Comprehensive coordination chemistry II vol 2

Introduction to Volumes 1 and 2
In this first two volumes of Comprehensive Coordination Chemistry II we have endeavored to lay
down the fundamentals of coordination chemistry as it is understood in the early part of the
twenty-first century. We hope to have provided all the necessary fundamental background
information needed to prosecute coordination chemistry in the physical and theoretical laboratory
and to appreciate fully the information provided in the remaining volumes of this treatise.
These volumes contain 112 contributions from some 130 outstanding, internationally known,
contributors. They are subdivided into nine major sections whose content is described briefly
below. The contributors were asked to emphasize developments in the field achieved since 1980
and since the publication of CCC (1987).
1. LIGANDS – a survey of the syntheses, characterization, and properties of many of the more
commonly employed ligands.
2. SYNTHESIS, PURIFICATION AND CHARACTERIZATION OF COORDINATION
COMPOUNDS – including a detailed survey of aqua metal ions, the use of solvents,
chromatographic methods, and crystal growth techniques.
3. REACTIONS OF COORDINATED LIGANDS – dealing with the chemistry of molecules
such as oxygen, nitric and nitrous oxide, carbon dioxide, oximes, and nitriles
4. STEREOCHEMISTRY, STRUCTURE, AND CRYSTAL ENGINEERING – structure
and stereochemistry involving lone pair effects, outer sphere interactions, and hydrogen
bonding.
5. NEW SYNTHETIC METHODS – nine contributions dealing with a wide range of newer
methodologies from biphasic synthesis to sol–gel to genetic engineering.
6. PHYSICAL METHODS – a very extensive chapter incorporating 34 contributions detailing
the enormous breadth of modern physical methods.
7. THEORETICAL MODELS, COMPUTATIONAL METHODS, AND SIMULATION –
17 contributions illustrating the wealth of information that can be extracted from a range of
computational methods from semi-empirical to ab initio, and from ligand field theory to metal–
metal exchange coupling to topology, etc.
8. SOFTWARE – a brief glimpse of some of the packages which are currently available.
9. CASE STUDIES – putting it all together – eight studies which reveal how the many physical

and theoretical techniques presented earlier in the volume can be used to solve specific
problems.
The creation of these volumes has been an exciting, challenging, time-consuming, and allabsorbing experience. The Editor hopes that it will also be a rewarding experience to the readership. Finally, the Editor is greatly indebted to Paola Panaro for her untiring assistance in the
considerable secretarial work associated with these volumes – without her it would have been
impossible. He is also much indebted to his wife Elaine Dodsworth for her emotional support!
A B P Lever
Toronto, Canada
March 2003

xvii


COMPREHENSIVE COORDINATION CHEMISTRY II
From Biology to Nanotechnology
Second Edition
Edited by
J.A. McCleverty, University of Bristol, UK
T.J. Meyer, Los Alamos National Laboratory, Los Alamos, USA

Description
This is the sequel of what has become a classic in the field, Comprehensive Coordination Chemistry. The first
edition, CCC-I, appeared in 1987 under the editorship of Sir Geoffrey Wilkinson (Editor-in-Chief), Robert D.
Gillard and Jon A. McCleverty (Executive Editors). It was intended to give a contemporary overview of the
field, providing both a convenient first source of information and a vehicle to stimulate further advances in the
field. The second edition, CCC-II, builds on the first and will survey developments since 1980 authoritatively
and critically with a greater emphasis on current trends in biology, materials science and other areas of
contemporary scientific interest. Since the 1980s, an astonishing growth and specialisation of knowledge
within coordination chemistry, including the rapid development of interdisciplinary fields has made it
impossible to provide a totally comprehensive review. CCC-II provides its readers with reliable and informative
background information in particular areas based on key primary and secondary references. It gives a clear

overview of the state-of-the-art research findings in those areas that the International Advisory Board, the
Volume Editors, and the Editors-in-Chief believed to be especially important to the field. CCC-II will provide
researchers at all levels of sophistication, from academia, industry and national labs, with an unparalleled
depth of coverage.

Bibliographic Information
10-Volume Set - Comprehensive Coordination Chemistry II
Hardbound, ISBN: 0-08-043748-6, 9500 pages
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Volumes
Volume 1: Fundamentals: Ligands, Complexes, Synthesis, Purification, and Structure
Volume 2: Fundamentals: Physical Methods, Theoretical Analysis, and Case Studies
Volume 3: Coordination Chemistry of the s, p, and f Metals
Volume 4: Transition Metal Groups 3 - 6
Volume 5: Transition Metal Groups 7 and 8
Volume 6: Transition Metal Groups 9 - 12
Volume 7: From the Molecular to the Nanoscale: Synthesis, Structure, and Properties
Volume 8: Bio-coordination Chemistry
Volume 9: Applications of Coordination Chemistry
Volume 10: Cumulative Subject Index

10-Volume Set: Comprehensive Coordination Chemistry II


COMPREHENSIVE COORDINATION CHEMISTRY II

Volume 2:
Fundamentals: Physical Methods,
Theoretical Analysis, and Case Studies
Edited by
A.B.P. Lever
Contents
Section I - Physical Methods
Nuclear Magnetic Resonance Spectroscopy (P. Pregosin, H. Rueegger).
Electron Paramagnetic Resonance Spectroscopy (S.S. Eaton, G.R. Eaton).
Electron-Nuclear Double Resonance Spectroscopy and Electron Spin Echo Envelope
Modulation Spectroscopy (S.S. Eaton, G.R. Eaton).
X-ray Diffraction (W. Clegg).
Chiral Molecules Spectroscopy (R.D. Peacock, B. Stewart).
Neutron Diffraction (G.J. Long).
Time Resolved Infrared Spectroscopy (J.J. Turner et al.).
Raman and FT Raman Spectroscopy (I.S. Butler, S. Warner).
High Pressure Raman Techniques (I.S. Butler, S. Warner).
Resonance Raman: Coordination Compounds (J. Kincaid, K. Czarnecki).
Resonance Raman: Bioinorganic Applications (J. Kincaid, K. Czarnecki).
Gas Phase Coordination Chemistry (P.B. Armentrout, M. Rodgers).
X-Ray Absorption Spectroscopy (J. Penner-Hahn).
Photoelectron Spectroscopy (Dong-Sheng Yang).
Electrochemistry: General Introduction (A.M. Bond).
Electrochemistry: Proton Coupled Systems (K.A. Goldsby).
Electrochemistry: Mixed Valence Systems (R.J. Crutchley).

Electrochemistry: High Pressure (T.W. Swaddie).
Ligand Electrochemical Parameters and Electrochemical-Optical Relationships (B. Lever).
Mossbauer: Introduction (G.J. Long, F. Grandjean).
Mossbauer: Bioinorganic (E. Muenck et al.).
Optical (Electronic) Spectroscopy (C. Reber, R. Beaulac).
Stark Spectroscopy (K.A. Walters).
Electronic Emission Spectroscopy (J. Simon, R.H. Schmehl).


Magnetic Circular Dichroism (W.R. Mason).
Magnetic Circular Dichroism of Paramagnetic Species E.I. Soloman et al.).
Solvation and Solvatochromism (W. Linert et al.).
Mass Spectrometry
Neutralization-Reionization Mass Spectrometry
Electrospray Mass Spectroscopy
Magnetism: General Introduction
Electronic Spin Crossover
Excited Spin State Trapping (LIESST, NIESST)
Notes on Time Frames

Section II - Theoretical Models, Computational Methods and Simulation
Ligand Field Theory
Angular Overlap Model (AOM)
Molecular Mechanics
Semiempirical SCF MO Methods, Electronic Spectra and Configurational Interaction (INDO)
Density Functional Theory (DFT)
Time Dependent Density Functional Resonance Theory (DFRT)
Molecular Orbital Theory (SCF Methods and Active Space SCF)
Valence Bond Configuration Interaction Model (VBCI)
Time-dependent Theory of Electronic Spectroscopy

Electronic Coupling Elements and Electron Transfer Theory
Metal-metal Exchange Coupling
Solvation
Topology: General Theory
Topology: Assemblies
Electrode Potential Calculations
Comparison of DFT, AOM and Ligand Field Approaches
MO description of Transition Metal Complexes by DFT and INDO/S

Section III - Software
AOMX - Angular Overlap Model Computation
GAMESS and MACMOLPLT
CAMMAG
LIGFIELD
ADF
DeMON
Survey of Commercial Software Websites

Section IV - Case Studies
Spectroscopy and Electronic Structure of [FeX ] n (X=CI,SR)(E.I. Soloman, P. Kennepohl).
4
Mixed Valence Dinuclear Species (J.T. Hupp).
Mixed Valence Clusters (Tasuku Ito et al.).
Non-biological Photochemistry Multiemission (A. Lees).
Nitrosyl and Oxo Complexes of Molybdenum (M. Ward, J. McCleverty).
Structure of Oxo Metallic Clusters (R.J. Errington).
Iron Centred Clusters (T. Hughbanks).
The Dicyanamide System (R.J. Crutchley).

2.1
Nuclear Magnetic Resonance
Spectroscopy
¨ EGGER
P. S. PREGOSIN and H. RU
ETH Ho¨nggerberg, Zu¨rich, Switzerland
2.1.1 INTRODUCTION
2.1.2 SOLUTION NMR
2.1.2.1 Detecting Less Sensitive X-nuclei
2.1.2.2 Chemical Shifts
2.1.2.3 Coupling Constants
2.1.2.4 Structural Applications
2.1.2.5 Dynamics
2.1.2.6 NOE and Exchange Spectroscopy
2.1.2.7 Special Topics
2.1.2.7.1 High-pressure studies
2.1.2.7.2 Molecular hydrogen and agostic complexes
2.1.2.8 Relaxation
2.1.3 NMR DIFFUSION MEASUREMENTS
2.1.3.1 Introduction
2.1.3.2 Methodology
2.1.3.2.1 Spin-echo method
2.1.3.2.2 Stimulated echo method
2.1.3.2.3 Derived sequences
2.1.3.3 Study of Complex Nuclearity
2.1.3.4 Study of Ion Pairing
2.1.3.5 Study of Hydrogen Bonding
2.1.3.6 Concluding Remarks
2.1.4 SOLID-STATE NMR SPECTROSCOPY
2.1.4.1 Introduction

2.1.4.2 Principles and Methodologies
2.1.4.3 Spin-1/2 Metal Nuclei
2.1.4.4 Quadrupolar Metal Nuclei
2.1.4.5 Ligand Nuclei
2.1.4.5.1 1H NMR
2.1.4.5.2 2H NMR
2.1.4.5.3 13C NMR
2.1.4.5.4 15N NMR
2.1.4.5.5 17O NMR
2.1.4.5.6 19F NMR
2.1.4.5.7 31P NMR
2.1.4.6 Applications of Two-dimensional NMR Spectroscopy
2.1.5 OUTLOOK
2.1.6 REFERENCES

1

2
2
2
3
6
7
9
10
11
11
13
13
15

15
15
15
16
16
17
18
19
19
19
19
20
21
21
22
22
22
22
23
23
23
23
26
26
26


2
2.1.1

Nuclear Magnetic Resonance Spectroscopy
INTRODUCTION

For more than 50 years, NMR spectroscopy has provided a major aid in solution structure analysis.
Starting from modest, 40 MHz machines, one can now measure on instruments approaching the
gigahertz range. Coordination chemists have been somewhat slow in profiting from this method, as
many of the metal complexes of the first transition series are paramagnetic, and thus only sometimes suitable for this methodology. Further, sensitivity was initially a problem, i.e., many metal
complexes are only sparingly soluble; however, the advent of polarization-transfer methods, highfield magnets, and improved probe-head technology have more or less eliminated this difficulty.
Measurements of 1H, 13C, 19F, and 31P spins on ca. 1–2 mg of sample, with molecular weights in the
range 500–1,000 Da, are now a fairly routine matter.
The spin I ¼ 1=2 nuclei with the largest magnetic moments and natural abundance are still
favored in the inorganic community, e.g., 1H, 13C, 19F, 31P, 111,113Cd, 195Pt, and 199Hg; however,
15
N, 29Si, 77Se, 103Rh, 107,109Ag, and 183W are now all fairly routine candidates.1–4 The 103Rh
literature is expanding rapidly;5–11 however, for other nuclei, e.g.,107,109Ag, the results continue to
develop slowly.12–14 57Fe15,16 and 187Os17–19 both represent examples of spins with considerable but
not insurmountable difficulties, primarily due to their small magnetic moments (see Table 1). There
are ongoing efforts on quadrupole nuclei,20,21 e.g., 67Zn,22,23 55Mn,24,25 99Ru,26,27 and 95Mo.28
Slowly, multidimensional methods are increasing in popularity within the inorganic
community; however, while several of these may be necessary to properly characterize a specific
complex, they are not all equally useful. COSY measurements connect coupled proton spins and
are thus useful for assignments. However, NOESY data can provide three-dimensional structure
features and also reveal exchange phenomena, thereby making these much more valuable for the
coordination chemist.
The number of solid-state measurements has increased exponentially, due both to interests in
heterogeneous catalysis and to the number of interesting complexes with very limited solubility.
Further, relatively new NMR methods are finding application, e.g., PHIP and PGSE diffusion studies,
so that the sections which follow cannot do justice to the individual topics, because of space restrictions.
We have tried to emphasize results since about 1990. This will undoubtedly have resulted in
some unfortunate omissions.

2.1.2
2.1.2.1

SOLUTION NMR
Detecting Less Sensitive X-nuclei

The most sensitive and now routinely used method for obtaining spin I ¼ 1/2 NMR signals for
less sensitive nuclei involves double-polarization transfer (I!S!I ), and uses one of the twodimensional NMR sequences shown in Figures 1 and 2.33–35
Table 1 Relative sensitivities for selected nuclei of common interest.
Nucleus
1

H
Si
57
Fe
59
Co
95
Mo
103
Rh
109
Ag
119
Sn
183
W
187

Os
195
Pt
199
Hg
29

Abundance (%)
99.9
4.7
2.2
100
15.7
100
48.2
8.58
14.4
1.6
33.7
16.8

a
Both direct and indirect methods (INEPT, HMQC, . . . , etc.) are in use.
broad due to the quadrupole moment of the metal.

Commenta

Rel. sensitivity
1
7.84 Â 10À3

3.37 Â 10À5
0.28
3.23 Â 10À3
3.11 Â 10À5
1.01 Â 10À4
5.18 Â 10À2
7.20 Â 10À4
1.22 Â 10À5
9.94 Â 10À3
5.67 Â 10À3
b

Most efficient via indirect methods.

Bothb
Indirect
Directc
Directc
Indirect
Indirect
Bothb
Indirect
Both
Both
c

Lines can be


3

Nuclear Magnetic Resonance Spectroscopy

The I-spins are assumed to be a high receptivity nucleus, most often 1H, i.e., one needs a nJ(X,
H) interaction, n ¼ 1–4. The data are detected using the proton signals and the spectra are usually
presented as contour plots, as shown in Figures 3 and 4. Occasionally, 31P or 19F are suitable
alternatives to protons. Specifically, for metal complexes containing phosphorus ligands in which
the 31P is directly bound to the metal center, one occasionally has a relatively large 1J(M,P) value
of the order of 102À103 Hz.36–38 Consequently, one need not be restricted to molecules revealing
suitably large proton–metal coupling constants. The time Á is set to 1/(2 J(S, I )), and the time t1
represents the time variable for the second dimension. These sequences provide a theoretical
enhancement of (
I/
S)5/2. For nuclei such as 57Fe, 103Rh, and 183W this means factors of 5,328,
5,689, and 2,831, respectively.
1

2.1.2.2

Chemical Shifts

Once obtained, the signals need to be interpreted. The general subject39 of metal and heavy-atom
NMR chemical shifts is approached by noting that the magnetic field, B, experienced by nucleus
X differs from that of the applied field, B0, as shown in Equation (1):
B ¼ B0 ð1 À t Þ

ð1Þ

The screening constant, , is a scalar quantity which is the trace of a second-rank tensor, i.e.,
 ¼ 1=3ðxx þ yy þ zz Þ

ð2Þ

In a high-resolution NMR solution experiment one normally measures the average, ii, due to
rapid molecular tumbling. The total screening constant consists of two components d and p,
such that:
 ¼ d þ p

(a)

(c)

I

I

S

∆

t1

ð3Þ

S

(b)

(d)

I

I

S

S

Figure 1 Heteronuclear multiple quantum correlation (HMQC) pulse sequences: (a) sequence for small
J(I, S) values; (b) for larger, resolved J(I, S) values and phase-sensitive presentation; (c) zero or double
quantum variant for the determination of the I-spin-multiplicity; (d) with refocusing and optional S-spin
decoupling.

(a)

(b)

I
S

I
t1

S

Figure 2 Heteronuclear single quantum correlation (HSQC) pulse sequences with optional decoupling of
the S-spin: (a) standard sequence; (b) modified for the I-spin-multiplicity determination.


4

Nuclear Magnetic Resonance Spectroscopy

The diamagnetic screening constant, d, involves the rotation of electrons around the nucleus
and is important for proton NMR. These electrons may be immediately associated with the atom
in question, or with circulating electrons associated with proximate functionalities, i.e., anisotropic
effects. For the paramagnetic screening constant, p (which makes the major contribution to the
nuclei 13C, 15N, 31P, 57Fe, 103Rh, 119Sn, 195Pt, . . . etc.), the average energy approximation, for an
atom A is often made, i.e.,
A p / À < rÀ3 > ÆB QA;B =ÁE

ð4Þ

The term QA,B represents the bond order charge-density terms, r is an average distance from
nucleus A to the next atoms, and ÁE an averaged energy difference (between suitable filled and
empty orbitals). Equation (4) indicates that energies, bond orders, and distances all contribute to
Ap. As ÁE can be relatively small (perhaps due to a small n–* or –* separation), the
observed range of chemical shifts is often hundreds of ppm for donor atoms, and thousands of
ppm for transition metals. It is not unusual to find several terms in Equation (4) which change as
a function of ligand complexation, so that a thorough understanding of heavy-atom shifts

1

H

1

13

H{ P}

15

1

–374

31

N- H{ P}-HMQC

–372

–148

–146
ppm
ppm

–20.0

–20.2

–20.4

–20.6

–20.8

Figure 3 15N,1H {31P} HMQC for the [IrH2(8-aminoquinoline)(PPh3)2]þcation. The two hydride ligands are

trans to the two N-donors, thereby affording relatively large, selective 2J(15N,1Hhydride) values. The vertical
scale shows the 15N chemical shift.


5

Nuclear Magnetic Resonance Spectroscopy

OT f

Ru

P
Ph 2
CH 2
Ph
O
CH 3
OH
P

δ

δ
Figure 4 31P,1H COSY for the complex shown. Note that the two POCH2methylene protons are diastereotopic and that one of these happens to fall exactly under the solvent (THF) signal. However, the correlation
readily reveals two types of cross-peaks and thus the chemical shift of the hidden proton. There are also
correlations to POH, and ortho and meta protons of the P-phenyl.

requires a more detailed consideration of their source than for proton chemical shifts. It is
insufficient to interpret metal chemical shifts using concepts such as ‘‘local electron density’’ at

the atom in question, as this approach can be misleading; e.g., the 13C chemical shift of the
anionic carbon in Li(CPh3) is at a higher frequency than that for CHPh3.40 It is clear from the
literature41–49 that it is now possible to calculate screening constants (and thus chemical shifts, ,
of heavier atoms) fairly accurately.
Often, heavy-atom chemical shifts are considered empirically. The range of metal chemical
shifts is usually of the order of thousands of ppm and is very sensitive to changes in, and close to,
the local coordination sphere. Simple ligand-field-type considerations result in significant changes
in energy levels at a metal center when the donor atoms are changed. This will clearly affect the
ÁE term in Equation (4), e.g., the Co(H2O)63þ 59Co resonance is found at ca. 15,000, whereas the
Co(CN)63– 59Co resonance is at ‘‘0’’ ppm. Further, the Rh(H2O)63þ 103Rh resonance is at 9,924,
whereas the Rh(CN)63– 103Rh resonance is at 340. Crude correlations relating the metal chemical
shift with oxidation state or stability50 have been found, e.g., for Pt(CN)42À the 195Pt resonance is
at À4,746, whereas for Pt(CN)62À the 195Pt resonance is at À3,866 (both vs. PtCl62À); however,
ambiguities exist, so that each case should be viewed on its own merits.
Solvent effects on metal resonances are routinely tens of ppm, and changes in temperature
during a measurement result in large enough shifts (often in the range 0.1–0.5 ppm  CÀ1) that fine
structure on the resonance is readily lost. Isotope effects (e.g., 35Cl vs. 37Cl, 16O vs. 18O, or 1H vs.
2
H) on metal resonance positions51–55 are sufficiently large that the different chemical shifts from
the individual isotopomers are often well resolved. These effects are not so marked in donor-atom
NMR spectra, i.e., for 13C, 15N, or 31P complexed to a metal center, solvent effects are normally a
few ppm or less.
For the two donor atoms nitrogen and phosphorus, the normal chemical-shift range is of the
order of hundreds of ppm. A change in hybridization from sp3 to sp2 will be associated with new
orbitals. These represent orbitals, e.g.,  and *, whose energy separation will strongly affect the
chemical shift. As an example, the 15N resonance for trialkyl amines, R3N, is at À300 to À390,
whereas the 15N resonance for pyridines is found at þ 80 to À175, both classes relative to
CH3NO2.56 Moreover, complexation of a sigma donor, e.g., either an aliphatic nitrogen or a
tertiary phosphine donor, simultaneously changes both the lone-pair energy and the local geometry at the donor atom, so that interpretation can be complicated. For pyridine (or related
heterocyclic ligands with sp2 donors14), complexation to a metal usually affords a shift to low

frequency, whereas for triphenyl phosphine complexation there is normally a high frequency
change. There exist compilations of both 14,15N56 and 31P36–38 chemical shifts. Electronegative
groups on these donors, and inclusion in various ring sizes, as well as the size of the substituent on


6

Nuclear Magnetic Resonance Spectroscopy

the donor atom, all play important roles in determining the chemical shift. As there are literally
hundreds of reported nitrogen chemical shifts and thousands of measurements for the 31P spin,
the reader is advised to consult the reviews noted.
The special case of carbon as donor, i.e., alkyl, phenyl, alkynyl, allyl, CO, olefin (or arene or
Cp, . . . etc.), and carbene ligands, continues to attract significant attention and several articles57–63
have been written on this subject. Nevertheless, Equation (4) is valid. CO derivatives are
often found in the region  ¼ 150–250. Carbene compounds have 13C positions at relatively
high frequency, usually >200 ppm, and this special position is often diagnostic. Aryl complexes
reveal the coordinated ipso carbon at high frequency, with representative values between 130 ppm and
180 ppm. Complexed olefins show their 13C positions over a wide range, with coordination chemical
shifts as small as 10–15 ppm, but often 30–70 ppm or more. The oxidation state of the metal
(and thus the d–* back bonding) is important in determining 13C frequencies for these complexes.
Given that both the metal centers and parts of the ligands can contain strongly anisotropic
regions, ligand complexation often has a significant effect on proton chemical shifts. Individual
protons can be forced into environments which result in marked high- or low-frequency resonance
positions. The axial positions in square-planar complexes often afford high-frequency proton
shifts,64,65 e.g., as in (1); and, of course, phenyl ligands (or aromatic substituents), as well as
donors such as pyridine or triphenyl phosphine—which contain aromatic fragments—can
strongly affect the local environments of proximate protons, e.g., as in (2).
(EtO)2 1
P

O

P2Ph3
Pd
Cl

M

M
L

L

H

D
H

H

(1)

(2)

8.22 ppm
J(P1,H) = 5.8 Hz, (P2,H) = 7.3 Hz

Me

(3)

D = C or N

Even simple ligands such as chloride can influence the position of proximate protons, e.g.,
in structure (3), the proton indicated might be expected at around 7 ppm, but it appears above
8 ppm.66
Metal–metal multiple bonds can also be strongly anisotropic with respect to protons.67 In the
quadruply bonded Cr and Mo complexes shown in (4), the NH protons appear at  ¼ 3.46 and
 ¼ 3.04, instead of at  ¼ 8.04 and  ¼ 6.44 in the free ligand and Li salt, respectively.

2
N
H

N

N

M

M

N

N

H
N
2

(4) M = Cr or Mo
Apart from transition-metal hydride compounds, which appear at very low frequency, most
proton chemical shifts are relatively routine.

2.1.2.3

Coupling Constants

The theory for spin–spin interactions between a spin I ¼ 1/2 metal and an appropriate ligand
atom follows directly from the description developed by Pople and Santry. Currently a number of
mathematical methods68 are in use which allow the calculation of various J-values.


7

Nuclear Magnetic Resonance Spectroscopy
A modified form of the Pople and Santry expression is given in Equation (5) and
occ unocc

1

JðM; LÞ /
M
L j s ðMÞð0Þj2 j s ðLÞð0Þj2 S
j

S ðEk À Ej ÞÀ1 CðMÞks CðLÞks CðMÞj s CðLÞj s

ð5Þ

k

reveals that the one-bond interaction depends on the metal and ligand atom magnetogyric ratios,
, the s-expectation values, , the occupied, j, and unoccupied, k, molecular orbital energies, and
the s-coefficients of the atomic orbitals used in making up the molecular orbitals.
Given that the
and s-expectation values, , depend markedly on the individual metal and
ligand atoms under consideration, the values of these spin–spin interactions vary over several
orders of magnitude, e.g., 1J(195Pt, 1H) is often >1,000 Hz, but 1J(103Rh, 1H) is usually <30 Hz.
1 195
J( Pt, 31P) is often >2,000 Hz, but 1J(103Rh, 31P) is usually <300 Hz. Since both the
and
s-expectation values for the 31P atom are relatively large, one finds spin–spin interactions of the
order of 102–104 Hz, depending upon the metal and the nature of the phosphorus ligand. There is
an extensive literature on 1J(M, 31P),36–38 although much work has involved platinum and
rhodium complexes. Metal–metal one-69,70 and two-bond71 coupling constants can be surprisingly
large and, in some cases, are 20,000–40,000 Hz.69–72 Complexes (5) and (6) are clear, albeit
somewhat extreme, examples of this idea. With the possible exception of complexes containing
31
P, (e.g., see (3) above), long-range coupling constants such as 3J(M, (spin ¼ 1/2)) have not
received as much attention as 1J(M, L). Nevertheless, spin I ¼ 1/2 metals and ligands can easily
couple to protons and other nuclei over three, four, and sometimes more bonds (and these
interactions can be quite useful for determining metal chemical shifts of e.g., 119Sn,73 109Ag,74
183
W,75–77 195Pt,78,79 and 199Hg.80

L
L

Ir

Pt
Cl3Sn

ClHg

L

1J(Pt,Sn)

SnCl3

Cl

SnCl3

CO
L

= ca 20,000 Hz

2J(Hg,Sn)

= ca 40,000 Hz

L = P(OEt)3

L = PPh3

(5)

2.1.2.4

(6)

Structural Applications

In terms of applications, the subjects of chemical equivalence and symmetry still deserve honorable mention in that one can use the relative number and NMR multiplicity to assign structure,
e.g., trigonal bipyramidal, (7), vs. square pyramidal, (8), in ‘‘ML5’’ complexes (especially where L
is a spin I ¼ 1=2 donor).
For ligands with suitable proton, fluorine, or phosphorus atoms, low-temperature NMR
studies are informative and reveal either the 3:2 or 4:1 ratio.
A useful empiricism involves chemical shifts and/or one-bond coupling constants to spin I ¼ 1/2
metal centers in square-planar, (9), or octahedral, (10), compounds.
L

L
L

M

L
L

L

M

L

(7)

M
L

L
(8)

Spin = 1/2 nucleus

L
L

M

Spin = 1/2 nucleus

L
(9)

(10)

There is sometimes a dependence of either  13C, 15N, or 31P, . . . etc. and/or 1J(M,
spin ¼ 1=2 nucleus) on the trans influence of L.81,82 For stronger L-donors the chemical shift


8

Nuclear Magnetic Resonance Spectroscopy

moves to lower frequencies, whereas the value of 1J(M, spin ¼ 1=2 nucleus) can be markedly
reduced. This is the case for NH3 (or amine) complexes of Pt(II) and, specifically, for (11)
and related amino-acid complexes. It has been suggested that O, N, and S donors, in the
trans position, can be distinguished by the chemical shift of the 15NH3 signal. Sadler and
co-workers83–89 have been very active in this area.
In general, 15N chemical shifts in platinum complexes have received increasing attention and
most reports use indirect methods of detection, even on enriched materials. The development
of cis-PtCl2(NH3)2, and related cancer drugs, has been accompanied by a renewed interest in
1 195
J( Pt, 15N).90–97 This parameter varies by ca. one order of magnitude between 80 Hz and about
800 Hz. 15N data can also be used to recognise unique three-center interactions98 in Pt chemistry,
e.g., (12), or to identify an enol form of the amide, e.g., (13), an amino-quinoline Ir(III)
derivative.
Ph
P
NH3
Pt

Pt +

Ph

P

CF3SO3
H
N

Ph

L

Ph

CH3

N

N
L
Ir

L

L = PPh3

H

H
(12)

Me
O

H
O

(11)

N

(13)

In the latter complex, the expected one-bond NÀH interaction, found in acetamide complexes,
is absent.99 This type of complex shows a rarely observed 2J(15N,1H) value. Given the interest in
organometallic and catalytic chemistry, there are many reports on 1J(M, 13C)100–103 and
1
J(M, 31P).104,105
Many applications of spin–spin interactions through two bonds center on the empiricism that
2
J(X, Y)trans ) 2J(X, Y)cis, i.e., the trans coupling in (14) is greater than the cis coupling in (15).
This is most likely to be valid only for the second- and third-row transition metals. Moreover, it is
thought that the signs of these two 2J interactions are different. 2J(31P, X), X ¼ 1H, 13C, or 31P
represent the most abundant examples. There are relatively few modern, detailed studies on this
subject, and Field and co-workers106,107 have used 2-D methods to obtain some useful data on
signs and values of nJ(X, Y) in organometallic complexes of RuII and RhI.

I = 1/2 spin
M

M
>>

I = 1/2 spin
(14)

I = 1/2 spin

I = 1/2 spin
(15)

Inserting and/or exploiting specific NMR-active isotopes still attracts attention. In both monoand polynuclear complexes, one can occasionally use the integrated intensities of e.g., 29Si,73
117,119
Sn,108–110 or 195Pt,111,112 satellites, arising from two- or three-bond interactions together
with integrals relative to the center band, to obtain a quantitative determination of the number of
metals in the cluster; see Figure 5. In all of these examples, the structural information derives
from the integrals and/or the presence of coupling constants, and not from the positions of the
signals.
Both chemical shifts and coupling constants have been used113 to characterize the novel Pt–
pyrazolyl borate formyl complex, (16). The observed coupling constant from the Pt atom to the
formyl proton, 327 Hz, is relatively large.
The 13C NMR parameters for the Pt–methyl group provide an interesting contrast when
compared to those of the formyl group. The methyl carbon resonance is found at 0.48 ppm,
with 1J(Pt, C) expected to be in the range 620–710 Hz.


9

Nuclear Magnetic Resonance Spectroscopy

195

Pt NMR

119
–4,700.0

Figure 5

195

imp.

117

–4,750.0

–4,800.0

–4,850.0

117

–4,900.0

–4,950.0

119
–5,000.0

Pt NMR spectrum of the [Pt(SnCl3)3(2-methylallyl)]2Àdianion. The intensities of the
satellites reflect the number of complexed tin ligands.

117,119

Sn

N
13C

O
H– B

J(Pt, C) = 1,260 Hz

C

N
N

1H

H

Pt

CO = 237 ppm

1

formyl = 12.66 ppm

2J(Pt,

Me

H) = 327 Hz

(16)

2.1.2.5

Dynamics

NMR spectroscopy allows the coordination chemist access to a variety of dynamic phenomena
via spin–lattice, T1, and spin–spin, T2, relaxation times, plus line-shape analyses and phasesensitive exchange (NOE) spectroscopy. The spin–lattice relaxation time, T1, can be correlated
to molecular tumbling and rotations. Classical T2 measurements, together with the Swift and
Connick equations for paramagnetic metal systems, lead to ligand-exchange-rate information.114–116
An example of the latter type of application concerns proton and phosphorus T2 relaxation
enhancement in several phosphite ester anions by manganese paramagnetic complexes. These
compounds contain the fragment (17) shown, and analysis of the various relaxation data allows
the determination of metal/ligand association rate constants without temperature studies.117 The
important subject of NMR studies on paramagnetic complexes in biological systems, i.e., the
rather special consequences of porphyrin, phosphate, and amino-acid derived ligands, has been
reviewed several times.118,119

O

Mn
O
OH

31PT

2

P

H
OCH3

1 H-P T

2

(17)
Since 1970 or before, chemists have relied on classical, detailed temperature-dependent lineshape analyses.120,121 Indeed, fundamental contributions to our understanding of the dynamics of
fluxional metal complexes with -hydrocarbon ligands,122 tertiary phosphorus donors,123 as well
as -allyl anions,124–126 all stem from these types of measurement. Their contributions to metal
carbonyl dynamics and rearrangements in cluster compounds is even more pronounced, and we
cite selected studies in this very large area of organometallic chemistry.127–148 For slow exchange


10

Nuclear Magnetic Resonance Spectroscopy

between two sites and negligible overlap of the signals, expressions such as Equation (6)120 (or
more complicated versions149) have served well:
W ¼ ð1=Þðk þ 1=T2 Þ

ð6Þ

(W ¼ bandwidth at half height, k ¼ first-order rate constant)
In the early reports, line-shape studies predominated; however, many of the more recent reports
use 2-D exchange spectroscopy.

2.1.2.6

NOE and Exchange Spectroscopy

Nuclear Overhauser effects, NOEs, involve dipole–dipole relaxation phenomena which result in
signal enhancements.150 For two interacting protons, the maximum NOE, max is:
max ¼ ð5 þ !2  2c À 4!4  4c Þ=ð10 þ 23!2  2c þ 4!4  4c Þ

ð7Þ

(! ¼ frequency,  c ¼ correlation time).
For small molecules with short  c values (extreme narrowing limit), this equation reduces to
max ¼ þ50%. This is rarely achieved for a single proton in coordination compounds, as there are
often a number of spins contributing to the relaxation of an individual proton and the  c values
are not always so short. Clearly, if the quantity (5 þ !2 c2 – 4!4 c4) ¼ 0, then there is no NOE. It
is well known150 that max can pass through zero and the limiting value is À100%. This can be the
case for biological or other macromolecules. Further, a negative NOE is also possible for higher
molecular weight metal complexes, e.g., MW > 1,000, and/or in viscous media (perhaps due to
low-temperature studies). In these cases ROESY spectra150,151 can be useful.
Although selective 1H NOE studies and magnetization-transfer experiments are still frequently
in use,150 the simple three-pulse (phase-sensitive) 2-D NOESY sequence, given in Figure 6, is
finding increasing popularity.152–159 The mixing time should be chosen such that exchange can
take place without losing too much signal intensity. Practically, this often means values in the
range 0.4–1.0 seconds, although individual T1 values and temperature will require that this
parameter be constantly adjusted to suit the coordination compound in question.
Wherever coordination chemistry problems overlap with those of organic chemistry, e.g., conformational analysis, 1H NOE studies will have their classical value. Chiral inorganic complexes
have been studied with emphasis on inter- and not intra-ligand NOEs.155,156,160–166 These results
allow the determination of the 3-D structure of the complex and thus, for enantioselective catalysts,
the shape of the chiral pocket offered by a chiral auxiliary to an incoming organic substrate. Since
many such auxiliaries possess phenyl phosphine donors, the interactions between the ortho protons
of the P-phenyl group and those from a second ligand make a decisive contribution to the structure
determination. Structure (18) shows a hypothetical Pd(chiraphos)-(allyl) cation, and it is easy to see
how NOEs, from the three allyl protons to the P-phenyl ortho protons, can provide useful structural

data. The four phenyl groups, two pseudo-axial and two pseudo-equatorial, are all nonequivalent.

(a)
t1

t mix

t1

t mix

(b)

Figure 6 Pulse sequences for nuclear Overhauser and chemical exchange spectroscopy: (a) NOESY;
(b) ROESY.


11

Nuclear Magnetic Resonance Spectroscopy

For complexes of modest size which tumble relatively rapidly, 2-D NOESY methods
distinguish between NOE and exchange phenomena via the phases of the signals. The diagonal
and exchange peaks have the same phase in contrast to those due to NOE. Since the 2-D
methodology is not selective, i.e., all of the spins are excited simultaneously, the exchange map
can reveal several species in exchange with each other as well as two or more different processes.
A nice example is provided by the tetranuclear Ir-cluster anion (19).167 The CO ligands are
involved in several temperature-dependent exchange processes.
g
e

e
ax

letters = different CO ligands

Ir

Me Me
+
Pd

P
eq

"merry-go-round" =
eq

P
d
ax

H
H

b
Ir
c

H

Ir
a

Ir
Br

R
(18)

d

a

c

a
d
b
d
a

to d,
to b,
to d
to a and
to f

f

(19) [Ir4(CO)11Br]–

One of these, the so-called ‘‘merry-go-round,’’ selectively exchanges the bridging and terminal
CO ligands, a, d, b, and f, in the pseudo-equatorial direction. Since the various 13CO signals can
be assigned, 2-D 13C NOESY spectroscopy reveals exchange cross-peaks connecting all four of
these signals, thus identifying this selective process, as indicated in the drawing.
A unique aspect of this form of exchange spectroscopy concerns the ability to detect species
whose concentration is so low that they escape detection in a conventional one-dimensional
experiment. Figure 7 shows a section of the 1H NOESY spectrum for a mixture of isomeric
palladium phosphino–oxazoline, 1,3-diphenylallyl complexes.168 One observes a major component in exchange with a visible minor component (ca. 10% of the more abundant isomer).
However, there are additional, very broad, exchange cross-peaks from the main isomer to an
‘‘invisible’’ species, which would easily have gone undetected.
Interest in 19F, 1H NOEs in coordination chemistry is developing,169,170 and several interesting
examples of 31P, 31P exchange spectroscopy have been reported.171–173

2.1.2.7
2.1.2.7.1

Special Topics
High-pressure studies

NMR studies under high pressure have increased markedly in the last two decades. Technically, these
measurements are most frequently carried out using sapphire NMR tubes, and this methodology has
been modified over the years.174–179 These pressure experiments are usually carried out with the joint
aims both of determining activation volumes and of shifting chemical equilibria. Occasionally, details
with respect to the pressure dependence of NMR parameters are published.180
Measuring rate constants vs. pressure allows the determination of activation volumes, and thus
gives a hint as to whether the reaction mechanism is associative or dissociative.
lnðkI Þ ¼ lnðkI ; 0Þ À ÁVI‡ P=RT

ð8Þ

Much work has been done on solvated metal complexes by Merbach and co-workers.178,181–189
These pressure studies have been extended to organometallic CO190–192 and SO2193 complexes
plus, interestingly, the first dihydrogen aqua-complex, Ru(H2)(H2O)52þ, (20),194 produced as
shown in Equation (9):
RuðH2 OÞ62 þ þ H2 ! RuðH2 ÞðH2 OÞ52 þ

ð9Þ


12

Nuclear Magnetic Resonance Spectroscopy

8a

8a
8b

8b

8c

8c
4.5

5.0

5.5

ppm
ppm

5.5

5.0

4.5

Figure 7 Section of the phase-sensitive 2-D NOESY for isomeric palladium phosphino-oxazoline,
1,3-diphenylallyl cationic complexes. The major isomer (8a) (which does not correspond to (8) in the text)
is clearly exchanging with (8c). However, (8a) is also exchanging with an unknown compound (broad
exchange peaks).

The 1J(H, D) value of 31.2 Hz in the H2 ligand allows an estimation of the H–D separation,
ca. 0.90 A˚, using the relationship:
dðHÀDÞ % À0:01671 JðH; DÞ þ 1:42

ð10Þ

suggested by Maltby et al.195 It is probably useful to remember196 that correlations with activation volumes may not be straightforward. Elsevier and co-workers27,170,197–199 have used high
pressures in connection with supercritical fluids, and have studied effects on line widths and other
NMR parameters.
Homogeneously catalyzed hydrogenation chemistry, often under an overpressure of gas, has
been followed by proton NMR for decades, and frequently important intermediates go undetected due to their relatively low concentration. Since the para hydrogen induced polarization,
(PHIP) signal magnification can be several orders of magnitude, Bargon,200–207 and the Duckett
and Eisenberg groups208–222 plus others have studied in situ reactions using parahydrogen under
mild hydrogen pressure. The major limitation arises from the necessity for the two parahydrogen
atoms to be transferred pairwise. The PHIP effect has also been recently shown to be useful

for 13C, as well.200
The PHIP approach has been used to help identify the cationic Rh(I) dihydrido-bis-solvento
complex shown, (21).222
This type of dihydrido-phosphine chelate complex is often mentioned in mechanistic
discussions on enantioselective hydrogenation, but was previously thought to be not very stable.


13

Nuclear Magnetic Resonance Spectroscopy

H OMe
+
P
H
Rh
P
OMe
H
H

PPh2
P
= PHANEPHOS =
P
PPh2

(21)

2.1.2.7.2

Molecular hydrogen and agostic complexes

Much effort has been invested in the use of NMR methods to study molecular hydrogen
complexes.223–241 The identification of an LmM(2–H2) often requires variable temperature,
deuterium enrichment, and T1 studies. The deuterium incorporation is useful in that the value
of 1J(H, D) can be diagnostic, as noted above.
In polyhydride complexes, exchange between hydride and complexed molecular hydrogen often
leads to observable dynamics in their 1H NMR spectra. In many cases these processes are
associated with relatively low activation-energy barriers.242 In the complex IrH2X(H2)(PR3)2,
(22), X ¼ Cl, Br, or I, the exchange can proceed via either hydride/hydrogen exchange leading
to (23), or oxidative addition leading to (24).

H

H

X

PR3

Ir

H

X

R3P

H

H

R3P

H

H

(22)

PR3

Ir

R3P

H H

X

PR3

Ir

H
H

(23)

H

(24)

C
C

M
H
(25)

Si

M

M

H

H
(26)

(27)

It is only a small extrapolation to move from side-on complexed H2 to side-on complexed
XÀH, and Crabtree243 has commented on how these interactions are related. The name ‘‘agostic’’
is often used244–246 for the case of X ¼ a suitably substituted carbon atom. There are also a
number of examples of X ¼ a suitably substituted silicon atom.247–250 The agostic interaction of a
CÀH bond, (25), results in a low-frequency shift of the proton resonance (due to the development
of ‘‘hydride-like’’ character) and substantial reduction in the one-bond coupling constant, 1J(13C,

1
H). This reduction can be 50% or more. Similarly, for X ¼ SiR3, the one-bond, 1J(29Si, 1H) value
decreases. In the solid state one finds the CÀH bond as a donor to the metal. There are many
examples of this type of interaction.251–261

2.1.2.8

Relaxation

Relaxation times can be useful for coordination chemists. For our discussion it is sufficient to express
the longitudinal relaxation rate of a nucleus, R1, ( ¼ 1/T1), as the sum shown in Equation (11):262
R1 ¼ R1DD þ R1CSA þ R1SR þ R1SC þ R1Q þ R1EN þ R1other

ð11Þ


14

Nuclear Magnetic Resonance Spectroscopy

with the various contributions defined as follows: DD ¼ dipole–dipole; CSA ¼ chemical-shift
anisotropy; SR ¼ spin rotation; SC ¼ scalar coupling; Q ¼ quadrupole; and EN ¼ electron–
nuclear. It should be noted, however, that for coupled-spin systems, this simple sum is no longer
valid.263–265
The measurement of the relaxation rate gives the coordination chemist access to parameters
related to the anisotropic interactions described by the spin Hamiltonian which, in solution, are
averaged to their isotropic values or even zero. In principle structural information can thus be
retrieved, since R1DD and R1E render information with respect to the separation to other nuclei or
unpaired electrons, respectively, e.g., via the 1/r6 distance dependence shown in Equation (12).
Frequently, a number of dipoles contribute to relaxation, so that a sum is necessary:

R1DD /  c =Ær6

ð12Þ

The R1CSA term describes the substitution pattern and the local stereochemistry. R1SR leads to
moments of inertia, and the scalar and quadrupolar coupling constants are obtainable from R1SC
and R1Q, respectively, with the latter describing the electric-field gradient at the site. Beside this
wealth of structural information, each of the individually contributing rates correlates to
molecular tumbling, via a correlation time,  c, plus global and local rotations and other dynamic
phenomena.
In practice, however, it is often difficult to separate or exclude some of the contributing
pathways unless one of the interactions is clearly dominating.
The R1DD term can usually be evaluated. Consequently, data from one- and two-dimensional
nuclear Overhauser spectroscopy studies contribute to the coordination chemists understanding
of three-dimensional solution structures152–166 and molecular association phenomena such as ion
pairs.169,170,266–269 Distance constraints are usually qualitatively established, based on cross-peak
intensities or volumes. Occasionally monitoring the build-up rates is preferred, in order to
quantify internuclear distances.266,268
The determination of R1DD, and in particular the maximum rate, i.e., the T1 minimum, is
popular for the determination of the HÀH distance in molecular hydrogen complexes, as the
intraligand HÀH separation is much shorter than other interproton distances.270 The HÀH
distances are calculated from the T1 minima according to two models involving static271 or
fast-rotating hydrogen ligands,272 respectively. Distances thus derived should be considered as
semiquantitative, as additional spins (e.g., other hydride ligands in polyhydrides) or dipolar
coupling to NMR active metal centers may shorten T1.273 Other relaxation contributions, such
as the spin-rotation mechanism, may not be ruled out. Moreover, the exact nature of ligand
dynamics (classical vs. quantum-mechanical rotation and tunneling of hydrogen) is not settled.270
R1CSA is an important contributor to the relaxation of heavy nuclei, particularly for the
transition metals, and can be separated from the other contributions due
R1CSA / B20  c

ð13Þ

to its unique B02 dependence (see Equation (13)). Structural conclusions have been derived from
this parameter, e.g., linear, trigonal, and tetrahedral Pt(PR3)n complexes can easily be
distinguished from their 195Pt T1CSA values.29
R1Q is normally the dominating relaxation pathway for quadrupolar nuclei. For a series of
metal deuterides, quadrupole coupling constants have been determined using this method, thus
shedding light on the size of the electric-field gradient at the D nucleus. These results reflect the
characteristics of the MÀD bond, in particular ionic vs. covalent contributions.274–276
R1EN is responsible for relaxation of the nuclei in a paramagnetic complex and depends
strongly on the relaxation rate of the unpaired electrons, correlation times for molecular reorientation, ligand-exchange rates, the bonding situation, and the electron–nucleus distance. The study
of various enzymes containing paramagnetic metal centers,118,119,277–283 and the use of complexes
of rare-earth metal ions as contrast agents in magnetic resonance imaging,284–287 represent two
important applications of this methodology.
The term R1other summarizes other possible contributions to spin–lattice relaxation, e.g., a spin–
photon Raman scattering mechanism has been proposed for relaxation of the 205Pb nucleus in
lead nitrate and other heavy spin-1=2 nuclei in solids.288


Nuclear Magnetic Resonance Spectroscopy
2.1.3

15

NMR DIFFUSION MEASUREMENTS

2.1.3.1

Introduction

The determination of relative molecular size in solution remains a subject of considerable interest
to the coordination chemistry community, in particular with respect to the formation of polynuclear complexes, ion pairs, and otherwise aggregrated species. Apart from classical methods
such as mass spectrometry289 (see Chapter 2.28) and those based on colligative properties290 —
boiling-point elevation, freezing-point depression, vapor and osmotic pressure—the Pulsed Field
Gradient Spin-Echo (PGSE) methodology291,292 has recently resurged as a promising technique.
PGSE measurements make use of the translational properties, i.e., diffusion, of molecules and
ions in solution, and thus are directly responsive to molecular size and shape. Since one can
measure several components of a mixture simultaneously,293,294 PGSE methods are particularly
valuable where the material in question is not readily isolable and/or the mixture is of especial
interest.
PGSE methods were introduced in 1965 by Stejskal and Tanner295 and, since then, have been
widely used. In the 1970s this approach was used to determine diffusion coefficients of organic
molecules.296 In the following decade, variants of the technique were applied to problems in
polymer chemistry.297–300 Since then, diffusion data on dendrimers301–306 and peptides,307–310 as
well as on molecules in various environments, e.g., in porous silica311 and zeolites,312 have been
obtained. Recent applications of PGSE methods in coordination and/or organometallic chemistry
have emerged.169,313–326

2.1.3.2

Methodology

The basic element of an NMR diffusion measurement consists of a spin-echo sequence,327 in
combination with the application of static or pulsed field gradients.295,328 Several common
sequences are shown inFigure 8, and we discuss these only briefly as the subject is covered in
several reviews.291,292,329–334

2.1.3.2.1

Spin-echo method

In the Stejskal–Tanner experiment,295 Figure 8a, transverse magnetization is generated by the
initial /2 pulse which, in the absence of the static or pulsed field gradients, dephases due to
chemical shift, hetero- and homonuclear coupling evolution, and spin–spin (T2) relaxation. After
application of an intermediate  pulse, the magnetization refocuses, generating an echo. At this
point the sampling (signal intensity measurement) of the echo decay starts. Fourier transformation of these data results in a conventional NMR spectrum, in which the signal amplitudes are
weighted by their individual T2 values and the signal phases of the multiplets due to homonuclear
coupling are distorted. Both effects are present in the diffusion experiment; however, due to the
fixed timing, these are kept constant within the experiment.
(a)

(c)

(b)

(d)

∆

∆

Figure 8 Pulse sequences commonly used for PGSE measurements: sequences with (a) spin-echo;
(b) stimulated echo; (c) stimulated echo and longitudinal eddy-current delay (LED); (d) stimulated echo
with bipolar pulsed field gradients and LED. Narrow and wide black rectangles represent /2 and  radiofrequency pulses, respectively. Narrow and wide open rectangles are field-gradient pulses of duration /2 and
, respectively, and strength G.


16

Nuclear Magnetic Resonance Spectroscopy

The application of the first pulsed linear field gradient results in an additional (strong) dephasing
of the magnetization, with a phase angle proportional to the length () and the amplitude (G) of the
gradient. Because the strength of the gradient varies linearly along, e.g., the z-axis, only spins
contained within a narrow slice of the sample acquire the same phase angle. In other words, the
spins (and therefore the molecules in which they reside) are phase encoded in one-dimensional
space. The second gradient pulse, which must be exactly equal to the first, reverses the respective
phases and the echo forms in the usual way. If, however, spins move out of their slice into
neighbouring slices via Brownian motion, the phase they acquire in the refocusing gradient will
not be the one they experienced in the preparation step. This leads to incomplete refocusing, as in
the T2 dephasing, and thus to an attenuation of the echo amplitude. As smaller molecules move
faster, they translate during the time interval Á into slices further apart from their origin, thus
giving rise to smaller echo intensities for a given product of length and strength of the gradient.

2.1.3.2.2

Stimulated echo method

The second experiment, shown in Figure 8b,328 works in quite the same way, with the difference
that the phase angles which encode the position of the spins are stored along the z-axis in the
rotating frame of reference by the action of the second /2 pulse. Transverse magnetization and
the respective phases are restored by the third /2 pulse. This method is advantageous in that
during time Á, T1 as opposed to T2 is the effective relaxation path. Since T1 is often longer than
T2, a better signal/noise ratio is obtained. Furthermore, phase distortion in multiplets due to
homonuclear coupling is attenuated.

2.1.3.2.3

Derived sequences

The accurate determination of diffusion coefficients for large, slow-moving species requires strong
gradient amplitudes. The resulting eddy-current fields can cause severe errors in the spatial phase
encoding. The sequence shown in Figures 8c335,336 and 8d337,338 contains an additional, so-called
longitudinal eddy-current delay (LED) element, i.e., magnetization is again stored along the z-axis
during the decay time of the eddy currents. Disturbance of the field-frequency lock system can be
minimized by the use of bipolar field-gradient pulses, Figure 8d.
Technically, all of the above experiments are performed by repeating the sequence while
systematically changing the time allowed for diffusion (Á), or the length () or the strength (G)
of the gradient. Mathematically, the diffusion part of the echo amplitude can be expressed by
Equation (14):


 
I

2 2
¼ Àð
Þ G Á À D
ln
I0
3

ð14Þ

(G ¼ gradient strength, Á ¼ delay between the midpoints of the gradients, D ¼ diffusion coefficient,  ¼ gradient length).
The diffusion coefficient D is obtained from the slope of the regression line by plotting ln(I/I0)
(I/I0 ¼ observed spin-echo intensity/intensity without gradients) vs. either Á –/3, 2(Á –/3), or
G2, depending on the parameter varied in the course of the experiment. Although slopes and
diffusion coefficients differ by a proportionality factor depending on the experimental parameters,

it is often convenient (for visualization) to group several measurements recorded under identical
settings in one figure. Compounds which possess smaller hydrodynamic radii move faster, show
larger diffusion coefficients, and reveal steeper slopes: see Figure 9.
The diffusion constant D can be related to the hydrodynamic radii of the molecules via the
Stokes–Einstein Equation (15):
D¼

kT
6rH

ð15Þ

(k ¼ Boltzmann constant, T ¼ absolute temperature,  ¼ viscosity, rH ¼ hydrodynamic radius).
The validity of hydrodynamic radii obtained from NMR diffusion measurements was
demonstrated by comparison with radii calculated from either crystallographically determined


17

Nuclear Magnetic Resonance Spectroscopy
ln(I/I0)
0.0

–1.0

–2.0

–3.0

–4.0

–5.0

–6.0

–7.0
0.00

0.01

0.02

0.03

0.04

0.05

0.06
2
2 –2
G (T m )

Figure 9 Plot of ln(I/I0) vs. the square of the gradient amplitude. The slopes of the lines are related to the
diffusion coefficients, D. The five lines stem from CHCl3 and the four Pd–arsine complexes PdCl2L2,
L ¼ AsMexPh3Àx, x ¼ 3, 2, 1, 0 (increasing molecular volume from left to right). The absolute value of the
slope decreases with increasing molecular volume.

volumes,322,324,325 analogous complexes, or from calculated structures.324 The agreement between
the two parameters—see Figure 10 and Table 2—is generally acceptable: perhaps even too good,

given the assumption that all of the complexes have spherical shapes.
Given favorable receptivity and T1 and/or T2 relaxation times, one is not limited in the choice
of the nucleus measured. Although most studies in coordination and organometallic chemistry
involved the observation of 1H, the use of alternative or additional nuclei often gives a complementary view. Studies based on 7Li,325 13C,324 and 19F169,316,322,326 have appeared.

2.1.3.3

Study of Complex Nuclearity

The determination of molecular size in solution is a frequent problem for coordination compounds; e.g., in lithium and copper, as well as in transition-metal carbonyl and hydroxo/oxo
chemistry, one finds numerous examples of polynuclear species. Increasingly, use is made of
NMR diffusion measurements to directly assess molecular volumes in solution.
Venanzi and co-workers320 characterized the equilibrium between the monomeric RuCl2(mesetph)—mesetph ¼ (C6Me3H2)P{CH2CH2PPh2}2—and the dinuclear [Ru2(-Cl3)(mesetph)2]Cl
complexes, based on the 1.23 ratio of their diffusion coefficients indicating a doubling of the
volume for the latter. The structures of the mixed-ligand dinuclear complexes (MeOBiphep)RuCl(-Cl2)RuCl(6-p-cymene)316 and [(Duphos)(6-p-cymene)Ru(-Cl)RuCl(6-p-cymene)]Cl326
were postulated from identical diffusion rates for both subunits and their larger volumes compared to, e.g., [(Duphos)(6-p-cymene) RuCl]Cl and Ru2(-Cl)2(Cl)2(6-p-cymene)2. Interesting
applications in zirconocene chemistry involved (i) the characterization of the dinuclear intermediate
[{Cp2ZrCl}2(-O2CH2)] in the course of the CO2 reduction with Cp2Zr(H)Cl324; and (ii) the
observation of ion quadruples for Cp2Zr(Me)2 in the presence of a Lewis acid like B(C6F5)3.313
Diffusion measurements also showed that addition of isonitrile to coordinatively unsaturated
tetrameric copper(I) complexes proceeds with the retention of the square Cu4S4 core.321


18

Nuclear Magnetic Resonance Spectroscopy
rX-ray

M

7.0
L

K
6.0

I

J

H
F

G

5.0
E
4.0

D
B
C

3.0

A

3.0

4.0

5.0

6.0

7.0

r hydr.

Figure 10 Plot of hydrodynamic radii obtained from PGSE experiments vs. the radii calculated from
crystallographic data. For compounds D, E, G, and H, the radii in the solid state were estimated using
reported structures for analogous phosphine, instead of arsine. For C and J the value was calculated from
minimized gas-phase structures (PM3).

Experimental diffusion coefficients for the dimeric and tetrameric THF solvated n-butyllithium
aggregates, [n-BuLi]2ÁTHF4 and [n-BuLi]4ÁTHF4, respectively, agree well with those calculated
from X-ray or PM3 structures.325 In terms of larger species, Valentini et al.317 investigated
dendrimeric ferrocenylphosphine ligands, while in a bioinorganic application, Gorman et al.301
estimated the hydrodynamic radii of iron–sulphur-cluster-based dendrimers with the cube Fe4S4
core. The largest examined particles containing coordination compounds result from the selfassembly of 30 {R3P}2{CF3SO3}Pt–(C6H4)n–Pt{CF3SO3}{R3P}2, n ¼ 1 and R ¼ Et, or n ¼ 2 and
R ¼ Ph; and 20 tri(40 -pyridyl)methanol into dodecahedra with 55 A˚ and 75 A˚ diameter.314

2.1.3.4

Study of Ion Pairing

Occasionally one can determine the diffusion coefficients for cations and anions separately, and
thus determine whether they move together as ion pairs or separately as free ions. Frequently,
coordination compounds in use in homogeneous catalysis possess anions such as PF6À, BF4À,
CF3SO3À, or BArFÀ, and 19F PGSE experiments represent an alternative and complement.

Table 2

Hydrodynamic and crystallographic radii.

Compound
A
B
C
D
E
F
G
H
I
J
K
L
M

ZrCl2(Cp)2
{Cp2ZrCl}2(-O)
ZrCl(OMe)(Cp)2
PdCl2(AsMe3)2
PdCl2(AsMe2Ph)2
TpMe2W(CO)3H
PdCl2(AsMePh2)2
PdCl2(AsPh3)2
PdBr(C6F5)(MeOBiphep)
{Cp2ZrCl}2(-O2CH2)
Pd2(dba)3

PdBr(C6H4CN)(Binap)
[Ru2(-Cl3)(mesetph)2]Cl

rH
324

3.0
3.7324
4.2324
4.2317
4.8317
4.6317
5.4317
5.8317
6.0317
6.3324
6.2317
7.1317
7.8320

rX-ray
3.1339
3.9340
3.6324
4.1342
4.8342
5.0343
5.4344
5.8345
6.2322

6.1324
6.3346
6.8347
7.5348


Nuclear Magnetic Resonance Spectroscopy

19

Macchioni and co-workers,315 in pioneering work, measured diffusion coefficients of the structurally
closely related complexes trans-[Ru(PMe3)2(CO)(COMe)(pz2CH2)]BPh4 and trans-[Ru(PMe3)2(CO)(COMe)(pz2BH2)], and found clear evidence for ions in nitromethane, ion pairs in chloroform at low
concentrations, and ion quadruples in the latter solvent at high concentration. Ion quadruples were also
mentioned by Beck et al.313 for zirconocene compounds in benzene solution. An interesting solvent
dependence was noted for the complexes [RuCl(6-benzene)(PBu3)2]PF6 and [Pd(diphenylallyl)
(Duphos)](CF3SO3).322,326 In CD2Cl2 the diffusion coefficients are quite different, with the anions
moving much faster, whereas in CDCl3 they are the same within experimental error, suggesting that
free ions and ion pairs are present in the two solvents, respectively. Effective doubling of the volume was
observed when replacing the chloride anion in [(Duphos)RuCl(6-p-cymene)]Cl with BArF, a fluorinecontaining derivative of tretraphenylborate.322 The conclusion that the BArF analog is present as a
relatively tight ion pair is supported by the 19F diffusion measurement on the anion giving almost the
same diffusion coefficient derived from the 1H study.322 Ion pairing with the BArF anion has also been
reported for a series of iridium complexes, whereas analogs with PF6À are separated.169
Given that there are several known examples of anions that affect results from homogeneously
catalyzed reactions,349–351 studies of ion-pairing effects assume new significance.

2.1.3.5

Study of Hydrogen Bonding

Yet another promising area concerns hydrogen bonding in metal complexes.

The two triflates in complex (28), were found to move at almost the same rate.322 Although
tight ion pairing could be an explanation, it was concluded that hydrogen bonding to the P–OH
fragment carries the noncoordinated triflate effectively along with the cation.322

2.1.3.6

Concluding Remarks

Conventional NMR methods depend on the interpretation of interactions explicitly included in
the spin Hamiltonians, i.e., chemical shifts, scalar, dipolar, and quadrupolar coupling constants.
An empirically well-established parameter-to-structure relationship is generally essential for
elucidating complex molecular structures. As the spin interactions tend to be rather local, it is
often tedious to describe overall molecular properties such as size, shape, mass, and charge. In
this respect, the size- and shape-sensitive NMR techniques based on pulsed field-gradient spinecho methods add an invaluable tool to the coordination chemist’s armory. With (i) the widespread availability of self-shielded gradient equiment, (ii) the proven reproducibility of results,
and (iii) the straightforward interpretation of ‘‘size,’’ PGSE methods will find frequent application
in solving problems in coordination chemistry.

2.1.4
2.1.4.1

SOLID-STATE NMR SPECTROSCOPY
Introduction

Since about 1980, NMR spectroscopy of coordination compounds in solution has been increasingly used on a routine basis to address a multitude of new and older chemical problems. The
introduction of two-dimensional correlation methods afforded quick access to parameters for
relatively rare spin-1=2 nuclei. Further, three-dimensional solution structures can now routinely
be solved, including not only their constitution but also all aspects of configuration, conformation, and intra- and intermolecular dynamics.
Although there are now hundreds of publications on the applications of solid-state NMR
spectroscopy in coordination chemistry, this technique has not yet made a similar transition. It
still remains mostly in the realm of ‘‘specialists,’’ often more interested in the physical properties

itself than in their chemical significance. This is certainly partly due to the additional equipment
and knowledge required, but also due to the neglect of chemists who define structural chemistry
as X-ray crystallography. At the moment, solid-state NMR exists only as a tool for bridging the
gap to solution studies, thereby overlooking the inherent wealth of information available.
Naturally, but certainly not exclusively, solid-state NMR spectroscopy is the method of choice
for all those materials that are neither crystalline nor soluble, e.g., coordination complexes