摘要:

Chemical Society Reviews Editorial Board Professor H. W. Kroto FRS (Chairman) Professor M. J. Blandamer Dr. A. R. Butler Dr. E. C. Constable Professor B. T. Golding Professor M. Green Professor D. M. P. Mingos FRS Professor J. F. Stoddart Consulting Editors Dr. G. G. Baht-Kurti Professor S. A. Benner Dr. J. M. Brown Dr. J. Burgess Dr. N. Cape Professor A. Hamnett Dr. T. M. Herrington Professor R. Hillman Professor R. Keese Dr. T. H. Lilley Dr. H. Maskill Professor Dr. A. de Meijere Professor J. N. Miller Professor S. M. Roberts Professor B. H. Robinson Dr. A. J. Stace Staff Editors Mr. K. J. Wilkinson Dr. J. A. Rhodes Dr. M. Sugden University of Sussex University of Leicester University of St. Andrews University of Cambridge University of Newcastle upon Tyne University of Bath Imperial College London University of Birmingham University of Bristol Swiss Federal Institute of Technology, Zurich University of Oxford University of Leicester Institute of Terrestrial Ecology, Lothian University of Newcastle upon Tyne University of Reading University of Leicester University of Bern U n ivers ity of Sh eff ieId University of Newcastle upon Tyne U n iversity of G ott ingen Loughborough University of Technology University of Exeter University of East Anglia University of Sussex Royal Society of Chemistry, Cambridge Royal Society of Chemistry, Cambridge Royal Society of Chemistry, Cambridge It is intended that Chemical Society Reviews will have the broad appeal necessary for researchers to benefit from an awareness of advances in areas outside their own specialities.Deliberate efforts will be made to solicit authors and articles from Europe which present a truly international outlook on the major advances in a. wide range of chemical areas. It is hoped that it will be particularly stimulating and instructive for students planning a career in research. The articles will be succinct and authoritative overviews of timely topics in modern chemistry. In line with the above, review articles will not be overly comprehensive, detailed, or heavily referenced (ca.30 references), but should act as a springboard to further reading. In general, authors, who will be recognized experts in their fields, will be asked to place any of their own work in the wider context. Review articles must be short, around 6-8 journal pages in extent.In consequence, manuscripts should not exceed 20-30 A4/American quarto sheets, this length to include text (in double line spacing), tables, references, and artwork. An Instruction to Authors leaflet is available from the Senior Editor (Reviews). Although the majority of articles are intended to be specially commissioned, the Society always considers offers of articles for publication. In such cases a short synopsis, rather than the completed article, should be submitted to the Senior Editor (Reviews), Books and Reviews Department, The Royal Society of Chemistry, Thomas Graham House, Science Park, Milton Road, Cambridge CB4 4WF. @ The Royal Society of Chemistry, 1993 All Rights Reserved No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form, or by any means, electronic or mechanical, photographic, recording, or otherwise, without the prior permission of the publishers. Typeset by Servis Filmsetting Ltd. Printed in Great Britain by B lack bear Press Ltd.

ISSN:0306-0012    

DOI:10.1039/CS99322FX017

出版商:RSC    

年代:1993

数据来源: RSC

摘要:

Guest EditoriaI Special Issue on Electron Paramagnetic Resonance Spectroscopy The Electron Spin Resonance Group of the Royal Society of Chemistry celebrated its 25th anniversary with a meeting at Sheffield in March 1993, in which the plenary lecturers were invited to review the present standing of their subject. A selection of these lectures is collected in this issue. They illustrate the importance of the technique in all the main branches of chemistry. Atherton’s Bruker Lecture on nuclear Zeeman inter- actions, McLauchlan’s lecture on radical pairs, and Roduner’s on muon spin resonance deal with the physical side of spectros-copy. Davies’s lecture on organic radical ions continues the traditional interest of EPR spectroscopists in organic 7r-electron systems, and Marsh’s on spin-labelled lipids illustrates the rapidly increasing application of EPR spectroscopy in biological chemistry. The power of the technique in inorganic chemistry is demonstrated by Mabbs’s paper on transition metals and Edwards’s on alkali metals. The collection ends with a review by Nonhebel on the ring-opening of cyclopropylmethyl radicals. We look forward to the developments and application of the EPR technique that the next 25 years may bring! N. M. Atherton A. G. Davies

ISSN:0306-0012    

DOI:10.1039/CS993220X019

出版商:RSC    

年代:1993

数据来源: RSC

ISSN:0306-0012    

DOI:10.1039/CS99322BX020

出版商:RSC    

年代:1993

数据来源: RSC

摘要:

BRUKER LECTURE. The Nuclear Zeeman Interaction in Electron Resonance N. M.Atherton Department of Chemistry The University of Sheffield Sheffield S3 7HF U.K. I Introduction Elementary accounts of electron paramagnetic resonance (EPR) emphasize the hyperfine splitting in the spectra and explain how it arises and how it may be interpreted. This is quite proper for the hyperfine splitting often yields useful information very directly and in a fairly unsophisticated way. The analysis of spectra to extract hyperfine coupling constants can often be done under the assumption that the AMs = 1 AMI = 0 selection rule is valid. This selection rule implies that the transitions can be described using an energy level diagram which takes no account of the nuclear Zeeman energy and this in turn implies that the levels themselves are the eigenvalues of a Hamiltonian which does not contain the nuclear Zeeman interaction. The A Ms = 1 AM = 0 selection rule provides an adequate basis for analysing the spectra of species in solutions and in some solids. However it has been known for many years that it can be inappropriate for solids where the dipolar component of the hyperfine interactioh contributes to the hyperfine splitting and that this condition occurs when the hyperfine interaction is comparable to the nuclear Zeeman energy.The effect was first observed and understood by McConnell Whiffen,2 and Gordy3 and their collaborators for radicals of general structilre RR’CH which at the time were of especial interest as models of the aromatic CH fragment. Apart from practitioners of solid state ENDOR and ESEEM most practitioners of EPR have been able to get along very nicely without troubling about the matter and it has not featured prominently in the literature for some years. However recent technological developments have made it possible to measure spectra at much higher fields than those traditionally used for example at fields of 3.4,5.4,and 8.9 T corresponding to electron Larmor frequencies of 95,4 150,5 and 250 GHz6 respectively for g= 2. Since increasing the magnetic field increases the nuclear Zeeman energy while leav- ing the hyperfine interaction unchanged it seems possible that in high field experiments one may run into regimes where the two interactions become comparable and where the behaviour of the system in electron resonance experiments may be quite different from that which is observed at say X-band. In view of these considerations it appears timely to review the role of the nuclear Zeeman interaction in electron resonance. It may be a comfort to those who are not familiar with these Neil Atherton MJUSbrought up in Redcar where he attended Sir WilliamTurner’s School and was a student of the University of Birmingham. He has been active in the field of electron spin resonance and its appli- cations since he began Ph.D. research under the supervision of Professor D. H. Whiflen in 1956. After a postdoctoralyear with Professor S. I. Weissman at Washington University St. Louis he went to the University of Shefield as an ICI Fellow in 1960 and eventually became Professor of Physical Chem- istry there in 1975. He is cur- rently Dean of the Faculty of Pure Science at Shefleld. 293 matters if we emphasize at this point we will be dealing with solids or situations where the rotational correlation is long and that for any effect to show there must be considerable anisotropy in the hyperfine interaction. 2Theoretical Considerations In order to illustrate the points which we wish to emphasize it will be sufficient for us to consider an S = + system described by the spin Hamiltonian where the three terms describe respectively the electron Zeeman hyperfine and nuclear Zeeman interactions. For full generality we should add a term describing the nuclear quadrupole interac- tion but the important physical points are best perceived if it is omitted. We now assume that the electron Zeeman interaction is by far the largest term.This means that we neglect the field due to the nucleus at the electron and take the electron spin to be quantized in a field determined by the applied field as transformed by the operation of the g-tensor.The quality of this assumption improves with increasing strength of the applied field. We will comment on the effect of the anisotropy of the g-tensor later but for the moment take it to be isotropic. Now the electron spin can be taken to be quantized along the applied field and (1) becomes where Ms = ++ and 1is a unit vector defining the orientation of the applied field B in the axis system in which A is expressed. The eigenvalues of this Hamiltonian are which gives rather cumbersome expressions for the energies of the AMs = 1 EPR transitions but a rather more elegant one for the squares of the AMI = I ENDOR frequencies. These results are obtained quite readily by making a judicious choice of the quantization axis for the nuclear spin and this point is implicit or explicit in all the literature treatments. 3.73 It is not necessary to rehearse the argument here but the important point to be realized is that the orientation of this axis depends on the electron spin state.The physical basis of this is clear when one considers the magnetic fields at the nucleus as illustrated in Figures la b.The total field at the nucleus BI is the resultant of the applied field B and the hyperfine field Bs which is itself in general compounded of an isotropic compo- nent parallel to B and a dipolar part. Figures la and 1b may be taken to represent the Ms = -+ and Ms = ++ states respecti- vely. It is clear that both the magnitude and orientation of BIare dependent on the electron spin state when the hyperfine interac- tion is anisotropic. It follows from all this that one must be careful with the nuclear spin eigenfunctions. For consistent calculations one needs them expressed in the same basis for the two electron spin states. For example if we chose the set ~MF),i.e. the eigenfunc- tions of Iz for Ms = -3,as the basis then the eigenfunctions for Ms = ++ are linear combinations of these with admixture coefficients which depend on + the angle between By and Bf Figure Ic. For I = + one finds CHEMICAL SOCIETY REVIEWS 1993 C Figure 1 (a) (b) Magnetic fields experienced by a nucleus having an anisotropic hyperfine interaction with an electron spin S= $The applied field B and the hyperfine field Bs combine to give a resultant Bfwhich provides the quantization axis for the nuclear spin For the two electron spin states the Bs vectors have the same magnitude but are antiparallel so the resultants B are different in both magnitude and orientation for them (c) Definition of the angle 4between the axes of quantization of the nuclear spin for the two electron spin states with the second function determined by the orthogonality requirement and where y’B2 -(1/4)(IA A I)cos f$ = [{(1/4)(IA A I) + y’B6)’ -y2B6(IAf)2]”2 (5) One may readily verify that when the hyperfine coupling is isotropic or when B lies along a principal value of the hyperfine coupling then B and B are collinear for both electron spin states 4 = 0 or 7~ Further when Bs and B are identical in length B,f and By are orthogonal so that cos(4/2) = sin(4/2) = 2-4 These are the main points we need for the discussion which follows However before proceeding it is convenient to tidy up the effect of g-anisotropy When there is g-anisotropy the electron is quantized along an axis which is not collinear with B and the orientation of the field Bs at the nucleus reflects this misalignmentThe result is that g enters into all the expressions for the eigenvalues and eigenfunctions where for example I A is replaced by 1g A/(Igg I)) However the essential physical point is not changed the axis of quantization of the nuclear spin depends in general on the electron spin state 3 EPR Absorption Spectra The disposition of the local fields at a nucleus depicted in Figure la is switched into that of Figure lb when an EPR absorption occursThe nuclear spin state after the transition will be either A4,f = +3or A4; = -3with relative probabilities determined by 4 If I = 3there are now two observable transitions for each initial nuclear spin state From equation 4 we can see that the transition moments are sin(4/2) and cos(4/2) so that the intensit- ies of the two transitions are (+)(1 fcos+) It may be discerned from equation 5 that the two transitions have equal intensity when the nuclear Zeeman energy is equal to one half of the effective hyperfine interaction (1 A A I)$ Further the intensity- weighted mean position of the two transitions is equal to one half of the effective hyperfine interaction It is clearly wrong- headed to speak of these transitions as being ‘allowed’ or ‘forbidden’ we will refer to them as (M,,M;)transitions which may be strong or weak The stick spectra depicted in Figure 2 exemplify the sort of behaviourjust describedThey are calculated for the a-proton of TX Am = 30MHz n Ayy = 90MHz AZ = 60MHz ZX plane X band v1 = 14 5 MHz Y I I I I 70’ Figure 2 Orientation-dependence of the EPR spectrum for an a-proton at X-band a C-H fragment at X-band (v = 14 5 MHz) for the field exploring the plane containing the axis of the singly occupied 2p orbital (X) and the C-H bond (Z) It was assumed that Axx = -60 MHz AZz = -30 MHz values which have long been accepted as typical for the C-H fragment When the field is close to X the hyperfine coupling is relatively large and to all intents and purposes the AM = 0 selection rule applies However as the field approaches Z weak (M,,M;) transitions begin to show appreciable intensity although the spectrum becomes simple again when it lies along 2 Figure 3 shows the development of the spectrum for the field lying 50”from Z as a function of increasing field corresponding to electron Larmor C-H ZXplane 50’ 0 14.5 I 1 ~ ~~~ 20 11 I 22.45 I I II 30 I I 40 I 53 Figure 3 Field-dependence of the EPR speLtrum for an a protonThe figures indicate the value of Vf/MHz 14 5 MHz corresponds to X band 53 MHz to Q-band When V = 22 45 MHz C$ = x 2 THE NUCLEAR ZEEMAN INTERACTION IN ELECTRON RESONANCE-N M ATHERTON frequencies in the range X-band to Q-bandThis covers the field at which the nuclear Zeeman energy is half the effective hyper- fine interaction We note that at the highest field the weak outer transitions have become ‘proton spin flip’ transitions their separation approaches a limiting value of 2vI lo * All this is familiar for protons and it is clear that for them going to high fields causes no complications especially as virtually all of the protons in systems of interest have smaller couplings than the one in the C-H fragment so that the nuclear Zeeman interaction dominates to determine the axis of quanti- zation However this will not be so for other nuclei essentially all of which have smaller magnetogyric ratios As an I = + example we consider SN this is not unrealistic for there can be merit in using isotopically substituted nitroxides as probes Figure 4shows the appearance of the spectra at several frequen- ciesThey were calculated assuming that the field lies 70”from a principal hyperfine coupling of 129 MHz in a plane containing a second principal coupling of 24 55 MHz these values having been scaled from those typical of the 4Ncouplings in nitroxides 15NtZ .I AzZ = 129MHz >N-O-+ X Am = 24 55 MHz 700 95 1.51I 1 35 I I 5.55 95 I I I 15051 150 1 I I I 2375 250 I 39.58 I Figure 4 Field-dependence of the EPR spectrum of an 15N-labelled nitroxideThe figures on the left indicate vs/GHz those on the right v,/MHz Of course nitroxides containing 14N are of crucial interest Figure 5 indicates spectra calculated for the same orientation of the field as that defined above for the 5Nisotopomer for the fields used in recent EPR experiments The relevant princi- pal values of the hyperfine tensor were taken to be 92 and 17 5 MHz It is interesting to note that at an EPR frequency of 150 GHz where for this orientation the critical condition on the relative values of the effective hyperfine coupling and the nuclear Zeeman energy is close to being met the intensity of the ‘MI= 0’ hyperfine component is very smallThe intensity would be exactly zero if the condition were exactly met 4 = n/2 the reason being that the nuclear spin is oriented perpendicular to the quantization axis for the MI = 0 nuclear spin state and there is zero probability of it finding the equivalent orientation when the quantization axis IS flipped by ~/2 It is not difficult to identify other nuclei quite familiar in X-and Q-band EPR whose Zeeman energies are considerable at the highest fields at which EPR experiments have now been done It would seem prudent to consider whether this is signifi- cant in any experiment being carried out at high fields For example the detailed shapes of powder spectra should reflect the occurrence of any transitions which are ‘forbidden’ at low field Again when the principal axes of the g-and A-tensors are not lo 150 I 16.48 1 11 250 I I Figure 5 Field-dependence of the EPR spectrum of an 14N-nitroxide AZz = 92 MHz Axx = 17 5 MHz same orientation as in Figure 4 The figures on the left indicate v,/GHz those on the right v,/MHz collinear then hyperfine features appearing at a g-extremum in a powder spectrum which may well stand out very clearly at high field may not simply reflect the effective hyperfine splitting 4 Electron Spin Echo Envelope Modulation (ESEEM) The occurrence of (MI,M;)transitions is the cause of ESEEM The experiment was conceived implemented and analysed by Mims some 20 years ago,’ but several years were to pass before it came into widespread use The origin of the modulation of the echo observed following d -2-pulse (~/2T -n)sequence can be understood from Figure 6 Here we show the evolution in the rotating frame of an S = 4 I = 3 system whose EPR spectrum comprises four (MI,M;) transitions In this figure the time evolution is to be read from the top and instead of the dephasing and rephasing of the coher- ences being depicted in the conventional manner showing their t r 27 Figure 6The formation of a modulated echo in a (~/2 7 n) pulsed experiment on an S = $ I = $ system whose EPR spectrum comprises (M,,M;)transitions See text for a detailed explanation movement on a circle we use a linear representation so that the horizontal axes in the diagrams represent angleThe top diagram depicts the magnetization lying along 1. after its rotation from z by the ~/2 pulse along xThe system is then allowed to evolve and the four coherences corresponding to the four (M,M;)transitions fan out at rates determined by their Larmor frequencies until the x pulse assumed to be applied along y is applied at time 7 This pulse has two effects The first the normal one in echo experiments is to rotate coherences about y by 7~The second effect which is the crucial one for ESEEM is that it creates new coherences which are in the 'wrong' place that is their angular displacement from 1is not that which they would have achieved had they moved at their Larmor frequencies during the interval T These new coherences are indicated by the short arrows in the third diagram Further evolution of the system now takes all the coherences back towards the origin y but they do not all refocus simultaneously at time 27 the new coherences arising from the second pulse arrive back earlier or later and the echo envelope is modulated It is clear that the modulation depends on the occurrence of the (MI,M;)transitions if the AMs =l,AMI =0 selection rule applied so that the spectrum consisted of just two transitions then all the spins would refocus simultaneously The experiment was analysed by Mims,' his result for the form of the echo modulation function can be written* 47)-M4 +M4 +2M M2{COS wlZr+cos -M M2 {cosw7 7 +cosw 7; (6) where M+ and M-are the transition moments for the two (M,,M;)transitions w12 and w~~ are the two ENDOR frequen- cies and w +and w -are their sum and difference Recalling that the squares of the transition moments sum to unity we see immediately that the depth of modulation at the ENDOR frequencies should be a maximum when the two transition moments are equal z e when the nuclear Zeeman energy is half the effective hyperfine interactionThere is thus an optimum field for ESEEM measurementsThis conclusion is also reached from analysis of the 3-pulse ESEEM experiment in which the stimulated echo is detected The important use of ESEEM is to complement ENDOR in the measurement of small hyperfine interactions such as those which obtain for ligand nuclei in transition metal complexes Taking 14N as an example X-band is clearly a good frequency to use for couplings of the order of 1 MHz since V is also 1 MHz However for other nuclei with comparable hyperfine interac- tions but with larger magnetogyric ratios there may well be no advantage in going to high field and for studying small hyperfine couplings to 'H and 19Fit may very often be advantageous to make ESEEM measurements at lower frequencies than X-band 5 Coherence Spectroscopy (COSY) Two-dimensional (2D) magnetic resonance experiments were conceived by Jeeneri2 and have become established as an indispensable part of NMR spectroscopy l3Their development for EPR lagged behind that for NMR on account of the more demanding technology required to cope with the much shorter characteristic timescales but notable progress has been made in the last few years In particular Freed and his collaborators have implemented and analysed the EPR analogues of several established NMR experiments l4 while a review by Schweiger gives a comprehensive overview of developments up to 1991 The NMR COSY experiment is a valuable way of unravelling the couplings in complex spin systems * The experiment com- prises two ~/2 pulses separated by an interval and the free induction decay is detected over the time regime t following the second pulse Fourier transformation with respect to the time regimes tl and t yields the 2D spectrum in which the appear- ance of off-diagonal or cross peaks indicates coupling between pairs of spins In the absence of strong relaxation processes the COSY spectrum of an S =3system in which there is hyperfine CHEMICAL SOCIETY REVIEWS 1993 coupling to a single nucleus and in which the AMs =1 AM =0 selection rule holds is not expected to show cross peaks this has been confirmed by Gorcester and Freed14 l7 for a nitroxide in solution However if the EPR spectrum comprises (M,,M;) transitions then cross peaks should be observed up to the time of writing this experiment does not appear to have been implemented 6 MagnetizationTransfer Experiments Dynamical processes transfer magnetization from one part of a spectrum to another Chemical exchange is a transparent ex- ample but here we will concentrate on the transfer effected by slow rotational diffusion for a great deal of attention has been paid to devising and analysing EPR experiments to study and characterize such motion We will list three classes of experiment and comment on the implications for them of the occurrence of (M,,M;) transitions An approach which is very direct and conceptually straight- forward is the frequency-swept ELDOR experiment of Hyde et ul l8The principle may be understood by reference to Figure 7 which depicts very schematically the rigid lattice limit powder spectrum of a nitroxide radical having assumedly uniaxial anisotropic magnetic interactionsThe spectrum is pumped at a point corresponding to a particular orientation for say the MI = -1 hyperfine component for example at up and the response at another point for example o0,is monitored The strength of that response is determined by the effectiveness at which saturation is induced at up,and thus by T and then the competition between spin-lattice relaxation and the rate at which slow rotational diffusion transfers the saturation to the observing point Data are collected by varying the separation between and w0 and so this CW experiment is very time- consuming A great improvement in this respect can be obtained if a pulsed technique is used and it should be possible to do this using an experiment implemented by Freed and his group l4 Generically the experiment belongs to the class of 2D experi- ments which were introduced by Jeener et a/ for the study of chemical exchange,19 and which are known as EXSY (from exchange spectroscopy) but which Freed very appropriately refers to as 2D-ELDORThe method has been used to study freely tumbling nitroxides and the potential for studying slow motion has been appreciatedi4 but the experiment does not yet seem to have been implemented for the slow motional regime It is interesting to note in passing that this pair of experiments a I// M =+I T TO -I OP Figure 7The construction of the powder EPR spectrum for a hypotheti-cal uniaxial nitroxide The spectra for the perpendicular and parallel orientations are indicated at (a) and (b) respectively the idealized powder absorption spectrum at (c) THE NUCLEAR ZEEMAN INTERACTION IN ELECTRON RESONANCE-N M ATHERTON frequency-swept ELDOR and 2D-ELDOR form a very pleas- ing illustrdtion of the complementarity of double resonance and 2D experiments The third type of experiment we wish to mention is saturation transfer EPR (ST-EPR) 2o Here one detects typically the out-of-phase absorption at the second harmonic of the modulation frequency the sampling of different parts of the spectrum being achieved because the field is modu- lated This is a CW method and so is very widely available although it needs to be handled with care 21 In all of these experiments the nature of the response depends on the transition moments of the transitions being excitedThe transition rate depends on the transition moment in exactly the same way irrespective of whether the oscillating field driving the trdnsition derives from coherent radiation or from stochastically fluctuating magnetic interactions and it follows that the spin- lattice relaxation time is longer for a weak (M,,M;) transition than it is for a strong one It is clear from Figures 4 and 5 that the rigid lattice limiting spectra of nitroxides at high fields must contain contributions from (M,,M;) transitions and so one might expect to see manifestation of their occurrence through compdrison of magnetization transfer experiments performed at different frequenciesThe point has been appreciated in respect of ST-EPR5 but it would appear that there is considerable scope for further study of the matter 7 ENDOR Transition Moments The core of this essay has been the fact that the orientation and magnitude of the field experienced by a nucleus depends on the clectron spin state and the orientation of the applied field with respect to the hyperfine tensor We move towards a conclusion by considering the consequences for ENDOR transition moments In the usual experimental arrangement for ENDOR the r f field is delivered by a coil whose axis is perpendicular to the applied field B so that the r f field oscillates in a plane perpendicular to B In general this plane will not be perpendicu- lar to the axis of quantization of the nuclear spin If the angle between the r f field and the quantization axis is $ then the trdnsition moment contains a factor sin 4 and the r f -induced nuclear trdnsition probability lies in the range 1 3sin2$ 30 It follows that when the hyperfine and nuclear Zeeman energies are compdrdble the intensities of ENDOR transitions can be strongly orientdtion-dependentThis effect which will be fami- liar to anyone who has made ENDOR measurements on single crystals has been recognized and understood for many years 22 Considerdtion of this matter has not figured prominently in andlyses of the results of orientation-selected ENDOR experi- ments whereby one seeks information about anisotropic hyper- fine interdctions from powder samplesThe method which was initially developed by Hoffman Kreilick and Yordanov and their c~llnborators,~~ following up earlier work by Rist and Hyde,24 is now firmly established 25 The principles can be understood by considering the idealized case of a uniaxial ligand hyperfine coupling in a complex with a uniaxial g-tensor Vdnadyl complexes may approach this ideal limit and we use one as an example in Figure 8 The EPR spectrum of a vanadyl complex is shown in Figure 8a it is a typical example The ESR dbsorption dt point B ,the low field extremum arises from those complexes in the MI= -7/2 nuclear spin state for which B lies along ,g dnd the ENDOR response at that point arises from those complexes only If the angle between the axes ofg and A is u then the ENDOR response is crystal-like for in all the complexes contributing to the response B is inclined at uto the axis of the hyperfine coupling cf Figure 8b Such a response is shown in Figure 8d which is the high frequency * 33Cs ENDOR signdl observed from vanadyl-doped CsCl (the low frequency component occurs close to zero frequency) If the field is set to point B of the EPR spectrum the ENDOR response is from complexes in which the field is inclined at 0 tog but now as can be seen from Figure 8c this covers a range of orientations from (8 +U)to (0 -a),of the field with respect to A We thus expect a a Iz Bo 91,25mT' 1i b C I? n d e Figure 8 Orientation-selected ENDOR (a) Powder EPR of a vanadyl complex (b) and (c) orientation of the applied field with respect to tensor axes for the points marked B and Bg respectively (d) and (e) corresponding ENDOR spectra obtained from vanadyl-doped CsCI 120 K A full commentary is given in the text powder ENDOR signal but from a limited range of orien- tations An example is shown in Figure 8e which was obtained from vanadyl-doped CsCl for a setting of the field corresponding toe= 11" One could hope to be able to read directly from spectra like that of Figure 8e the extrema in the ENDOR frequencies for the particular value of 8 and analysis of these as a function of 8 should enable A and u to be determined However it is not necessarily clear which points on the spectrum actually corres- pond to the extrema in the ENDOR frequencies so to optimize the quality of the analysis it seems necessary to cdrry out simulations It seems clear that in general the detailed shape of the simulated spectra will depend on whether or not the orien- tation dependence of the ENDOR transition moment is included in the calculationsThe sensitivity of the calculated spectra to the transition moment will depend on the particular case but preliminary calculations indicate that there are realistic circumstances where the inclusion of the transition moment can have a significant effect on the shapes of simulated spectra 26 It would appear that there is scope for further investigation of this matter 8 Conclusion The role of the nuclear Zeeman energy in both well-established and modern electron resonance experiments has been surveyed In conclusion two further areas which may bear thinking about will be mentioned The first point concerns the Breit-Rabi levels When the nuclear Zeeman energy is about half the effective hyperfine splitting the low frequency ENCOR transiton lies at zero frequency which implies an (avoided) crossing of Breit-Rabi levelsThe occurrence of such a crossing is exploited in muon level crossing experirnent~,~~ following up a suggestion due to Abragam 28 It remains to be seen whether interesting and useful effects reflecting the magnetic field dependence of the nuclear Zeeman energy conventional electron resonance experiments The final point is on the evolution of the magnetization of radical pairs and the polarization of their EPR spectra 29 Discussion of this for the case where the EPR spectra contain (M,,M>) transitions might be interesting and relevant to the behaviour of pairs in the solid state or possibly the slow motional regime NOTE ADDED IN PROOFThe comment about COSY made at the end of Section 6 has been overtaken to some extent by recent work (S Lee B R Patyal and J H Freed J Chem Phys 1993,98 3665) 9 References 1 H M McConnell C HellerT Cole and R W Fessenden J Am Chem SOC 1960,82,766 2 N M Atherton and D H Whiffen Mol Phys 1960,3 1 3 I Miyagawa and W Gordy J Chem Phys 1960,32,255 4 0 Burghaus E Haindl M Plato and K Mobius J Phys E Sci Instrum 1985 18 294 5 Ya S Lebedev in ‘Modern Pulsed and Continuous Wave Electron Spin Resonance’ ed L Kevan and M K Bowman Wiley New York 1990 p 365 6 D E Budil K A Earle and J H Freed in Advanced EPR Applications in Biology and Biochemistry’ ed A J Hoff Elsevier Amsterdam 1989 p 307 7 W Gordy ‘Theory and Applications of Electron Spin Resondnce Wiley New York 1980 8 N M Atherton ‘Principles of Electron Spin Resonance Ellis Horwood Chichester 1993 9 H M McConnell and J Strathdee Mol Phys 1959,2 129 CHEMICAL SOCIETY REVIEWS 1993 10 GTTrammell H Zeldes and R Livingston Phys Rev 1958 110 530 11 W B Mims Phys Rev 1972 B5,2409 1972 B6,3543 12 J Jeener Ampere International Summer School 197 1 Basko Polje Yugoslavia 3 R R Ernst G Bodenhausen and A Wokaun ‘Two Dimensional Nuclear Magnetic Resonance in Liquids’ Oxford University Press 1987 4 J Gorcester G L Millhauser and J H Freed in ‘Modern Pulsed and Continous Wave Electron Spin Resonance’ ed L Kevan and M K Bowman Wiley New York 1990 p 119 5 A Schweiger Angew Chem Int Ed Engl 1991,30,265 16 see e g R K Harris ‘Nuclear Magnetic Resonance Spectroscopy’ Longman London 1986 17 J Gorcester and J H Freed J Chem Phys 1988,88,4678 18 J S Hyde M D Smigel L R Dalton and L A Dalton,J Chem Phys 1975,62 1655 19 J Jeener B H Meier P Bachmann and R R Ernst J Chem Phys 1979,71,4546 20 see eg L R Dalton B H Robinson L A Dalton and P Coffey Adv Mugn Res 1976,8 149 21 D Marsh and L Horvath in ‘Advanced EPR Applications in Biology and Biochemistry’ ed A J Hoff Elsevier Amsterdam 1989 22 see e g D H Whiffen Mol Phys ,1966,10,595 E R Davies andT Rs Reddy Phys Lett 1970,31,398 23 B M Hoffman R A Venters and J Martinsen J Mugn Res 1985,62 537 T A Henderson G C Hurst and R W Kreilick J Am Chem Soc 1985 107 7299 N D Yordanov and M Zdrav- kova 1984 Proc XXII Congr Ampere Zurich p 612 24 G H Rist and J S Hyde J Chem Phys 1970,52,4633 25 Electron Magnetic Resonance in Disordered Systems ed N D Yordanov World Scientific Singapore 1992 26 N M Atherton and C Oliva unpublished work 27 S F J Cox G H Eaton J E Magraw and C A Scott Chem Phys Lett 1989,160 85 28 A Abragam Compt Rend Acad Sci (Paris) 1984,299,95 29 see eg K A McLauchlan in ‘Modern Pulsed and Continuous Wave Electron Spin Resonance’ ed L Kevan and M K Bowman Wiley New York 1990 p 285

ISSN:0306-0012    

DOI:10.1039/CS9932200293

出版商:RSC    

年代:1993

数据来源: RSC

摘要:

The Electron Paramagnetic Resonance Spectra of Organic Radical Ions Alwyn G. Davies Chemistry Department, University College London, 20 Gordon Street, London, WCI H OAJ, U.K. 1 Introduction Organic radical ions have played a key role in organic EPR spectroscopy. Neutral radicals in fluid solution usually self-react at a diffusion-controlled rate and have a lifetime of much less than a second. If their EPR spectra are to be recorded, they therefore have to be continually generated within the cavity by special methods such as in situ irradiation with electrons or with UV light, or by flow mixing of the reagents as they enter the cavity. Radical anions and cations on the other hand are usually longer lived, sometimes indefinitely so, and it is relatively easy to obtain strong, well-resolved spectra.It was natural then that much of the early work on the EPR spectra of organic radicals should be focused largely on radical ions. The first set of papers, by Weissman in 1953,’ included the naphthalene, anthracene, and mono-, di-, and tri-nitrobenzene radical anions and Wurster’s nitrogen-containing radical cation, and the second set, by Fraenkel in 1955,2was concerned with the semiquinone and semidione radical anions. Most of the principles concerning hyperfine coupling which are used today were derived from studies on radical anions in the 1950s and 1960s and are discussed in Gerson’s book on High Resolution EPR Spectroscopy (1970),3 and in Kaiser and Kevan’s edited volume on Radical Ions (1968).4Since then there have been few major developments in matters of principle, but the experimental techniques have improved greatly, particularly in relation to radical cations, and the studies have been extended to many more structural types.An extensive, though not com- prehensive, listing of the EPR data on organic radical ions, with references, is given in three editions of Landolt-Bornstein. The major development in technique has been the generation of radical ions by gamma-irradiation of dilute solutions of substrates in frozen matrices such as ethers for radical anions, or Freons for radical cations.6 As the radical ions are immobilized, the spectra are anisotropic; this anisotropy provides further information about the electron configuration, but it also causes the lines to be relatively broad.The technique is most useful for smaller molecules, and it can be used for generating radical cations from compounds with high ionization energies, such as alkanes5It is less useful for generating the radical cations from Professor Davies did his B.Sc London. and his Ph.D. with degree at University College Sir Christopher Ingold. His research has included work on organic peroxides, organome- talk chemistry, and free radi- cal reactions, and the EPR spectra of organic radicals and radical ions. He is a Fellow of the Roval Society, and holds the Organic Reaction Mechan- isms prize of the Royal Society of Chemistry, and is the present Chairman of the ESR Group.He will be spending a year from November 1993 at the Univer- sity of Freiburg as the holder of a Humboldt Award. 299 larger n-conjugated compounds, where the resolution of com- plex spectra containing a large number of closely spaced lines is often important. A second technique which is being increasingly used is the generation of radical cations in activated zeolites.’ It can be used for substrates with ionization energies up to about 11 eV. The reactant must be small enough to enter the channels of the zeolites, and the hindering of rotation may again give rise to anisotropic spectra. This review will concentrate on the EPR spectra of radical ions in fluid solution. 2 Generation The orbital occupancy by the electrons of a n-conjugated molecule and its corresponding radical anion and cation are illustrated in Figure 1.In principle, the radical anion is formed by addition of an electron into the LUMO, and the radical cation by removal ofan electron from the HOMO, but less direct routes to the radical ions can often be used if the parent compound is not available. -Antibonding Bonding#--e-M +e-Mi --M-Radical cation Radical anion Figure 1 Orbital occupancy in M, Ma+, and Ma-. A fundamental problem in generating a radical anion or cation from a substrate M is that of avoiding back electron transfer from the radical anion to the oxidized reductant, or to the radical cation from the reduced oxidant. For the radical anions this problem is easily solved by using an alkali metal as the reductant (see below), and up to about 1980 many more radical anions than cations had been studied.In recent years new techniques for generating radical cations have been developed, and that situation has now been partly redressed.* 2.1 Radical Anions The principal techniques for generating radical anions in fluid solution are shown in Table 1. Table 1 Generation of radical anions (1) Reduction with an alkali metal (2) Photoassisted electron transfer (3) Deprotonation of a neutral radical (4)Electrolysis CHEMICAL SOCIETY REVIEWS, 1993 Experimental Methods for Generation of Radical Ions If UV irradiation is to be used, the working part a of the cell must be made of high grade silica (eg Suprasil, ca 3 mm o d ) which will not itself develop a signal under irradiation The silica cell a is joined to the Pyrex upper section through the graded seal b Solvents can be transferred by pipette or syringe, or on a vacuum line Typical procedures are as follows Radrcal Catrons The solvent (eg TFAH, ca 0 5 cm3), Hg(TFA), (ca 10mg), and the substrate (1-2 mg) are successively added to the cell A, and then flushed with nitrogen or degassed on the vacuum line The cell is stoppered at c or sealed at d, and transferred to the EPR cavity which is equipped for m situ photolysis Radical Anions In straightforward cases, it may be sufficient to add the substrate (1-2 mg) to the cell A, and a clean piece of potassium at 6, too large to pass into the silica section a The solvent (egpotassium4ried THF, ca 0 5 cm3) is then distilled into the cell on the vacuum line and sealed at d The solution is washed over the metal until the colour and the spectrum of the radical ion develop, sonication in a cleaning bath may be used to accelerate the process For more demanding substrates, the apparatus B may be used, the purpose of the coarse sintered glass filter e is to prevent fragments of metal passing into the working part of the cell a, and that of the bypassfis to avoid an air lock The sample is introduced into a and the metal into the side arm h which is then stoppered The cell is connected to the vacuum line at dand then sealed under vacuum at I The side arm g is warmed with a luminous flame to distil the metal as a mirror onto the wallsat] The side arm h is removed by sealing at k, The formation of a radical anion by treating a substrate with an alkali metal is very general (e g equation 1) All the alkali metals can be used, including sodium/potassium alloy, and sodium amalgam, and a more polar solvent (eg diethyl ether or tetrahydrofuran rather than a hydrocarbon) helps to solvate the ions which are formed A good ligand for the metal cation, particularly a crown ether, will further stabilize the metal cation, and the electron transfer can be assisted by sonication The alkali metals all have nuclear spin, and frequently hyper- fine coupling can be observed to the metal counter cation This is discussed below If the parent molecule M is not accessible, the radical anion M -can sometimes be prepared by photo-induced electron transfer An example is illustrated in Figure 2 Photoionization of hydrazine in liquid ammonia/THF in the presence of potassium t-butoxide leads to the formation of the diazene radical anion by the sequence of reactions shown in equations 2-4 H,N-NH, + Bu'O +H,N-NH + Bu'OH (2) H,N-NH % H,N-NH + esolv (3) H,N-NH + Bu'O +HN=NH + Bu'OH (4) The spectrum shows hyperfine coupling by two equivalent nitrogen atoms [I = 1, a(2N) 7 9 GI, and two equivalent protons [a(2H) 11 3 GI, together with, at high field, the singlet due to the solvated electron A radical anion can be regarded as the conjugate base of a protic neutral radical, and equation 5 illustrates the application of this principle in the preparation of the radical anion of di-t- butylsilanone'O by the abstraction of a hydrogen atom and a proton from the corresponding silanol by a t-butoxyl radical (from the photolysis of di-t-butyl peroxide) and a t-butoxide anion respectively .P d b a the solvent is distilled into a on the vacuum line and the cell is sealed at d The radical anion is then generated as before After use, the cell should be cut open, and the residual metal cautiously dissolved in an alcohol, t-butyl alcohol should be used for potassium The cell can then be reconstructed and reused , solv 10 G' U -Figure 2 EPR spectrum of the diazene radical anion in liquid NH,/ THF, showing, as marked, the singlet due to the solvated electron (Taken, with permission from ref 9) Few chemists appear to be confident in both electrochemistry and EPR spectroscopy, and the electrolytic generation of radical anions and cations deserves more attention A convenient cell for zn sztu electrolysis has been described by Ohya-Nishiguchi * * The technique has the advantage of being applicable under neutral conditions over a wide range of temperature It has been particularly successful for preparing radical ion salts for X-ray crystallography, the salt may separate on the appropriate elec- trode, and be used without further handling l2 2.2 Radical Cations There is no single method equivalent to the alkali metal route to radical anions, by which radical cations can be prepared A variety of methods is available as shown in Table 2,* and the choice between these is still largely empirical The electron transfers in methods 1-5 may all be promoted by photolysis Mere dissolution of a substrate in a protic acid (CF,CO,H, H,SO,, CF,SO,H/SO,, FSO,H/SO,), may be sufficient to THE EPR SPECTRA OF ORGANIC RADICAL IONS-A G DAVIES Table 2 Generation of radical cations (1) With protic acids (2) With Lewis acids (3) With oxidizing metal ions (4)With n-conjugated electron acceptors (5) With aminium radical cations (6) Protonation of a neutral radical (7) Electrolysis generate the radical cation, the substrates with the higher ionization energies need the use of the stronger acids For example, the NMR and EPR spectra of anthracene in FSO,H/ SO, show that the cation resulting from addition of a proton at the 9-position, and the radical cation resulting from removal of an electron, are both present l3 When trifluoroacetic acid (TFAH) is used as the solvent, nucleophilic attack on either species may have the result that the EPR spectrum of the aryltrifluoroacetate [eg 9-trifluoroacetoxy- and 9,lO-bis(tri- fluoroacetoxy)-anthracene +I is observed l4 The mechanism or mechanisms by which protic acids bring about oxidation is not certain (and the possible effect of daylight has often been ignored) The suggestions which have been made include electron transfer to ground state or photoexcited sub- strate (equation 6),l ,and electron transfer from the photoex- cited substrate to the dimer of trifluoroacetic acid, which avoids back electron transfer by dissociating into trifluoroacetate anion and dihydroxytrifluoroethyl radical (equation 7) M+MH+-+M++MH (6) M* + (CF,CO,H), -+ M + CF,C(OH), + CF,CO, (7)+ A variety of Lewis acids behave in the same way Aluminium trichloride has been most widely used, particularly in dichloro- methane, and, without photolysis, will bring about the oxidation of substrates with ionization energies less than ca 8 eV Other reagents which have been used include AsCl,, BF,, BCI,, SbCI,, and SbCl, Oxidation with metal ions has been carried out with silver(r), cobalt(IrI),* cerium(rv),' mercury(~~),' and thallium(IIr),20 usually in TFAH.and with lead(1v) in FSO,H,' the oxidizing power is in the sequence CeIV > TI"' > Hg" Cobalt(rI1) and cerium(1v) have been used only under flow conditions which is expensive in solvent, reagent, and substrate, but is sometimes uniquely effective Modifications of this method, using other cobalt and cerium salts under static, photolytic conditions might repay investigation Mercury trifluoroacetate or thallium trifluoroacetate in static, usually photolytic systems have been used extensively The mechanism is illustrated for Hg(TFA),/TFAH in equation 8, it involves photoassisted electron transfer within a charge-transfer complex, energy-wasting back electron transfer being avoided by loss of trifluoroacetate ion from the reduced metal complex MH + Hg(TFA), +[MH Hg(TFA),] -+ MH + ++ Hg(TFA), -+ MH + Hg(TFA) + TFA Under these conditions, a number of substrates undergo mercu- ration in the aromatic ringz2 the reaction occurs at the CH ring position where, in the SOMO, the electron density (and hence the hyperfine coupling constant) is highest The ionization energies of the mercurated species are often close to those of the parent molecules, and the EPR spectra which are observed may be of MH +,or MHg(TFA) +,or both With some substrates, the mercuration under photolytic conditions is faster than that in the dark, and hence the reaction can apparently proceed through the interaction of the radical ion pair as well as through the neutral molecules, both processes giving the same Wheland intmnediate M(H)Hg(TFA), (equation 9) There appears to be 30 1 no report of the observation of the analogous arylthallium radical cations in experiments with TI(TFA), + TFAH (9) The generation of radical cations by electron transfer to TT-electron acceptors has not been widely used, and should be capable of being extended For example, when a few drops of TFAH are added to a solution of thianthrene and of 2 3-dichloro-5,6-dicyanobenzoquinone(DDQ) in dichlorometh- ane, a purple colour develops, and the spectrum of the thianth- rene radical cation can be observed 23 Presumably protonation of the DDQ radical anion to give the neutral radical overcomes the reversibility of the electron transfer Triarylamininium radical cations, Ar,N will remove an elec- + tron from a substrate with an appropriately low ionization energy, and provide a useful route to radical cations under mild conditions Tris(4-bromopheny1)aminium hexachloroantimon-ate, (4-BrC,H4),N + SbC1, ), is commercially available, and the tris(2,4-dibromophenyl)aminiumhexachloroantimonate is readily prepared Solutions of the aminium salt and substrate are mixed at low temperature, then allowed to warm when the spectrum develops 24 The formation of a radical cation by the protonation of a neutral radical is a useful concept, though many of the reactions which might appear to follow this mechanism in fact adopt an alternate route For example, the photolysis of pentamethyl- cyclopentadiene under neutral conditions shows the formation of the pentamethylcyclopentadienyl radical, and it was pre- dicted that the same reaction in TFAH should show the spec- trum of the pentamethylcyclopentadiene radical cation (equa- tion 12) ls Indeed it does, but the reaction appears to involve oxidation of the substrate Me,C,H by the photoexcited cation Me,C,H: As mentioned above the electrolytic technique appears to be capable of further development One of its advantages is that it can avoid the strongly acid conditions of most of the other techniques, and in principle it can be used for acid-sensitive substrates such as organometallic compounds However, one of the principal decay routes of radical cations involves loss of a proton to give a highly reactive neutral radical, and acid conditions may be necessary to avoid this problem 3 Interpretation of Spectra3 The hyperfine coupling (a)for a proton in the U-or /3-position to an unpaired electron is given by the McConnell and Heller- McConnell equations (equations 13 and 14) where p is the electron spin density at the carbon centre, and Q is the McCon- nell constant In equation 14 8is the dihedral angle between the axis of the 2p orbital and the CH bond, if, in a series of related compounds, 0 may be assumed to be constant, equation 14 can be reduced to equation 15 If any two of the three terms in equation 13 or 15 are known, the third can be calculated, and in a conjugated system, the spin densities over all the n-centres should sum to unity One use of these relationships is to predict and to help in the analysis of the spectra of new radical ions, a second is to check the performance of MO calculations of local electron densities As a first approximation, the spin density may be taken to be equal to the Huckel electron density (c2)at the n-centre, but in a conjugated system it will depend also on the electron density at the other n-centres, and allowance for this can be made by McLachlan's method Values of the constant Qahave been derived by Gerson3 from the regression lines of plots of observed coupling constants against HMO electron densities or McLachlan spin densities, and are (-)26 9 and (-)2 1 8 G respectively for radical anions, and (-)35 1 and (-)25 4G respectively for radical cations The larger values for the radical cations are ascribed to the effect of the positive charge on the spatial distribution of the porbital on carbon, or the sorbital on hydrogen The predictive value of the two calculations is illustrated in Table 3 for the spectrum of the radical anion of ful~alene~~ which is shown in Figure 3 Pro-Table 3 Observed and calculated values of a(Ha)/G in the fulvalene radical anion a(H-2,2', 5,5') U( H-3,3',4,4') Observed 155 37 Calculated (HMO)" -185 -331 Calculated (HMO/McLachlan)" -1 05 -3 25 Taking Q = -30 G as it IS in the cyclopentadienyl radical CHEMICAL SOCIETY REVIEWS.1993 grammes for the calculation of Huckel electron densities and McLachlan spin densities, and for the simulation of EPR spectra are available for microcomputers In strong simple spectra, the satellite lines due to 13Chyper-fine coupling in natural abundance can sometimes be observed The analysis can be based on relative intensities and on the values predicted by a calculation which sums the spin polariza- tion contributions from the spin densities on the a-and 6-carbon atoms in the n-system An example (for the biphenylene radical cation) is given in reference 26 4 Counterion Coupling As mentioned above, radical anions may show hyperfine cou- pling to an alkali metal counterion [7L1 (92 6%), 23Na (loo%), 39K (93 l%), all with I=3/2, ssRb (72 8%) I= 5/2, s7Rb (27 2%) I= 3/2, 133C~(100%) I= 7/21 An example is shown in Figure 4 27 Irradiation of the dianion of dihydropentalene with UV light induces electron transfer to the lithium cation (equation 16), and the spectrum of the pentalene radical anion can be observed There is a nodal plane in the SOMO passing through the 2- and 5-positions The spectrum therefore consists of a quintet [a(4H) 7 76 GI of narrowly spaced triplets [a(2H) 0 90 GI (at -48 "C),and each line is further split into a 1 1 1 1 quartet by coupling with the lithium counter ion (Figure 4a), if 12-crown-4 is added, this complexes the lithium cation and breaks the coupling, and the quartets are reduced to singlets (Figure 4b) n The interaction with the counterion is usually reduced at lower temperature (as the dielectric constant of the solvent (a LI+ I Figure 4 EPR spectrum of the pentalene radical anion showing (a)the presence of hyperfine coupling to the lithium counterion and (b) the Figure 3 EPR spectrum of the fulvalene radical anion absence of this coupling when 12-crown-4 IS added THE EPR SPECTRA OF ORGANIC RADICAL IONS-A G DAVIES increases) and when the coordinating power of the solvent is increased (e g when THF is replaced by DME) The effect that the counter cation has on the spin distribution, and hence the hyperfine coupling constants, in the radical anion is usually small, but in some special cases it may lead to a concentration of the unpaired electron density in one particular region of the molecule This appears to be the cause of the complications which are observed in the EPR spectrum of the tetraphenylene radical anion 28 It is interesting that there appear to be no reports of the observation of hyperfine coupling of a counteranion with a radical cation Part of the explanation may be that whereas the alkali metal cations are poor electrophiles for the carbanions, the common counter anions are better nucleophiles for the radical cations, and lead to chemical reaction such as the mecuration or trifluoroacetoxylation which is mentioned above 5 Chemical Interactions and Reactions It must be remembered that the EPR technique is very sensitive -the spectra illustrated in Figures 2 and 4 are derived from solutions ca M in radical ions The spectrum which is observed will be that of the substrate in solution with the lowest ionization energy or electron affinity, and impurities in low concentrations can cause misleading results For example, tetra- phenylene prepared from the thermolysis of biphenylene continues to show the EPR spectrum of the biphenylene radical cation until it is purified by chromatography, and radical anions prepared from sodium or potassium which has been stored under tetralin or decalin may show the spectrum of the naphtha- lene radical anion One must equally beware of the interactions and the unimole- cular and bimolecular reactions which the radical ions may undergo in solution These are rare with radical anions, but common with radical cations, also of course the strongly acid conditions which are often used for generating radical cations may induce reactions of the substrates also by non-radical Ioutes The most common phenomenon that is observed is the charge-transfer interaction of a radical cation and its precursor (equation 17) M +M-(M), (17)+ + The hyperfine coupling constants in, for example, the anthra- cene dimer radical cation are the same as those which are observed in the cyclophane where two anthracene structures are held in eclipsing positions,29 and it is assumed that, in the absence of steric repulsion between substituents, the two mole- cules similarly are eclipsed in the dimers M, +,idealizing the overlap of the SOMO and HOMO The electron is equally shared between the two molecules, and the spectrum shows hyperfine coupling to twice the number of protons (or other nuclei) of each type, at approximately half the coupling constant shown by M Thus the benzene radical cation with a(6H) 4 44 + G forms (C,H,),+ with a(l2H) 2 16 G, and the anthracene radical cation with a(2H) 6 47 G, a(4H) 3 08 G, a(4H) 1 38 G gives (C,,H,,),+ with a(4H) 3 25, a(8H) 1 42 G, a(8H) 0 71 G In favourable examples M may associate with a number of+ parent molecules M, and with coronene, complexes up to (C,,H, 2)4+ have been identified by electrolysis at low temperature 30 If the arene carries substituents, as in pyracene or l-methyl- naphthalene, steric interference between the substituents may lead to dimers with lower structural symmetry Similar dimer radical cations, M2+, are known for sulfur- ~entred,~ and phosph~rus-centred~~ ’nitr~gen-centred,~~ radi-cal cations No equivalent interaction to give the dimeric species M, has been reported for radical anions, although when two arenes are held closely parallel in a cyclophane radical anion, the unpaired electron is delocalized over both rings 29 The SOMO would now have the same symmetry as the LUMO of the substrate and this interaction is apparently less bonding than is the SOMO/ HOMO interaction in radical cations One contributory factor may be that in the anion, the p-orbitals are more diffuse than in the cations The dimers Mi+ may interact further by covalent bonding For example dialkylacetylene radical cations react with their parents to give tetraalkylcyclobutadiene radical cations (equa- tion 18),34 and treatment of benzene with Hg(TFA),/TFAH leads to the radical cation of biphenyl (equation 19) 35 Radical cations may also be formed with intramolecular rearrangement, though it is often not clear whether this occurs through a cation or radical cation Thus di-t-butyl acetylene with aluminium chloride shows the spectrum of the hexamethyl- butadiene radical cation (equation 20),3 diphenylacetylene shows the spectrum of the triphenylazulene radical cation (equation 21),37 and 1,4-dimethylcyclohexene shows the radical cation of the Diels-Alder adduct between the parent and 2,5- dimethylcyclohexadiene (equation 22) 38 Me, ,Me ; Me3CC CCMe3 (20) ~e‘ Me More deep-seated rearrangements can sometimes be observed, and bis(pentamethylpheny1)methane and a variety of related systems containing polymethylated benzene derivatives all show the spectrum as the octamethylanthracene radical cation 39 6 References 1 D Lipkin, D E Paul, J Townsend, and S I Weissman, Science, 1953, 117,534 2 B Venkataraman and G K Fraenkel, J Am Chem Soc ,1955,77, 2707, J Chem Phys ,1955,23,588 3 ‘High Resolution ESR Spectroscopy’, F Gerson, Wiley Verldg Chemie, Weinheim, 1970 4 ‘Radical Ions’, ed E T Kaiser and L Kevan, Interscience, New York, 1968 5 ‘Landolt Bornstein, Numerical Data and Functional Relationships in Science and Technology’, Vol II/l, 1965, Vol II/9dl, 1980, Vol II/ 9d2, 1980, Vol II/17f, 1988, Vol II/17h, 1990 6 M C R Symons, Chem Soc Rev, 1984,13,393 7 E Roduner, L M Wu, R Crockett, and C J Rhodes, Catal Lett, 1992, 14,373 304 8 A G Davies and J Courtneidge, Acc Chem Res , 1987,20,90 9 J C Brand, B P Roberts, and R Strube, J Chem SOC, Perkin Trans 2, 1985, 1659 10 A G Davies and A G Neville, J Organomet Chem ,1992,436,255 I I A Terahara, H Ohya-Nishiguchi, N Hirota, and A Oku, J Phys Chem , 1986,90, 1564 12 e g H P Fritz, et a1 ,Z Naturforsch , 1978, 33b, 498 13 A G Davies and C J Shields, J Chem SOC,Perkin Trans 2, 1989.1001 14 P D Sullivan,E M Menger,A H Reddoch,andD H Paskovich, J Phys Chem , 1976,82, 1158 15 J L Courtneidge, A G Davies, C J Shields, and S N Yazdi, J Chem Soc , Perkin Trans 2, 1988, 799 16 L Eberson and F Radner, Acta Chem Scand , 1992,46,630 17 R M Dessau, S Shih, and E I Heiba, J Am Chem Soc 1970,92,~ 412 18 W T Dixon and D Murphy, J Chem Soc , Perkin Trans 2, 1976, 1823 19 W Lau, J C Huffman, and J K Kochi, J Am Chem SOC,1982, 104, 5515 20 I H Elson and J K Kochi, J Am Chem SOC , 1973,95,5060 21 W Lauand J K Kochi, J Org Chem ,1986,51,1801, J Am Chem Soc , 1986, 108,6720 22 A G Davies and D C McGuchan, Orgunometallics, 1991,10,329 23 K L Handoo and K Gadru, Curr Sci , 1986,55920 24 e g S F Nelsen and C R Kessel. J Chem SOC Chem Commun , 1977,490 25 A G Davies, J R M Giles, and J Lusztyk, J Chem Soc Perkin Trans 2, 1981, 747 CHEMICAL SOCIETY REVIEWS, 1993 26 D V Avila, A G Davies, M L Girbdl, and D C McGuchdn, J Chem Reseurch (SJ,1989,256 27 D Wilhelm, J L Courtneidge, T Clark, and A G Davies, J Chem Soc Chem Commun , 1984,810 28 W Huber and K Mullen, Acc Chem Re.5 , 1986, 19, 300, Gescheidt and M Scholz, unpublished work 29 F Gerson, Top Curr Chem .1983. 115.57 30 H Ohya-Nishiguchi, H Ide, and N Hirota, J Chem Phi 5 1979, 66, 581 -31 B C Gilbert, D K C Hodgeman, and R 0 C Normdn, J Chem Soc , Perkin Trans 2, 1973, 1748 32 F Gerson, G Gescheidt, J Knobel, W B Martin, L Ncumdnn, dnd E Vogel, J Am Chem Soc, 1992,114, 7107 33 W B Gara and B P Roberts, J Chem Soc Peihin Trans 2. 1978 150 34 J L Courtneidge, A G Ddvies, E Lusztyk, dnd J Lusztyk J Chem Soc Perkin Trans 2, 1984, 155 35 J L Courtneidge, A G Davies, T Clark, and D Wilhelm, J Chem SOC,Perkin Tranr 2, 1984, 1197 36 J L Courtneidge and A G Ddvies, J Chem Soc Chem Commun . 1984, 136 37 C J Cooksey, J L Courtneidge, A G Davies, J C Evans, P S Gregory, and C C Rowlands, J Chem Soc Per Xiri Ti am 2, 1988, 807 38 A G Davies and R Hay-Motherwell, J Chem SOC Perkin Trans 2, 1988,2099 39 L Eberson, F Radner, and M Lindgren, Acta Chem Scand , 1993, 47,835

ISSN:0306-0012    

DOI:10.1039/CS9932200299

出版商:RSC    

年代:1993

数据来源: RSC

摘要:

On the Possibility of an Insulator-Metal Transition in Alkali Metal-Doped Zeolites P. P. Edwards and L. J. Woodall The School of Chemistry, The University of Birmingham, Edgbaston, Birmingham, B I5 2TT U.K. P. A. Anderson University Chemical Laboratory, Lens field Road, Cambridge, CB2 I EW, U.K. A. R. Armstrong lSlS Science Division, Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX1 I, U.K. M. Slaski School of Physics and Space Research, The University of Birmingham, Edgbaston, Birmingham, B I5 2TT U.K. 1 Introduction Conventionally a metal may be viewed through the notional separation of its constituent atoms into a regular array of ions and a gas of itinerant Although neither exists in practice, a close approximation to the former is a dehydrated zeolite, where cations connected on only one side to an anionic framework line the inside of a series of regular, interconnected cavities (Figure These white solids are, of course, insulators.The most effective route for the controlled and continuous doping of ‘excess electrons’ -possibly localized, possibly itiner- ant -into these pristine solids is through their reaction with alkali metal ~apour.~- We will illustrate here that where the incursive atoms of the vapour of, for example, Na, K, Rb, or Cs, enter a dehydrated zeolite containing a large number of framework cations (gener- ally Na + or K +), they are spontaneously ionized by the intense electric fields within the host matrix.’ The incoming metal atoms Peter Edwards is Professor of Inorganic Chemistry at the University of Birmingham.He was born in Liverpool and obtained his B.Sc. and Ph.D. degrees from Salford University. FolloMing periods at Cornell, Oxford, and Cambridge he took up his present position in 1991. He has been the recipient ofthe Corday Morgan (1985) and Tilden (1993) Medals of the Royal Society of Chemistry. M. Slaski A.R. Armstrong P.A. Anderson L.J. Woodall P.P. Edwards (MO) are to all intents and purposes ‘dissolved’ and the resultant entities M+ and e- are totally integrated into the solid host structure in a manner reminiscent of the spontaneous dissolu- tion of these same alkali metals in liquid amm~nia.~.~ At low doping levels of alkali metal vapour, the released excess elec- trons are then at liberty to interact with a number of framework cations leading to the formation of well defined, and spatially localized paramagnetic clusters of the former M;(“- I)+, where M’ is the framework alkali cation and n = 2,3,4,5,6.The intro- duction, of alkali atoms into the receptive host zeolite can therefore be considered both to increase the cation density and to ‘titrate’ excess electrons into the structure.At some critical stage of metal loading, one expects enhanced electron-electron interactions and one may further envisage the possibility of a ‘matrix-bound’ Insulator-Metal Transition lo,’ within the zeolite host. The possibility of such an intriguing ‘metallization’ transition occurring within the intracrystalline Marcin Slaski was born in Krakow, Poland and obtained his undergraduate and graduate degrees from the Jagellonian University.Following periods in the U.S.A. and Norway he became SERC Postdoctoral Fellow at Birmingham in 1991. Robert Armstrong was born in Scunthorpe, England. He obtained his B.A. from Magdalen College, Cambridge, and his Ph.D. in 1991 (with PPE) from this same institution. He is presently SERC Postdoctoral Fellow with Professor W.I.F. David at the Rutherford Appleton Laboratory. Paul Anderson was born in County Antrim, N. Ireland, and educated at Coleraine Academical Institution and King 3 College, Cambridge. He completed his Ph.D. thesis in 1990 (with PPE) at Cambridge. At the time ofpublication ofthis article he becomes Royal Society Research Fellow at the University of Birmingham.Lee Woodall was born in Rochdale, England. He graduated ,from Oxford University (St. Catherines College) in 1991 and moved to Birmingham in 1992 to begin his Ph.D. in Inorganic Chemistry. 305 Faujasite (zeolites X and Y) Figure I The structures of the zeolites discussed in this work are shown along with those of the related mineral sodalite. The vertices of the polyhedra are occupied by silicon or aluminium atoms: the frame-work oxygens and exchangeable cations are omitted for clarity. channels and cavities of nanoporous zeolites is the focus of this present report. Its experimental verification is, as yet, unproven, although there are very strong precedents for this proposal.’* Just what degree of metal loading is required -and indeed what type of ‘metal’ ensues -is currently unknown.Obviously, this is not a report of completed work on a well developed subject. It cannot be, for many of the key experiments (most notably electrical transport measurements) are yet to be undertaken. However, we can report recent and substantial advances not only in the determination of the crystal structure of these intriguing solids, but also in the nature of the electronic proper- ties conferred upon the zeolite system through the controlled doping with alkali metals. For the latter, we review ESR, NMR and magnetic susceptibility studies which, in combination, directly probe the electronic nature of the excess electrons.These magnetic and resonance measurements also have a funda- mental advantage in that they are non-intrusive/non-destructive interrogators of the electronic structure of solids -a major consideration in the study of these highly reactive, moisture-, and air-sensitive materials. The experiments are difficult, but one feels that the reward will be new contributions to our understanding of the Insulator-Metal Transition and, indeed, to the very nature of the metallic state itself. Thus, instead of providing definitive answers we can, at this juncture, outline the current emerging views. Before reviewing our current knowl- edge of the title systems, it is appropriate to set comparisons with other, perhaps more established systems which undergo Insu- lator-Metal Transitions. 2 Matrix- Bound lnsu lator-M eta I Transit ions In a ‘pure’, one-component vapour (e.g.Na or Cs metals under supercritical conditions) very high densities are generally required to effect the transition from insulating to metallic beha~i0ur.l~The particular examples of expanded Cs and Hg are included in Figure 2 which illustrates the Insulator-Metal Transition for a range of systems as detected by the concent- ration dependence of the electrical conductivity. As one can CHEMICAL SOCIETY REVIEWS, 1993 Conductivity/R-’cm-1o4 Cs at 2273 K I’ I 1o3 I II 1o2 II I 10’ Iat1823K I 1oo I I Ilo-‘ I I I 1 o-2 I II Electron (or donor) density/ecm-3 1019 1020 lo2’ 1023 Figure 2 The Insulator-Metal Transition, showing the concentration dependence of the electrical conductivity for the expanded metals Hgand Cs, and the matrix-bound transitions in Si:P and NH,:Na. The appropriate observation temperatures are also given (from ref.15). see from this figure, transitions from insulating to metallic behaviour occur as some parameter of the system, or some external variable, is continuously changed. Of particular concern to us will be the precise location of this electronic phase transition, as well as the temperatures generally used in probing such a transition to -and from -the metallic state. Importantly, all of these parameters are intrinsically system-dependent and derive from subtle differences in the physics and chemistry of the problem.We will amplify these comments in the paragraphs below. The vast majority of such experimental systems (Figure 2) are best described as ‘matrix-bound’ in that they comprise an assembly of, for example, one-electron impurity or donor centres embedded in a host material (eg. elemental Si, liquid NH,). Within this description, one encompasses the examples of expanded (supercritical) alkali metals, alkali metal-ammonia solutions, and doped group 14 semiconductors.’ A prototype example of a matrix-bound Insulator-Metal transition is seen in the metallic condensation of the lattice of hydrogen-like impur- ity centres (e.g. P, As, Sb) in the hosts silicon and germa- nium. 6.1 In all of these systems, the chemical nature of the host matrix is of paramount importance from two counts.18 First, it dictates the precise form of the (localized) excess electron wavefunction at low doping levels.Secondly, and at higher densities, it influences (part through the preceding effect) the critical conditions for the transition to the metallic state. Another venerable example is that of sodium-ammonia solu- tion~.~,~Most chemists are aware that at low concentrations of sodium, these solutions are blue and electrolytic; at high con- centrations they are bronze-coloured with a conductivity rivall- ing that of liquid mercury. As we hinted in Section 1, we believe there are strong links to the present example of alkali metal ‘solutions’ in zeolites. An appreciation of the semiconductor, or matrix-bound analogy for Na-NH, was given some 35 years In this view liquid NH, is viewed as a dielectric host ON THE POSSIBILITY OF AN INSULATOR-METAL TRANSITION-P P EDWARDS ET AL matrix in which the alkali atom simply takes on the role of a donor or impurity state, this is a complementary description to the chemical 'dissolution' of the element in liquid ammonia 2o In the case of expanded metals, eg caesium and mercury (Figure 2) one can view the system as 'metal-doped vacuum' and this, once again, provides the direct semiconductor/matrix- bound analogy for which the 'host' dielectric constant now becomes unity l3 Returning to the case of the doped semiconductors, the ground state wavefunction for the localized (low density) impur- ity centre (e g Si P) is characterized by an extremely diffuse, hydrogen-like function having a characteristic Bohr radius, a8 of ta 20 8, in Si and ca 45 A in Ge A concomitant weak binding energy (typically <0 005 eV) for the localized electron centre necessitates extremely low temperature measurements (typically 10 mK) to probe the natural evolution of the Insulator-Metal Transition within the silicon matrix (Figure 2) 21 In the case of 'sodium-doped ammonia' (NH, Na) the excess or donor solvated-electron wavefunction at low doping levels is generally described as being strongly localized in a void or cavity in the host liquid, having a characteristic Bohr radius of ca 2-3 8, 2o Here typical binding energies would be in the region 1-3 eV In the case of the solvated electron, the wavefunction is strongly localized on the highly polarized entourage of solvent molecules, the species can be written as (NH,), There are interesting comparisons to be made between, for example, Nai + and (NH,),These fundamental differences in the nature, extent and binding of the localized electron wavefunction in all of these systems has a profound bearing on the critical density (n,) and location of the Insulator-Metal Transition at high densities Of course, the term 'high' is purely relative, samples of Si P become metallic at densities above ta 3 x loi8 elec cm 3, NH, Nd solutions attain metallic status at densities exceeding lo2' elec cm (Figure 2) It was Mott who first described a simple criterion linking a&to the critical density, n,, at the Insulator-Metal Transition, I'lZ 10 22 Although more complicated theories have been developed, Mott's view unquestionably describes the basic physics of the problem and at the same time It has the attraction of transpar-ently describingjprescribing the transition in a wide variety of matrix-bound systems The experimental data linking ah and n, (both determined experimentally) for the systems discussed above (and others) are shown in Figure 3 Edwards and Sienko18 found that, for these wide variety of condensed phase systems, the transition from Insulator to Metal is successfully predicted by a scaled form of the Mott criterion, ni aft = 0 26 f0 05 (2) This criterion appears to be upheld over almost eight orders of magnitude in n, and three orders of magnitude in a& Such considerations will be important guides to our discussion of a possible metallization transition in alkali metal doped zeolites We now turn to the case in hand, and outline how alkali doping brings about changes in the electronic properties of the host system Our aim will be to sharpen our emerging descrip- tion of these new solids by comparison -and contrast -with the above, more-established systems 3 The Electronic and Geometric Structure of Alkali Metals in Zeolites 3.1 Low Concentrations: Coordination and Ionization The characteristic pink to red coloration and ESR spectrum of 13 lines characteristic of Naif were first observed by Kasai4 upon irradiation (under vacuum) of dehydrated sodium-Y I"''1" "' \ \.(CHx) M W0,:N: Ar-Cu'.\ 14 16 18 20 22 Log [critical concentration, n,] (~rn-~) Figure 3 A logarithmic plot of the effective Bohr radius, a; vs the critical concentration for metallization, n,, in a variety of systems (from refs 2, 18, 20) (Na-Y) with y, or X-rays Both the number of ESR lines and their intensities are in excellent agreement with those expected from a system of four equivalent nuclei with I = 3/2 (23Na) In Na-Y this means that the ESR spectrum originates from an excess electron trapped between four equivalent sodium cations Similar reasoning leads to the identification5 of the correspond- ing potassium species, Ka+ (Figure 4) Recent neutron diffraction studies23 suggest that the partici- pating ions in KZ are for the most part drawn from outside the + sodalite cage and held there under the influence of the unpaired electron in four tetrahedrally arranged cations Figure 5 shows the structure of the sodalite cage in KJK-A (K, notation denotes an additional five potassium atoms per primitive unit cell) showing a tetrahedron of potassium ions inside a sodalite Figure 4 The ESR spectra of Na:+ and K:+ showing both first-and second-derivative presentations (from ref 5a) CHEMICAL SOCIETY REVIEWS, 1993 Observed Calculated Figure 5 The sodalite cage in KJK-A showing a tetrahedron of K+ ions inside the cage (dark circles) with faces capped by another tetrahedron of K+ ions outside the cage (pale circles) (from ref 23) cage (dark circles) with faces capped by a further tetrahedron of potassium ions outside the cage (pale circles).To further highlight the solvent/matrix duality of the host zeolite, the following equations are useful descriptions for the processes under consideration -+(Mo-Zeolite ) Mo+ 4Na + (zeol,te) M + + Nai + Mo+4K+(zeollte)-+ M+ + K:+ (M =Na,K,Rb,Cs) (MO-NH, ) Mo+xNH, M+ +(NH,); --f A particularly ‘clean’ example of the ESR spectrum from a localized non-interacting Nai centre (without interference + from other resonances) derives from the product obtained from low temperature reaction of Rb vapour with Na-Y;‘j RbO + 4Nac:eol,te) Rb+ + Na:+ (3)-+ This reaction is also important since it illustrates that, to first order, the role of the added alkali atoms is simply that of an electron donor.Clearly the fate of the ensuing Rb+ -presum-ably integrated into the host structure -may have some effect at the higher doping levels. We view the zeolite, therefore, as a solid ‘solvent’ for the dissolution of alkali metals; in much the same way the Nai+ centre can be viewed as an ‘electride’ derived, for example, from a solution of alkali metals in various non-aqueous solvents 24 In the vast majority of cases studied to date,23 we find that the added ‘guest’ cation occupies accessible cationic sites in the zeolithic framework. It appears that the incursive alkali atoms, once ionized, are able to benefit from the considerable coordina- tion of the guest cation to the oxygen ions on the zeolite framework.It seems likely that, for example, a 3s electron on a sodium atom, entering the zeolite and subject to the intense electrostatic fields generated by the host lattice, finds itself effectively under the influence of a group of ions, rather than just a single one, as in the case of the parent atom. This is, after all, the situation one finds for the four known electron traps in lightly doped sodium zeolite, Nap- l)+ (n= 3,4,5,6).This behaviour is dramatically illustrated by our discoveryz5 of a family of clusters, Na;+, Nai+, in zeolite Na-X and Na-Y (Figure 6). Given the degree of vibrational and translational mobility that is well established for zeolite cations, even at room temperature, one may conclude that the excess electron at low densities would be able to pass from one group of ions to another throughout the crystal, before finding a stable site in one of the established clusters.There is clear evidence that, even at exceptionally long distances between Nai + centres, electrons in these traps are able Figure 6 A family of ionic clusters In Na/Na-X the observed ESR spectrum is shown on the lefthand side (a) first derivative and (b) second derivative The simulated ESR spectra for an equal mixture of Nat + and Naz are shown on the right hand portion of the diagram + (from ref 25) to interact with each other. Here again, one detects strong similarities with the situation for metal-ammonia solutions, where electron4ectron interactions become discernible at extremely low metal concentrations.8 It is to these matters that we now turn.3.2 Intermediate and High Concentrations: Interacting Electrons, Spin Delocalization, and the Onset of an Insulator-Metal Transition The onset of substantive electron4ectron interactions in alkali doped zeolites is highlighted by several experimental obser- vations on samples of progressively increasing alkali metal content. The exposure of, for example, dehydrated Na-Y to sodium vapour causes the white solid first to turn pink, then bright red, deep red, and eventually blue/black. In Figure 7 we reproduce the salient features6 of the ESR spectra from such products formed upon the controlled reaction of Na-Y with 3,8, 13, and 32 (extra) sorbed sodium atoms per unit cell (P.u.c.). The pink to red solids, obtained by the treatment of zeolite-Y with relatively low concentrations of metal (< 1 additional sodium atom P.u.c.) exhibit the fingerprint ESR spectrum of Nai+, and at higher metal concentrations, typically 3 atoms g= 2 g= 2 Figure 7 The evolution of the ESR spectrum of Na/Na-Y containing (a) 3, (b) 8, (c) 13, and (d) 32 extra sodium atoms per unit cell ON THE POSSIBILITY OF AN INSULATOR METAL TRANSITION-P p u c and above, a singlet resonance appears whose relative intensity grows with increasing sodium content, eventually to eclipse the spectrum of 13 hyperfine lines From detailed stu- diesz6 of the microwave power saturation characteristics of these signals, it is clear that the singlet resonance makes an important contribution to the spectrum, even at metal concent- rations as low as 3 atoms p u c This change in ESR behaviour, represented by the emergence of the singlet resonance, is caused by the interaction of Na:+ centres such that unpaired electron spin hops between centres effectively ‘scrambling’ the individual sodium hyperfine components This exchange narrowing becomes more and more effective as the electron spin extends over larger and larger numbers of trapping sites It is important to stress that although the faujasite unit cell contains 8 potential sites (sodalite cages, Figure 1) for Na:+, the ESR singlet is already important at concentrations as low as 3 atoms p u c and dominant at 8 atoms p u c when all the sodalite cages should be filled with Na:+ centres Thus, the ESR singlet emerges at just the stage when the probability of two Na:+ centres occupying adjacent sodalite cages becomes significant At first sight the emergence of a single ESR line from the hyperfine multiplet might be invoked as evidence of the transi- tion to genuine itinerant electrons in a truly metallic system z7 28 There is no question that ESR (and indeed NMR) measurements are potent indicators of the transition from spatially localized to completely itinerant electron states l3 29 However, it is important to point out that ESR is sensitive also to spin delocalization involving the extension of the excess electron wavefunction over several centres l7 30 31 For such interactions to be detected, the exchange energy between contributing paramagnetic centres need only be of the order-of-magnitude of the magnetic hyperfine interaction (energy) This contrasts with the situation, for example, in d c conductivity measurements whereby complete electron delocali- zation requires the creation of an electron-hole pair at the Mott transition l7 31 There are clearly large energy differences between the two processes Such spin -not necessarily charge -delocalization over a finite number of centres is again reminiscent of the situation found, for example, in doped semiconductor^^^ and metal solutions In the former case, this embryonic spin delocaliza- tion was regarded by Slichter30 as “ simply the first step in the process of turning into a metal” This may be a good summary of the situation shown in Figure 7 Paradoxically, there is ample evidence that the isolated elec- tron traps such as Na: +,may have quite considerable spatial extent leading to recognizable electron-electron interactions, even at quite low loading levels In sodalite, for example, pulsed ENDOR and spin-echo measurements have dem~nstrated~~ bouring cavities in the zeolite The clusters form an electronic network coupled by inter-cluster exchange interactions in the P EDWARDS ET AL 0 10 20 30 40 50 60 70 80 90 Tern perature/K Figure 8 The reciprocal ESR intensity (directly related to the electron spin susceptibility) of Na:+ as a function of temperature The sample was Rb/Na-Y (from ref 6) between centres in adJacent sodalite cages whose midpoints are a mere 12 8, apart (Figure 1) Evidence for such strong interac- tions, leading now to the formation of diamagnetic singlet (S= 0) states results from recent measurements on the magnetic and spin susceptibilities of these samples 34 Briefly, the picture that emerges is that a large fraction of excess electron spins (ca 90Y0)are ‘frozen out’ in electron spin singlet states with only d very small (but immediately recognizable, Figure 4)fraction of paramagnetic, and interacting (Figure 9) Na: + centres The turn-over, or cusp in the magnetic susceptibility data at low temperature^^^ (ca 10 K, Figure 9) is reminiscent of spin- glass behaviour This observation hints at the disordered nature of these electronic states For although the host matrix is unquestionably crystalline, the doping with alkali metals to generate Na:+ is random in the sense of the occupation of sodalite cages It is interesting to note similar behaviour in the paramagnetic spin susceptibility of SI P at temperatures around 0 02 K,35this scaling in temperature between the two systems may originate from the large differences in binding energies for the excess electron states in Si P and alkali metals in zeolites (Figure 9) Recent 23Na NMR of sodium-doped Na-X at these low temperatures also reveal direct evidence of inter-site intcr- actions Nuclear relaxation measurements reveal d rapid relaxa- tion component of likely electronic origin At sub-helium tem- peratures, there is an abrupt disappearance of the NMR signal, suggestive of a magnetic phase transition The onset of this phase transition is highlighted by the temperature dependence of the nuclear relaxation rate (Figure 10) The existence of these magnetic phase transitions once again emphasizes the import- ance of interactions between paramagnetic clusters in neigh-isotropic hyperfine interactions with sodium nuclei located in neighbouring sodalite cages (Figure 1) Evidence that electrons +in Nai do indeed interact over relatively large distances is also energy range 0 0001-0 001 eV (See also ref 37 ) forthcoming from measurements of the relative electron spin All the indications are that at these accessible levels of loading, susceptibility (xS)for the dilute sample Rb/Na-Y A plot of l/x, the systems are indeed close to an Insulator-Metal Transition vs T has, when extrapolated, an intercept of -25K on the The majority of the effects discussed above may be viewed in negative temperature axis, consistent with weak antiferromag- terms of (embryonic or spin) delocalization As yet there are no netic coupling between the isolated Na:+ centres (Figure 8) firm measurements on electrical transport properties which This observation is given yet more weight by the fact that the would constitute strong experimental evidence for a transition Na: centres at this level of loading can occupy no more than to a true ‘metallic’ state in the zeolite channels + & of the sodalite cages and are, therefore, on average, at least As we have outlined, in the case of both silicon doped with 24 8, apart! phosphorus,’ 30 and metal-ammonia solution^,^ an import- Given the anticipated air; for the Na:+ centre in zeolites (see ant distinction has been drawn between ‘spin delocalization’ and below) this means that the onset of significant (z e measurable in ‘charge transport delocalization’ which defines the compound as magnetic measurements) electron4ectron interactions sets in a genuine ‘metal’, able to conduct a current In both cases, the when the average distance between participating centres is former has been shown to occur before the latter z 10 x a6 This is again reminiscent of the conditions for the Applying the Edwards-Sienko’ criterion to the case of Nai + onset of electron spin-pairing in metal-ammonia solutions at centres in zeolites, and using the estimatesz7 of Xu et a1 for ah, extremely low metal concentrations Interestingly, electron we can predict that a transition to metallic behaviour should transfer In biological systems also generally involves hop dis- occur at concentrations between lo2] and centres cm-3 tances of between 10 to 20 8, for the electron to go from The concentration of sodalite cages in the faujasite structure is membrane surface to an opposite surface 33 about 5 x 1020cm and so a sample of Na-Y containing a +Logically, a much stronger interaction can be expected perfect array of sodalite cages each filled with an Na: centre is 310 3 Oe-7 a.l 2 5e-7 I h lcu a IEa v I C0-2 Oe-7 a I -s Q) I 0) 8 l ar“ a 8 1 5e-7-a..a 1 Oe-7. 0 10 20 30 40 50 7 (K) (b) Temperature{ mK} 20 100 200 1000 2000 10000 20, I I L f: 18-cnc. C5. 16-I E! 14-m Y m 9!9 12-lo)oa 1 2 3 4 log{Temperat ure[m K]} Figure9 (a) The temperature dependence of the total magnetic suscepti- bility (recordedas the magnetization) as a function of temperature for a sample KJK-A (from ref 34) (b) The logarithm of the ESR integrated area is plotted against log temperature for a sample of Si P with a composition (3 2 x 10l8cm 3), very close to the Insulator Metal Transition (from ref 35) Note the differencesin temperaturescales for (a) and (b) not yet expected to be metallic In samples containing more included metal, however, the concentration of excess electrons introduced to the zeolite may well reach -or even exceed -the critical values just mentioned In summary, no experimental evidence, to date, has yet been collected which suggests that any compound of sodium metal in zeolites is indeed ‘metallic’ Our own magnetic data, coupled with the optical work of Srdanov3*39 et a1 suggests that we are indeed very close to an incipient Insulator-Metal Transition However, such statements are not as conclusive as they may sound If genuine charge transport were to occur in such materials, with their interpenetrating aluminosilicate lattice and less than one electron for every two cations, it would constitute a rather unusual metal indeed For example, even if the channels and cavities of the zeolite were filled with a truly metallic phase, it is by no means clear what sort of physical properties would be expected of this filamentary and highly electron deficient, diluted metallic state Clearly further magnetic and transport studies are urgently needed, these will have to be allied with viable synthetic options aimed at maximizing the amount of doped alkali metal in the zeolite CHEMICAL SOCIETY REVIEWS. 1993 I I I I I, I,, 1 10 100 Temperature (K) Figure 10 A log log plot of the 23Na nuclear spin-lattice relaxation rates versus temperature for Na/Na Y (solid points) and Na/Na-X (open points) The shaded region indicates the approximate tempera-ture range at which the resonance vanishes in Na/Na Y (from ref 36) Crystal structure data, to which we now turn, lend strong support to the picture of a gradual buildup towards metalliza- tion, which has been developed from magnetic measurements At low concentrations of added metal, powder neutron diffrac- tion studies have established the presence of included potassium in K,/K-L in cationic sites indistinguishable from those occu- pied in dehydrated K-L, direct proof of the incorporation and ionization of alkali metals within the zeolite pores 40 At high concentrations Sun et a1 41 have determined the structure of caesium-loaded zeolite X by single crystal X-ray diffraction Although the zeolite cavities were in this case said to be filled with caesium atoms, virtually all were found in sites coordinated to the anionic zeolite framework, suggesting that they were predominantly cationic in character The distribution of the cations was such that each supercage contained an icosahedron of caesium ions ostensibly linked to form a ‘cationic continuum’, with caesium+aesium distances in the range 3 89-7 27 A The electronic properties of this compound remain unknown The same group has similar features in potassium- loaded zeolites but the interpretation of these results is ham- pered somewhat by a lack of control over the composition of the final products Using high-quality powder neutron diffraction data, we have determ~ned~~ the structure of potassium zeolite A saturated with potassium metal (K,/K-A) Although each sodalite cage in zeolite A contains eight equivalent cationic sites, only four potassium ions can be accommodated, and it is this intrinsic topological constraint which leads to cation ordering and the subsequent self-assembly of a potassium superlattice (Figure 1 I) Alternate a-cages are thus found to contain either 8 or 12 cations, those containing 8 retain, more or less, the structure of the parent zeolite, whilst those containing 12 are much more densely packed Although potassium-potassium nearest neighbour distances, ranging from 4 24-4 88 A, cluster closely around the potassium metal value of 4 54 A, bond valence sums calculated for the various potassium sites suggest that cations located in the more densely packed fraction of a-cages may be significantly electron-rich compared with those in the remainder, which appear to carry a full ionic charge 23 The possibility that the observed segregation may be electronically as well as structurally driven is of particular importance in the current context, as structural instability and phase separation are frequent harbingers of an incipient Insulator-Metal Transition lo 4 Concluding Remarks Barrer first expounded the view12 43 of dehydrated zeolites as “ crystals porous on the scale of molecules” Here we have ON THE POSSIBILITY OF AN INSULATOR-METAL TRANSITION-P P EDWARDS ET AL 31 1 Figure 11 The origin of the potassium superlattice in K,/K-A A fragment of the crystal structure showing neighbouring a cages and a sodalite cage (see also Figure 1) The much less open structure of the lefthand cage is readily apparent (ref 23) illustrated the efficacy of zeolites as porous hosts for atoms of the alkali metals The incoming alkali atoms give up their ns valence electron to the solid in return for a framework coordination site for the resulting cation.The reaction with alkali metal vapour can thus be considered to simultaneously increase the number of cations in the zeolite framework and introduce excess electrons, both processes are fundamentally important in the evolution of electron delocalization Our review of the current structural magnetic and magnetic resonance data leads us to propose that these systems are close to an Insulator-Metal Transition It may be possible -via judicious choice of zeolite and synthetic routes -that one can engineer a genuine metallization transition within this continuous porous host structure We therefore place alkali metal-doped zeolites in the realms of other chemical systems’ close to and spanning, the Insulator-Metal Transition What is clear is that the electronic properties of these systems -and indeed the metallization conditions -will depend not only upon details such as electron density and screening (a la Mott, etc ) but also upon the geometrical constraints imposed by the host zeolite.One can anticipate very interesting electronic properties for such systems Acknowledgements We thank the S.E R C and B.P. (V R U ) for support and Professor R J P. Williams, F R S for drawing our attention to ref 33 References N W Ashcroft and N D Mermin, ‘Solid State Physics’, Saunders College, Philadelphia, 1976 P P Edwards and M J Sienko, Znt Rev Phys Chem , 1983,3,83 R M Barrer, ‘Zeolites and Clay Minerals as Solvents and Molecular Sieves’, Academic Press, 1978 Early pioneering work in this area (a) J A Rabo, C L Angell, P H Kasai, and V Schomaker, Discuss Faraday SOC, 1966,41,328 (b)P H Kasai, J Chem Phys , 1965,43, 3322 (a) P P Edwards, M R Harrison, J Klinowski, S Ramdas, J M Thomas, D C Johnson, and C J Page, J Chem SOC,Chem Commun, 1984, 982 (b) M R Harrison, P P Edwards, J Klinowski, D C Johnson, and C J Page, J Solidstate Chem , 1984, 54, 330 6 P A Anderson and P P Edwards, J Am Chem SOC, 1992, 114, 10608 7 J W Mortier and R A Schoonheydt, Prog Solid State Chern , 1985, 16, 1 8 J C Thompson, ‘Electrons in Liquid Ammonia’, Clarendon Press, Oxford 1976 9 P P Edwards, Adv Inorg Radiochern , 1982,25, 135 10 N F Mott, ‘Metal-Insulator Transitions’, Taylor and Francis, London, 1990 1 1 P P Edwards and C N R Rao, eds ,‘The Metallic and Nonmetallic States of Matter’, Taylor and Francis, London, 1985 12 R M Barrer, J Inclusion Phenomena, 1983, 1, 105 13 P P Edwards in ‘Physics and Chemistry of Electrons and Ions in Condensed Matter’, 1984, p 297, ed J V Acrivus, A D Yoffe, and N F Mott, NATO (DAVY) ASI, D Reidel, Netherlands 14 W Freyland and F Hensel in ref 11, p 93, for a recent review, see F Hensel, M Stolz, G Hohl, R Winter, and W Golzlaff, J de Physique ZV, Colluque C.5, supplement, 1991, 1, C5-191 15 D M Holton and P P Edwards, Chem Brit, 1985,21, 1007 16 ‘Metal Non-Metal Transitions in Disordered Systems’, ed D P Tunstall and L R Friedman, 1978, Scottish Universities Summer School in Physics, Vol 19 17 M N Alexander and D F Holcomb, Rev Mod Phys , 1968, 40, 815 18 P P Edwards and M J Sienko, Phys Rev B , 1978, 17,2575 19 K S Pitzer, J Am Chem Soc , 1958,80, 5046 20 P P Edwards and M J Sienko, J Am Chem Soc ,1981,103,2967 21 T F Rosenbaum, K Andres, G A Thomas, and R N Bhatt, Phys Rev Lett , 1980,45, 1723 22 N F Mott, Phil Mag , 1961,6,287 23 A R Armstrong, P A Anderson, and P P Edwards, submitted manuscript 24 J L Dye, in ‘Valency’, XXXII Robert A Welch Foundation Conference on Chemical Research, 1988, p 65, (see also comments on p 90) R A Welch Foundation, Houston, Texas 25 P A Anderson and P P Edwards, J Chem Suc , Chern Commun , 1991,915,P A Anderson,R J Singer,andP P Edwards.ibid ,914 26 P A Anderson, Ph D Thesis, University of Cambridge, 1990 27 B Xu and L Kevan, J Phys Chem ,1992,96,2642, B Xu, X Chen.and L Kevan, J Chem Soc ,Faraday Trans, 1991,87, 3157 28 K W Blazey, K A Muller, F Blatter, and E Schumacher, Euruphys Lett, 1987,4, 857 29 R N Edmonds,M R Harrison,andP P Edwards,Ann Rep Prog Chem , Sect C, 1985,82, p 265 30 C P Slichter, Phys Rev, 1955,99,479 31 P P Edwards, J Phvs Chem , 1980,84, 1215 32 J B A F Smeulders, M A Hefni, A A K Klaassen, E de Boer, U Westphal, and G Geismar, Zeolites, 1987, 7, 347 33 R J P Williams, Mol Phys, 1989,68, 1 34 (a)L J Woodall, M Slaski, E K Sinn, P A Anderson, and P P Edwards, submitted for publication (b) see also Y Nozue, T Kodaira, and T Goto, Phys Rev Lett, 1992,68, 3789 35 D P Tunstall and P J Mason, ‘Heavily doped silicon, phosphorus ESR at millikelvin temperatures’, companion proceedings for this conference, J Chem SOC,Faraday (in press) 36 G Schafer, W W Warren, jnr, P A Anderson, and P P Edwards, J Non Crystalline Solids, in press 37 Y Nozue, T Kodaira, S Ohwashi, T Goto, and 0 Terasaki, Phys CHEMICAL SOCIETY REVIEWS, 1993 Rev B, 1993, in press 38 V I Srdanov,K Haug,H Metm,andG D Stucky,J Phys Chem, 1992,96,9039 39 G D Stucky, Prog Inorg Chem , 1992,40,99 40 P A Anderson, A R Armstrong, and P P Edwards, manuscript submitted for publication 41 T Sun, K Seff, N H Heo, and V P Petranovskii, Science, 1993, 259,495 42 T Sun and K Seff, J Phys Chem , 1993,97,5213 43 R M Barrer, Pure Applied Chem , 1986,58, 13 17

ISSN:0306-0012    

DOI:10.1039/CS9932200305

出版商:RSC    

年代:1993

数据来源: RSC

摘要:

Some Aspects of the Electron Paramagnetic Resonance Spectroscopy of &Transit ion Meta1 Com pou nds F. E. Mabbs Chemistry Department University of Manchester Manchester M 13 9PL U.K. 1 Introduction Electron paramagnetic resonance (EPR) spectroscopy is an extremely powerful probe of the electronic structures of mater- ials with unpaired electrons. There is a variety of EPR tech- niques each of which has some particular advantages. The most popular because of its availability is continuous wave (CW) EPR spectropscopy. 1~2In this technique the microwave radia- tion used to induce transitions is applied to the sample con- tinuously. A fixed frequency is used although different fixed frequencies may be used for specific reasons. When the unpaired electrons are mainly associated with the metal centres CWEPR is the preferred technique. Although CWEPR can give infor- mation when the unpaired electrons are delocalized onto sur- rounding atoms which have non-zero nuclear spin it has some serious limitations which will be discussed later.These limi- tations can often be overcome by the use of other methods such as multiple resonance3 or pulsed techniques. With the avail- ability of commercial instrumentation there is an increasing use of electron nuclear double resonance (ENDOR) and electron spin echo envelope modulation (ESEEM) spectroscopies. In essence these two techniques record the NMR spectra of (highly) paramagnetic materials. With respect to d-transition metal ions EPR spectroscopy is widely used to study coordination and organometallic com- plexes and metal ion centres in biological materials and in catalysts.The various EPR techniques can be applied at a number of different levels of sophistication; from merely detect- ing the presence of unpaired electrons through identifying atoms associated with those unpaired electrons to detailed descriptions of electronic structures. At whatever level is being considered it is important that the user realises both the potential and the limitations of the particular technique. Incor- rect or over-interpretation should certainly be avoided. Equally so should under-interpretation when with some extra effort more information can be reliably abstracted from the experi- mental spectra. Frank Mabbs is a graduate (B.Sc./Ph.D./D.Sc.) of University College London. His postgraduate research (1957-60) super-vised by thenow ProfessorThe Lord Lewis Kt. F.R.S. concerned the magnetic properties of transition metal complexes. After three years as a Technical Oficer with British Titan Products at Billingham he moved to the University of Manchester as a NATO Research Fellow and was subsequently appointed to a Lectureship. He is currently a Senior Lecturer in Inorganic Chemistry. His research inter- ests are in the broad area of the coordination chemistry of d transition metals and the structures reactivities and spectroscopic properties (es-pecially EPR) of coordination compounds. 313 This review will deal with both the commonly and not so commonly occurring interactions which have an effect on exper- imental EPR spectra. Because the subject area is vast only cases where an individual metal ion has one unpaired electron will be dealt with. Special attention will be given to CWEPR since this is most widely used. However the circumstances under which it will be either profitable or indeed essential to use other EPR techniques will be discussed more briefly. The discussion will be divided into three areas (1) dilute mononuclear paramagnets (2) the effects of surrounding para- magnets and (3) ligand atoms with non-zero nuclear spin. 2 Diluted Monomeric Paramagnets The main interactions which will be considered as contributing to the EPR spectra are (i) the electronic Zeeman effect and (ii) that between the electron and the metal nuclear spin. For some systems it may also be necessary to include the metal nuclear Zeeman and quadrupole interactions. For any one paramagnet the electronic Zeeman interaction is expressed via the g-tensor. 5a There are three mutually orthogonal principal values of g.The deviation of theseg-values from the free electron value of 2.0023 carries information concerning the orbital angular momentum of the electron i.e. information concerning the electronic struc- ture.The interaction between the electron spin and the metal nuclear spin (the metal hyperfine interaction usually denoted by A) is expressed via the A-tens~r.~~ This is also characterized by three mutually orthogonal principal values. As will be shown in the next section the directions of the three principle values of g and of A need not coincide.Their coincidence or otherwise is in part determined by the point symmetry at the metal ion. 2.1 The Effects of Point Symmetry In this context it is important to make the distinction between point symmetry and the more commonly used descriptions of the shapes of complexes. For example we may have two complexes MA and MA,B where the ligand atoms are at the corners of a square plane. The common description of both of these complexes would be square planar. However MA would have D4,,point symmetry whereas MA,B would have either C or Dzh point symmetry for cis and trans arrangements respectively. The point symmetry at the metal determines whether or not any of the principal values ofg or of A are required to be equal to each other. Also it determines whether or not any of the principal axes of g and A are required to be coincident.These criteria are summarized in Table 1 along with the accepted nomenclature for EPR behaviour and their associated point symmetries. The importance of these relationships is that each type of EPR behaviour is associated with a restricted number of point symmetries. This in turn places constraints upon the geometrical structures of the paramagnet. For example if we can experimentally demonstrate that a paramagnet really has say rhombic EPR symmetry then the associated geometry must belong to one of the point groups Dzh C, or D,. It would be incorrect to assign a structure which belongs to a more sym- metric arrangement e.g. D, which is strictly axial. Table 1 Relationships between g and A tensors EPR symmetry and the point symmetry of paramagnets EPR Symmetry g and A Coincidence of TensorsTensor Axes Isotropic g = gyy= g All coincident Ax = A = A,Axial g = gJ,f g All coincident A = A f A Khombic g f gVvf g All coincident Ax # A # A,,Monoclinic gxx + gyy # g One axis ofg and A # A # A A coincident Triclinic gxx # g # gz CompleteA # A # A non-coincidence Axial gxx = gyy # g Only g and A,,non-collinear A = A # A coincident 2.2 The Experimental Determination of EPR Symmetry The previous section has set out the theoretical relationships between EPR symmetry and point symmetry For a system of unknobn structure if the EPR symmetry can be determined we have invaluable structural information since the paramagnetic can only belong to a restricted range of point symmetriesThe problem is a practical one of how to obtain reliably the above type of information As in all spectroscopic techniques there is often a lack of uniqueness in the interpretation of the experimen- tal data This may arise either from the inadequacies of the data or from different combinations of interactions leading to the same spectrum With this in mind the next two sections explore the usefulness and the limitations of experimental CWEPR spectra 2 21 Spectra from Powders or Frozen Solutions These types of spectra are the ones most commonly encountered when investigating materials of unknown structure In this article the term powder spectrum will be used to cover spectra from either powders or frozen solutions For these types of measurement to be useful three essential criteria must be satisfied (1)There must be no magnetic interactions between the para- magnets the effects of such interactions are discussed in Section 3 Since such interactions usually arise from the close proximity of the paramagnets this means that they must be in low concentration i e magnetically dilute The dilution must be at the molecular level Thus for powders no matter how finely they are powdered mechanical mixing is unsatisfactory (11)The methods for interpreting the spectra require there to be completely random orientations of the paramagnets in the sample Thus the diluted solids must be powdered sufficiently so that there are no preferential orientations of small crystallites Similarly solutions must be frozen to form a glass thereby avoiding the formation of crystallites (111) The randomness of the paramagnets in the sample should always be checked by repeating the spectrum after the sample has been turned through an angle for example of about 20" If the two spectra are not identical then the paramagnets in the sample are not completely randomly oriented The determination of the EPR symmetry from spectra is the next important step This step is often inadequately performed leading to possible incorrect assignments of the EPR symmetry and hence the electronic and geometric structures With the aid of some selected samples both the power and the limitations of methods of determining the EPR symmetry from powder spec- tra will be shown The simplest situations arise when there are no hyperfine interactions In these cases it is usually a question of determining whether or not the paramagnet has axial or rhombic g values CHEMICAL SOCIETY REVIEWS 1993 Isotropic Axial1 v gxx = gyy = szz 911'SL sxx f syy f Qzz Qll < 91 Figure 1 Idealized EPR patterns for different EPR symmetries consider- ing g anisotropy only For axial EPR symmetry g =g and g = g.r = g When the resonances for the principal g values of the paramag- net are sufficiently well separated compared to the linewidths of the resonances then this presents no problemsThis situation is represented by the simulated spectra in Figure 1 However if the anisotropy in for example two of the g values is such that at a particular microwave frequency the resonance magnetic fields are not well separated compared with the linewidths then the spectra could be (mis-)assigned to an EPR symmetry which is too high An example of this is in Figure 2a where the spectrum at X-band could easily be mistakenly assigned to axial EPR symmetry When spectra appear to correspond to axial EPR symmetry at X-band it is important to do at least one but preferably both of the following (I) a full simulation of the spectrum including linewidths and lineshapes as variables should be performed (11) the spectrum should be obtained at a higher microwave frequency For the particular example shown in Figure 2 the Q-band spectrum clearly demonstrates that the paramagnet concerned has rhombic g values see Figure 2b Note that when only the g value anistropy is the experimental observable there is a much greater choice of associated point symmetries For example for rhombic g values the point symmetry of the molecule could be any of those corresponding to the EPR symmetries rhombic monoclinic or triclinic I will return to the example used in Figure 2 a little later to show how an analysis of both theg and A tensors can narrow the choice of point symmetries A I--\'\/ Figure 2 A comparison of (a) the X-and (b) the Q-band spectra of the I= 0 isotopes of molybdenum (the parts of the spectra within the dashed lines) for [LMoOCl,] where L = hydrotris (3,Sdimethyl-pyrazo1yl)borato The presence of a metal hyperfine interaction can be extremely useful in two particular ways It provides (I) an additional means of detecting anisotropy in the system and (11) the possibility of determining the coincidence or otherwise of the principal axes of the g and A tensors Let us first consider a typical visual difference between the spectra of an axial and a rhombic paramagnet Figure 3 shows X-band spectra for two vana- dium(1v) species one of which has axial and one which has SOME ASPECTS OFTHE EPR SPECTROSCOPY OF d-TRANSITION METAL COMPOUNDS-F E MABBS Figure 3 A comparison of the experimental powder EPR spectra (a) an axial system represented by [VO(imid),Cl] in CH,CN/imid where + imid = 1 vinylimidazole and (b) a rhombic system represented by [VO(Mequin),] where Mequin = 2-methylquinolin-8-olato rhombic or lower EPR symmetry In these cases the major differences between the spectra are the splittings which occur in the rhombic spectrum of those features corresponding to those labelled ‘I’in the axial spectrum An example which represents a severe test of the combined use of more than one microwave frequency and of spectrum simula- tion is provided by H,[V(R,R-HIDPA],] diluted in the corres- ponding zirconium compound see Figures 4and 5 An initial look at both the X-and Q-band spectra suggests that the system has axial EPR symmetry since the features in the region of the spectra associated with the x and y directories (equivalent to those labelled ‘I’in Figure 3) of the system are not split However all attempts to simulate both the X- and Q-band spectra based on axial EPR symmetry are not entirely satisfac- tory compare Figures 4a and 4b and Figures 5a and 5bThe introduction of a small anisotropy into both g, g and A, A,,,produces an improved simulation at both frequencies see Figures 4c and 5c Although the rhombicity is small it is consistent with the known structure of the compound From the crystallography the highest possible point symmetry at the vanadium is C The following two examples also provide additional reasons for performing detailed spectrum simulationsThe features in a powder spectrum arise from turning points in the angular variation of the resonance fields within the systemTurning points in S = 1/2 systems occur when the magnetic field is parallel to the principal axes of the g and A tensorsThese features are marked X Y or Z on the simulated spectra in Figures 6 and 7 However for some combinations of the principal g and A values there may be turning points at other orientations I e ‘off-axis’ turning pointsThis is illustrated in Figure 6 giving rise to what is termed an ‘overshoot’ feature Such features are often observed in the X-band spectra of copper(I1) species In Figure 7 there are also ‘off-axis’ turning points but these now occur at the low field end of the spectrum and can thus be termed ‘undershoot’ featuresThe features attributed to the ‘off-axis’ turning points can have greater amplitudes in the powder spectra than some of those which belong to the principal directions At first sight it would be tempting to assign the ‘overshoot’ or ‘undershoot’ features to the principal directions Such an assignment would either lead to incorrect principal values of g and A if the spectra were interpreted by simply ‘reading off’ magnetic field positions or to an inability to interpret all the features in the spectra We now turn our attention to the much more difficult task of trying to determine whether or not the g and A tensors are coincident It is important that any putative non-coincidence should be confirmed by spectrum simulation Are there any guidelines with respect to the form of a powder spectrum which might suggest the presence of non-coincidence?The answer is 1 2 z xb::xxzxxII I : z 2I 1z 1 288 320 352 384 416 BlmT 1 1 7 Iv=9245GHz I1 II III II IllZ YXXKXXDPIXYXYZ z Z 288 320 352 384 416 BlmT Figure 4 A comparison of the experimental and simulated X-band powder EPR spectra of H,[V(R,R-HIDPA),] diluted in the zirconium analogue where HIDPA = hydroxyiminodipropionate (a) Simu- lated assuming axial EPR symmetry and g = 1 9195 g = 1 9839 A = 17 15 mT A =4 9 mT AB(pp) =2 0 mT AB(pp) = 1 6 mT (b) experimental (c) simulated assuming rhombic EPR symmetry and g = 19195 grx= 19848 g = 19829 A = 17 15 mT A,,=46 mT A = 52 mT AB(p-p) =20 mT dB(p p)xx= AB(pp) = I 6 mT A Gaussian lineshape function was used In the simulations yes under some circumstancesThe first indication of non- coincidence is usually that there appear to be either too many features in the spectrum or that there are features in the wrong place compared to those predicted from simple considerations with the g and A tensor axes coincident Examples of this are in Figures 8 and 9 In these two cases extrapolating the positions of the hyperfine features starting from either end of the spectrum produces either some features which are unaccounted for (see Figure 8) or predicted positions where no features appear in the spectrum (see Figure 9) Some caution is advised with this approach as we must be sure that any extra features are not due to impurities or that failure of the extrapolated features to match those in the spectrum is not due to second-order effects An additional indication that there is non-coincidence is the inability to simulate spectra assuming coincidence However this is a negative reason and the lack of success in the simulation could be due to other reasons Also if this lack of success were taken as a starting point for trying to discover non-coincidence relying on further spectrum simulation could be very time consuming The considerations in the previous paragraph require suitable simulation programs and also considerable effort However if the information concerning non-coincidence of the g and A tensor axes can be obtained it restricts further the point groups to which the paramagnet can belong For example we have found this approach particularly useful in the series of oxo- molybdenum(v) compounds of formula [LMoO(X,)] where L = hydrotris(3,5-dimethylpyrazolyl)borato When the donor CHEMICAL SOCIETY REVIEWS 1993 (a) XhXx xzx x x x 2 2 2 z 2 IIIIIIIII I 1 I I I aXXX2WmXYXY 2 2 2 2 z ll,llllllllllllll I I I I I 1 1'~TLY~~~~YYGH~~XXYZUXiXYXY Z ZI 2I ZI 2 90 -. .- --.- T Ig (4 ......Ia ......_..._ I._...... 7i 75-........ ..;;j ;-off-axis r....3 .... ........ turning.........' 60.-.... ........ .-point.I. -~ru ............ 1......_.E .... ._...._..._. B/mT 240 280 320 360 400 BlmT Figure 6 Simulated powder spectrum showing the 'overshoot' feature in an axial paramagnet with S = 1/2 I =312 g =2.300 g =2.050 K 19.0 mT K = 1.0 mT isotropic dB(pp) =4.0 mT v =9.250 GHz. (a) Variation of the resonance fields with 0 (b) the powder spectrum. Resonance fields at the axes are marked Z for the parallel direction and X for the perpendicular direction. Any features not marked in this way belong to 'off-axis' turning points. nlxlx xzx XlX,X~Z-Z-z~Z~Z 1248 1280 1312 1344 1376 BlmT Figure 7 Simulation of an axial powder spectrum of a vanadiuni(1v) species showing the 'undershoot' features. (a)The angular variation of the resonance field with B('off-axis' turning points are denoted by *). Simulation parameters were g = 1.9195 g = 1.9839 A 17.15 mT A =4.9 mT dB(pp) =5.2 mT dB(pp) =2.4 mT Gaussian lineshape. Resonance fields at the axes are marked Z for the parallel direction and X for the perpendicular direction. Any features not marked in this way belong to 'off-axis' turning points. I1 111111 1 1 11 I I1 I I I I I atoms represented by X are either monodentate ligands or bidentate ligands with a symmetric donor set the powder spectra are interpretable in terms of monoclinic EPR sym-metr~.~This indicates that these molecules have C,/ C or C point symmetry. For C point symmetry the only symmetry element is a mirror plane. Where X-ray structures are available the presence of a mirror plane or very nearly mirror symmetry is found for those compounds where powder EPR spectra indicate monoclinic EPR symmetry. In case the discussion so far gives the impression that powder EPR spectra will always provide detailed information on point symmetry a word of caution must be injected. If the angle of non-coincidence is small say <lo" then it may be difficult to detect from powder spectra. Experience has shown that the simulated spectra are often insensitive to such small angles of non-coincidence particularly when the anistropy in both the g and A tensor elements being rotated is small. Sometimes the lower the experimental microwave frequency the easier it is to detect the presence of non-coincidence. If we wish to use the information from powder spectra to discuss the details of electronic structure then there are some SOME ASPECTS OFTHE EPR SPECTROSCOPY OF d-TRANSITION METAL COMPOUNDS-F E MABBS ‘Monoclinic [LMoOCl,]/toluene compare -+‘Rhorn bic’ (d) si mulation t-80mT v = 9 250 GHz 304 320 336 352 368 BlmT Figure 9 Powder type spectra at 77 K of [LMoOCl,] where L = hydro-tris(3,5-dimethylpyrazolyl)borato,dissolved in (a) [LSnCl,] and (c) tolueneThe arrows in (c) indicate the extrapolated positions of the hyperfine features starting from either end of the spectrum (b) and (d) are simulations using the parameters g = 1 971 g = 1 941 g = 1934 A = 71 4 x cm A = 18 1 x cm-’ =A = 38 1 x cm-’ dB(p-p) = 3 0 mT ~lB(p-p),~ dB(p p) = 2 5 mT and (b) the angle of non-coincidence between g ,/A and g,,/A equal to 33” (d) complete coincidence of the g and A tensors A GdUSSidn lineshape function was used in the simulations additional considerations At best the powder EPR spectra give the values of the g and A tensors and their relationship to each other However we have no direct means of assigning a given tensor element to any particular direction in the paramagnet This is especially true in low symmetry systems where it cannot be assumed that the principal axes of the tensors will correspond to metal-ligand directions If we wish to discuss the electronic structure in detail then it is essential not only to know the geometric structure of the paramagnet but also to know the orientation of the tensors with respect to the atomic framework A detailed single crystal study on crystals for which the X-ray crystal structure is known is now required 2 2 2 Single Crjstal Spectra Single crystal measurements are often performed in three mutually orthogonal planes AB BC AC with respect to the orthogonal axes A B and C It is convenient but not essential for A B and C to be the orthogonalized crystallographic axes The electronic Zeeman effect and the hyperfine interaction are expressed in the measuring axis system via the symmetric tensors where (glJ>’= kJI)’ and (KLg2)lJ= (K2g2)Jlfor f J In most cases it is possible to obtain only the magnitudes but not the signs of the above tensor elements *The usual reason for this is that there may be magnetically inequivalent but chemi- cally identical paramagnets in the crystalThis creates a problem of relating the signals to specific paramagnets in the different measuring planes in the crystalThe sdme situation arises if the crystal has to be remounted or if more than one crystal has to be usedThese problems are equivalent to uncer- tainties in the positive or negative senses of rotation with respect to the A B C measuring axesThe result is that we do not know the relative signs of the off-diagonal elements within either of the tensors but the relative sign of equivalent (glJ)zand (K2gZ),Jis determinedThus for this type of measurement apriori there are eight alternative solutions for each of the tensorsThese alterna- tives correspond to all possible sign combinations of the off-diagonal elements The inter-connection between these alterna- tives is shown in Scheme 1 I 1 Single crystal in three orthogonal planes with respect to a chosen set of axes e g ABC Schonland Lund & Vanngdrd Alternative (I) for principal Alternative (11) for principal Four possible sets of direction Four possible sets of direction cosines These sets arise from cosines These sets arise from ambiguities in the senses of ambiguities in the senses of rotation in the three planes of rotation in the three pldnes of measurement measurement The ambiguity is equivalent to not knowing the positive and negative When reldting the directions of the principal values of g and A it is necessary to consider the four distinct assignments of the measuring axes relative to those used in the crystal structure determination Scheme 1 How can the correct alternative be found?The ambiguities in the signs of the off-diagonal elements can be removed by tdking measurements in a fourth plane in the crystal The choice of this plane with respect to the original ABC axes will depend upon the alternatives to be distinguished and upon the ability to orient accurately the crystal in the chosen plane Measurements such as these may resolve the ambiguities in both the values dnd orientations of the tensors with respect to the measuring axes If for any reason a suitable fourth plane cannot be measured a choice between the two sets of values can often be made IVU d comparison of the experimental powder spectrum and simula- tions based on the two alternative sets of values An example of this is illustrated for [LMo{V)O(Et,dtc)] where Et2dtc = N N-diethyldithiocarbamateThe alternative values are given in Table 2 and the comparison between the experimental and simulated powder spectra is in Figure 10 In this pdrticular example this comparison rules out Alternative I However with this procedure we are still left with deciding which of the four alternative orientations of the tensors with respect to the measur- ing axes is the correct one This is equivalent to not knowing the positive and negative senses of the measurement axes with respect to the crystallographic axes 318 CHEMICAL SOCIETY REVIEWS 1993 Table 2The principal values direction cosines and angles between the g and A tensors for [LMo(V}O(Et,dtc)] (The axes for measurement were assigned as a b c*) Alternative I U b C* g = 1958 0 9388 0 3320 -0 0918 Angles (") between the g and A tensors g22= 1980 0 1678 -0 6735 -0 7199 A 1 A22 A33 g = 1 988 0 3009 -0 6604 0 6880 g11 176 1 88 7 86 4 g2 2 91 5 178 4 89 5 A = 1503 -0 9220 -0 3555 0 1533 g3 3 86 4 89 5 36 ,A2 = 766 -0 1407 0 6767 0 7227 IA = 22 0 3607 -0 6448 0 6739 Alternative II a b C* gl = 1958 -0 9219 -0 3508 0 1646 Angles (") between the g and A tensors g = 1 983 0 3636 -0 6364 0 6803 A 1 A22 A33 g = 1 986 -0 1339 0 6870 0 7143 g11 31 93 0 89 2 g2 2 87 0 31 89 6 lAlli = 151 9 -0 9032 -0 3742 0 2101 g3 3 89 2 89 6 179 1 = 530 0 4109 -0 6126 0 6752 lA22~ lA331= 51 0 0 1239 -0 6962 0 7071 The A values are in units of 10 cm Estimates errors f0 001 for g values and f0 5 x 10 cm for A values When the four alternative sets of orientations have been trans- formed into the crystallographic framework extra criteria are required in order to choose the appropriate orientation of the tensor axes with respect to the atomic framework For example 7in the molecule [LVO(Et,dtc)] the crystal structure shows that although it is not a crystallographic requirement there is an '111 1 27T approximate mirror plane in the molecule I e the molecule approximates to Cs point symmetryTherefore the alternative having one g and one A tensor axis nearly mutually coincident and perpendicular to the approximate mirror plane in the molecule was the one chosen lo 3The Effects of Surrounding Paramagnets This topic could be wide ranging but because of restrictions on space the discussion will be confined to magnetic interactions between paramagnetic centres (I) within isolated dimers and (ii) in undiluted solids The mechanisms whereby the magnetic interactions occur will not be discussed Figure 10 Comparison of (a) the room temperature spectrum of a 3.1 Isolated Dimers diluted powder of [LMo{V)O(Et,dtc)] with simulations for (b) Alter-The important interactions within a dimer which determine the native ZZ,and (c) Alternative IinTable 2 In addition to the parameters form of the EPR spectrum are usually the electronic Zeeman in Table 2 an isotropic dB(pp) = 1 0 mT and a Gaussian lineshape effect the metal hyperfine interaction electron4ectron dipole function were used interactions and magnetic exchange The particular form of the spectrum will depend upon the relative magnitudes of these interactions The following discussion will be restricted to The next stage of the analysis from either of the above dimers composed of chemically equivalent metal centres approaches is to relate the experimental orientations of the tensor axes to the atomic framework of the paramagnet If we have an unambiguous orientation of the tensors with respect to 3 1 1 Magnetic Exchange and Metal Hyper-ne Interactions in the measuring ABC axes then all that remains is to transform Dimers in Fluid Solution these orientations into the crystallographic frameworkThe The case of an isotropic system (or an anisotropic system directions of the tensors can then be compared with metal- tumbling rapidly in solution) will be treated for the effects of ligand directions calculated from the crystallography To do this isotropic magnetic exchange metal hyperfine interaction and it is essential that the relative orientations of the positive ABC magnetic field These interactions are expressed via the spin- measuring axes and the positive crystallographic axes are known Hamiltonian (1) unambiguously If the experiment has left us with four alternative sets of orientations then the choice of the correct one is more difficultThis is because in general we cannot assume that the tensor axes will coincide with any particular orientations with The exchange interaction gives rise to an electronic spin singlet respect to the atomic framework of the paramagnet The reasons and an electronic spin triplet The spin singlet (S = 0) is lowest for the alternative answers were the ambiguities in the senses of for antiferromagnetism whilst the spin triplet (S = 1) is lowest rotation in the measurement framework This is equivalent to for ferromagnetism The spin functions required for the dimer not knowing the positive senses of the measurement axes with must specifically include the nuclear spins of the two centres i e respect to the positive directions of the crystallographic axes IS,Ms,Z ,m,(1),Z2,mX2)) a total of (21 + 1)(2Z2+ 1) functions SOME ASPECTS OFTHE EPR SPECTROSCOPY OF d TRANSITION METAL COMPOUNDS-F E MABBS 3 19 for each electronic spin function In the case of a dimer consist- ing of two s lV nuclei (I= 7/2),an example which will be used shortly there are a total of 256 functions to consider Obtaining the energies and spin functions exactly by applying (1) would require the diagonalization of a 256 x 256 matrix This is poss-ible with modern computers but it makes it difficult to produce closed form expressions for the resonance magnetic fields If we assume that a first order calculation will suffice then (1) can be re- written as The problem now reduces to a 4x 4matrix for each combi- nation of mX1)and mX2),and this can be diagonalized algebrai- callyThe result is that for each possible combination of mX1) and mX2) there are four allowed transitions These are summar- ized in Table 3 Within the approximations above the resonance fields and their relative intensities are valid whatever the relative BhT 180 240 300 360 420 480 I --300mT . ~=9252GHz v = 9 252 GHz 307mT I v=9252GHz v = 9 252 GHz v = 9 252 GHz 1lr-j values of J and A This type of treatment has been applied to a number of nitroxide biradicals l2 Some simulated spectra for a vanadium(rv) dimer are shown in Figures 1 I and 12 When Table 3 Resonance magnetic fields resonance type and relative intensities of the allowed transitions Resonance Relative Resonance FieldType B = B + [J+ R-A(rnl(1) + m,(2))]/2g,f3e S B = B + [J-R-A(rnX1) + rnl(2)}]/2g/3e T B = B -[J + R+ A(rnX1) + ml(2))]/2g/3e S B = B -[J -R + A(mX1) + rnl(2)}]/2g/3e T Intensities (R -414~ (R + 414~ (R-414~ (R + 414~ S resonances and T resonances are those for which the predomindnt spin functions belong to the spin singlet state and spin triplet states respectively R = {J2 + AZ(dm)Z}zAm = {rndl)-m,(2)} BhT 280 300 320 340 360 380 1 1mmT v = 9 252 GHz Figure 11 Simulated spectra showing the effect of varying lJl/lAl for a Figure 12 Simulated spectra showing the effect of varying IJ / A for d vanadium(1v) dimerThe values of 1 Jl/lAl are (a) 0 (b)2 (c) 4(d) 6 (e) vanadium(1v) dimer The values of lJl/lAl are (a) 20 (b) 30 (c) 50 (d)8 (f) 10 (g) 18 An MI independent dB(pp) of 2 1 mT and a 70 (e) 100 (f) 500 (g) 1000 An Mrindependent dB(pp) of 2 1 mT Lorentzian lineshape function were used and a Lorentzian lineshape function were used 1J1 = 0 the spectrum is that expected for a monomer and when IJ1 >> IA we obtain the number of lines and the relative intensities which are usually regarded as characteristic of a dimer. In between these limits the predicted form of the spec- trum depends upon lJ~/iAl.When IJl and 1Al are comparable weak S resonances are predicted and they provide12 a useful way of measuring IJI. As IJI becomes larger than IAl the intensities of the S resonances rapidly decrease to zero.The T resonances also show a dependence on ,J’/Al a dependence which persists after the S resonances are too weak to observe. However eventually the T resonances become insensitive to increasing iJl/iAl. In the example shown this occurs for lJi/lAl greater than about 100. The simulated spectra in Figures 11 and 12 have assumed the same linewidth for all transitions. However it is well established that linewidths are MI dependent for anisotropic species which are tumbling see for example Figure 13. This MI dependence usually takes the form dB(pp) = a +bM +c(M,)* (3) where dB(p-p) is the peak-peak linewidth and for a dimer :dI= mkl) +mX2).The imposition ofsuch a linewidth function is to modify the appearance of the spectra in Figures 11 and 12. The most noticeable effect on the simulated spectra is the significant broadening of the features at the extremities of the spectra particularly at the high field end. I I I v=9.252GHz 280 300 320 340 360 380 BhT Figure 13The effect of M dependent linewidths on the simulated spectrum of (a) a vanadium(1v) monomer and (b) a vanadium(rv) dimer. The linewidth parameters in equation 3 were a = 2.20 mT h = 0.2 mT c = 0.01 mT. A Lorentzian lineshape function was used. If the exchange interaction fluctuates with time about the static value IJI then there may be additional linewidth effects. These have been observed in some nitroxide biradicals and they result in an alternation of the amplitudes of the lines in the derivative spectrum.12 In the limit of very rapid exchange ( J’ > Ai) the expression for the linewidth in the dimer becomes dB(pp) = a +b(rn/(l)+rnX2)}2 +c{mXl)+m/(2)}2 +d(rnA1) -rn/(2)}2 (4) The last term in (4)is the one responsible for the alternation of the amplitudes.The parameter d contains the information concerning both the fluctuation of the exchange about its static value Jl and the correlation time for the fluctuation. Unusual relative amplitudes in EPR spectra can also occur for transition metal dimers. Three selected examples which exhibit slightly differing effects are given in Figure 14. CHEMICAL SOCIETY REVIEWS 1993 Figure 14 Experimental fluid solution X-band spectra at room tempera- ture of (a) [{LVO(pzh)}(p-malonato){LVO}] (b) [{LV0(pzh)t2(p-acetylenedicarboxylato)] (c) [{LVO(pzh)}2(p-benzene- 1,4-dicarboxy- lato)] where pzh = 3,5-dimethylpyrazole and L = hydrotris(3,5-dimethylpyrdzoly1)borato.The scan range on each spectrum is 100 mT. 3.2 Undiluted Solids For reasons which will become apparent as the discussion progresses it is often thought that obtaining the EPR spectrum of an undiluted solid is a waste of time. One of the major reasons for this view is the presence of inhomogeneous line broadening which occurs as a result of interactions which affect the energies of the spin states involved in the EPR transitions. However adopting a pragmatic view a preliminary investigation of the spectrum (preferably at more than one microwave frequency) is always worthwhile. Occasionally there are interesting surprises and sometimes even unpromising looking spectra can yield information. For d transition metal compounds the most common causes of line broadening in undiluted solids are electron4ectron dipolar and exchange interactions. For any given paramagnetic centre the dipole-dipole interaction due to surrounding para- magnets creates a magnetic field at that paramagnet.This is an additional field which is superimposed on the applied magnetic field. In a solid it is unlikely that all the paramagnets in the sample will experience the same additional field. and hence the spectrum is broadened. Electronic exchange between paramag- nets due to orbital overlap may also lead to line broadening but under some circumstances (exchange) narrowing can result. Both dipole-dipole and exchange effects depend primarily on the distance between the paramagnets.These effects can be reduced by diluting (at the molecular level) the paramagnet in a diamagnetic host. The first ‘casualties’ of decreasing magnetic dilution are usually ligand hyperfine structure (because it is usually the smallest interaction) followed by the metal hyper- fine structure. The individual hyperfine lines broaden overlap and finally produce a single broadened line. A few selected examples which illustrate the effects of the different magnitudes of dipole-dipole and exchange interactions compared to those of the metal hyperfine and the electronic Zeeman effect are given in the following sections. 3.2.1 Electron-Electron Dipole Interactions Less than the Metal Hyperfine but no Exchange An example of this situation can be found14 in the single crystal EPR spectra of [VOCl,(tppo),]. Here the spectra are essentially those expected for a diluted vanadium(1v) centre. However the dipole-dipole interaction makes a contribution to the peak- peak linewidth dB(pp) which supplements the inherent line- widths for the molecule.These effects are orientation dependent. When the total dB(pp) and the metal hyperfine splitting are comparable in magnitude the resulting spectrum may have an SOME ASPECTS OF THE EPR SPECTROSCOPY OF d-TRANSITiON METAL COMPOUNDS-F E MABBS 12 1 unusual appearance Instead of the expected (2Z+ 1) lines it may be difficult to recognize any specific number of hyperfine components Some selected examples of such spectra are in Figure 15 VV Figure 15 Spectra showing the effect of linewidth versus hyperfine splitting A for a selection of orientations in an undiluted single crystal of [VOCl,(triphenylph~sphineoxide)~](a) A = 19 33 mT dB(pp) =7 68 mT (b) A =9 71 mT dB(pp) =9 53 mT (c) A = 7 19 mT dB(pp) =9 74 mT 3 2 2 Weak Extended Exchange Occasionally in undiluted crystals which apparently consist of isolated monomeric centres we observe EPR spectra unlike those expected for a monomer or for any discrete polymeric unitThese unusual spectra are often explicable in terms of electron4ectron dipole and exchange interactions which are less than or equal to the metal hyperfine coupling Here the exchange extends throughout the crystalline lattice in either one two or three dimensions (I e weak extended exchange)The first reported' example of such a system was the weak one-dimen- sional exchange system [N(B~"),],[~~Cu(mnt)~] mnt =maleo-nitriledithiolate A weak two-dimensional exchanging system' is provided by [H tmen][VO(malonato),(H,0)] 2H,O where H tmen = N,N,N',N'-tetramethylethylenediaminium The single crystal spectra of each of these compounds are both orientation- and temperature-dependent The vanadium com- pound provides a particularly rich spectrum and examples of its temperature variation when the magnetic field is parallel to the V=O direction are shown in Figure I6 Apart from the spectra in the temperature range ca 200 to 180K none of these spectra have the appearance expected for an isolated monomer or for any discretre polymeric unitThe methods required to interpret such spectra are beyond the scope of this review but they are well documented -v U' 50mT 50hT 50iT Figure 16 The temperature variation of the EPR spectrum when the applied magnetic field is parallel to the terminal VO direction in a single crystal of undiluted [H,trnen][VO(malonat~)~(H~O)]2H20 3 2 3 Exchange Greater than the Metal HyperJne Splitting When the exchange interaction is greater than the metal hyper- fine splitting but it is less than the microwave energy (IK(8)l <iJ/ <hv) then a broad unstructured resonance may be observedThe peak-peak linewidths in the spectra are however less than those expected for total resolution of all the hyperfine components An example of this is provided'* by undiluted [VO(Mequin),] where Mequin =2-methylquinolin-8-olato In this compound a single broad line is observed at all orientations of the crystal The peak-peak linewidths range from ca 10 mT to 45 mT depending upon the crystal orientation The expected spread of the spectrum for complete resolution of the mctdl hyperfine lines would be 38 mT to 121 mT It is possible to estimate IJl from the linewidth dependence if three dimensional exchange is assumed ' Under these conditions where dB(p-p) is the peak-peak separation in the first derivative spectrum IJI is the exchange interaction and M2(t)=M2(d)+M2(h) with M,(h) equal to the second moment of the hyperfine interaction and M2(d) is the second moment of the dipolar interaction M2(d) can be cdlculated from the crystal structure data using Van Vleck's equation,20 whilst M,(h) is obtained via the g and A tensors from d diluted single crystal study and Slichter's general method of cdlculating moments For the above compound this type of analysis gave d value of 38 mT for J 3 2 4 Exchange Greater than the Microwave Energj When IJI exceeds the energy of the microwave radiation the separate identities of chemically identical but magnetically inequivalent paramagnets at a general orientation may be lost Where two separate signals are expected in the absence of exchange there is now only one which occurs with a g value which is the arithmetic mean of the g values of the individunl paramagnets at that orientation Under these conditions it is important to note that the principal g values are apropertj of the crystal and these will not generally correspond to the principal values for the individual paramagnets Even in a single crystal the exchange interactions destroy valuable information since the principal g values for the individual paramagnets can only be obtained from the principal crystal g values if the direction cosines of the former are already known 22h When IJI >>hv and the exchange takes place over a very large number of centres throughout the crystal we mdy observe d single sharp line when a more complicated spectrum is expected This phenomenon is known as exchange narrowing 2oThe exchange causes rapid motion of an individual electron spin throughout the solidThis has the effect of completely averaging metal hyperfine and electron4ectron dipolar interactions which would otherwise have a broadening effect It is sometimes possible to estimate (Jl from the peak-peak linewidth For a three dimensional exchange the relationship for a Lorentzidn shaped line is where M,(d) is the second moment of the dipolar interaction 4 Ligand Hyperfine Interactions In d transition metal compounds the ligand hyperfine interac- tion (designated by a) is usually smaller than the metal hyperfine interaction this relative order of these interactions will be assumed throughout the present discussion Initially the use and the limitations of CWEPR will be explored One of the major disadvantages of CWEPR is the effects of inhomogeneous line broadening which often prevent the observation of ligand hyperfine splittings However let us initially put aside these problems and examine some of the effects which we expect to observe Starting with any given spectrum in the absence of ligand hyperfine interactions we then expect additional split- tingsThus each line in the basic spectrum will be split into a number of new components depending on the types of ligand nuclei with which the unpaired electron interactsThus a single ligand nucleus with nuclear spin I will cause a splitting into 21 + 1 lines of equal relative intensity If the interaction of the unpaired electron is with n equivalent nuclei each with nuclear spin 1,then we should observe a splitting into (21,dmax) + 11 lines where I,dmax) = nlThe relative intensities of these new lines will not be equal but will be determined by the coefficient of yM/ in the following expansion (r'+x' 1 +x' 2 + +x '+I +x 1)" (7) An example of this is shown in Figure 17 for the frozen solution spectrum of [VO(ded t~)~] where ded tp = diethyldi thiop hos- phate There are two equivalent phosphorus atoms in this compound which results in each of the vanadium hyperfine lines being split into a 1 2 1 triplet (31Pis in 100% natural abundance with I= 1/2) 16mT Figure 17The X band spectrum of [VO{S,P(OEt),},] in tolueneat 77 K The above example is one in which the ligand hyperfine splitting is significantly greater than the linewidths of the individual resonances When the linewidths (due to inhomoge- neous line broadening mechanisms) become comparable to or greater than the ligand hyperfine splittings we obtain either incomplete resolution of the ligand hyperfine splittings or fail to resolve any of the splittings An example23 where the ligand hyperfine splitting is comparable to the linewidth is provided by the diluted crystals of [InC1(VO)C12(tmu)2] where tmu = N N N' N-tetramethylurea In a powder sample of this compound no ligand hyperfine components could be resolved see Figure 18 However at selected orientations in a single crystal each vanadium hyperfine line showed further splittings see Figure 19These extra splittings can be accounted for in terms of two equivalent chloride ligands 23 20 0 mT-Figure 18 The Q-band powder spectrum of [InCl{VO}C12(tmu),] where tmu = N N N N' tetramethylurea at 298 K v = 34 974 GHz This last example highlights at least one major problem associated with powder CWEPR although improvements in resolution can sometimes be obtained by taking measurements at low microwave frequencies 24 However if CWEPR fails to resolve ligand hyperfine splittings when their presence is sus- pected then other methods have to be triedThese other methods are multiple resonance techniques such as electron nuclear double resonance (ENDOR) and pulsed techniques such as electron spin echo envelope modulation (ESEEM) Although these methods are technically more difficult than CWEPR they are less sensitive to line broadening effects and in addition they provide a more direct measure of nuclear quadru- pole and nuclear Zeeman effects These latter techniques look CHEMICAL SOCIETY REVIEWS 1993 more directly at the energy separations (due to nuclear effects) in the individual msmanifolds Indeed they measure the nuclear magnetic resonance (NMR) spectrum of the (highly) paramag- netic system The essential differences in the way in which the various types of spectra arise are illustrated in Figures 20 to 22 via simplified examples In the CWEPR experiment the sample is continuously irra- diated with a fixed microwave frequency whilst varying the magnetic field When the condition dE= hv and the selection 126T -II//Illl 80mT -80mT 1 26T Figure 19 A comparison of the experimental (upper) and simulated (lower) spectra in the AC plane of a single crystal of [InCl (VO}Clz(tmu),] where tmu = N N N' N'-tetramethylureaThe rela- tive orientations were (a) 170" (b) 150" (c) 60" ,'!! v = 9250 GHz L I 320 324 328 332 336 340 BImT Figure 20 Diagram showing the origins of the hyperfine lines in CWEPR spectrum for a system with S = 1/2 and I = 1/2 (a) energy levels (b) first derivative spectrum The dashed lines refer to the situation in the absence of the hyperfine interaction SOME ASPECTS OFTHE EPR SPECTROSCOPY OF d-TRANSITION METAL COMPOUNDS-F E MABBS rule Ams = f1 AmI = 0 are both satisfied there will be an absorption of microwaves This leads to the EPR spectrum in Figure 20b In an ENDOR experiment the magnetic field is set at the value for an EPR transition for example the (ms = -1/2,mI= 1/2) -(mS = 1/2 mI = 1/2) transition in Figure 21a If the micro-wave power is high enough to give significant saturation of the EPR signal and the system is swept with radiofrequency radia-tion then when the radiofrequency equals the frequency for transitions between the energy levels in each mSmanifold there will be an increase in the EPR absorption When this absorption is recorded as a function of the radiofrequency the spectrum in Figure 21b will be observed In this example for a < 2vN,where a is the hyperfine coupling constant and vN is the free atom resonance frequency at the magnetic field of the experiment the two observed frequencies are 25 V = vY -a12 v2 = vN + a12 In an ESEEM experiment we again set the magnetic field at a value corresponding to an EPR transition but now the system is subjected to a sequence of intense pulses of microwave radia-tionThe subsequent free induction decay signal obtained as a function of the delay time between the initial pair of pulses is modulated by the superposition of frequencies corresponding to those for transitions between the energy levels in each of the ms manifolds 26This is illustrated in Figure 22b by the simulated example of a three pulse experiment where the free induction decay has been subtracted This spectrum is in the time domain The frequencies associated with the modulations are obtained by a Fourier transform of this spectrum into the frequency domain The result of this is shown in Figure 22c There is an approximate hierarchy of the usefulness of EPR techniques in relation to the magnitude of the hyperfine interac-tion CWEPR is best for measuring large interactions (> ca 0 5mT) ENDOR is most useful in the approximate range 0 5-0 1 mT whilst ESEEM is more suited to measuring even smaller hyperfine interactions However the ranges over which these techniques are applicable do overlap In a system where there are several different magnitudes of hyperfine interactions the use of all three techniques may be required in order to measure the full I I -1 1 2’ 2 <-a ->>“N VR Figure 21 An illustration of the origins of ENDOR transitions in a system with J = 1/2 and I = 112 (a) Energy levels at a fixed magnetic field for a < 2vN,(b) ENDOR spectrum as a function of the applied radiofrequencyThe dashed line represents the EPR transition which is being monitored 1_-_-1 7’ 7 ’ -0 1 2 3 4 ClS (4 a 30 25 11 *! 20 1C-15 I I! 5 ‘0 5 10 I!‘ 20 25 30 MHZ Figure 22 An illustration of the origins dnd the form of the ESEEM spectrum from a system with S = l/2 and Z= 1/2 (a) Energy levels dt d fixed magnetic field for a < 2v (b) the three-pulse spectrum in the time domain ignoring the decay (c) the Fourier transform of the spectrum in (b)The dashed line represents the EPR transition which is being monitored range of interactions An example of this is the single crystal CWEPR ENDOR and ESEEM studies2’ of [TcNCl,]- diluted in the diamagnetic compound [Ph,As][TcOCI,] Where appropriate the hyperfine tensors the quadrupole tensors dnd the nuclear Zeeman effects on 99Tc 35 37Cl,and l4 ISN were measured These data allow a detailed description of the bond-ing in the high symmetry (C4v)[TcNCl,] ion Thus the com-bined use of CWEPR ENDOR and ESEEM can give a very detailed description of the electronic structure of transition metal complexes AcknowledgementsThe author wishes to thank Drs M S Austerberry D Collison J R Morton and K J T Taylor and Mr S S Turner for helpful discussions 4 References 1 F E Mabbs and D Collison ‘Electron Paramdgnetic Resondnce of d Transition Metal Compounds’ Elsevier Amsterdam. 1992 2 J R Pilbrow ‘Transition Ion Electron Paramagnetic Resondnce Clarendon Press Oxford 1990 3 Ref 2 chapter 9 C P Poole Jr and H A Farach Appl Spec u0.w Rev 1983,19 167,A Schweiger Struct Bonding (Berlin) 1982,51 1 4 Ref 2 chapter 10 A Schweiger Agneu Chem Znt Ed Engl 1991 30,265 L Kevan ‘Time Domain Electron Spin Resonance’ ed ,L Kevan and R N Schwartz Wiley New York 1979 chapter 7 L Kevan ‘Modern Pulsed and Continuous Wave Electron Spin Reso-nance’ Wiley New York 1990 chapter 5 A Schweiger ihirl chapter 2 5 Ref 1 (a) chapters 2 and 4 (b) chapters 3 and 5 6 E M Armstrong M S Austerberry D Collison S N Ertok,C D Garner M Helliwell and F E Mabbs J Chem Soc Chem Commun ,submitted for publication 7 D Collison F E Mabbs J H Enemark and W E Cleldnd Jr Polyhedron 1986,5,423 D Collison D R Eardley F E Mdbbs K Rigby and J H Enemark Polyhedron 1989 8 1833 D Collison F E Mabbs and K Rigby Polyhedron 1989 8 1830 8 D S Schonland Proc Phys Soc London 1959,73 788 A Lund andT Vanngard J Chem Phjs 1965,42 2979 9 J R Morton and K F Preston J Magn Reson 1983,52,457 10 D Collison F E Mabbs K Rigby and W E Cleland Jr ,J Chrm Soc Faraday Trans 1993 accepted for publication 11 N M Atherton ‘Electron Spin ResonanceTheory dnd Appli- cations’ Ellis Horwood Chichester 1973 p 182 12 G R Luckhurst Mu1 PhJs,1966,10,543,S H Glarum and J H Marshall J Chem Phys 1967 47 1374 A Hudson and G R Luckhurst Chem Rev 1969,69 191 13 D Kivelson J Chem Phjs 1960 33 1094 R Wilson dnd D Kivelson J Chem PhLs ,1966,44,154 Ref 1p 1 179 and references there1 n 14 B Gdhandnd F E Mabbs J Chem Soc Dalton Trans ,1983,1713 15 K W Plumlee B M Hoffmann J A Ibers and Z G Soos J Cheni Phis 1975,63 1926 16 D Collison B Gahan and F E Mabbs J Chem Soc Dalton Tranr 1983 1705 17 B Gahanand F E Mabbs J Chew1 Soc Dalton Trans 1983,1695 Ref 1 chapter 17 18 D Collison B Gahan and F E Mabbs J Chern Soc Dalton Tranr 1987 111 19 G F Kokoska ‘Low Dimensional Cooperative Phenomend’ ed H CHEMICAL SOCIETY REVIEWS 1993 J Keller Plenum New York 1975 p 171 P M Richards ibid p 147 20 J H Van Vleck Phys Rev 1948,74 1168 2 1 C P Slichter ‘Principles of Magnetic Resonance’ Harper and Row New York 1963 p 50 and 3rd Edition Springer-Verlag Berlin 1990,~ 71 22 (a) D M S Bagguley and J H E Griffiths Proc Roy Soc (London) 105 A201 366 (b)Ref 1 p 73 23 D Collison F E Mabbs and J Temperley Spectrochim Acta 1991,47A 691 24 Ref 2 p 51 25 Ref 11 p 366 26 W B Mims Phys Rev B 1972,52409 1972,6 3543 27 R Kirmse K Kohler U Abram R Bottcher L Golic and E DeBoer Chem Phys 1990 143 75 R Kirmse K Kohler R Bottcher U Abram M C M Gribnau C P Keijzers and E DeBoer Chem Phis 1990,143,83

ISSN:0306-0012    

DOI:10.1039/CS9932200313

出版商:RSC    

年代:1993

数据来源: RSC

摘要:

Why can Transient Free Radicals be observed in Solution using ESR Techniques? Keith A. McLauchlan Physical Chemistry Laboratory University of Oxford South Parks Road Oxford OX1 3QZ U.K. 1 Introduction Initial studies of the ESR spectra of free radicals were in the solid state in which the radicals were isolated by the matrix and unable to annihilate each other by reaction. This limited the range of radicals which could be studied and inhibited studies of their essential characteristic their reactivity. In consequence methods were devised by which reactive free radicals could be studied directly. These have involved photolysis of samples with continuous wave light preparation of radicals in rapid flow systems electrolysis and more recently flash photolysis and pulse radiolysis. It is the object of this paper to examine the processes for radical production and to see why these particular experimental methods have arisen. It is hoped that this may provide insight to improving technique and extending the range of the radicals which may be observed routinely. No systematic consideration of this problem seems to have been made previously. 2 How Free Radicals are Created Whether primary or secondary free radicals are observed in experiments they result from a seminal event in which a pair of doublet entities is produced. In normal chemistry and photo- chemistry this is a pair of radicals whereas in radiation chemistry one member may be an electron.The primary process in the former cases is the breaking of a chemical bond.This has not received the attention it deserves from chemists particularly ESR scientists who have by-and-large simply accepted that the bond does break under the correct conditions without enquir- ing into the consequences and implications. It has been known for 70 years that to form a chemical bond requires the two electrons which comprise it to have antiparallel spins but only comparatively recently was the question asked as to what happens to the spin orientations when the bond is broken and the electrons find themselves on different radicals. It was first asked in the abstract in radiation chemistry’ but then became a prerequisite to the understanding of the magnetic resonance phenomena Chemically Induced Dynamic Nuclear Polarization Keith McLauchlan obtained his B.Sc. and his Ph.D. from Bristol University before holding a post-doctoral fellowiship at the N. R.C. in Ottai4u. In 1960 he joined the National Physical Laboratory working on NMR before mov- ing to Oxford in 1965. He ufterwwrds pioneeredjlash pho- tolysis ESR and was a co-discoverer of electron spin polarization in chemical reac- tions. His other interests include Spin Chemistry Reac- tion Yield Detected Magnetic Resonance (R YDMR) and the efSects of magneticjields on chemical biochemical and bio- logical systems. He is a Fellow of the Royal Society and is President of the International EPR (ESR) Society. (CIDNP),2.3 and Chemically Induced Dynamic Electron Polari- zation (CIDEP).4 In fact electron spin orientation is normally conserved on chemical reaction and the radicals are formed in a pair which at the time of its creation possesses the same electron spin multiplicity as did its molecular precursor.This together with the existence of rigid spin selection rules for chemical reaction (normally the radical pair must be in the singlet state with antiparallel electron spins on the radicals for reaction to occur) forms the entire basis of the new research field ‘spin chemistry’. It underlies why magnetic fields affect radical reac- tion~~and why the techniques of Stimulated Nuclear Polariza- tion (SNP),6 Optically Detected Magnetic Resonance (ODMR),’ and Reaction Yield Detected Magnetic Resonance (RYDMR)8 exist.The effects may have wide technical appli- cation in industrial processes9 involving free radicals and may be the source of environmental field effects on man.Io The implications to ESR observations of transient radicals seem not to have been appreciated save for the causation of electron spin polarization in reactive systems. In normal chemistry most free radicals result from bond-breaking in the ground (normally singlet state) molecule and this produces a pair of free radicals with antiparallel electron spins as shown for the molecule R R below Since two radicals which may recombine with small activation energies appear to be formed side-by-side with their electron spins correctly aligned for reaction it might be expected that they would immediately back-react to re-form the reactant and no radicals would be observed in experiments performed on a timescale greater than the reaction lifetime (i.e.all experiments). Luckily however the energy of the reaction causes some spatial separation of the radicals and not all vanish immediately but even so some 90% of the radicals re-combine in the first few hundred pico-seconds after they have been created as a result of re-encounters during short-term diffusion.This has been demonstrated by direct observation using pico-second flash photolysis with optical detection techniques and predicted theoretically.12 It is only those radicals which survive this very rapid geminate period of the reaction which later became the free radicals in the system and are observed and it is a sobering thought that this represents only a small fraction of those originally produced.The object of the ESR scientist is to maximize this fraction. Why then do not all the radicals recombine in this very early period of reaction?To some extent this is because not all diffusion paths lead to re-encounters in the geminate phase of the reaction. More importantly however a mechanism exists for making a proportion of those encounters that do occur unproductive in leading to reaction. This happens by the radi- cals becoming unable to react by virtue of their spin state having changed in the brief period after they were formed the radical pair having converted into a triplet configuration by the time the encounter occurs. It is precisely those radicals which fail to react at re-encounter as a result of then being triplet-correlated which exhibit radical pair mechanism CIDEP in experiments.This phenomenon provides direct evidence for the detailed history of the radicals being described. The essential feature needed for the highest possible concentration of radicals to survive the initial geminate period and be observed as free radicals in an experi- CHEMICAL SOCIETY REVIEWS 1993 ment is consequently singlet-triplet interconversion in the pair Since the re-encounter probability of two radicals formed together diminishes rapidly in time afterwards the faster the singlet-triplet mixing the greater the concentration of radicals which escape initial recombination The overall process following dissociation of the precursor molecule may be represented 'M +{ I{R,' + R2*}+3(R,'+ R2*}} +RT' + Rt' where M is the precursor molecule and the asterisk denotes that the radicals are electron spin polarized and exhibit CIDEP in their ESR spectrumThe outer brackets enclose what is now known as the 'spin correlated radical pair' a species which exists throughout the geminate period of the reaction It is a true if unusual reaction intermediate which occurs in all radical com- bination reactions Singlet-triplet interconversion can be caused in several differ- ent coherent and incoherent (spin relaxation) ways In the coherent sense it happens as a result of the spin state of the radical pair developing under the action of the spin Hamiltonian (XM)which for the majority of the lifetime of the pair is time- independentThat is it can be written in the form familiar to ESR scientists in terms of interactions at the two radicals considered separately with simply the Zeeman interactions and their hyperfine coupling terms included This is equivalent to saying that the coupled spin state of the radical pair evolves in time with the two electrons independent of each other This is normally a good approximation since the electron exchange interaction between the electrons in the pair falls off rapidly with distance and therefore time as the radicals separate and it is assumed that any anisotropic interactions are rotationally aver- aged to zero For a radical pair created in a pure spin state (and it is always formed either in the singlet or one or more of the triplet states) the wavefunction at a later time t can be written l3 where IS) and IT,)are the pure singlet and triplet functions and c(t) is a time-dependent coefficient whose product with its complex conjugate yields the fractional contribution of the state to the overall wave function at a given time There are three independent triplet functions which in the high-field limit are the Zeeman states To and T*l Here we have chosen to write the wavefunction of the radical pair in the coupled representation rather than to talk of the spins of the individual electrons because it is the spin multiplicity of the pair considered together which determines the reaction probabilityThe wavefunction is obtained by solution of the time-dependent Schrodinger equation The three different triplet states may mix with the singlet one if the radicals are produced in low or zero magnetic fields This implies that the singlet has three accessible non-reactive triplet states If on the other hand they are created inside the magnetic field of an ESR spectrometer the Zeeman interaction lift< the degeneracies of the magnetic Ti states sufficiently to prevent their mixing with the others and only the Sand Tostates are left to evolve in time Now the singlet can turn into only one triplet state and the reaction probability has increased In this situa- tion solution of the equation gives cs(t) = cs(0)cosQt-icro(0)sinQt and cro(t)= cro(0)cosQt-zcs(0)sinQr where Here the symbols have their usual significance with for exam- ple mp,/representing the magnetic quantum number of the nth nucleus in radical 1 which exists in the overall nuclear spin state (4In carbon-centred radicals with similar g-values in the 0 33T field of an X-band spectrometer the dominant interaction is almost always the hyperfine coupling and even in a pair of chemically identical radicals the overall nuclear hyperfine state of the two radicals usually differs With couplings typical of these radicals complete state interconversion takes 1-10 nano-seconds and so it is those re-encounters which occur at about this time that are ineffective in leading to reaction A more strict description would say that immediately after the radical pair is formed in the pure singlet state the states start to mix and the probability of reaction at a subsequent re-encounter depends upon the singlet character of the radical pair at that time Nevertheless the implication is that the process is not very efficient for producing observable free radicals since most re- encounters occur before the triplet character is appreciable 10 nanoseconds being a long time on the timescale of molecular diffusionThis has unfortunate implications for the observation of free radicals produced in thermal reactions and in particular due to the low concentrations which might anyway be expected in enzyme reactions This theory now may be extended to obtain an expression for the overall reaction probability inside the geminate period of the reaction We again use the model in which the exchange interac- tion can be neglected and in which the spin and molecular dynamics (diffusion) are assumed to occur on different time- scales so that the effects of the two are separable In this case the total reaction probability of geminately created radicals is given by' PR = ASP,(t)P,(r)dt 0 where X is the probability that two radicals which encounter in the singlet state actually react Ps(t) is the probability that the system is in the singlet state at the time of the re-encounter and P,(t)dt is the probability of a re-encounter in the time-interval dr at that timeThe probability of free radicals escaping reaction and being observable in the ESR experiment is simply (1 -PR) This formulation is useful for it reminds us very directly that diffusion is another factor in the whole process and that it can be adjusted empirically in experiment either to enhance reaction probability in the geminate period or to decrease it so as to optimize the number of free radicals in the systemThis can be accomplished in several ways such as change in solution visco- sity and encapsulation of the radicals inside micelles The description is however an approximate one for in most cases spin evolution and molecular diffusion occur simultaneously This situation can be analysed using the stochastic Liouville equation which is however capable of analytical solution only in some simple cases l4 The coherent processes drive the spin mixing continuously in time under the influence of a constant interaction provided that the hyperfine states are not changed during the geminate pair lifetime as a result for example of fast degenerate electron hopping processesThese have been observed to affect spin state evolution in CIDEPl and RYDMR experiments16 which therefore provide the means to study them on the timescale of the geminate pair lifetime A similar result has been reported from fast energy transfer processes in a study of the RYDMR and magnetic field effect (MFE) behaviour of electronically excited radicals l7These are specific examples of relaxation processes which by contrast with the coherent ones cause WHY CAN TRANSIENT FREE RADICALS BE OBSERVED IN SOLUTION USING ESR7-K A McLAUCHLAN random changes in the local fields leading to spin flips and a stochastic generation of spin mixing It happens however that for small carbon-centred radicals in solutions of normal visco- sity at room temperature and with no such very fast reactions occurring the relaxation times are typically of the order of 1-2 ps so that the coherent process is faster and dominates Relaxation effects on spin mixing are however well known in MFE experiments conducted in viscous or micellar solutions where the geminate lifetime is extended sufficiently long for them to be observed If the electron is centred on an atom different from carbon relaxation may be sufficiently fast to compete successfully with the hyperfine-driven spin mixing We shall return to the beneficial effects of relaxation in some instances below Many of the methods that ESR spectroscopists use to produce radicals do not involve observation of the primary radicals in the system but rather secondary ones produced from their reaction Nevertheless the concentrations of the radicals which are observed are determined by the primary processes that have been discussed above But if a sufficient concentration of primar- ies is obtained the production of secondary radicals is not a spin selective reaction but typically proceeds through H-abstraction addition etcThe same principles of spin selectivity and conser- vation no longer apply (although the secondaries are formed with the electron spin state of their progenitor' 8) and so it is the detailed understanding of the primary processes which are the basis for optimizing radical production even when it is second- ary radicals that are of interest The methods used in the laboratory are the results of empiri- cal experiments it has simply been found how to produce sufficiently high concentrations of radicals for observation We now turn to the understanding of these methods using the principles outlined above 3The Methods for Radical Production used in ESR 3.1 Photochemistry Whether using flash-photolysis in time-resolved experiments or continuous wave methods to produce radicals for spectroscopic study the majority of experiments have involved classical photochemical processes A typical reaction involves the absorption of radiation by a singlet ground state molecule leading by an electronic transition with spin conservation to an excited singlet state Here the radiative lifetime is short and the excitation energy would be lost if the molecule did not undergo rapid intersystem crossing into a triplet state whose phosphor- escence is spin-forbiddenThe molecule therefore persists for a comparatively long time in this state and it is the one which is normally the source of the ensuing photochemistry Its common fate is to react with a suitable substrate to form a pair of radicals In contrast to the situation discussed above in which the ground state molecule dissociated to form radicals the radical pair is now formed with electron spin conservation in a triplet-correlated state For example 'Me,CO -+ 'Me,CO* -+ 3Me,CO* followed by 3Me,C0 + Me,CHOH -+ 3{Me,COH + Me,CO€ I The radicals cannot react immediately and although a small proportion re-encounter after triplet-singlet interconversion has occurred and form product most survive the geminate period and lead to high and observable free radical concent- rations It is no coincidence that the triplet reaction route has been found to yield high concentrations of radicals If on the other hand the geminate product was the desired result of the chemical reaction the dissociation through the singlet state would be more effective Such considerations have possible wider implications to the use of radicals in chemistry for example in radical-initiated polymerizations where clearly the triplet state dissociation would be best Control of the spin state of the spin-correlated radical pair at the moment of its formation should be an important part of the design of chemical reactions and physical observations which involve radicals Despite the argument for triplet state reactivity given above and which can be found in any photochemistry text-book it is often possible to push the reaction through the singlet route simply by arranging for the reaction rate to form radicals to compete with that of the intersystem-crossing stage in the precursor moleculeThis has been demonstrated in a number of CIDEP experiments where radicals produced from singlet precursors have been detected in observations on transient species It happens facilely if the triplet state is not reactive (usually a XX* state19) or if the excited singlet is able to react with the solvent or by fast electron transfer as in radical ion pair systems 2o Usually however the signal strengths are low when compared with triplet-generated species Not all photochemical processes involving free radical pro- duction for ESR study do proceed through triplet reaction pathways an exception being the dissociation of a peroxide to form an initial pair of oxygen-centred radicals Why this is possible is discussed below 3.2 All Other Methods The photochemical method involving triplet state reaction appears unique in controlling the proportion of radicals which fail to undergo recombination in the geminate period by taking advantage of the adverse initial spin state of the radical pair All the others entirely serendipitously appear to work by causing extremely rapid spin state interconversion for they typically involve reactions of ground state molecules or singlet excited statesThe most successful method for producing transient radicals for study in steady state concentrations in flow systems has undoubtedly been that where the radicals are produced by use of a transition metal/peroxide couple *l Here the primary process in radical production involves either the transition metal ion itself or a hydroxyl radical produced extremely quickly after the reaction is initiated Both of these species have extremely short relaxation times as a result of orbital degeneracy and in a singlet-correlated radical pair the system attains triplet char- acter on a timescale which competes with or is faster than the coherent mixing process described aboveThis inhibits reaction during the crucial early period after radical pair formation when re-encounters are at their most probableThe result is that although the inital bond-breaking produces a singlet-correlated primary pair (whatever its nature) many of the radicals survive the geminate period and can be used to produce secondary radicals for subsequent study In addition the mixing of the solutions in the flow system usually occurs outside of the main magnetic field of the spectrometer in a low ambient field in which coherent spin mixing might convert the singlet radical pair into any of the triplet sub-states which would also lead to a decrease in reaction probability in the initial phase of the reaction Nevertheless it is the incoherent contribution to the spin mixing which is usually the most significant The peroxide case referred to above is a simple example of this and it occurs whether the radicals are produced by thermo- lysis of the ground state or photolysis involving an electroni- cally excited singlet stateThe result of a symmetrical bond scission is to create a singlet-correlated pair of radicals in which the electron is centred upon the oxygen atom and is conse- quently liable to fast relaxation so as to form the unreactive triplet state It is quite common in our experience for the radical concentrations from peroxide-initiated reactions to be low and this can be understood by an extension of the arguments given aboveThere it was not pointed out specifically that the singlet triplet mixing process interconverts these two states with the radical pair wavefunction continuously changing between the two pure states Damping occurs only if the radicals diffuse apart and never re-encounter or if they re-encounter in the singlet state and react In consequence with very fast relaxation inside the field of the spectrometer and with the radical system prepared in the singlet state the system thereafter jumps ran- domly between the triplet and singlet states Converting from the initial singlet to the triplet is effective in eventual free radical production only if a substrate which reacts to form the observed secondary radical encounters the radicals when they are triplet- correlated for as soon as they re-attain the singlet state and encounter they reactThis implies that a further criterion must be satisfied the substrate must react with the radicals on a timescale that is not dissimilar to the singlet-triplet interconver- sion rate driven by the random relaxation process In turn this implies employing a diffusion-controlled reaction with the substrate in high concentrationTypical examples of this in action are the production of phosphorus-22 or sili~on-centred~~ radicals by reaction with substrates with easily abstracted hydrogen atomsThese can then be used to create further generations of radicals in the system The substantive point is that the secondary radical in these situations normally has a comparatively long relaxation time and so radical pairs consist- ing of two such radicals do not convert to the singlet and react on this same very fast timescale Although this last aspect has been discussed specifically in the context of peroxyl radicals the principle is general and applies to all the other situations including that of the metal/peroxide couple It is less important in the photochemical generation of carbon-centred free radicals from a triplet state reaction since the spin state interconversion is much slower and diffusion controlled rate processes in the classical sense are able to compete with the rate of coherently driven return to the singlet state Similar principles to those described in this whole section apply to radiolytic production of free radicals where one of the initial species may be either the solvated electron or in aqueous solution the hydroxyl radical once more and also to the electrolytic production of radical ions 4 Conclusions Although it has long been accepted that free radicals can be produced in suitable concentrations for direct observation this is in fact a cause for wonder since it is not what would be expected from a detailed consideration of the processes that occur immediately after radicals are first formed in solutionThe methods that have been evolved to produce them for ESR study can be understood by consideration of these fundamentals and unknowingly we have made use of spin selectivity on reaction on the one hand and relaxation effects on the other Now that these principles are understood it should be possible to invent new methods and to appreciate how to create radicals in sufficient concentration for study by ESR One of the driving forces for the study of free radicals has been their importance as reaction intermediates and yet our methods have evolved to observe them in high concentrations It may now be possible to move smoothly between one situation and the other by small changes in reaction conditions so as to be sure that the radicals which are observed are indeed relevant to the reaction proceed- ing under its usual conditions Radical combination rate constants are often obtained from kinetic ESR studiesThey have been treated in the past as CHEMICAL SOCIETY REVIEWS 1993 empirical constants which can be interpreted in terms of the activation energy of the reaction on the one hand and diffusion on the otherThis is largely adequate for the slower diffusion- controlled reactions which occur in solution By this is meant those reactions which result from radicals which are formed in different regions of the solution and later encounterThere is however a much more fundamental very fast process which occurs between radicals created together in the geminate period of the reaction The rate constants of radical combination reactions are actually time-dependent with these two different processes happening on very different timescales Where the geminate reactions are concerned a detailed interpretation of the rate constants is possible in terms of spin-mixing on the one hand and very short-term diffusion on the other With organic radicals hyperfine-driven coherent spin mixing occurs at a very definite and calculable rate and observations of geminate kine- tics can consequently be used to explore the nature of diffusion in solution on the nanosecond timescale 24 Spin considerations apply to the classical diffusion-controlled radical combinations too but here the long-range diffusion is the rate-controlling step 5 References 1 B Brocklehurst Nature 1969 21 921 2 G L Closs J Am Chem Soc 1969,91,4552 3 R Kaptein and L J Oosterhoff Chem Plzbs Lett 1965 4 195 4 Chemically Induced Magnetic Polarization ed LT Muus P W Atkins K A McLauchlan and J B Pedersen D Reidel Dor- drecht 1977 5 U E Steiner and T Ulnch Chem Re1 1989 89 51 6 R Z Sagdeev Yu N Molin and K M Salikhov Bull Mugn Reson 1980,2,66 7 A D Trifunac and R G Lawler Mugon Reson Rev 1982,7 147 8 0 A Anisimov V M Grigoryants V K Molchanov and Yu N Molin Chem Phys Lett 1979,66 265 9 N J Turro M F Chow Ch -J Chung and Ch -JTung J Am Chem Soc 1983,105 1572 10 K A McLduchlan Phvsrcs World 1992 5 41 11 T J Chuang G W Hoffman and K B Eisenthal 1974 Chem Phys Lett 1974,25201 12 Z Schulten and K Schulten J Clzem P~JS 1977. 66,4616 13 F J Adrian Ref 4 p 77 14 K A McLauchlan and U E Steiner Mol Plzjs 1991,73 241 15 S N Batchelor H Heikkila C W M Kay K A McLauchlan and I A Shkrob Chem Phys 1992,162,29 16 S N Batchelor K A McLauchlan and I A Shkrob. Mol Phis 1992,75 50 1 17 S N Batchelor K A McLauchlan and I A Shkrob Mol P~JF 1992,77 75 18 K A McLauchlan in 'Modern Pulsed and Continuous-Wave Electron Spin Resonance,' ed L Kevan and M K Bowman Wiley New York 1990 p 336 19 C D Buckley and K A McLauchlan Mol Phrs . 1985 54 1 20 S N Batchelor K A McLauchlan and I A Shkrob 2 Ph~s Chem 1993 in the press 21 W T Dixon and W A Waters 1962 Proc Chem Soc London 1962 253 and numerous successor papers especially by R 0 C Norman and B C Gilbert 22 K A McLauchlan and N J K Simpson J Chem Soc Perhin Trans 2 1990 1371 23 P J KrusicandJ K Kochi,J Am Chem Soc 1969,91 3938,and numerous successor papers especially by B P Roberts 24 S N Batchelor K A McLauchlan. and I A Shkrob Mol Phl.~ 1992 75 531 and references quoted therein

ISSN:0306-0012    

DOI:10.1039/CS9932200325

出版商:RSC    

年代:1993

数据来源: RSC

摘要:

Progressive Saturation and Saturation Transfer ESR for Measuring Exchange Processes of Spin-Labelled Lipids and Proteins in Membranes Derek Marsh Max- Planck- lnstitut fur biophysikalische Chemie, Abteilung Spektroskopie, 0-37077Gottingen, Germany I Introduction The conventional electron spin resonance (ESR) spectra from spin-labelled biomolecules are sensitive to rotational motions on the timescale of 10-to lops s, which is determined essentially by spin-spin (i.e. T,) relaxation processes arising from modula- tion of the nitroxide hyperfine and g-value anisotropies (see e.g. ref. 1). The success of the technique depends in part on the versatile chemistry of the stable nitroxide free radical as a reporter group (see e.g. ref. 2). Typical spin-labelled biological lipids and reagents for covalent modification of protein side chains are shown in Figure 1.Conventional spin label ESR spectroscopy has therefore found wide application as a probe method for studying lipid chain motions in membranes and conformational changes in proteins, as well as in other areas of biophysical chemistry (see e.g. ref. 3).Extension of the motional sensitivity to slower time scales is possible by determining the microwave saturation properties of the ESR spectrum that are governed by the nitroxide spin-lattice relaxation time, T,, which for the relevant cases lies in the microsecond time regime. Such methods have already been exploited in the determination of slow rotational diffusion rates by using saturation transfer ESR spectroscopy in which the non-linear ESR signal out-of-phase with respect to the field modulation is detected under conditions of partial microwave ~aturation.~ One of the most fruitful examples of the standard use of spin label saturation transfer ESR spectroscopy is in the study of the rotational mobility and aggregation states of proteins in membranes (see e.g.refs. 1 and 5). In the present article, attention is concentrated on a different set of continuous wave saturation experiments which are aimed at determining slow exchange processes. Such applications are new and therefore deserve a detailed presentation of the meth- ods of analysis. Both two-site exchange and Heisenberg spin exchange are considered, since these offer the possibility of determining not only apparent unimolecular, but also true bimolecular rate constants.The motivation for such studies lies principally in determining slow exchange and translational diffusion rates involving membrane proteins, since these are not readily accessible by the more usual methods of spin label ESR Derek Marsh is a member of the research staffof the Spectroscopy Department at the Max Planck Institute for Biophysical Chemistry, Gottingen. Dr. Marsh obtained his B.A. degree in physics from the University of Oxford in 1967 and his D.Phi1. degree from the same institution in 1971. He worked subsequently at the Astbury Department of Biophysics, University of Leeds; at the Biology Division of the National Research Council of Canada, 0ttm.a; at the Max Planck Institute in Gottingen; and at the Biochemistry Department of the University of Oxford, before moving to his present position in 1975.Dr. Marsh's current research interests centre around studies of the structure and dynamics of biological membranes and of lipid bilayer model membranes, using diferent biophysical tech- niques, the principal being spin label electron spin resonance spectroscopy. 329 / 0 I1 H2C-0-P-0-X Ib0-CH IMO-CH I 2 0 0 N=C=S A-Figure 1 Typical spin-labelled phospholipids (upper structure) and reagents for reaction at nucleophilic centres in amino acid side chains of proteins (lower three structures). spectroscopy. For Heisenberg exchange, the spin exchange frequency not only of a single labelled species but also of two labelled species may be determined, hence yielding information on the relative location and mutual accessibility of the labelled groups.The methods employed are either the progressive satu- ration of the conventional ESR spectrum with increasing microwave power, or the determination of the integrated inten- sity of the saturation transfer ESR spectrum, which is an unconventional but more sensitive technique. Because of the inhomogeneous broadening associated with spin label powder patterns, both sets of experiments are best analysed in terms of the integrated spectral intensity. Applications range from stu- dies of the lateral diffusion of membrane proteins, via the exchange of lipids associated with membrane proteins, to the insertion of proteins in membranes, and many further appli- cations in biophysical chemistry are to be anticipated. The methods for analysing such experiments and the associated rate equations are presented here.CHEMICAL SOCIETY REVIEWS, 1993 2 Continuous Wave Saturation Classically, the saturation of the intensity of the conventional ESR spectrum can be described in terms of the population differences, n,, between the Ms,= f 3 levels of the ith spin system, where n, = N; -N: with N,’ being the spin popula- tions of the two levels (see Figure 2). The standard expression for the steady-state population difference under continuous wave (CW) irradiation of the kth spin system is:6 where nko is the Boltzmann equilibrium population difference and W is the rate at which transitions are induced by the microwave H, field.The latter is given from standard radiation theory by:’ where y is the electron gyromagnetic ratio, w is the angular microwave frequency and g(W -Wk) is the line shape function for the spin packet centred at Wk. Equation 1 serves to define the effective spin-lattice relaxation time, q$,in a CW saturation ESR experiment. Because the ESR absorption is proportional both to Wand to n (i.e. to the microwave susceptibility), the line height of the absorption spectrum is given by: where the absorption line height in the absence of saturation is obtained by putting = 0. For Lorentzian spin packets, as is the usual case, the normalized line shape is given by: where Tz,k is transverse (spin-spin) relaxation time.From equations 3 and 4 the saturation of the integrated intensity of the ESR absorption line shape, Sk = Sa(w -wk).do, is given by: where So$ is the integrated intensity of the ESR absorption in the absence of saturation, and offf= y2H;c$T,,k is the effective saturation parameter. Since the individual spin packets saturate independently and contribute additively to the total intensity, equation 5 holds good irrespective of the degree of inhomoge- neous broadening, and also for anisotropic powder patterns if anisotropy in TI and T, may be neglected.8 This is not true, however, for the saturation curves normally deduced from the absorption line heights, because these depend strongly on the degree of inhomogeneous broadening relative to that of the saturation br~adening.~ Thus in complex spin systems, the CW rr -1 wei Figure 2 Energy levels, spin populations (N,*)and transitions for two spin environments, i and j, in the ESR line shape.The spin population difference is given by: n, = N; -N,+ The transition rate for spin- lattice relaxation is 2We = l/T,O. The rate of Heisenberg spin exchange between spins i andj is 2KxN,+N,T, and that for chemical (or physical) exchange is N,T,-= NTJJ -l. , I / / / I I I I 0 I l l 1 I I I I I ( I I , I 0 5 10 15 P ’I2(rnW”2) Figure 3 Continuous wave ESR power saturation curves for a spin- labelled lipid in different membrane systems.Data are given for the lipid membrane alone (e),the delipidated protein alone (0),and the lipid-protein membrane complex (m). The straight dashed lines correspond to the predicted dependences for no saturation and for half saturation (upper and lower, respectively). The full lines are non- linear least squares fits of the saturation data to equation 5, and the dashed curved line is the dependence predicted for the lipid-protein complex according to equation 6 from the fits to the two single- component data sets. The data were recorded at a low temperature in the gel phase, for which the lipid exchange between the two environ- ments is very slow. (Data from ref. 14). saturation is best analysed in terms of the second integral of the conventional first-derivative absorption spectrum.Typical microwave power saturation curves for a spin-labelled lipid in different membrane systems are given in Figure 3. In treating multicomponent systems, the integrated intensity of the absorp- tion spectrum has the further advantage of being directly additive, the saturation of the total integral in such multicompo- nent systems being described by: wheref; and So,totare the fractional intensity of componenti and the total integrated absorption intensity, respectively, in the absence of saturation. An alternative expression in terms of relaxation enhancements, which are of principal interest, is: (7) I where ol0and q,,are the effective saturation parameter and T,, respectively, in the absence of additional relaxation enhance- ment.In this case, it is assumed, appropriate to the cases to be considered, that T, is unchanged because it is far less sensitive to the additional relaxation processes than is T,. An example of the saturation behaviour of a two-component system, in compari- son with that of the individual single components is given in Figure 3. 3 Saturation Transfer ESR Intensities The normalized integrated intensity of the phase-quadrature, second harmonic, absorption (V,’) saturation transfer ESR spectrum is defined by: O PROGRESSIVE SATURATION AND SATURATION TRANSFER ESR-D. MARSH 33 1 where V, represents the conventional in-phase, first harmonic, absorption ESR signal.Theoretical simulations of the V,' saturation transfer spectra4 have shown that the intensity is approximately proportional to the effective spin-lattice relaxa- tion time, Gff.Experimental support for this relation has come also from the linear dependence of l/lsTfor the spin label on paramagnetic ion concentration, confirming that 1 /IST corres-ponds to the spin-lattice relaxation rate of the spin label that is enhanced by paramagnetic relaxation. The dependence of the saturation transfer integral intensity on the effective spin label T, can therefore be expressed as: where QT.kand q,kare the intrinsic saturation transfer integral and spin label T,, respectively, in the absence of additional relaxation enhancement.Comparison of equations 5 and 9 thus indicates that the integrated intensity of the V,' saturation transfer spectrum is more sensitive to changes in T, than is the saturation of the conventional Vl ESR spectrum. The direct linear dependence on T, also allows simplifications in the analysis of more complex systems, since the total integrated STESR spectral intensity for a multicomponent system (cf. equation 7) is given simply by: wheref; and QT,tot are the fractional intensity in the conventional V, spectrum of component i and the total saturation transfer integral, respectively, in the absence of additional relaxation processes. The usefulness of this method has been demonstrated experimentally both for two-component lipid membranes'O and for reconstituted lipid-protein membranes.o,l 4 Two-site Exchange and Heterospecies Heisenberg Spin Exchange Kinetically, physical exchange between two inequivalent sites and the Heisenberg spin exchange between spin labels in two inequivalent sites are found to be indistinguishable. Physical exchange between two sites, b and f, is considered first: -1 b-f 7tJ where T; (i = b or f) is the pseudo-unimolecular rate of transfer per unit time from site i (cf. Figure 2). IfJ; is the fractional population at site i, then the rate constants are related by detailed balance: where fb +ff = 1. Because physical exchange occurs with conservation of spin orientation, the rate equation for the population difference at site b is given simply by: dnb/dt = -nb7b' + nfrf (12) and similarly for the population difference at site f.The situation for Heisenberg spin exchange is somewhat more complicated. Heisenberg exchange between spin labels at the two sites takes place between spins of opposite orientations (i.e. cross relaxation): KXbi f' where K, is the bimolecular rate constant for spin exchange (cf. Figure 2). The net rate equation for the population difference at site b is therefore: dnb/dt = -2Kx(N, Nf' -Nb+ NC) (13) This may be rewritten as:13 where the notation Ni = NC + Nc, with i = b or f, is used, and a similar rate equation can be derived for the population differ- ence at site f. The spin exchange frequency is defined in the usual bimolecular formalism by: 7;' = K,(Nb + Nf).It can then be seen that equations 12 and 14 are formally equivalent, with the identities TC~=fp&' and =fb7G1, which are fully consis- tent with equation 11. Thus only two-site physical exchange need be considered to cover both cases. 5 Saturation with Two-site Exchange If transitions of the spins at site b are induced by the H, microwave field, the net steady state condition for the spin population difference at this site is: where the first term on the right represents the transitions induced by the microwave field, the second is the spin-lattice relaxation and the final terms represent the exchange between sites (cf. Figure 2). The corresponding steady state condition for spins at site f which is not irradiated by the microwave field is: Solution of equations 15 and 16, together with equation 11, yields the standard expression for the saturation of the spin system at site b (i.e.equation l), where the effective spin-lattice relaxation time, q$,at site b is given by (cf.ref. 13): The corresponding result for two-site Heisenberg spin exchange is: which is obtained from the identities between the exchange rates in the two cases. Equivalent expressions can be derived for site f by permutation of the indices. Equations 17 and 18 are exactly of the form required for analysis of progressive saturation or saturation transfer ESR measurements by using equation 7 or 10, respectively. Equation 17 may be expressed in terms of a single exchange rate, Tb-or 7f as required, by means of the relation given in equation 11.Equation 18 is already in this form. Additionally, if the ratio c,f/c,b is known, e.g. from the ratio of the saturation transfer ESR intensities in the absence of exchange (cf. equation 9), the effective T, may be expressed solely in terms of a dimensionless exchange rate, e.g. q,bT, l. As an illustration, representative dependences of the saturation transfer ESR integral on the rate of two-site exchange are given in Figure 4. Depending on conditions, useful sensitivity can be obtained for exchange rates up to five times the intrinsic spin-lattice relaxation rate. The largest sensitivity is found at low exchange rates, less than the intrinsic spin-lattice relaxation rate.The method has been applied successfully to detecting the physical exchange of spin-labelled lipids at the hydrophobic interface with integral proteins in membranes, l4 as is illlustrated diagrammatically in Figure 5A. The lipid exchange rates are found to lie in the range of the intrinsic spin-lattice relaxation rate ( M lo6 s-l) and to reflect the thermodynamic selectivity of different lipid species for the protein. In gel phase membranes, where the lipid chain mobility is drastically reduced, the lipid exchange rates are found to be vanishingly small, or at least are CHEMICAL SOCIETY REVIEWS, 1993 0.8 0.6 I-9 2 cn 0.4 0.2 0.0 0.0 2.0 4.0 6.0 8.0 10.0 T 1.bO%-' Figure 4 Dependence of the normalized saturation transfer integral intensity, ZsT, for a two-component spin label system (b and f) on the scaled exchange rate, Ty,b~b-of component b.Dependences are l, given for ratios of the saturation transfer integrals of the two components in the absence of exchange of ZgT.f/ZgTT.b= 0.1 (full lines) and 0.5 (dashed lines), where from upper to lower curves the fraction of component b isf, = 0.8, 0.5, 0.2. Calculated from equations 10 and 17. very strongly reduced relative to those in normal fluid lipid membranes. Heisenberg spin exchange between different sites has also been studied recently in the binding of a spin-labelled precursor protein to negatively charged lipid membranes con- taining spin-labelled lipids, as is illustrated diagrammatically in Figure 5B.The spin exchange frequency of the spin label on the protein was found to depend sensitively on the position of the spin label in the lipid molecule with which spin exchange was taking place (cf. Figure 5B).In this way, it was possible to define the degree of penetration of the protein into the membrane, which is likely to be a determining parameter in the translocation of the precursor protein across the membrane. The mature holoprotein was found to be located at the membrane surface and not to penetrate the membrane significantly. 6 Saturation with Heisenberg Spin Exchange The effects of Heisenberg spin exchange between spin labels of a single species on their ESR saturation properties are now Figure 5 Diagrammatic illustration of spin-label exchange processes in biological membranes.(A) Two-site exchange for a spin-labelled (-NO) lipid molecule between sites at the lipid-protein interface and in the lipid bilayer regions of the membrane. The spin label has different relaxation times in the two environments. (B) Heisenberg spin exchange between spin-labelled lipids and a spin-labelled mem- brane-penetrating protein. The highest (collisional) spin exchange frequency is obtained for the spin-label group on the lipid that is positioned at the same depth in the membrane as that on the protein. considered. In contrast to the two-site case, many different distinct transitions are coupled by spin exchange. These may correspond to different hyperfine states, or to different orien- tations of the spin labels relative to the external magnetic field direction in a powder sample (see Figure 6).Effectively, equa- tions 15 and 16 must then be summed over all these states undergoing mutual spin exchange. Using the spin exchange formalism, the general steady rate equation for the population difference of the ith transition is: where N = EN, and n = En,. In this equation, transitions are assumed to be induced by the microwave field in the kth spin system, i.e. 81,k = 1 for i = k and is zero otherwise. Summing equation 19 over all i gives the following relation: Solution of equations 19 and 20 for i = k yields the standard expression for the saturation of the kth spin system (i.e.equation l), with the effective spin-lattice relaxation time being given by: where the exchange frequency is: 7G1= KJV, and zk = Nk/N is the fractional population (or degeneracy) of the transition being saturated.For powder saturation transfer ESR spectra from unoriented systems (e.g. membranes), the effect of this relaxa- tion enhancement is to reduce the intensity of the spectrum without appreciable changes in line shape (see Figure 6 and ref. 16). Representative dependences of the effective spin-lattice relax- ation rate, and hence of the saturation transfer ESR integral (cf equation lo), on the Heisenberg spin exchange frequency are given in Figure 7. When the degree of degeneracy is low (zk z 0) a linear relation between the effective relaxation rate and spin Figure 6 Exchange between spin packets, i and k, in a powder spectral line shape from randomly oriented spin labels.A given spin packet, k, undergoes Heisenberg spin exchange with all other spin packets, i. This results in a powder line shape given by the long-dashed line (cf. ref. 16).For rotational diffusion, a spin packet at position k undergoes an angular displacement to position i, where the size of the displace- ment depends on the diffusion mechanism. For Brownian diffusion, this produces a powder line shape given by the short-dashed line (cf. ref. 16). PROGRESSIVE SATURATION AND SATURATION TRANSFER ESR-D. MARSH NO NO W I I I I I I I I 0 2 4 6 8 10 T 1O/%x Figure 7 Dependence of the normalized effective spin-lattice relaxation rate, fl/Tiff,on the scaled Heisenberg spin exchange frequency, GT;l, obtained from equation 21.From upper to lower, the values of the degeneracy factor are: Z, = 0,0.05,0.1,0.2, and 1/3. exchange frequency is obtained, as would be expected for a true relaxation enhancement, rather than a cross relaxation, because the redistribution of saturation between the different exchange- coupled states does not limit the effective relaxation. In this limiting case, the saturation transfer integral intensity is given by the following expression: which is found to be applicable in many cases of interest where the spin exchange frequency is low. At high exchange frequen- cies, on the other hand, qstends to a limiting value of Zkc that represents the maximum redistribution of saturation through- out the various distinct spin label states.Beyond this limit, the spin-spin relaxation time, T,, then becomes sensitive to the spin exchange process and the exchange frequency can be determined conventionally from the line widths and line shapes of the in- phase ESR spectra. ’ The principal application of this saturation transfer ESR method is in the determination of slow bimolecular collision rates between spin-labelled molecules, for which the exchange frequency is too low to affect T2and hence is not amenable to the usual lineshape analysis. Whereas the latter is suitable for determination of translational diffusion rates of spin-labelled lipids in membranes (cf.ref. 17), it cannot be applied to the slower translational diffusion of spin-labelled integral mem- brane proteins which are more dilute and have broader ESR lines. The viability of the saturation transfer ESR method for such measurements has been verified from the viscosity and temperature dependence of the translational diffusion coeffi- cients of a spin-labelled protein in homogeneous solution. A strategy for measurement with integral membrane proteins is indicated in Figure 8. Solubilized spin-labelled protein is com-bined with unlabelled membrane protein at different relative proportions and membranes are then reconstituted at the same total proteinllipid ratio in order to ensure a constant effective intramembrane viscosity. The dependence of the saturation transfer ESR integral intensity on relative spin concentration in the reconstituted Na,K-ATPase membranes was found to con- form to that given in equation 22.19 The local translational diffusion coefficients deduced from the resulting bimolecular collision rate constants were in the expected range ( M 2 x 1 1 NO NO NO NO Figure 8 Scheme for measurement of the translational diffusion rate of the Na,K-ATPase in reconstituted membranes of the same protein/ lipid ratio, but different fractions of spin-labelled protein.Solubilized spin-labelled protein is mixed with solubilized unlabelled protein at different proportions and the membranes then are reconstituted by precipitation from the detergent solution. The Heisenberg spin exchange frequency is determined by the relative concentration of spin-labelled protein and the collision rate between proteins in the membrane.cm2s-l), but were much larger than corresponding values found for the long-range diffusion coefficients in whole cell systems, indicating considerable barriers to long-range diffusion in the latter case. A further application is the use of equation 22, with suitable calibrations, to determine the local concentrations of spin-labelled probe molecules in heterogeneous systems. This approach has been employed successfully to a study of the kinetics of the nucleation and growth of lipid domains in a model membrane system. O 7 Slow Rotational Diffusion and Saturation Studies It was shown above that two-site physical exchange and Heisen- berg spin exchange are kinetically equivalent.Rotational diffu- sion of a spin labelled molecule can be approximated as physical exchange in small steps. This results in a spectral diffusion of saturation which is analogous to that of the Heisenberg spin exchange between distinct transitions in an anisotropic powder spectrum of a single spin-labelled species (cf. Figure 6),which was treated in the immediately preceding section. This equiva- lence has led to a simple description of the standard saturation transfer ESR experiment used for the determination of slow rotational diffusion rates, particularly of membrane proteins and supramolecular aggregates, that is outlined below.2 The spectral diffusion rate arising from spin label rotation is determined by parameters governing the angular dependence of the resonance positions and the width of a spin packet, and is inversely proportional to the rotational correlation time, T~, which is defined by 7R = 1/(6DR)where DRis the rotational diffusion coefficient.22 This spectral diffusion rate (ccT< l) is equivalent to the spin exchange frequency, ~&l,introduced above. However, because the spectral diffusion rate depends on the angular dependence of the resonance positions, the extent of the resulting reduction in intensity varies throughout the spec- trum, producing a large change in the saturation transfer ESR line shape (see Figure 6).Thus the effects of rotational diffusion on the saturation transfer ESR spectrum can be distinguished readily from those of Heisenberg exchange when both spectral line shapes and intensities are taken into account.A standard method of extracting rotational correlation times from the saturation transfer ESR spectrum is viathe ratios of the line heights at the most sensitive part of the spectrum to those at the extreme turning points in the spectrum that are insensitive to rotational diffusion (cf. Figure 6). Since the line heights and intensities of the saturation transfer ESR spectra are directly proportional to the effective T, (cf.equation 9), the spectral line height ratios and integrated intensities, R, that are normally used for establishing rotational correlation time calibrations (cf.reis. 4 and lo), therefore may be expressed from equation 21 in the following general form: where R, is the value of the measured parameter R in the absence of rotational diffusion, a and b are constants to be fitted that depend only on intrinsic spectral parameters, and the ratio a/bis equal to the orientational degeneracy parameter ( = sine). Equa- tion 23 describes very well the dependence on rotational correla- tion time of the diagnostic line height ratios and intensities of the saturation transfer ESR spectra from spin-labelled haemoglo- bin in glycerol-water mixtures, as is seen from Figure 9.21It therefore can be used to give the following simple expression for the correlation time calibrations of the experimental STESR spectra: where values of the calibration constants, k, R,, and 6, for the different spectral parameters can be found in ref.23. This is a, much more readily accessible form than hitherto has been presented and has the additional advantage of reflecting directly the underlying spectral diffusion process. I II..-" Figure 9 Rotational correlation time (TR) calibration obtained with spin-labelled haemoglobin for the low-field diagnostic line height ratio, L"/L, of the second-harmonic, 9O0-out-of-phase, absorption saturation transfer ESR spectrum (Vi-display). The full line is a non-linear least-squares fit of the data to equation 23, with the fitting parameters: (L"/L)o= 1.88, a = 6.18 ps and b = 67.9 ps (m,= + 1 hyperfine manifold). From ref.2 1. Slow rotational diffusion of spin-labelled molecules also may be studied from the power saturation of the conventional ESR spectra. Squier and tho ma^^^>^ have demonstrated the feasibi- lity of this approach and have made calibrations of the rotatio- nal correlation time by using spin-labelled haemoglobin. The parameter measured, R',is the ratio of the second integrals of the conventional first-derivative ESR spectra recorded at low (sub- saturating) and high (partially saturating) microwave powers, where both effectively are normalized to the values in the absence of saturation. The low and high microwave powers were CHEMICAL SOCIETY REVIEWS, 1993 chosen to correspond to values of H, at the sample of 0.032 and 0.25 gauss, respectively.From equation 5, the low/high power second integral ratio is therefore given by: where aeffis the saturation parameter at the high (partially saturating) microwave power. It is found that such conventional ESR saturation measurements are also amenable to the analysis presented above for the effects of slow rotational diffusion on saturation transfer ESR spectra.26 As before, equation 25 can be written in terms of the relaxation enhancement as: where 0, and are the saturation parameter at the high (partially saturating) microwave power and the value of T,, respectively, in the absence of rotational diffusion. For slow rotational diffusion, T, remains essentially unchanged in equa- tion 26. Making the same substitution as was done immediately above for the value of qffin the presence of rotational diffusion, then yields: where the parameters to be fitted are a and b,as previously, and 0,.As for the saturation transfer ESR spectra, this equation is capable of describing the correlation time calibration for the saturation of the conventional ESR spectrum with a reasonably high degree of accuracy. The fitted values for a and b are reasonably close to those obtained for the saturation transfer ESR integral intensity,26 as for consistency they should be, hence giving further support to the method used in the analysis. The corresponding rotational correlation time calibration for the saturation of the conventional ESR spectrum is then given by: where k' = 116.6 ps, = 3.12 and b = 46.8 ps.It is to be anticipated that this readily accessible formulation will facilitate further applications of this alternative new form of saturation transfer ESR spectroscopy. Conclusions Continuous wave saturation of spin label ESR spectra is exquisitely sensitive to slow physical exchange and weak Heisen- berg spin exchange processes which lie in the characteristic frequency range of the spin-lattice relaxation rate. Such situa- tions occur widely in the biological applications of spin label ESR methodology. Measurements are made of the integrated spectral intensity, either with progressive saturation of the conventional in-phase ESR spectrum, or from the out-of-phase saturation transfer ESR spectrum.The effects of (two-site) physical exchange and Heisenberg spin exchange on the effective spin-lattice relaxation have equivalent formulations, which lead also to a simplified description of the response of the saturation transfer ESR spectra to slow rotational diffusion. There is thus a very direct connection between the spin dynamics that are reflected by the ESR saturation properties and the molecular dynamics of the spin-labelled system of interest. The appli- cations are likely to be many and currently include studies of lipid-protein interactions, protein translational and rotational diffusion, and lipid domain formation in biological membranes. 9 References I D. Marsh and L. I. Horvath in 'Advanced EPR. Applications in Biology and Biochemistry', ed.A. J. Hoff, Elsevier, Amsterdam, 1989, pp. 707-752. 2 B. J. Gaffney in 'Spin Labeling. Theory and Applications', ed. L. J. PROGRESSIVE SATURATION AND SATURATION TRANSFER ESR-D. MARSH Berliner, Academic Press, New York, 1976, pp. 183-238. 3 D. Marsh in ‘Membrane Spectroscopy’, ed. E. Grell, Springer- Verlag, Berlin-Heidelberg-New York, 1981, pp. 51-142. 4 D. D. Thomas, L. R. Dalton, and J. S. Hyde, J. Chern. Phys., 1976, 65, 3006. 5 P. F. Knowles and D. Marsh, Biochem. J., 1991,274,625. 6 C. P. Slichter, ‘Principles of Magnetic Resonance’, 2nd. Edn., Springer-Verlag, Berlin-Heidelberg-New York, 1978. 7 A. M. Portis, Phys. Rev., 1953, 91, 1071. 8 T. Pali, L. 1. Horvath, and D. Marsh, J. Magn. Reson., 1993, A101, 215. 9 T. G. Castner, Jr., Phys. Rev., 1959,115, 1506. 10 L. I. Horvath and D. Marsh, J. Magn. Reson., 1983,54,363. 11 T. Pali, R. Bartucci, L. 1.Horvath, and D. Marsh, Biophys. J., 1992, 61, 1595. 12 L. I. Horvath, P. J. Brophy, and D. Marsh, Biochim. Biophys. Acta, 1993,1147,277. 13 D. Marsh, J. Magn. Reson., 1992,99, 332. 14 L. I. Horvath, P. J. Brophy, andD. Marsh, Biophys.J., 1993,64,622. 15 M. M. E. Snel, B. De Kruijff, and D. Marsh, Biophys. J., 1993,64, A16. 16 D. Marsh and L. I. Horvath, J. Magn. Reson., 1992,97, 13. 17 D. Marsh in ‘Biological Magnetic Resonance. Spin Labelling Theory and Applications’, ed. L. J. Berliner and J. Reuben, Vol. 8, Plenum, New York, 1989, pp. 255-303. 18 V. V. Khramtsov and D. Marsh, Biochim. Biophys. Acta, 1991,1068, 257. 19 M. Esmann and D. Marsh, Proc. Natl. Acad. Sci. USA, 1992, 89, 7606. 20 T. Pali, R. Bartucci, L. I. Horvath, and D. Marsh, Biophys. J.,1993, 64, 1781. 21 D. Marsh and L. I. Horvath, J. Magn. Reson., 1992,99,323. 22 P. Fajer, D. D. Thomas, J. B. Feix, and J. S. Hyde, Biophys. J.,1986, 50, 1195. 23 D. Marsh, Appl. Magn. Reson., 1992,3, 53. 24 T. C. Squier and D. D. Thomas, Biophys. J., 1986,49,921. 25 T. C. Squier and D. D. Thomas, Biophys. J., 1989,56,735. 26 D. Marsh, 1993, to be published.

ISSN:0306-0012    

DOI:10.1039/CS9932200329

出版商:RSC    

年代:1993

数据来源: RSC

摘要:

Polarized Positive Muons Probing Free Radicals A Variant of Magnetic Resonance E. Roduner Ph ysikalisch -Chemisches lnstitut der Universitat Zurich Winterthurerstrafie 190 CH-8057 Zurich Switzerland 1 Introduction What is an elementary particle which is classified as anti-matter and constitutes the main component of our exposure to cosmic rays on Earth good for in chemistry? Its microsecond lifetime makes it too elusive to allow the production of bottles of new compounds. Nevertheless as will be shown here the exotic particle forms the nucleus of an atom which is chemically well behaved. It can be substituted for protons in molecules where it acts as a spy radiating off information of interest to the chemist. The positive muon (p+)is a particle with a mass of one-ninth the proton mass with spin +and an associated magnetic moment which is 3.18 times the proton moment and a lifetime of 2.2 ps. Its availability in the form of energetic beams with a spin polarization close to 100% at the ports of suitable accelerators led to its successful application as a magnetic probe in matter. The four major accelerator facilities which operate such beams are found atTRIUMF in Canada at PSI in Switzerland at RAL in England and at KEK in Japan. The experimental technique has been dubbed pSR which stands for Muon Spin Rotation (or Resonance or Relaxation). In various materials the thermalizing muon captures an electron and forms a hydrogen-like one-electron atom with the muon as a nucleus. It has been dubbed muonium (Mu =p+e-). Since its ionization potential and its Bohr radius are within 0.5% the same as those of H it is in a chemical sense a light hydrogen It reacts with unsaturated bonds by addition as in leaving thereby the muon as a polarized spin label chemically bound in a free radical. In this way it has proven particularly useful for the investigation of structure reaction kinetics and reorientational dynamics of organic radical^.^ Given the fact that the chemical and magnetic properties of a positive muon are completely analogous to those of the proton it is evident that the behaviour of the two nuclei in a magnetic field is also analogous and that phenomena of magnetic resonance such as precession free induction decay and relaxation can be described in much the same way in both cases. Whereas this is true in principle there are important differences which should be kept in mind.The short lifetime of the muon puts a severe limit ~______ Emil Roduner is a physical chemist with interest in the for-mation structure and dyna- mics of organic free radicals in solid liquid and gaseous environments. In 1978 he made the first observation of muon-substituted free radicals. Since then he has been using positive muons as probes and in 1988 he was awarded the Werner Prize and Medal for the deve- lopment of the muon spin ro-tation technique to a universal method in radical chemistry. on the spectral resolution and has the consequence that it is not possible to distinguish between different diamagnetic muon- substituted molecules since chemical shifts or nuclear couplings are not resolved.The muon is implanted in the sample as a polarized species.There is therefore no need to first create spin coherence using a high frequency preparation pulse. The time resolution is thus significantly increased over that of more conventional techniques. Furthermore one has close to the full muon polarization at all temperatures and it is independent of the Curie factor which normally imposes a fatal limit on the experimental signal-to-noise ratio. This makes the muon tech- nique extremely sensitive so that it is possible -and in time resolved experiments required -to work with a concentration of a single muon in the sample at a time.The immediate advantage of such low concentrations in radical chemistry is the absence of bimolecular termination reactions which has the consequence that the kinetics are always of first or pseudo-first order and that the signal of surface-adsorbed radicals is not depleted under conditions of high radical mobility. Signal detection via energy absorption measurement is of course not feasible under conditions where one has a single muon in the sample but fortunately advantage can be taken of the asymmetric muon decay with emission of the decay positron preferentially in the instantaneous muon spin direction. On this basis a single particle counting technique borrowed from par- ticle physics allows monitoring a free induction decay signal in a transverse field experiment with a typical time resolution of ca. 1 ns or to detect a time-integrated forward-backward decay asymmetry as a function of a longitudinally applied magnetic field. The potential of the transverse field technique has been reviewed previ~usly.~ Emphasis will therefore be given here to the longitudinal field variant which takes advantage of the special effects encountered near avoided crossings of energy levels.They were first encountered in optical spectroscopy5 but are used routinely in nuclear analytical methods6 and in NMR in particular together with fast field cycling methods.’ They are also important for the mixing of radical pair singlet-triplet (S-T-states in experiments studying electron polarization effects8 and have found applications in many other areas of ~pectroscopy.~There are also other techniques which make use of nuclear spin polarized beams which compared with NMR leads to an increased sensitivity in surface studies.6 2Theoretical Background 2.1 Hamiltonian for a Radical with Axial Hyperfine Symmetry In order to demonstrate the analogy of pSR with conventional magnetic resonance we concentrate on a system where the unpaired electron of a radical is coupled by hyperfine interaction to the muon and to one additional magnetic nucleus. Further magnetic nuclei introduce no major new aspects they are omitted here to reduce the number of indices and summation signs in the formulae. Also for simplicity we shall restrict the discussion to a system with tensors of coincident axial hyperfine symmetry as is found for a species undergoing fast uniaxial rotation.This is characterized by the Hamiltonian 337 CHEMICAL SOCIETY REVIEWS 1993 where ve+k = ye+,! x B are the electron muon and nuclear Zeeman frequencfes I,n _terms of their gyromagnetic ratios and the external field B,. S,Pkare the corresponding spin operators Agf their Fermi contact interaction and the principal components of the tensor describing the magnetic dipole interaction of the muon (nuclear) point-dipole with the unpaired electron which is smeared out in its orbital which is often the p,-type. In polar coordinates the terms A -F take the form O where 4 is+the azimuthal angle 8 is the angle between the unique axis and B and M = ms+ mr + mkis the quantum number for the z-component of the total angular momentum.The selection rules used referred to in this work are characterized by AM.They follow immediately from t_he_structu_re ,Of the operators. Note that operators of the type S+I-and %I+ which correspond to AM = 0 arise both from dipolar (term B) and from isotropic interaction (equation 2). Electron g-factor anisotropies are usually small but signifi- cant in organic radicals. Despite this the electron Zeeman term was written as a scalar in the Hamiltonian. While this is not normally correct it is justified for pSR applications at high external fields where as will be seen later the electron Zeeman term cancels out in all relevant expressions to first order since we observe pure muon (nuclear) transitions. 2.2The Basis for an Investigation of Reorientational Dynamics Owing to the nature of the dipolar magnetic interaction the hyperfine coupling tensor has a fixed orientation with respect to the radical. It provides the handle for the study of reorientatio- nal dynamics since any motion which is fast compared with the inverse anisotropy leads to partial or complete averaging of the anisotropy. Little advantage of this fact has been taken hitherto to investigate radical motion. Interaction between two point-dipoles depends on the angle 8 between the line connecting the two dipoles and the direction of the external magnetic field and it is proportional to (3 cos2 8 -1). It is well known that for protons in the a-position to the radical centre the positive component of the dipolar interaction lies in the direction of the connecting bond and that it adopts a value of + 30MHz for the malonyl radical.'The component parallel to the p,-orbital is close to zero and the third one therefore -30 MHz. The situation for P-protons is slightly more complicated since their position is usually not fixed to the nodal plane. As is shown in Figure 1 the two lobes of the p,-orbital containing the unpaired electron are best accommodated in the posjtive cone of the function (3 cos2 8 -1) when the external field B is close to parallel to the line connecting the /?-nucleus with the radical centre.The two other components are negative and it is found experimentally that they are often of the same magnitude so that the coupling tensor is approximately axial with D,,pointing from the nucleus to the radical centre. Also because of the (Y-3 dependence it is reduced in magnitude compared with that for a-nuclei. DI for 8-protons in rigid localized radicals is found to be typically + 7.5 MHz. Any fast motion averages partly the hyperfine anisotropy. Figure 1 Dipolar interaction of the hydrogen nucleus in ,%position a point-dipole with the unpaired electron which is 'smeared out' in ap,- orbital. The orientation of the cone function (3 cos' -1) is shown for the situation when the magnetic field is roughly parallel to the direction of the positive component of the hyperfine anisotropy tensor. Oo = 54.7" is the magic angle where the dipolar coupling disappears. Specifically rotation about an axis perpendicular to D,,makes Dlthe new DF = -o.5Dl,,i.e.the motion reduces the anisotropy by a factor of two and changes its sign. On this basis recent quantitative analysis of anisotropic ESR spectra gave evidence for rotational motion of the tetramethylethylene radical cation in ZSM-5 zeolite.' 2.3 Evolution of Spin Polarization The time evolution of muon polarization P(t),in the presence of a static external field has been evaluated previously using a density matrix approach.12 Expressed in a basis of Zeeman product states (Clm = &,x it is obtained for transverse fields as the expectation value of the Pauli spin operator ($) which leads to For longitudinal fields (&)gives Poy is the initial muon polarization of the species of interest N = 4nk(2P + 1) the dimension of its energy matrix 8qk = (xB.~~xJ',~)the Kronecker delta and A = A + A' represents the relaxation on the transition frequency vnrn= (En-Ern)/h. A = 0.4551 ps-is the inverse muon life time and A' is the first- order rate constant which accounts for chemical reaction into a state with different resonance conditions. 2.4 Simplification in Zero Magnetic Field In the absence of an external magnetic field the Zeeman terms in the Hamiltonian vanish. Furthermore the energy spectrum of the system is independent of its orientation in a laboratory frame. While conventional magnetic resonance usually avoids zero field conditions pSR has taken advantage of the unique situation for isotropic systems with equivalent nuclei,12 or for anisotropic systems in the absence of magnetic nuclei. The simplest system is that of a muon-electron two-spin-+ system. In the isotropic case three of the four eigenstates form a degenerate triplet which is separated by Ak from the singlet state. Spin polarization oscillates between muon and electron and the only non-zero frequency is expected at AK~.This POLARIZED POSITIVE MUONS PROBING FREE RADICALS-E corresponds to 4463 MHz for vacuum-like Mu and needs special experimental effort to resolve while the reduced hyperfine interaction in radicals is more easily accessible In the presence of axial anisotropy the triplet splits into a doublet and another singletThree frequencies at Ago -205 Ago + D5,and 305 are expected for this case In Section 4 1 3 Mu@C will serve as an example for this case The situation becomes immediately more complex when further magnetic nuclei are present It is no longer possible to read coupling constants directly off the spectrum For the case of an arbitrary number of equivalent protons in addition to muon and electron however it has been possible to work out analyti- cal expressions for frequencies and transition amplitudesThe case will be treated further in Section 3 1 and is illustrated in Figure 5 2.5 General Behaviour in High Magnetic Fields Because of the simplification of spectra it is convenient as in magnetic resonance in general to work in high fields where U >> A& Ato Except for the special conditions encountered near avoided crossings of energy levels the muon is then decoupled from the other magnetic nucleus Eigenstates y5 are pure individual product states x,,i e the expansion coefficients c in equations 5 and 6 take the values 0 and 1 In longitudinal fields the time dependence vanishes and the muon polarization P_(B,t) = Po becomes staticThe time dependence in transverse fields is governed by a’”,(see equation 5) which mixes states which differ in the muon but not in the electron or nuclear spin quantum numberThis is expressed by the selection rules I Amp I = 1 AmSk= 0The corresponding transition frequencies are given to first order by v* = /vI1f j[Ak + D“11 -3 cos*8)]1 (7) More accurate expressions are found in the specialized literature l2 l3 The frequencies correspond to the two ENDOR transitions of the muon in the radical Because of the high field condition they are independent of nuclear Zeeman or hyperfine terms each line is therefore degenerate by a factor (21k+ I) and has an ampli- tude of 0 5PThe line shape is given by the Fourier transform of the exponentially damped cosine functions in equation 5 which is a Lorentzian with full width at half maximum 2h The muon hyperfine parameter is obtained directly as the sum (or differ- ence depending on the relative magnitude of the terms in equation 7) of the two frequencies In polycrystalline material the distribution of &values leads to powder patterns of asym- metric shape 2.6 Behaviour at Avoided Level Crossings (ALCs) The theory for ALC resonances of isotropic systems containing a spin polarized muon has been developed by Heming et a1 l4 and extended to more general cases in solids by Kiefl15 and by Roduner Dynamic effects have also been treated Only a brief outline is given here At true crossings of magnetic energy levels in high fields eigenstates are pure Zeeman product states but near avoided crossings they are mixtures of the two crossing statesThe normal high field approximation is thus no longer valid This leads to a broadening or even to a splitting of one of the transverse field lines l5 In longitudinal fields too the system is not prepared in dn eigenstate and it therefore oscillates at a frequency given by the energy difference between the two mixing states In the time-integrated forward-backward decay asym- metry this leads to a resonance at the field which meets the ALC condition As can be seen by inspection of the Hamiltonian and in particular of equation 4 there are three types of resonances characterized by the selection rules IAMI = lA(mp + mk)I = 0 1 2The resonance field is given to first order by RODUNER Higher order terms have to be taken into account for quantita- tive work but the corrections are usually on a level < 1% The amplitude as a function of field is determined from the time integral of equation 6The field dependence of the expansion coefficients c leads to resonances of Lorentzian shape which are broadened in the presence of relaxation or chemical reaction In polycrystalline material the different orientations lead again to powder patterns The three types of avoided crossings are shown in the energy level diagram of Figure 2 Outside the resonances the energies vary linearly with magnetic field and the states are pure Zeeman states as indicated by the labelling Only the four states with electron spin a are shown the others are well separated in energy E spin flip-flip (AM= 2) rn uo n-p roton spin flip-flop (AM= 0) B P B Figure 2 High-field energy level diagram for a three-spin system of an electron e positive muon p and proton k Muon avoided level crossing resonances occur when states with opposite muon spins become near-degenerate in energy allowing the system to oscillate between them The simplest case is the AM = I ALC lineTwo states which belong to the same electron and nuclear spin but diffe! in the muon spin are mixed by operators of the form SJs The elements C and D of the Hamiltonian (equations 2 and 4)are of this form They are non-zero in the presence of muon hyperfine anistropy (except for the special orientations 8 = nn/2 for integer n) Muon hyperfine anisotropy therefore leads to an avoided crossing of this type but in the absence of anisotropy the levels are not mixed and the corresponding resonance will be absent The resonance is therefore especially suitable to study anisotro- pic reorientational motion of radicals in orienting environ- ments even in polycrystalline or amorphous states l9The critical time for the averaging process is given by the inverse anisotropy D5 The AM = 0 line a muon-nuclear spin flip-flop transition is allowed only in second order since the H;miltonian provides no direct matrix elements which mix the two Zeeman states The degeneracy at the crossing is lifted by isotropic coupling of the two states to a third distant state with opposite electron spin (I/3,apa,_) tor the case shown in Figu_re :) and the active element is At”,,S+P combined with A$&& Resonances of this type are observed also in liquids where rapid tumbling averages the anisotropy to zero Inspection of equation 8 shows that the resonance position depends on the relative sign of the muon and the nuclear hyperfine interaction terms Since the radicals are formed in a way which leaves the muon in a position of the molecule where At”,,is normally positive it allows the determi- nation of the sign of nuclear coupling constants which is unique in magnetic resonance The last type is the ldMI = 2 muon-nuclear spin flip-flip transitionThe crossing is avoided again indirectly as in the AM = 0 case but it occurs only in the presence of anisotropy (terms Eand Fin equation 4) It is usually weak and narrow and has therefore not found practical applications yet 3 ExperimentalTechniques Several variants of experimental techniques have been deve- loped They have in common that they all stop energetic muons of a spin polarized beam from an accelerator port in the sample to be investigated To monitor the signal they are all based on the detection of the decay positrons which are emitted preferentially along the instantaneous spin direction when the muon decays The first such experiment was reported by Garwin et a1 2o in their verification of the parity violation in pion decay A scheme of the experimental set-up for the two main variants is shown in Figure 3 In both cases the muon enters from the left with its spin polarized in the direction of flight and the decay positrons are detected by a set of scintillation counters which surround the sample placed in the centre of a magnetThe scintillator pulse sequences are logically analysed in a fast electronics and good events are stored in a multi channel analyser or computer memory in the form of a time histogram or field scan as shown in the insets 3-P+ [,,pol Figure 3 Block scheme of apparatus for time-resolved transverse field muon spin rotation (TD-pSR left) and for time-integrated longitudi- nal field avoided level crossing resonance (ALC-pSR right) 3.1 Time Differential Muon Spin Rotation (TD-pSR) The left-hand side of Figure 3 shows the set-up for TD-pSR It is used most often in transverse but occasionally also in longitudi- nal or even in zero external magnetic fieldThe incoming muon triggers the backward counter b and starts the clock for a lifetime measurement The decay positron if detected in the forward counter f stops this clock Good events are counted in the proper channel of the histogram Bad events in particular those where more than a single muon has been detected in the sample during a time window of several microseconds are eliminated by the logical circuit The principal content of the histogram is a radioactive decay curve which corresponds to the muon lifetime The muon precesses in a transverse magnetic field and therefore the detection probability for decay positrons sweeps past the forward counter which leads to a modulation of the decay curve with the muon precession frequenciesThis superimposed signal represented by equation 5 is the analogue CHEMICAL SOCIETY REVIEWS. 1993 of a free induction decay following a ~/2pulse for a selected nucleus in Fourier transform magnetic resonance As in NMR it is often the Fourier transformed FID rather than the raw time histogram which is displayed An instructive set of TD-pSR frequency spectra obtained with a sample of liquid vinylene carbonate in various magnetic fields is shown in the Figures 4 and 5 In a high transverse field (1600 Gauss top of Figure 4)we observe three frequencies The intense line up at 21 7 MHz is due to muons which have come to rest in a diamagnetic environment and therefore precess at the muon Zeeman frequency of 13 55 kHz/Gauss Owing to the short muon lifetime chemical shifts or nuclear couplings are not resolved so that this signal usually has to be assumed to be a superposition of contributions arising from muons in various environments For the present case it is plausible to assume that it represents muons which have been trapped in the lone pairs of the oxygen atoms Alternatively one can imagine that a Mu atom has substituted a hydrogen atom in the molecule in a hot atom reaction or that it has abstracted H so that the muon is actually present as MuH A pair of lines R corresponds to the radical formed by Mu addition to the double bond of the moleculeThey are centred at +Ago = 178 7 MHz and displaced approximately by up as is seen in equation 7 for the isotropic case with D? = 0The higher of the two frequencies has a lower amplitude as a consequence of the limited time resolution of the experiment The muon hyperfine coupling constant As = 357 5 MHz is obtained directly by taking the sum of the two frequencies The second spectrum was obtained in a field of 117 Gauss where the high field condition for muon decoupling from the protons no longer applies The radical lines are still centred at +A$ but they are much further apart and each line is split into a doublet of doublets by the two protons By numerical diagonali- zation it is possible to derive from the line positions sign and magnitude of the two proton coupling constants (here -39 8 MHz for the a-proton and 98 4 MHz for the ,&proton) The most general case is found for a field of 20 G which corresponds to about the proton hyperfine fields at the electronThe muon polarization is now distributed over 56 transitions of different intensities which leaves very little for an individual line A /o-/ H -398MHz L I I I I V 0 100 I 200 300 MHz Figure 4 TD-pSR spectrum obtained with liquid vinylene carbonate at 300 K in a magnetic field of 1600 Gauss (top) and 117Gauss (bottom) vI”is the Zeeman frequency for muons In diamagnetic environments R IS a pair of lines arising from radicals formed by Mu addition to the vinylene double bond The numbers next to the formula are the hyperfine coupling constants which for the muon has been reduced by a factor pp/pp= 3 1833 to make it directly comparable to the proton value POLARIZED POSITIVE MUONS PROBING FREE RADICALS-E I I I ,I V Figure 5 Simulated and observedTD-pSR spectra of the Mu adduct to vinylene carbonate in a low transverse and in zero field The apparent increased noise level at high frequencies is a consequence of a deconvolution for instrumental time resolution comparison between simulation and experiment gives satisfac- tory agreement (top of Figure 5) A more favourable situation is attained in zero field where because of degeneracy of states the number of transitions reduces to 12 only (bottom of Figure 5) The example demonstrates that it is possible in simple cases to extract from a zero field spectrum the entire information on coupling constantsThis option is particularly attractive for powders which normally give rise to broad lines in an external field -in zero field they are expected to give single crystal like features Reduction of & by the muon-proton relative magnetic moments pJpP = 3 1833 gives a value of 112 3 MHz which compared to the 98 4 MHz for the proton in the equivalent position reveals a hyperfine isotope effect of 14% This effect has been ascribed to the length of the C-Mu bond which in the dynamic average of a Morse oscillator exceeds that of an equivalent C-H bond by nearly 5% 21 3.2 Time Integral Avoided Level Crossing Muon Spin Resonance (ALC-pSR) The right-hand side of Figure 3 shows the ALC-pSR set-up in a longitudinal magnetic field The incoming muon is not detected only the decay positrons are counted in the two detectors f and b There is thus no principal limit on the muon flux as in the case of TD-pSRThe field is scanned in small steps and for each field value the muon polarization is measured It is proportional to the experimental asymmetry d,where Nf -Nb.d= -(9)N,-+ Nb' and Nfbare the total number of positrons counted in the two counters Figure 6 displays a typical example of an ALC-pSR spectrum It was obtained with a liquid solution of 6,6-dimethylfulvene in diethyl ether 22 Eight clear resonances are resolved which because of the liquid state are all of the type AM = 0 A TD-pSR experiment of the same fulvene revealed two radicals with RODUNER 34 1 A& = 105 1 MHz and 203 4 MHz and with relative yields of 60% and 40% respectively Analysis of the resonance positions is based on equation 8 which for the isotropic case and when the nuclei are protons reduces to B = IAg -A$,I x 53 80 Gauss with Ag,k given in MHz It shows that the two radicals appear separated in the ALC spectrum and that the first resonance from the left is composed of two near-degenerate linesThe two structures and the assignment of the coupling constants which are entirely consistent with expectation for radicals of a penta- dienyl type and of a cross-conjugated ally1 radical are given on top of the figure A simulation is in excellent agreement with the experimental spectrum The dividing lines between resonances of positive and of negative proton couplings is indicated It should be noted that smaller couplings lead to less intense and often unobserved resonances so that a typical gap is normally observed around the dividing lines Furthermore the line width is proportional to lA& -Aio1 -so that negative proton cou- plings normally lead to narrower lines which can be used as a further help for the assignmentThe hyperfine isotope effect between the muon and the proton bound to the same carbon atom amounts again to ca 14% as was found and discussed above for the case of vinylene carbonate Comparison of TD-pSR with ALC-pSR shows that the two techniques are to some extent complementary Since the selec- tion rules are different one obtains different information Of the hyperfine parameters high transverse fields yield only the muon coupling constant whereas the ALC technique gives in isotropic media the muon-nuclear difference When radicals are too complex to allow the observation of zero-field spectra then the total information is obtained in a single experiment only from an ALC spectrum recorded under frozen conditions so that Ak is obtained from a AM = 1 type transition Integration in ALC spectroscopy removes the constraint which allows only a single muon in the sample at any given time It thus profits from the higher muon fluxes which have become availableThis is at a cost of the direct information about the time dependence It is often advisable to do both types of experiments If details of the relaxation function in longitudinal fields need to be known it is of course possible to combine the two experimental philosophies and to do a time resolved longitudinal experiment A further advantage of longi tudinal fields is the absence of transverse relaxation processes (T2)This usually simplifies things and in the case of slow radical forma- tion from the Mu precursor it avoids the loss of phase coherence and makes it possible that radicals can be observed which are formed in a microsecond instead of a nanosecond This should make a whole new class of radicals accessible to observation -11 46H 4000 6000 8000 10000 12000 Field (Gauss) Figure 6 ALC pSR spectrum obtained with 6,6'-dimethylfulvene in diethylether solution and comparison with a simulationThe struc- tures of the two radicals with the coupling constants (converted to Gauss) are given on top 4 Applications to Problems of Current Interest 4.1 Reorientation Dynamics in Solids 4 I I ALC-pSR of a Benzene Single Crystal The dynamics of benzene have been investigated in detail by NMR The dominating motion a jump reorientation about the sixfold axis of the molecule has an Arrhenius frequency factor of1 09 x 1014s-iandanactivationenergyof176kJmol-' 23 Figure 7 displays an ALC-pSR spectrum of frozen benzene at 263 K Based on the known isotropic coupling constants from work in the liquid phase the three resonances are easily assigned to the strong IdMl = I feature and to the two transitions with \AM1 = 0 2 arising from indirect interaction of the muon with the methylene proton Further ldMl = 0 lines are present at higher fields but outside the range of the figureThe inset shows a scan with increased resolution and on an expanded scale over the very narrow IdMI = 2 resonance which has a full width at half maximum of only 28 G All lines are of Lorentzian shape An excellent simulation is obtained with isotropic hyperfine para- meters ,4ko = 519 7 MHz A; = 126 5 MHz with correspond- ing anisotropies D? = 3 5 MHz and Dt = 0 9 MHz and with an angle of 8 = SO" between the external magnetic field and the hyperfine symmetry axis Both the width of the IdMI = 1 and the intensity of the ldM( = 2 line are strongly orientation dependent and leave an uncertainty of only 2" for 8 CHEMICAL SOCIETY REVIEWS 1993 results give a correlation time for jump rotation of 28 ps at this temperature Furthermore it is known that benzene often forms single crystals on simple coolingThe special alignment of the crystal was not always reproducible in further experiments but it is plausible that the presence of a high magnetic field or the shape of the sample cell initiated a preferred orientation On cooling the resonances broaden considerably and at 163 K there is an indication of developing structure but the signal also becomes very weak due to the reduced fraction of muons which end up in the radical The theory for quantitative analysis of these data has not yet been worked out but it is obvious that they bear dynamic information 4 I 2The Plastic Phase of Polycrystalline Norbornene Norbornene is a near-globular molecule and as a typical member of that family it exhibits a plastic solid phase with fast rotations of the molecules It has a hexagonal crystal structure between 129 K and the melting point at 320 K and its reorienta- tional dynamics have been investigated by means of depolarized Rayleigh scattering and NMR spin-lattice measurements No indication of any anisotropy was found and correlation times of the order of 10 s were derived with no discontinuity at the phase transition to the liquid TD-pSR measurements using a single crystal revealed an orientation dependence of the hyper- fine interactions of the ero and the endo Mu adduct radicals and yielded the first evidence of anisotropic motion 25 Large single 000r----=fl 000 -0 01 -0 02 -0 03 Y AM=1 18000 19000 20000 21000 Field (Gauss) Figure 7 Experimental spectrum obtained with frozen benzene at 263 K and simulation of a single crystal spectrum for a cyclohexadienyl radical with coaxial hyperfine interactions of Ago = 519 7 MHz D? = 3 5 MHz for the muon and Ago = 126 5 MHz Dp = 0 9 MHz for the corresponding methylene protonThe angle between the hyperfine axis and the external field IS 80" The inset shows the AM = 2 transition with the field axis expanded by a factor of three and the asymmetry axis by a factor of two Both the muon and the proton are bound to the methylene carbon and thus chemically equivalent It should be noted that equation 8 predicts degeneracy of the three transitions for the case where the corresponding hyperfine couplings scale with the muon-proton ratio of the magnetic momentsThe fact that they are well separated in the experimental spectrum is a direct visualization of the hyperfine isotope effect Observation of such a simple spectrum for simply frozen benzene is striking considering the fact that crystalline benzene has four molecules with different orientations per unit cell and that each molecule has twelve sites (six from each side) available for Mu addition The complexity of the situation has been demonstrated previously for the related case of a naphthalene single crystal which gives orientation-dependent multi-lineTD- pSR spectra 24 In the present case the observed spectrum is compatible with expectation only for the conditions of fast rotation of the radicals in the crystal and with the presence of a single crystal which has the crystallographic b axis parallel to the external field so that all four orientations become equivalent The condition of fast rotation is expected to apply as NMR crystals are difficult to obtain for many materials The potential of ALC-pSR was therefore tested using polycrystalline norbornene Figure 8 displays the AM1 = 1 resonance of the ern Mu adduct Similar lines were observed for the isomer with Mu in the endo position The resonance field is directly proportional to the muon hyperfine coupling and according to equation 8 scales as B = Ago x 36 90 GaussThe mere presence of these lines is proof for anisotropy of the motion on a time scale of (2nDJ At the lower temperatures the shape of the features is clearly asymmetric and agrees with expectation for a powder The fact that the steep flank is on the high-field side of the resonance shows that orientations with effective hyperfine couplings larger than the isotropic value occur more often Since Ako is positive it means that D? is also positive This immediately excludes the possibility that the unique axis of rotation is approximately 173 K I-I 15000 15200 15400 15600 Field (Gauss) Figure 8 ALC-pSR spectra obtained with polycrystalline norbornene in the plastic phase Displayed is the AM1 = 1 resonance corresponding to the Mu adduct in the eyo position of the double bond of norbornene POLARIZED POSITIVE MUONS PROBING FREE RADICALS-E. parallel to the line connecting atoms C and C and thus contradicts the original Analysis of the anisotropy of the AM = 0 resonances (which are not shown here) reveals that this unique axis is most likely roughly parallel to the line c,-c6 as indicated in the structural formula in Figure 8. The width of the powder patterns in Figure 8 is directly related to the muon hyperfine anisotropy.The corresponding para- meter from a fit of the theoretical line shape function agrees quantitatively with the result obtained from the single crystal TD-pSR experiment and this is encouraging in view of future ALC-pSR experiments with powder materials since single crystals of suitable size are often not available. It is of interest to obtain information about the type of motion of the radical or molecule in the crystal. For near-spherical species one might expect small-angle rotational diffusion. Recent theoretical work shows that onset of such a motion leads to broadening of a lAMI = 1 resonance and eventually to its disappearance at high temperatures as a very broad feature. This is not what we observe.The line narrows as temperature increases and the shape is the same as that of a static axial system with reduced effective hyperfine anisotropy. The averag- ing process must be fast on the experimental time scale and the amplitude of the averaging motion must increase with tempera- ture. Some sort of precessional jumps rather than rotational diffusion could explain the observed behaviour. 4.I .3 Probing the Dynamics oj Solid C,o Fullerene C70 is an ellipsoidal molecule which in the solid state could well be expected to form a plastic phase with the molecule reorienting in some way but little IS known about it so far. Molecular dynamics calculations reveal a complicated structural behav- iour associated with the presence of the anisotropy of the molecule. Being one of the materials which is available in high purity only in small amounts and not in single crystals and considering the fact that Mu adds by addition to form radi- cals,26C is an attractive candidate for study of its dynamics by means of ALC-pSR. Such an experiment has been carried out and is currently being analysed. Reorientational disorder of C70 sets in gradually in a manner which is much the same as in norbornene.There must be a fast averaging process such as for example the precessional motion which has been predicted by the moleculer dynamics calculation^.^^ Besides Mu adduct radicals endohedral Mu was also detected with fullerenes and it appeared to relax at the lower tempera- tures much more rapidly in C70 than in c60,26 which was taken as evidence that Mu@C is sensitive to the anisotropy of the cage.This was verified in zero field experiments. Example spectra are displayed in Figure 9. A fraction of the muons relax at close to zero frequency but at 200 K a clear peak is observed =at $0~0.76 MHI as expected for axial anisotropy t 0.0 0.5 1.0 1.5 2 0 2.5 3 0 Frequency (MHz) Figure 9 Fourier transform amplitude in arbitrary units of histograms measured with C in zero external magnetic field at two tempera- turesThe peak at 0 76 MHz is proof for anisotropic Mu RODUNER 343 (see Section 2.4) while the time resolution was not sufficient to detect also the high frequencies.28 Interestingly this peak dls- appears at the phase transition at 270 K which shows that above this temperature the fullerene cages reorient fast enough to make the system appear isotropic. The anisotropy can be described by admixture of ca. 1YOof 2p character to the 1s wave function. The resulting electron density distribution for Mu placed in the centre of C70 is shown in Figure 10.The spherical 1s contribution dominates in the centre but damps away more quickly than the 2p so that a slightly pinched shape is obtained which fits the cage walls very well. The anisotropy may be a consequence of the shape of the C cage or of the pronounced charge distribution which according to semi- empirical calculations leaves a pronounced positive charge at the equator carbon atoms. By locking to the orientation of the cage the Mu atom can monitor the reorientational dynamics of the fullerene. The increase in energy by 2p admixture is compar-able to the zero-point vibrational energy for the three-dimen- sional harmonic oscillator of the endohedral atom in the van der Waals potential of the cage.28 Figure 10 Electron density contour map of Mu@CThe Mu wave function is represented by YMu= 0 9954Y1 + 0 0959iY,pJ The con- tours represent values equal to and lo-' of the electron density at the muon 4.2 Diffusion and Reorientation Dynamics of Radicals on Surfaces Organic free radicals on surfaces can be observed by ESR at low temperatures where their dynamics are frozen. As soon as mobility sets in termination reactions lead to the disappearance of the radicals and the signal is lost. Conditions are more favourable in porous silica and in zeolites where pores and cages hinder translational diffusion. Because of the high sensitivity the pSR techniques can detect radicals at ultra-low concentrations where termination does not play a role. Observation is possible even at elevated tempera- tures which are more relevant to chemistry. Figure 11 shows an ALC-pSR spectrum of the cyclohexadienyl radical observed at 334 K on muon irradiation of a sample of spherical fused silica grains of 7 nm diameter covered with a nominal monolayer of benzene.Three beautiful resonances are detected. They are all of the AM = 0 type and involve the nuclei indicated by the arrows. The isosteric heat of adsorption of benzene on a hydroxylated silica surface amounts to ca. 43 kJ mo1-I and is considerably larger than the heat of vaporization of the liquid (34 kJ mol~ I). Benzene therefore condenses and spreads on the surface and does not form droplets or escape into the vapour phase.The radical is expected to behave the same way and the fact that the resonance positions are shifted slightly to higher fields compared with the liquid supports further the conclusion that the radical is Y-0 04 1 I I I 19000 20000 21000 29000 30000 Field (Gauss) Figure 11 ALC spectrum obtained with a mono layer of benzene on spherical SiO grains (Cab-0-Si1 EH-5) of 7 nm diameter at 334 K Only AM = 0 resonances of the cyclohexadienyl radical are observed and the arrows assign the protons involved adsorbed on the surface This certainly leads to a preferred orientation and it is known that benzene molecules lie flat on hydroxylated surfaces The radical should thus display anisotro- pic behaviour and we expect to find a JAM1= 1 resonance In contrast the resonances are all of ideal Lorentzian shape not much broader than in the bulk liquid and there is not the slightest indication of a lAMl = 1 line (heavy arrow in the figure) The methylene proton signal was measured at twelve tempera- tures from 334 K down to 139 K where it disappears 29The line broadens continuously but its shape remains Lorentzian at all temperatures The IAMI = 1 resonance which is the strongest in solid benzene (Figure 7) is detected as a very weak feature at best Both indicate that the conditions remain isotropic and that we are in the region of motional narrowing By translational diffusion on the surface of the spherical grain the radical samples all orientations and averages the hyperfine Hamiltonian Furth- ermore it is likely that flipping over of the disk-shaped species contributes to the absence of this signalThis motion leaves the Hamiltonian unchanged but in the case of the IAMI = 1 reso-nance changes the sign of the term driving the transition It thus reverses time evolution of muon polarization A quantitative theory based on a stochastic Liouville approach has been developed1s and used for the analysis of the experimental data Preliminary results show that the activation of diffusion and even the coefficient for translational diffusion is similar to that in the liquid at the corresponding temperature Silica is often used as a support for metal catalysts It is therefore attractive to attempt observation of radicals as poten- tial transient intermediates of catalytic processes adsorbed on the surface of real catalystsThis is indeed possible Figure 12 shows the ALC-pSR spectrum obtained with a nominal 5% layer of benzene on the surface of a platinum loaded silica catalyst Because of the low coverage the signal is small and therefore the derivative spectrum is displayed but the three resonances which have been observed with plain silica (Figure 1 I-(AM( ff= AM=O AM=O .,.I,... ... .. 12000 16000 20000 24000 ' '28000 Field (Gauss) Figure 12 Derivative ALC-$3R spectrum observed with a 5% layer of benzene adsorbed on the surface of 2 5% by weight Pt-doped silica at 303 K CHEMICAL SOCIETY REVIEWS 1993 11) are clearly seen In addition there is a small feature at the field where the IAMJ= 1 line is expectedThe resonance positions and thus the isotropic hyperfine interactions are the same as for plain silica at the corresponding temperature even the line widths are close to the same This certainly comes as a surprise It makes clear that even though the radical is highly mobile and must diffuse fast enough to find the metal clusters it is not influenced by their presence The platinum islands are obviously blocked by adsorbed benzene and the radicals avoid these islands or skim over rapidly without taking notice of the metal under the insulating benzene layer 4.3 Organic Radicals in the Gas Phase Radicals consisting of more than three to four atoms are not normally detectable in the gas by conventional magnetic reso- nance techniques since the spectra are complex and the signal is split over too many lines to be observable For the techniques using highly polarized muons the situation is more favourable The ethyl radical has been observed at roughly atmospheric pressures using both theTD-pSR and the ALC-pSR techniques An example for the latter is shown in Figure I3 which gives the two AM = 0 resonances for the ethyl radical in 1 5 bar pure ethylene and with small amounts of oxygen added Due to the spin-rotation interaction the lines have a width of about 500 Gauss in the absence of oxygen This is more than an order of magnitude greater than in the liquid but the resonances are still evidentThe radical reacts with oxygen chemically and by Heisenberg spin exchange and this leads to further broadening Taking advantage of the fact that the two processes have a different effect on the line shape the method provides a tool to measure radical reaction rate constants and contributes to an understanding of gas phase processes which are of relevance in the photochemical degradation of organic pollutants in the atmosphere v r 1 I12000 14000 19000 I 21000 23000 Field (Gauss) Figure 13 ALC pSR spectra obtained with 1 5 bar ethylene at three concentrations of oxygen The two resonances correspond to the selection rule AM = 0 and belong to the a proton (20750 Gauss) and the /3 proton (13750) Gauss) of the muonated ethyl radicdl 5 Comparison with other Magnetic Resonance Techniques Typical values for some of the important parameters which allow a comparison of pSR with ESR and NMR are given in Table 1 It is obvious that the principal advantage of pSR lies in the polarization of the muon beam which is close to unity independent of temperature whereas the other techniques nor- mally have to work with Boltzman populationsThis is import- ant in particular at elevated temperatures and in zero magnetic field Together with the short lifetime of the muon it has the consequence that the muon technique can work with extremely low radical concentrations of the order of twenty or even a single species in the entire sample at any given time Even the lowest concentration of a solute is thus not depleted by chemical POLARIZED POSITIVE MUONS PROBING FREE RADICALS-E Table 1 Comparison of typical parameters in pSR ESR and NMR PSR ESR NMR Polarization at 300 K %lo 10-3 10-5 Minimum number of spins for simple spectrum Frequency resolution 107 O5MHz 5 x 1010 50kHz 1017 0 1 Hz Time resolution 1 ns 20 ns IPS reactions during an experiment and kinetics of bimolecular reactions are always of ideal pseudo-first order Also self termination which imposes the principal limitation on radical concentrations for ESR experiments in solution is absent The muon lifetime of 2 2ps poses a principal limitation on the time scale of the processes to be studied by pSR It is responsible for the low frequency resolution which does not allow resolving chemical shifts and thus discriminating between different dia- magnetic muonated species Only fast processes can be moni- tored but it is of course exactly these which are usually the more difficult ones to study by conventional techniques The limitation on the time resolution in ESR and NMR comes from the necessity to first create spin coherence using a high frequency preparation pulse Muons are injected into the sample already polarizedTime resolution is determined by the rise time of photomultipliers and in particular by the size of scintillation counters as the length of the light paths from muons triggering the counter in different places varies and the distance travelled in one nanosecond is of the order of 20 cm in these materials In NMR and more and more frequently also in ESR one takes advantage of elaborate pulse sequences Pulsed techniques have been applied and are still being investigated for pSR but the muon lifetime again imposes a major limitationThe muon magnetic moment is only three times that of a proton so that it takes a significant fraction of the muon lifetime to tip it by 90° even when high RF powers are appliedThe technique may develop an advantage on pulsed muon beams and for special applications but up to the present it has shown no indication of becoming routine The vast majority of magnetic resonance work is based on high field conditions where eigenstates are pure Zeeman product states Inspection of the Figures 6 and 7gives the impression that avoided crossing effects are very common and that one might generally have to pay more attention to cross relaxation effects in conventional magnetic resonance of radicalsThis impression needs relativation First it is noteworthy that in high fields the electron spin a and the p manifolds are well separated in energy and that they therefore do not cross For this reason there can be direct additional contributions only to nuclear but not to electron relaxation For a discussion Table 2 gives coupling constants for a number of common nuclei which give rise to avoided crossings near a field of 3300 Gauss as is often used in ESR or in ENDOR Second in low viscosity liquid solution one has isotropic conditions and only avoided crossings which obey the selection rule AM = 0 We see from equation 8 that one needs nuclei with different magnetogyric ratios to produce such a transitionThe most common organic radicals contain only protons as magne-tic nuclei so that the effect will not be encountered For different nuclei (one of them is assumed to be H here) the mixing rate between the two states induces a maximum nuclear relaxation at the crossing of T = TA~,A~,/B,~,A relatively large effect is obtained for X = F for which T becomes ca 1 ps The situation is of much more concern in the case of static anisotropy or of slow reorientational dynamics The mixing rate at the maximum 1sorientation dependent and for a nucleus X it is in the absence of dynamics given byT; = 3~Dfsin 8 cos 8 For an anisotropy of 10 MHz one thus achieves relaxation times RODUNER 345 Table 2 Interference of avoided level crossings in an ESR experiment at 3300 Gauss X H 28 1 - D 43 23 8 3c 71 21 0 14N 20 26 1 19F 26 4 17 31P I1 4 16 7 79Br 70 21 I of the order of 10 ns While this value relates directly to the two levels which are near-degenerate and thus to the ENDOR line at close to zero frequency which is not usually our focus it is likely that in the complex relaxation scheme governing the ENDOR effect the high frequency line is also affected Furthermore a recent study of the effect of dynamics shows that the onset of reorientational motion leads to an extreme broadening of the AM= 1 resonance while their amplitude is only moderately affected For reorientational correlation times of the order of (3nDJ one finds a nearly flat background relaxation and it is only when motion becomes much faster that relaxation loses its importance * The enormous sensitivity of the pSR technique may be demonstrated by the following fictitious example Suppose we are irradiating a sample with lo5 muons per second as in a typical time resolved experiment and suppose we started to do this 1O1O years ago just after the Big Bang and that we have never ceased to do so Let us assume further that the muons have a lifetime as long as the protons and that they are thus still in the sampleToday we would have accumulated some 3 x muons which is one-twentieth of a mole or 5 5 mgThis is just to demonstrate that we have not reported on a new method for organic synthesis! Acknowledgements Support from the Swiss National Founda- tion for Scientific Research and by the Paul Scherrer Institute in Villigen is gratefully acknowledged I am particularly indebted to my numerous co-workers and collaborators for their dedi- cation and their practical and conceptual work The present work would have been impossible without their contributions 6 References 1 S F J Cox J Phys C SoIidStute Phys 1987,20 3187 2 D C Walker J Php Chem 1981,85 3960 3 D C Walker ‘Muon and Muonium Chemistry’ Cambridge University Press 1983 4 E Roduner ‘The Positive Muon as a Probe in Free Radical Chemistry Potential and Limitations of the pSRTechniques’ Lecture Notes in Chemistry Vol 49 Springer Heidelberg 1988 5 T G Eck L L Foldy and H Wieder Phqs Rev Left ,1973,6,239 6 R F Haglund Chem Rev 1988,88,697 7 S Clough A J Horsewill M R Johnson M A Mohammed T Newton Chem Phyy 1991 152 343 8 C A Hamilton K A McLauchlan and K R Peterson Chem Phis Lett 1989 162 145 9 Chem Phqs ,special issue 1991 152 229 337 10 A Carrington and A D McLachlan ‘Introduction to Magnetic Resonance’ Harper New York 1967 11 E Roduner R Crockett and L M Wu J Chem Soc FuruduyTrans 1993,89 2101 12 E Roduner and H Fisher Chem Phvs 198 1,54 26 1 13 N M Atherton ‘Electron Spin Resonance’ Wiley New York 1973 14 M Heming E Roduner B D Patterson W Odermatt J W Schneider H Baumeler H Keller and I M Savic Chem Phks Lett 1986 128 100 15 R F Kiefl Hyperfine Int 1986,32,707 16 E Roduner 1 D Reid M Ricco and R De Renzi Ber Bunwnges Phvs Chem 1989,93 1194 CHEMICAL SOCIETY REVIEWS 1993 17 M Heming E Roduner I D Reid P W F Louwrier J W 25 M Ricco R De Renzi and E Roduner Phys Lett A 1988 129 Schneider H Keller W Odermatt B D Patterson H Simmler B 390 Pumpin and I M Savic Chem Phys 1989,129 335 26 Ch Niedermayer I D Reid E Roduner E J Ansaldo C 18 S R Kreitzman and E Roduner Chem Phys ,to be submitted Bernhard U Binninger J I Budnik H Gluckler E Recknagel 19 E Roduner Chimia 1989,43,86 and A Weidinger Phys Rev B 1993,47 10923 20 R L Garwin L M Ledermann and M Weinrich Phys Rev 1957 27 T J S Dennis K Prassides E Roduner G Cristofolini and R De 105 1415 Renzi J Phys Chem 1993 97 in press 21 E Roduner and I D Reid Isruel J Chem 1989,29,3 28 K Prassides T J S Dennis C Christides E Roduner H W 22 C J Rhodes E Roduner I D Reid and T Azuma J Chem Soc Kroto R Taylor and D R M Walton J Phys Chem 1992 96 Chem Commun 199 1,208 10600 23 U Haeberlen and G Maier Z Naturforsch A 1967,22 1236 29 I D Reid T Azuma and E Roduner Nature 1990,345 328 24 I D Reid and E Roduner Structural Chemistry 1991 2,4 19

ISSN:0306-0012    

DOI:10.1039/CS9932200337

出版商:RSC    

年代:1993

数据来源: RSC