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Magnetic Resonance of Paramagnetic Complexes.

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or 0 2 , are partially dissociated by N 2 ( A 3 x 3 molecules 1104,1431
It has been suggested that the mercury 2537 A emission might be used as a test for N 2 ( A 3 3 ; ) [56,230-232J.
Excitation of NO by N?(A3C:) has been shown to
occur efficiently by
The importance of Nz(A3X:) molecules in active
nitrogen is, however, somewhat limited by their relatively low concentration, which is estimated to be
m 10-3 [N] 12041.
N2(A 3c:) t NO(X 211)
+ Nz(X
+ NO(A
Excitation of N O results in approximately one-half of
the de-exciting collisions of Nz(A 33:) with NO 12291.
Received: March 24, 1969
[A 744 IE]
German version: Angew. Chem. 82. 187 (1970)
[229] R. A. Young and G. A. S t . John, J. chem. Physics 48, 898
[230] A. Granzow, M . 2. Hoffman, N . N . Lichtin, and S . K.
Wason, J. physic. Chem. 72, 3741 (1968).
[2311 A . Granzow, M . 2. Hoffman, N . N . Lichtin, and S . K .
Wason, J . physic. Chem. 72, 1402 (1968).
(2321 R. A. Young and G. A . St. John, J. chem. Physics 48,2572
(1968); C. H. Dugan, Canad. J . Chem. 47, 2314 (1969).
Magnetic Resonance of Paramagnetic Complexes
By Heimo J. Keller and KarI E. Schwarzhans[*J
The line width of the E S R and N M R signals of paramagnetic transition metal complexes
is determined mainly by the electron spin-lattice relaxation time q-.Values of regreater
than 10-9 lead to E S R spectra that are readily resolved, while values smaller than 10-11
give N M R spectra having small line widths. Since fast relaxation processes are effective
in nearly all transition metal complexes with several unpaired electrons and in all complexes having an orbitally degenerate ground state, the N M R method has a wider scope.
The sign and magnitude of the electron-nucleus coupling can be determined with great
sensitivity from the N M R spectra, whereas only the magnitude of this interaction can be
determined from the E S R spectra. Free spin densities can be found very accurately from
the N M R shifts, and the method can therefore be advantageously applied to kinetic
measurements, e.g. on short-lived contact complexes.
1. Introduction
The use of both the electron spin resonance (ESR) and
the nuclear magnetic resonance (NMR) effects can lead
to the solution of a number of chemical problems in
connection with paramagnetic transition metal complexes. Several reviews of both methods have been
published in recent years, and results for transition
metal complexes have also been discussed 11-81, but
their combined application to paramagnetic complexes
[*I Dr. H. J. Keller and Dr. K . E. Schwarzhans
Anorganisch-chemisches taboratorium
d e r Technischen Hochschule
8 Miinchen 2, Arcisstrasse 21 (Germany)
[ l ] N M R , ESR: A. Carringfon and A . D. McLachlan: Introduction to Magnetic Resonance. Harper & Row, New York
[2] N M R : D. R. Eaton and W . D. Phillips, Advances magnetic
Resonance 1 , 103 (1965).
[3] N M R : M . L. Maddox, S. L. Sfafford, and H. D. Kaesz,
Advances organometallic Chem. 3, 1 (1966).
[4] N M R : E. DeBoer and H. van Willigen, Progr. nuciear
magnetic Resonance Spectroscopy 2, 111 (1967).
[5] N M R : A. Kowalsky and M . Cohn, Annu. Rev. Biochem.
33, 481 (1964).
[6] N M R : D. R. Eaton, A . D. Josey, and W . D. PhiNips, D I S CUSS. Faraday. SOC.
3 4 , 77 (1962).
has been largely ignored. A question of prime interest
to chemists is when to use N M R measurements in
practice, and when ESR.
2. Theoretical Principles
2.1. Resonance Conditions
The problems will be considered on the basis of the
simplest possible system, i.e. hydrogen atoms, assuming at first that these atoms are not influenced by their
neighbors, so that it is possible to discuss the resonance
properties of a single hydrogen atom.
It is well known that the hydrogen atom consists of one
proton and one electron. Each of these elementary
particles has a characteristic angular momentum
(spin), which, according to the quantum theory, can
only assume certain specific values. The angular momentum J , which differs in magnitude for the two
particles in question, is therefore, figuratively speaking,
[7] ESR: B. R. McGarvey, Transition Metal Chem. 3, 89
(1 966).
[8] ESR: W . Low: Paramagnetic Resonance in Solids. Academic Press, New York 1960.
Angew. Chem. internat. Edit.
1 Vol. 9
(1970) 1 NO. 3
restricted to two definite directions in space. Thus
there are only two possible ( 5 ) spin states for the
proton and for the electron ( J = 1/2).
Owing to the electric charge carried by the elementary
particles, the angular momentum is associated with a
magnetic moment, which can be calculated from
where eo is the charge on the elementary particle, m is
its mass, c is the velocity of light, and fi is the Planck
constant divided by 2n. However, the moments calculated from this equation, which are known as the
nuclear magneton and the Bohr magneton (P = PN and
PB) respectively, do not coincide with the magnetic
moments found for the proton and for the electron in
resonance experiments. These are given by the product
of the magneton (p) with a purely empirical correction
factor, the g factor.
Like the angular momentum vectors, the magnetic
moments of the proton and the electron are also
restricted to two directions. These two states, which
are represented by antiparallel arrows, have the same
energy provided that no external magnetic field is
acting, i.e. the energy levels of the oppositely oriented
magnetic vectors are degenerate (Fig. 1, a). Tn a
strong external magnetic field Ho, the energy of the
state in which the magnetic moment is parallel to the
external field is reduced by a certain amount, while
the energy of the state with the antiparallel orientation
of the magnetic moment is increased by the same
amount, i.e. the degeneracy is lost (Zeeman effect).
Magnetic electron levels IESRl
The splitting (AE1 or AE,) is proportional to the
magnetic moment and to the strength of the external
field (Fig. 1,b):
Since the magnetic moment of the electron, according
to eq. (I), is greater by a factor of -103 than the
moment of the proton, the splitting of the degenerate
energy levels for electrons in accordance with eq. (3)
is r n l O 3 times as large as the corresponding splitting
for nuclei. Figure 1 thus gives only a hint of the true
state of affairs.
2.2. Resonance Spectrum of a Hydrogen Atom
Absorption or emission spectroscopy can now be
carried out on the system chosen as our example. If
electromagnetic energy corresponding to the difference between the magnetic electronic or nuclear
levels (AE1 and AEz respectively) is supplied to the
system from a suitable source, the elementary particles
with the parallel spin can be raised to the higher levels,
with reversal of their magnetic moment into the antiparallel state. Two discrete frequencies are absorbed
from a broad frequency spectrum in accordance with
Since the transitions between the magnetic electronic
levels have a much higher energy than those between
the magnetic nuclear levels, ESR absorptions occur in
the microwave region (v rn l O 9 - l O l O Hz; HO rn l o 3
gauss), while NMR absorptions, even at higher field
strengths, occur in the radio wave region (v rn 106 Hz;
HOrn lo4 gauss). According to eq. (3), the magnitude
magnetic nuciear levels I N M R i
not observable
= g N PN
dE, =9.
a S
gN p, H, -112a,
AEL = g,,
H, +1/2a,
= g.
H, +1/2a,
- 1/2a,
Fig. I .
Zeeman levels of a hydrogen atom In a strong external field Ho.
Angew. Chem. internat. Edit.
VoL 9 (1970) 1 No. 3
of the splitting of the levels is determined purely by the
magnetic moments of the particles; this leads to differences in the methods used in ESR and N M R experiments. Nevertheless, the usual distinction between ESR and N M R spectroscopy does not seem to
be justified merely on the basis of experimental peculiarities. The rules applicable to the two methods are
qualitatively the same. The chemist is interested only
in the parameters of the spectra that contain essentially
chemical information; these are above all the shifts of
the resonance signals in NMR, which correspond in
practice to the g factor measured in ESR.
It has been assumed so far that the magnetic moments
of the electron and of the proton do not influence each
other. However, this is not so. There is in fact a strong
“contact interaction” between these magnetic dipoles,
which was first postulated by Ferrni for the interpretation of optical spectra [9J. This interaction has a finite
value only if the unpaired electron can be described by
a n orbital function with a finite probability for the
position of the nucleus, as e.g. for unpaired electrons
in s orbitals. The strength of the interaction depends
on the spin quantum operators of the electron s a n d
of the interacting nucleus as well as on the absolute
probability of finding the unpaired electron in the
position of the nucleus (j$(O)12):
This results in further splitting of the electronic and
nuclear levels. The electronic moments are now exposed to two different magnetic fields, i.e. the external
field HOplus the magnetic moment of the nucleus with
the nuclear moment parallel to the field direction on
the one hand, and HOminus the nuclear moment with
antiparallel orientation on the other. On insertion of
the electron-nucleus interaction, therefore, we obtain
the diagram shown in Figure 1,c, with the result that
further transitions become possible. The orientation
of the nuclear moment parallel to HOcorresponds to
MI = +1/2, while the parallel orientation of the electronic moment, because of the opposite charge, corresponds to Ms = -1/2. Thus a large number of independent hydrogen atoms would give a resonance
spectrum of four “allowed” lines. (Selection rules :
AM1 = =tl,AMs = 0 for nuclear transitions; AMs
il, AM1 = 0 for electronic transitions.) The absorption line of the nuclear transition and the absorption
line of the electronic transition exhibit splitting corresponding to equal energy differences. Two ESR lines
should be observed in the microwave region and two
N M R lines in the radio wave region (Fig. 1, c).
2.3. Relaxation
Unfortunately, this last view is still not sufficiently
close to reality, since the hydrogen atoms are also
appreciably influenced by time-dependent fields of
[9] E. Fermi, Z . Physik 60,320 (1930).
their environment. Each atom executes thermal
motions with a speed that varies with the temperature.
Since the atom has magnetic dipoles, this motion
produces an alternating electromagnetic field. If the
frequency \I, of this alternating field satisfies the
resonance condition (4), a resonance transition is induced by this radiation in neighboring atoms. In the
spectral region considered, induced emission and absorption are equally probable, so that both emission
and absorption are stimulated by the electromagnetic
“stray field”. Thermal lattice energy can thus be
converted into spin energy and vice versa. Fast transitions between the levels thus become possible, since a
particle that has been transferred to a higher level by
absorption of energy can return to the ground state by
radiationless loss of energy to the “lattice”. The lifetime of a given state is consequently shortened, sometimes to such an extent that according to the Heisenberg uncertainty relation
A E . At > %
its energy becomes uncertain. The line width of the
resonance signal increases considerably. With very
short lifetimes, this may have the result that the transitions can no longer be observed. Since the magnetic
moments of electrons are very large, a very strong
electromagnetic stray field prevails in paramagnetic
systems, as in our example of hydrogen atoms or in
dilute solutions of organic radicals, andcauses extremely
short nuclear lifetimes and hence broadening of the
NMR lines. The two absorptions expected in the radio
wave region cannot be detected. This led to the assumption that N M R spectra could not be recorded for
paramagnetic compounds. However, this is incorrect
above all for inorganic complexes [1-81; on the contrary, NMR lines of adequate sharpness are the rule in
this case.
The fact that the resonance signals of such compounds
can be detected experimentally is the result of fast
transitions between the electronic levels. If, for example, many such transitions occur during a specific
thermal motion of a hydrogen atom, i.e. if the electron
spin of this hydrogen atom changes its direction
several times during the motion, the influence of the
stray field produced by the thermal oscillation of the
magnetic dipoles on nuclear relaxation decreases.
Only a time average of all possible spin directions acts
during a translation or rotation.
For a quantitative treatment of this intuitive model,
it is necessary to define the relaxation time, i.e. the
time after which l i e of the excited spins have returned
radiationlessly to the ground state. If the spins are very
strongly coupled to the “lattice”, i.e. if a fast exchange
takes place between the energy of the spin system and
degrees of freedom of the environment, the spinlattice relaxation times are short. According to the
relation (6), resonance absorptions should then be
absent or extremely broad, as has been indicated for
the N M R absorption of the hydrogen atom.
If, however, unpaired electrons have extremely short
electron spin-lattice relaxation times, as in many
Angew. Chem. internat. Edit. / Vol. 9 (1970)
/ No. 3
transition metal complexes, i.e. if the direction oftheir
spin is reversed rapidly in comparison with the correlation time of the particles in the solution, the COUpling of the nuclear spin with the lattice is largely eliminated; the nuclear spin-lattice relaxation times again
become longer, and the line width of the N M R signals
accordingly decreases. N o ESR spectra are observed
in such cases. Thus in solutions of paramagnetic compounds, the question when N M R and when ESR
studies are possible is determined by the electron spinlattice relaxation time [10-141. With relatively long
electron spin relaxation times (down to about 10-9 s),
usable ESR spectra can be recorded, but only very
broad-lined N M R spectra. With relaxation times
shorter than 10-11 s, on the other hand, i.e. with extremely short electxon spin relaxation times, only
N M R spectra (usually with small line width) can be
recorded. The two methods thus complement each
other excellently [Is].
In addition to the intramolecular transitions, fast
intermolecular processes also have a similar averaging
effect o n the time-dependent internal fields. If, for
example, the unpaired electrons in a molecule are
strongly delocalized, the orbitals, which have a broad
probability distribution, may overlap slightly in concentrated solution; an exchange interaction, in which
the spin can also reverse rapidly, becomes possible.
The requirements for this are often satisfied by organic
radicals [16-1*1, but less often by complex compounds.
3. Electron Spin-Lattice Relaxation Times
We are thus faced with the question of the parameters
that govern the electron spin-lattice relaxation times
of metal complexes, in order to cIarify whether to
carry out N M R and/or ESR studies. The interpretation of the electron spin relaxation times of paramagnetic transition metal complexes has been discussed
only quite recentlyI191, so we will confine ourselves
here to just the essential aspects. Since the mechanisms
are more complicated for a n effective relaxation in
complexes containing several unpaired electrons (zerofield splitting), it seems reasonable to confine the dis[lo] N . Bloembergen, E . M . Purcel, and R . V. Pound, Physic.
Rev. 73, 679 (1948).
[I 11 I . Solomon, Physic. Rev. 9Y, 559 (1955).
[12] N . Bloembergen and L . 0 . Morgan, J . chem. Physics 34,
842 (1961).
[13] R . A . Bernheim, T . H . Brown, H . S . Gutovsky, and D . E.
Woessner, J. chem. Physics 30, 980 (1959).
1141 H . M . McConnell and R . E. Robertson, J. chem. Physics
29, 1361 (1958).
[15] D . R . Euron, J. Amer. chem. SOC.87, 3097 (1965).
[16] M . E. Anderson, G . E . Pake, and T . R . Tuttle, J. chem.
Physics 33, 1582 (1 960).
[171 G. J . Hoiitink and J . Townsend, J. chem. Physics 34, 507
[181 K . H . Huusser, H . Brunner, and J . C. Jochims, Molecular
Physics 10,253 (1966).
[191 W . B. Lewis and L . 0 . Morgan, Transition Metal Chem.
4, 33 (1968).
Angew. Chem. internat. Edit.
1 Vof. 9
/ No. 3
cussion to compounds with S = 112, i.e. with only one
free electron spin. As a rough simplification, we can
say that N M R absorptions with small line widths
should be obtained for most complexes containing
several unpaired electrons (the only exceptions are
ions with an S ground state, such as Mn2+ and Fe3+).
These complexes are therefore particularly suitable
for N M R studies [20-261.
On the other hand, in complexes having only one unpaired electron, the electron spin-lattice relaxation
time is largely dependent on the symmetry and strength
of the ligand field. According to an empirical relation [271
A s . 104
To =
the electron spin-lattice relaxation time T~ is determined mainIy by the energy difference between the highest
occupied and the lowest unoccupied electron levels (A)
and by the temperature. Reference was made earlier
to the dependence of the line width on the spin-orbital
coupling constant A in complexes with varying A
values [281; its effect on the relaxation time need not be
considered further here.
At the same temperature and at comparable magnetic
field strengths, ‘ce for various metal complexes depends
mainly on A. In paramagnetic complexes with orbitally degenerate ground states, the highest occupied
and the lowest unoccupied levels have the same energy,
so that A should be zero. Though thermal motion and
fields of neighboling molecules cause slight splitting,
all metal complexes with orbitally degenerate ground
states, according to eq. (7), have extremely short
electron spin-lattice relaxation times. ESR spectra
should therefore be expected only at extremely low
temperatures (a few OK), whereas N M R spectra
should be very easy to record for compounds of this
T o clarify this point further a short discussion of the
splitting of d orbitals in transition metal complexes
having different ligand field symmetries is given. According to a simple (electrostatic) ligand field
scherner291, the five d states (Fig. 2) split up into an
undistorted or tetragonally distorted octahedral ligand
field, as shown in Figure 3.
[20] G. N . La Mar and L . Sacconi, J. Amer. chem. SOC.89,2282
[21] G . W . Everett j r . and R . H . Holm, Inorg. Chem. 7, 776
1221 P. K. Burkert, H . P. Fritz, W . C. Gretner, H. J . Keller, and
K . E . Schwurzhans, Inorg. nuclear Chem. Letters 4, 31 (1968).
[23] F. A . Hart, J . E. Newberry, and D . Show, Chem. Commun. i967, 45.
[24] R . W . Kluiber and W . De W . Horrocks j r . , J. Amer. chem.
SOC.88. 1399 (1966).
[25] J . Happe and R . C. Ward, J. chem. Physics 39, 1211 (1963).
1261 G . N . La Mar, J. Amer. chem. SOC. 87, 3567 (1965).
1271 G . Schoffu: ESR in d e r Biologie. Verlag G . Braun, Karlsruhe 1964, p. 29.
[28] K . H . Hausser, Naturwissenschaften 48, 426 (1961);
2. Elektrochem., Ber. Bunsenges. physik. Chem. 65,636 (1961).
I291 C. J . Bullhausen: Introduction to Ligand Field Theory.
McGraw-Hill. New York 1962.
d orbitals (schematic).
are extremely difficult to obtain 130-331. On distortion
of the ligands toward a planar arrangement, the levels
split into an E and a Bz state (Fig. 4, b). The ground
state is not further orbitally degenerate, so the width
of the ESR lines must decrease with increasing
distortion, while that of the NMR lines increases,
since T~ increases with A [eq. (7)]. The field of the
ligands can be varied in the bis(2-alkyliminomethylphenolato)copper(II) compounds ( I ) (Fig. 5) by varying the N-substituent 1343.
1 d;
free metal
Fig. 3. Splitting of the five d orbital functions in an octahedral field
(a) and with tetragonal distortion (h).
If the lower T2gstates contain 1,2,4, or 5 electrons and
the higher Eg states 1 or 3 electrons, the result is an
orbitally degenerate ground state with A m 0. This
situation is found e.g. in regular octahedral complexes
of T P , VlV, or Cr" and in regular tetrahedral complexes of Cu", Ti"', and VI1, to give only a few
If the regular arrangement of the ligands is disturbed,
e.g. by a Jahn-Teller effect, the degenerate orbital
functions fan out farther, the distance A between them
increasing with increasing distortion. The electron
spin-lattice relaxation time is thus a function of the
degree of distortion. The line width in the NMR and/
or ESR spectra can accordingly be used indirectly to
deduce the arrangement of the ligands. For example,
on transition from an octahedral to a planar arrangement in dl or d2 complexes, the ESR lines are expected
to become narrower while the N M R lines should
become broader.
This expectation can be confirmed for CuII(d9) complexes with various ligand field symmetries. Cu2+ in
regular tetrahedral coordination, similarly to the octahedrally coordinated Ti3+ ion, is in a triply degenerate
2T2 state [291 (Fig. 4, a); ESR spectra of such complexes
Fig. 4. Energy of the one-electron orbital functions of a tetracoordinate d9 ion in the regular tetrahedral (a) and distorted tetragonal (h)
ligand fields.
In the comparison of the N-tert-butyl (la) with the
isopropyl derivative ( I b ) (Fig. 5), the former was
expected, on steric grounds, to exhibit a greater angle of
twist between the planes of the practically planar
ligands 1351, and hence also to give a greater ESR line
[30] C . A . Bates, W . S . Moore, K . J . Standly, and K . W . H .
Stevens, Proc. physic. SOC.79, 73 (1962).
[31] C . A . Bates, Proc. physic. SOC.83, 465 (1964).
[32] M . Sharnoff, J. chem. Physics 42, 3383 (1965).
[33] R . E . Dietz, H. Kamimura, M . D . Sturge, and A . Yariv,
Physic. Rev. 132, 1559 (1963).
[34] H . P . Fritz, B. M . Golla, and H. J . Keller, Z . Naturforsch.
21b, 1015 (1966).
1351 T . P . Cheeseman, D . Hall, and T . N . Waters, Nature (London) 205, 494 (1965).
Angew. Chem. infernaf.Edit. Vol. 9 (1970) No. 3
Fix. 7. 1H-N MR spectra of bis(2-isopropy1iminomethylphenolato)copper(i1) ( l b ) in CDCI, a t 70 (a) and 20°C (b).
Fig. 5 .
Structure of
As is shown in Figure 6, the two complexes give very
different line widths at the same temperature (77 OK),
i.e. 1.5 and 40gauss respectively. Contrary to expectation, therefore, ( l a ) appears to have a more coplanar arrangement of the ligands, despite the expected
50 gauss
50 gauss
Fig. 6. ESR spectra of (a) bis(2-rerf-butyliminomethylphenolato)copper(l1) ( l a ) and (b) bis(2-iso~ropyliminomethylphenolato)copper(11)
( I b ) incorporated into the corresponding ZnIr complexes in the direction
Ho 11 c a t 77 “K.
enhanced steric hindrance. This surprising result was
confirmed by X-ray studies, which show that the twist
angle is 45 in ( l a ) [361, as compared with 60” in
(Ib) (371. The line width of the ESR absorptions thus
provides important information about the symmetry
of the ligand field.
The observed large ESR line widths at room temperature suggest, on the other hand, that the compounds
(1) with an approximately tetrahedral ligand field
should give N M R spectra with reasonable line widths.
1H-NMR absorptions of these complexes are in fact
~[36] 7.P . Cheeseman, D . Hall, and T. N . Waters, J. chem. SOC.
(London) A 1966, 685.
[37] P. L. Orioli and L . Sacconi, I. Amer. chem. SOC.88, 277
Angew. Chem. infernal. Edit. / Vol. 9 (1970)J No. 3
readily observed having a line width of about 100 Hz
(20 “C) 1381 (Fig. 7, b).
These observations confirm the conclusion that the
N M R and ESR line widths of the spectra of paramagnetic complexes in solutions of equal concentration are
roughly inversely proportional to one another 1151.
This can be said of complexes which are accessible by
only one method as well as of species for which both
methods can be used 138-411.
The dependence of the line width on the temperature
can be seen from what has been said already. According to eq. (7), a temperature rise considerably shortens
the electron spin-lattice relaxation time. Complexes
( 1 ) with an approximately tetrahedral ligand field give
a very broad ( m 1000 gauss) structureless signal in the
ESR spectrum at room temperature, while the N M R
absorptions have line widths of about 100 Hz, which
become narrower with rising temperature (Fig. 7, a).
Well resolved N M R spectra are obtained at higher
temperatures, and well resolved ESR spectra at lower
temperatures, since the unstructured ESR line observed a t room temperature has a distinct hyperfine structure a t 77 OK. Both N M R and ESR studies can therefore be carried out on complexes of this type by varying
the temperature.
It should be noted that ‘ c ~i s large for complexes with
“strong” ligands; in these complexes, the orbital
moment, and hence the cause of effective relaxation, is
eliminated by substantially covalent metal-ligand
bonds. Thus most of the paramagnetic organometallic
complexes have long electron spin relaxation times and
behave in resonance experiments as free organic
radicals 142,431.
[38] H . P. Fritz, B. M . GoIIa, H . J . Keller, and K . E. Schwarzham, Z. Naturforsch. Zlb, 725 (1966).
[39] R. Prins, P . Biloen, and J . D . W . van Voorst, J . chem.
Physics 46, 1216 (1967).
[40] Y. S . Karimow, V. M . Tschibrikin, and I . F. Schtschegolew,
J. Physics Chem. Solids 24, 1683 (1963).
[41] H . P. Fritz, F. H . Kohler, and K . E . Schwarzhans, J. organometallic Chem. 16, 1 4 (1969).
[42] H . J. Keller, Z. Naturforsch. 236, 133 (1968)
[43] H . J. Keller and H. Wawersik, Z. Naturforsch. 2Ob, 939
20 1
Attempts to compare the line width of N M R absorptions of different nuclei in a given paramagnetic complex show that the line width is influenced above all by
the magnitude of the nucleus-electron coupling, i.e.
the interaction measured by the value of ai. Results of
N M R experiments on organic radicals suggest that the
line width increases with thevalue of a: c1.11713,187441.
This is obviously also true of the paramagnetic transition metal complexes. Owing to a “direct” interaction
(cf. Section 2.6), the protons nearest to the metal ion
often have the largest spin density, and hence also the
greatest value of ui.Fig. 8 shows the 1H-NMR spectrum
of bis(salicylaldehydato)bis(pyridine)nickel(Ir)
(Fig. 9).
dipoles have only a small effect on the electron levels.
They have an effect of second order on the position of
the ESR absorptions, but the number of fines observed
is determined by the number and nature of the nuclei
that interact with the unpaired electron. “Hyperfine
splitting” (measured as ai in the units gauss or Hz)
appears (Fig. 6), the magnitude of this splitting increasing with the probability of finding the unpaired
electron in the position of the nucleus with which it is
in interaction r**7,81.
As was mentioned earlier, narrow N M R lines can be
recorded only if the electron spin relaxation times are
extremely short, i e . if the transitions between the
electron levels are extremely fast. This leads to the observation that a nucleus situated in the neighborhood
of such a rapidly relaxing electron spin experiences
only an averaged magnetic field due to the unpaired
electron, and includes also the hyperfine fields if the
electron spin relaxation time is very short in relation
to that of the reciprocal nucleus-electron interaction
Fig. 8. IH-NMR
Fig. 9.
Structure of bis(salicylaldehydato)bis(pyridine)nickel(I
The signals of the high spin density protons close to
the metal ion exhibit more pronounced broadening;
this is true in particular of the signals of the pyridine
protons in the GI position, which almost dive into the
electron cloud of the Ni”. The line width can be used
for identification of the protons if the structure of the
complex is approximately known [45-471.
4. Number and Position of the ESR and NMR
For example, a proton cannot then distinguish between the various electron spin orientations. The
N M R splitting (Fig. 1, c) disappears. Only one absorption signal is then observed, situated at the center
of gravity of the intensities of the two original lines,
which had unequal intensity [481. This stems from the
fact that according to
, @ % p H @
< l/ai
exp ( g P Hn M l k T d
the population of the lower levels is significantly
greater at room temperature than that of the higher
levels. The transition with the higher energy (A& in
Fig. 1,c) thus gives a higher absorption intensity than
that with the lower energy (AE& which joins levels
with smaller differences in population. The center of
gravity of the intensities of the two lines is thus not
given by the arithmetic mean, but is situated at somewhat lower field strengths. Pictorially speaking, there
are more electrons with orientation parallel to the
external field than with the antiparallel orientation in
the neighborhood of the nuclei. The external field is
reinforced, and the process corresponds to shielding,
which results in a displacement to lower field strengths.
The displacements increase with falling temperature
[eq. (9)], and increase with the number of unpaired
electrons per molecule. They show the same trend as
the susceptibility of paramagnetic compounds 1491.
It can be seen from the above discussion that though
the magnetic levels of the nuclei are greatly influenced
by the strong magnetic electronic dipoles, the nuclear
[45] H . P . Fritz, W . C . Grentner, H . J . Keller, and K . E.
Srhwarzhans, Z. Naturforsch. 236, 906 (1968).
[46] H . P . Fritz, B. M . Gollu, H . J . Keller, and K. E. Schwarzhans, Z . Naturforsch. 22b, 216 (1967).
1471 H . P . Fritz, H . J . Keller, and K. E. Schwarzhans, J. organometallic Chern. 6, 652 (1966).
[48] H. M . McConnell and D . B. Chesnut, J. chern. Physics 28,
[44] K . H. Hausser, Proc. XIV. Colloque Ampere, Ljubljana
1966, p. 1169.
107 (1958).
[49] H. M . McConnell and C . H. Holm, J. chern. Physics 28,
749 (1958); 27, 314 (1957).
Angew. Chem. internut. Edit. / Vol. 9 (1970)
/ NO. 3
For comparison with the order of magnitude of ESR
splitting, one can define a paramagnetic shift 8,[181,
which at room temperature is
Free spin densities can thus be measured much more
accurately by the N M R method, since shifts of up to
0.01 ppm are readily detectable, whereas an ESR
splitting of less than 0.05 gauss cannot be detected.
Moreover the direction of the shift gives the sign of the
constant ai, and hence of the coupling, which is not
given by ESR spectra. The use of the NMR method
for paramagnetic complexes thus offers two important
advantages over ESR studies.
5. NMR Results
The first successful experiments were carried out o n
various paramagnetic bis(x-cyclopentadieny1)metal
complexes 1493.
Of the many examples reported so far[2,4,50--561,only
a few typical measurements on bis(aminotropinoiminato)nickel(rI) complexes will be discussed at first.
The metal ions have a 3T2 ground state (Fig. 4, a) in
the tetrahedral ligand field, but a diamagnetic 1 Al,
ground state with a square-planar arrangement of the
ligands. The N M R line widths are a few hertzr261.
The activation energy o f the change from the paramagnetic to the diamagnetic conformation and back
can be determined from the shifts found a t various
temperatures [21.
The spin density at various points in the molecule can
be calculated from the paramagnetic shifts of the
protons, so that it has been possible to clarify the
nature of the transfer of free spin density[*] to the
ligands. Both cs and x bonds between the central metal
and the ligand may be involved.
dition to spin transfer via metal-ligand bonds, strong
direct metal-hydrogen interactions are also possible.
By overlap of suitable metal orbitals with hydrogen
orbitals of adjacent ligand protons, spin density can be
transferred “directly” to these protons. The relationships are particularly clear in the bis(x-cyclopentadieny1)metal complexes [57-593.
According to the usual rules, which are based either
on MO or on VB models, some of the unpaired electrons of the central metal ions should be distributed,
via the metal-ligand bond, over the molecular orbitals
involving the carbon pz functions of the rings. These
orbital functions would then have a considerable
“positive” spin density, which should lead to strong
deshielding of the carbon nuclei, and hence to displacements to lower fields for any 13C absorption observed.
Neighboring protons are not affected by this interaction.
Differentiation between “positive” and “negative”
spin densities is found to be necessary when the interaction between protons and free electrons in carbon
orbitals is also taken into account. As is shown in
particular by the ESR spectra of organic radicals 111,
the magnetic electron levels are split by the moments
of adjacent protons (as shown in Figure 1, c for the
hydrogen atom). According to eq. (9,this is possible
only if the orbital function by which the unpaired
electron can be described has a non-zero value at the
position of the proton.
The problem is solved mathematically by admixture
of electronically excited states with the ground state
(configuration interaction) with the result that free
Table I. IH-NMR data
metal complexes.
for paramagnetic bis(rr-cyclopentadieny1)-
Whereas the spin densities on the aromatic ligands in
the tetrahedral nickel(I1) complexes mentioned, which
have alternating signs, clearly point to transfer by x orbital functions 121, predominant cs delocalization was
postulated in particular for the hexacoordinate
nickelfrr) and cobaltfn) complexes 1251.
- 24.8
- 30.0
However, the argument used to distinguish between cs
and x delocalization seems questionable a t first. In ad-
- 29.7
- 29.6
- 28.2
-- 120
- 36
- 16.0
[50] R. J . Fitzgerald and R. S. Drago, J. Amer. chem. SOC.90,
2523 (1968).
[51] G. N . La Mar, Inorg. Chem. 6 , 1921 (1967).
I521 B. 5. Wayland and R . S . Drago, Inorg. Chem. 7 , 628
[53] F. Rohrscheid, R. E. Ernst, and R . H . Holm, Inorg. Chem.
6 , 1607 (1967).
[54] B. 8. Waylandand W. L. Rice, Inorg. Chem. 5 , 54 (1966).
[55] P . 5.Burkerr, H . P . Fritz, W . Gretner, H. J . Keller, and
K . E. Schwarzhans, Inorg. nuclear Chem. Letters 4, 237 (1968).
f561 D . Shaw and E . W . Randall, Molecular Physics 10, 41
[*I T h e absolute magnitude of the probability of finding a n
unpaired electron a t a given point is generally referred to as
t h e “free spin density”.
Angew. Chem. internat. Edit. / Vol. 9 (1970) / No. 3
- 18.1
[a] At room temperature; the shifts are given relative to the corresponding protons in 1,l’-dimethylferrocene with the positive sign toward
higher field strengths.
[b] M . F. Rerrig and R. S. Drugo, Chem. Commun. 1966, 891.
[57] H . P . Fritz, H . J . Keller, and K . E. Schwarzhans, Z. Naturforsch. 22b, 891 (1967).
IS81 H . P . Fritz, H . J . Keller, and K . E. Schwarzhans, J. organometallic Chem. 7, 105 (1967).
1591 H . P . Fritz, H. J . Keller, and K . E. Schwarzhans, 2. Naturforsch. 23b, 298 (1968).
spin density is transferred via the C-H a bond into
suitable hydrogen orbitals. However, the positive spin
density in the pz orbital of carbon is so strongly
polarized by the paired electrons involved in the C-H
bond that the sign of the spin density at the proton is
reversed. The negative spin density shields the proton
from the field, with consequent signal displacement to
higher fields. It is clear from the 1H-NMR shifts given
in Table 1 for bis(x-cyclopentadieny1)metal complexes
that this model is unsatisfactory. Since these results
also cannot be explained by a “pseudo-contact interaction”[5*] or by polarization of the bonding electrons 1601, a novel mechanism was postulated.
According to a simple term diagram (Fig. lo), the
resonance properties depend solely on the number of
electrons in the degenerate non-bonding metal orbitals
0; and 8, and in the antibonding molecular orbital of
cIg ,n pg13d I
Fig. 10. Term diagram for [M(CsHshI (M
3d metal).
In V ( ? F - C ~ H ~three
) ~ , electrons are distributed over the
and 6,; these projecting
three orbitals of symmetry
vanadium orbitals, which are situated between the
cyclic ligands, can overlap with the sterically favorable
hydrogen orbitals of the ligand protons. The hydrogen-metal combination is occupied by an unpaired
electron. Unlike in the above-mentioned transition via
the carbon atoms, positive spin density can be transferred “directly” to the hydrogen atom in this way.
The protons of the ligand thus experience strong deshielding, and the resonance signal appears at a lower
field strength. This is true of all complexes with unfilled metal orbitals of 5g and 6, type. “Direct” spin
[60] D. A . Levy and L. E. Orgel, J.rnolecular Physics 3, 583
transfer is no longer possible if these metal orbitals,
which can interact favorably with the ring protons, are
fully occupied by electron pairs (ferrocene). According
to the term diagram given, further electrons (in the
complexes CO(X-C~H&and Ni(x-CgH5)~)are packed
into the antibonding molecular orbitals of the type xi.
The free spin density in these orbitals which involves
the ligand pz carbon functions and metal functions
comes from the central metal ion without spin reversal,
so that, as in the model described earlier, the ring C
atoms have a positive spin density, which is then transferred to the H atoms with sign reversal. The protons
are thus strongly shielded, and signal displacements to
higher field strengths result. The data in Table 1 are as
expected. The shifts of protons of substituted cyclopentadienyl ligands and paramagnetic bis(x-benzene)metal complexes also agree with this model [59J.
It seems worth mentioning the result of an electron
diffraction study on bis(x-cyclopentadieny1)metal
complexesr611, according to which the H atoms are
bent out of the plane of the ring and toward the central
metal atom. This could be explained by weak hydrogen
bonding between M and C.
On the basis of considerations such as this, it is at
least questionable whether it is possible to distinguish
between a delocalization via metal-ligand bonds and
the direct metal-hydrogen interaction corresponding
to “through-space” electron-nucleus coupling 1453. The
decay of positive spin densities with increasing distance from the central metal ion has until now been
regarded as a typical characteristic of 5 delocalization.
However, the same is to be expected for direct M-H
interaction, which is probably often the main cause of
shifts of the 1H-NMR signals. The direct interaction can
be averaged out, for example, in the rapidiy rearranging
“tetrahedral” nickel(rr) complexes, and pure x delocalization has in fact been found for these compounds [*I.
Thus though very small spin densities can be detected
experimentally, it is possible only in a few cases to
determine definitely how the unpaired electrons are
transferred to ligand atoms. From the chemist’s point
of view, however, it is usually most interesting to
know how many unpaired electrons are present and
how they are distributed, whilst the mechanism of
transfer is of less importance. Altogether, the small
contact shifts (a few ppm), though important in structure analysis, are not suitable as a source of information on the reactivity of a part of a molecule.
5.1. Pseudo-Contact Shifts
The NMR spectra of paramagnetic complexes are
influenced additionally by possible pseudo-contact
interactions 1143, whose magnitude in accordance with
[61] I . A . Ronova and N . V . Alekseew, 2. strukturnoj Chim. 7,
886 (1966).
Angew. Chem. internat. Edit. Vol. 9 (1970) J NO. 3
depends mainly on the steric relation of the nuclei to
the central metal ion and on the anisotropy of the g
factor. However, appreciable signal shifts occur only
for compounds in which the unpaired electrons are
largely localized on the central ion. These include
compIexes of the lanthanidesr22.231 and of the actinides [62,631, in which the unpaired electrons remain in
“inner” orbitals that are only slightly affected by the
ligands, and complexes of 3d metals with “weak”
ligands. It seems unlikely [671 from recent 14N-NMR
investigations on some ion associates [551 that the
IH-NMR shifts observed for these substances are
really due to pseudo-contact interactions 164-661.
5.2. Time-Dependent Systems
Since even small changes in spin density cause relatively large N M R shifts, it is possible to detect even
very short-lived complexes between a paramagnetic
and a diamagnetic molecule [2,4,54,55J.It is particularly advantageous here that under the conditions of
a fast exchange, i.e. when the diamagnetic partner is
present in a large excess, the line widths found are
relatively small. If, for example, excess pyridine is
added to the cobalt(rr) complex shown in Figure 9,
the absorption signals of the pyridine protons become
sharper (Fig. 11).
In the presence of small quantities of paramagnetic
metal ions, it is possible in this way to determine the
positions in the diamagnetic molecule where the metal
ion is particularly readily attached from the line widths
and shifts [2,41.
We are grateful to Professor H. P. Fritz, without whose
suggestions and constant encouragement our own work
would have been impossible. We also fhank the Deutsche Forschungsgemeinschaft and the Fonds der Chemischen Industrie for rheir generous financial support.
B. M . Golla, P . B. Burkert, and W . Gretner have contributed to the success of the investigations by discussion
and experiment.
Received: January 2, 1969
[A 747 IE]
German version: Angew. Chem. 82, 227 (1970)
Translated by Express Translation Service, London
- 50
Fig. 11. I H-N M R spectra of
cobalt(i1) with excess pyridine.
0 10
Angew. &hem. internat. Edit. / Vol. 9 (19701 ,INo. 3
I621 R . yon Ammon, B. Kanellakopulos, and R . D . Fisrher,
Chern. Physics Letters 2, 513 (1968).
1631 J. C . Sheppard and J . L . Burdett, Inorg. Chem. 5 , 921
1641 W . D . Horrocks jr.. R . H . Fisclier, J . R . Hutchison, and
G . N . La Mar, J. Arner. chem. S O C . 88, 2436 (1966).
1651 G. N . La Mar, J. chem. Physics 41, 2992 (1964).
1661 J. W . Larsen and A . C. Wahl, Inorg. Chem. 4,1281 (1965).
1671 H . J . Ke//er: NMR-Basic Principles and Progress. Springer, Berlin 1970.
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