approximations involved and the uncertainties in This implies that for these complexes d, is well below dz2and dy., K and a-c, these values are at best only rough estimates; they as indicated in Figure 9. Such an ordering of the d r levels is nevertheless provide an approximate understanding of the exindeed expected for bischelates consisting of five-membered chains. trend. In contrast, the largest gcomponent for the [ C O ( C ~ ~ H ~ N ~ ) ]perimental C~~ complex lies along the y-axis. This anisotropy is consistent with the a = 0 limit. On the orbital energy diagram, the rotation of (23) Hitchman, M . A . Inorg. Chim. Acta 1977, 26, 231
-+
Orbital Symmetry and g Factors in a Co(I1) Complex The fact that A, and A, are much larger than A, can be explained with simplified expressions in which the spin contributions to the A components are given the limiting values of a pure ZA,(dg) ground state. A, = P[-4(3'/')~6 - 2/71 A, = P[-4(3'iz)bc
A, = P[4ac
- Y7]
+ y7]
In these expressions, the product terms, which represent the direct dipolar coupling with the orbital angular momentum, are the same as in the g-tensor expressions of eq 4 and therefore parallel the trends of the g anisotropy. This explains the large value of A,,, in agreement with the y-orientation of the dominant g component. The second term in eq 11 describes the interaction between the nuclear magnetic moment of the cobalt atom and the electron spin in a d,z orbital. This term clearly explains the large value for A,. Finally, we note the presence of superhyperfine interactions due to the coupling between the unpaired electron and the magnetic moment of the chlorine nucleus on the z-axis. A precise evaluation of this term is outside the scope of the simple three-parameter model. Nonetheless, the fact that no coupling with the equatorial nitrogen atoms is observed is consistent with the localization of the unpaired electron in a 3 d Z r 4 shybrid orbital with its main density along the z-direction and only a small equatorial lobe.
V. Discussion The phase-coupled ligator model,2 on which the present treatment was based, relates the splitting of the d?r orbitals to direct orbital interactions between the metal d orbitals and suitable ligand ?r orbitals. This point has recently been criticized by Gerloch and co-workersz4who consider that mixing of metal and ligand orbitals is only a minor effect, so that ligand electron density is the primary source of the ligand field potential. These arguments follow from a more elaborate general analysis of the ligand field formalism by W o ~ l l e y . ~ ~ In our opinion, this analysis is designed typically for Werner-type complexes with hard ionic metal-ligand bonding. In contrast, the macrocyclic ligands in Table I1 with frontier ?r levels close to the metal Fermi level seem to adhere to a more covalent (24) Deeth, R. J.; Duer, M. J.; Gerloch, M. Inorg. Chem. 1987,26, 2573. ( 2 5 ) Woolley, R. G. Int. Rev. Phys. Chem. 1987, 6, 93.
The Journal of Physical Chemistry, Vol. 94, No. I, 1990 113 type of ligand field regime, as is often found in organometallic compounds. This is borne out also by recent X a calculations on Co( 11) complexes with Schiff base ligandsz1 These calculations indeed point to ligand delocalization of the metallic d,, and d,, orbitals as the origin of the d?r orbital splitting. On the experimental side, Gerlochz4has disapproved the accepted orientation of the g tensor in Co(amben). His assertion was based on the susceptibility anisotropy study by Murray and SheahanZ6of the analogous Co(C1-amben). However it should be made clear that the accepted g, >> g,,> g, order in Co(amben) (see Table I1 and Figure 9) was determined unambiguously by doped with Co(I1). single-crystalm e a s ~ r e m e n t s ~on~ ~Ni(amben) ~*'~ Although the crystal structure of these amben complexes is unknown, they have been shown to be isomorphous" with the known Co(C1-amben) structure, leaving little doubt about the assignment in Table 11. In conclusion, the clearcut reversal of magnetic anisotropy between a-disubstituted and 0-disubstituted bischelated complexes (see Table I1 and Figure 9) provides direct experimental proof for the existence of symmetry-controlled interactions between d orbitals and ?r orbitals of conjugated ligands. Similar evidence for the validity of the phase-coupled ligator model may be found in the ligand field spectra of trischelated Cr( 111) c o m p l e ~ e s , ~ ~ ~ ~ * containing unsaturated a-diimineZ9and @-diketonatesoligands. Acknowledgment. This work was supported by a research grant from the Belgian Government (Programmatie van het Wetenschapsbeleid). A.C. is indebted to the National Fonds voor Wetenschappelijk Onderzoek (NFWO) for a senior research associateship. F.D. acknowledges support from the Fonds National Belge de la Recherche Scientifique (FNRS). Thanks are also due to Prof. P. Piret for Weissenberg measurements. We thank Prof. A. von Zelewsky for information on the EPR measurements on Co(amben). Registry No. [Co(CloHmN8)]CIz,12354 1-8 1-1; [Ni(CloH,,N8)]CIz, 64057-11-0. (26) Murray, K. S.;Sheahan, R. M. J . Chem. Soc.,Chem. Commun. 1975, 475. (27) Ceulemans, A.; Bongaerts, N. Vanquickenborne, L. G. Inorg. Chem. 1987, 26, 1566. (28) Ceulemans, A.; Bongaerts, N.; Vanquickenborne, L. G. In Photochemistry and Photophysics of Coordination Compounds; Yersin, H., Vogler, A,, Eds.; Springer-Verlag: Berlin, Heidelberg, 1987; p 31. (29) Hauser, A,; MPder, M.; Robinson, W. T.; Murugesan, R.; Ferguson, J. Inorg. Chem. 1987, 26, 1331. (30) Atanasov, M. A.; Schonherr,T.; Schmidtke, H.-H. Theor. Chim. Acta 1987, 77, 59.
