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Study of the bonding in pentacarbonylmanganese derivatives by photoelectron spectroscopy

 

作者: S. Evans,  

 

期刊: Discussions of the Faraday Society  (RSC Available online 1969)
卷期: Volume 47, issue 1  

页码: 112-120

 

ISSN:0366-9033

 

年代: 1969

 

DOI:10.1039/DF9694700112

 

出版商: RSC

 

数据来源: RSC

 

摘要:

Study of the Bonding in Pentacarbonylmanganese Derivativesby Photoelectron SpectroscopyBY S . EVANS, J. C. GREEN, M. L. H. GREEN, A. F. ORCHARD AND D. W. TURNERInorg. Chem. Lab., and Phys. Chem. Lab., South Parks Rd., OxfordReceived 13th February, 1969The photoelectron spectra excited by helium 21.2 eV radiation in the complexes Mn(CO)5X,where X = H, C1, Br, I, CH3, CF3, COCF3 and Mn(C0)5, have been determined. The ionizationpotential data are discussed in terms of a simple molecular orbital description of the electronicstructures.The value of photoelectron (PE) spectroscopy as an electronic structural tool inorganometallic chemistry is virtually unknown. We have studied the PE spectraof a series of compounds Mn(CO),X, where X = H, C1, Br, I, CH3, CF3, COCF,and Mn(CO),, in order to explore the utility of this new technique for molecules ofconsiderable electronic complexity.EXPERIMENTALThe photoelectron spectrometer has been described.l The vapour of the compoundunder investigation was fed continuously into the ionization chamber at a pressure below2 0 0 ~ .Except for the hydride, Mn(CO)SH, the most volatile of the complexes studied, itwas necessary to place the sample as close as possible to the ionization chamber so as toallow free flow of its low pressure vapour. The spectra were calibrated by introducingxenon into the ionization chamber at the same time, as previously described.'12The compounds Mn(CO)5X were prepared and purified essentially by previousIy reportedand their purity ascertained from infra-red and mass spectra.8'12RESULTSThe photoelectron spectra are given in fig.1 and the ionization potential(1P)data are recorded in table 1. The accuracy of the LP data varies, but for the mostpart, the figures quoted in table 1 are correct within at least 0.25 eV (the maxima forrelatively sharp PE bands may be defined more accurately). In each of the PE spectrawe may distinguish three main regions of ionization, labelled A , B and C in table 1.The PE bands in region A have the relative intensities given in square brackets. Theseare rough estimates, and may be in error by as much as 10 %.Some of the spectra show a PE band centred at 12.6 eV due to the presence ofwater as a trace impurity. The spectrum of the chloride, Mn(CO),Cl, also containsa sharp band at 14.0 eV.This we attribute to trace amounts of carbon monoxide l3(see table 2), presumably arising from in situ decomposition of the sample. Boththe chloride and its bromine analogue are relatively involatile, so that small amountsof volatile impurities are readily detectable. There is apparently such tracecontamination in the spectra of each of these compounds.11TBLE IO IONIZATION POTENTIAL DATA a FOR THE Mn(C0)5XH C1 Br I CF 3 COCF38-80[2-0] 8.76[2*0] 8*35[2.5Ic8.6510.43 [2*0] 10*04[2*0] 9.57[2*0] 9.20[3] 9.011*00[1*0] 10-80[1.0] 10-37[1-0] 10.30[1](1 3-5-1 6.9) (14.0-1 7.0) (1 3.8-17.4) (1 3.7-17.6) (1 3517.6) (1 2-2-17.6)14.1 14.0 13.3 &[ 13*80 14.6 15.2 15.4 15.0 14.5 14.5C 17.97 18.7 18.6 18.6 18.5 18.514.4 14.315.6 15-4 15.016-419.9a Gross regions of ionization are in parentheses : otherwise the figures relate to PE band maxima.For the iodide, brackets. b The assignment, in terms of the m.0.ionized, does not refer to Mn2(CO)lo.This value gives the sum of the relative band areas for the two IP centred at 8.35 and 8.65 eV. d No114 PHOTOELECTRON SPECTRA OF Mn(CO)SXI =' IL . . . . . . . . . . . . . I21 20 19 10 I7 6 6 14 1) 12 I1 10 9 8Fig. 1 (a-d).I20 13 I6 I7 16 15 14 13 11 I 1 10 9 8I m' I11 20 I9 I0 17 I6 15 I 4 13 I2 I 1 I0 9 S 7Fi.2. 1 (e-h).FIG. 1 .-The photoelectron spectra of (a) Mn(CO)gH, (b) Mn(CO)5C1, (c) Mn(CO)sBr, ( d ) Mn(C0)5'1,( e ) Mn(CO)5CF3, cf) Mn(CO)SCOCF3, (9) Mn(CO)&H3, (A), Mn2(CO)I o.Horizontal scale givenin electron-volts (eV); the derived ionization potential data are given in table 1 .DISCUSSIONASSIGNMENT PROBLEMWe seek to explain the ionization potential (IP) data in terms of Koopman'sappro~imation,'~ according to which the individual vertical IP of closed-shellmolecules may be identified with the SCF energy eigenvalues of the occupied molecularorbitals (m.0.) from which the electrons are ejected. The molecular IP from whose rela-tion ships are strictly those of ionic energy levels, then receive a simple interpretationas one-electron orbital energies. The Koopmans approximation, however, sufferscertain deficiencies : in particular, errors arise from orbital rescaling, correlation andrelativistic effects.15 A substantial cancellation of the different errors does in facEVANS, GREEN, GREEN, ORCHARD AND TURNER 115occur, and is such that a Koopmans ab initio SCF estimate of a molecular IP isusually too large, e.g., see ref.(15), but not in a uniform and predictable fashion.Thus, if we use molecular IP empirically to diagnose the relative energies of theoptimum one-electron orbitals, we may not obtain the correct ordering of the SCFeigenvalues, see ref. (1 6). Nevertheless, an empirically established m.0. energylevel scheme, based on Koopmans' approximation, will have considerable allegoricalvalue : moreover, it should relate to semi-empirical m.0. theories which make realisticuse of atomic (or molecular) spectral and IP data.The empirical analysis of 1P data hinges upon the assignment question.Tofacilitate assignment we shall use group theory to establish the symmetry-dependentfeatures of the m.0. diagram tie., to construct the symmetry orbitals correspondingto a realistic choice of valence orbitals). We shall also invoke gross electronegativityarguments to limit further the possible form of the m.0. energy level scheme. Also,there js available a number of criteria for assignment of ionization bands, in thelight of conceivable m.0. schemes. In particular, we employ the following criteriarelating to orbital degeneracies. (1) The area under PE band, which reflects theionization cross-section of the occupied orbital concerned, should be simply relatedto orbital degeneracy.l3. l 8 The cross-sections should be similar for orbitals ofcomparable localization properties and energy.(2) Spin-orbit interactions mayresult in multiplet splitting of the ion term which, if resolved, will indicate the spatialdegeneracy of the ionized level. '-l If the effective spin-orbit coupling variessubstantially with position in the molecule the magnitude of the multiplet splittingmay indicate the localization tendencies of the ionized m.0. concerned : it may alsoenable one to distinguish between ionic terms having the same degeneracy butdifferent symmetries .Circumstantial evidence derived from the study of a series of related compounds,and related model systems, may also assist assignment. In addition, the analysis ofvibrational 3* (or vibronic) fine structure, relative IP band widths or the correlationwith electronic spectra, may often prove helpful.However, criteria concerning thelatter are of limited utility for the PE spectra of the Mn(CO),X speciesinvestigated here.Mn(CO),X PE SPECTRATABLE 2.-A GENERAL COMPARISON OF THE PHOTOELECTRON DATA * FOR CARBON MONOXIDE,Mn2(CO)lo AND Cr(CO),MndCO) 10 cr(c0) 6c CobA (7.9-9-3) 8.4 14.0 50B (12.8-16'4) (12.6-16.3) 16.9 17~C (17.3-18-5) (17.2-18.2) 19.7 40Unless in parentheses the data relates to ionization peaks.b We include the generally accepted one-electron assignment of the carbon monoxide IP.zoC The Cr(C0)6 PE spectrum shows vertical IP at 13.3, 14.1 and 17.5 eV.l8From the IP data in table 2, the PE spectra of Mn,(CO)lo and Cr(CO)6,18 eachshowing three main regions of ionization, have a strong resemblance. Unless thereis an inconceivably high effective charge on the metal atoms, the correspondencewith the PE spectrum of carbon monoxide l3 must be that indicated in this table.We assign the central region B in the Mn2(CO)lo and Cr(C0)6 spectra to ionizationsfrom m.0.of mainly carbonyl 50 and In character: the high energy region C weassociate with m.0. largely localized as the 40 112.0. of carbon monoxide. Weattribute the remaining structure (region A ) to ionization from m.0. of predominantlymetal 3d a.0. character. These general conclusions are reinforced by an extendedHiickel calculation on Cr(CO)6.2116 PHOTOELECTRON SPECTRA OF Mn(CO),XThe essential features of PE spectra of the Mn(CO),X compounds are alsoanalogous to those of Cr(C0)6.It therefore seems reasonable to suggest similar+ 3xe I EMnFIG. 2(a).-Av qualitative molecularorbital scheme for the Mn(C0); cationswith its 46 valence electrons. Thisbelongs to the C4" point group, and thecoordinate system is chosen centred atthe metal atom such that there are fourCO groups on the x and y axes and oneon the z axis (cf. table 3). The occupiedlevels are ringed, and orbitals of un-certain relative energy are bracketed.The Mn(C0); anion presumably has itstwo additional electrons in the 6alorbital.FIG. 2(b).-A qualitative view of the main features of the molecular orbital structures of Mn(C0)5Hand the halides, Mn(CO)5X, and their relationship with the Mn(C0); ion (cf.fig. ah))EVANS, GREEN, GREEN, ORCHARD AND TURNER 117assignments (see table 1). To be more explicit we refer our discussion to the m.0.diagrams, fig. 2(a) and fig. 2(b), for the Mn(C0)5 fragment, and the Mn(CO),Xspecies with monatomic X, respectively. Each molecule has C4" symmetry. WeTABLE 3The transformation properties and correlation of the metal valence orbitals in M(C0)6(Oh point group), square-pyramidal M(CO), (CaU) and M2(C0)10 with staggered (Dad)or with eclipsed (D4h) configurationametal a.o oh c4v D4d D4hdz2 eg" a1 a1+b2 a1g+a2udx2 - y 2 4 61 e; + eg bl,+bdUdXY 6 s b2 eg + e; b2,+blU4, t 4 g ea ed; + e: e,b+ e:4 2 t:9 eb ef + eg e:+ e,PS a19 a1 Q+b2 a 1 g - t a2uPz a1 a1 + b2 el g + a2uPxPYa The usual ccnventions are observed.Z2choose a valence orbital basis set restricted to metal 3 4 4s and 4p (transformationproperties given in table 3), together with the 4a, 5 0 , ln and 2n m.0.of carbonmonoxide. For halogen we employ valence-shell p (transforming as e+a,) ands ( a , ) a.o., and for hydrogen just the 1s (a,) a.0. Five carbonyl orbitals of csymmetry transform as 2a, + b , + e in the C,, point group : on the other hand, thecarbonyl n orbitals generate symmetry orbitals a , + a2 + bl + b2 + 3e. The detailedstructures of the m.0. diagrams reflect our conclusions, but are also based onqualitative arguments invoking overlap criteria, etc. In fig. 2(a), for example, the 6em.0. i s placed above 2b, on the grounds that the metal dyz and dzx orbitals interact lessstrongly with the carbonyl n* orbitals than does the dxy orbital.Those levels whichwe believe are of uncertain relative energy are bracketed in the diagrams.Certain details of the B and C regions of the PE spectra require special comment.Except for the methyl and perfluoroacetyl compounds, the Mn(CO),X spectraeach show a sharp edge at about 13 eV (see table 1). On overlap grounds this isprobably the adiabatic ionization from the 5e, m.0. mainly localized as carbonyl50. We also observe, for X = CH3, CF3 and COCF3, more structure in region Bthan appears in the other PE spectra. In particular, the methyl compound gives abroad band centred at about 12.6 eV which, by comparison with the methyl halidePE spectra,18 we assign to ionization of electrons essentially localized in the CH3a-orbitals.Similarly, we refer to the PE spectra of simple perfluoromethylderivatives,18 such as CHF3, and attribute the additional structure in region B ofMn(CO),CF3 to photo-ionization from orbitals that are largely fluorine 2p incharacter. The perfluoroacetyl compound, Mn(CO),COCF,, also exhibits additionalstructure in the region C of its PE spectrum : this may be associated either with theacyl CO group or with CF, itself.I8Apart from these observations, it appears that the general appearance and positionof the B and C regions of the PE spectra are relatively insensitive to the nature ofthe group X. In contrast, region A is markedly dependent on the nature of X, andis sufficiently resolved to permit the application of more detailed assignment criteria118 PHOTOELECTRON SPECTRA OF Mn(CO),XThe hydride, and also the methyl and perfluoro-methyl compounds, show twoPE bands in region A.The relative intensities of these bands are close to 2 : 1 inMn(CO),H, and about 3 : 1 in Mn(CO),CF3 : in the methyl compound, the intensityratio is inverted but approximately 1 : 2. Invoking our intensity criterion, (1)above, we therefore assign these two LP to the mainly metal e(dx,,dy,) and b2(dxy) m.o.,as shown in table 1. The hydride case is illustrated in fig. 2(b). The acyl compound,Mn(CO),COCF,, also apparently has two IP in region A , but these are incompletelyresolved. We presume they have the same origin as the IP of Mn(CO),H, etc.,assigned previously.The PE spectra of the chloride and bromide exhibit three low-energy bands,while Mn(CO),I has four bands. We assume that the first two bands of the lattercompound are the components, split under spin-orbit interactions, of a band whichcorresponds to the first band in the PE spectrum of either Mn(CO),Br or Mn(CO),CI.Now the only terms of the Mn(CO),X+ ion which are subject to multiplet splittingare the 2E species : and these should split symmetrically into states of equal degeneracy(the doublets E' and E"), which conforms with our observations.Moreover, sincespin-orbit effects must be much greater in the region of the iodine nucleus thanelsewhere in the molecule, we may also infer that the first IP of the halides relatesto ionization from an m.0.of largely halogen character. The observed doubletsplitting in Mn(CO),I is about 0.3 eV: if the orbital concerned were completelylocalized on the iodine atom, we would expect a splitting of some 0.6 eV (as calculatedfrom the free iodine spin-orbit coupling constant csp = 5070 ~ m - l ) ~ ~ , whereas for apure manganese 3d a.0. we expect a mere 0.03 eV (cJd = 240 cm-' for the Mn atom).The spin-orbit coupling constants being much smaller for chlorine and bromine (c3p = 590cm-', c4p = 2460cm-'), it is not surprising that we observe doubletsplitting only in the Mn(CO),I case. Thus, we assign the first IP in each of thehalide PE spectra to a 7e level, as shown in fig. 2(b). By analogy with the hydride,the remaining PE bands in region A, with relative intensities close to 2 : 1, are assignedto the 6e and 2b2 levels.Having assigned the essential features of the Mn(CO),X PE spectra, furtherdiscussion is warranted.With regard to the m.0. diagrams, fig. 2(u) and 2(b)on the acquisition of additional electron density in Mn(CO),X the energy levels of theparent Mn(C0): fragment will become more positive: and, since X interacts onlyindirectly with the CO groups, we expect the largely metal levels 2b2, fie, etc. torise further than those more localized on carbonyl. It is thus reasonable that theselatter m.0. are reiatively insensitive to the nature of X, as indicated by the PE spectra.In view of the relative Mulliken electronegativities of the monatomic X, weexpect the self-consistent charges on the manganese atom to diminish in the orderCl>Br>I>H. Therefore, the average of the 2b2 and 6e IP should be least inthe hydrides, and increase in the same sense.This is in accord with our observations.Also (table 1) the 6e-2b2 energy separation is less in the halides than in Mn(CO),H :for the mixing of halogen p , a.0. and the largely metal 6e level of Mn(C0)f mustreduce relatively the energy of the 6e m.0. of Mn(CO),X.The halide PE spectra also provide some evidence for metal-halogen d,-p,bonding on the bask of the following arguments. The inferred 7e (mainly halogenpn) m.0. energies, whilst in the expected order CI<Br<I, are distinctly higher andless differentiated than the energies of essentially halogen p n orbitals in simple halides :in the methyl halides, e.g., the relevant vertical IP are CH3Cl 11.30 eV, CH,Br10.54 eV and CH31 9.55 eV.18 The noticeably lower first IP of each of the Mn(CO),halides (table 1) may in general be associated with a higher electron density on halogen,but in particular with a substantial mixing of the halogen p x and the metal dxz,dyEVANS, GREEN, GREEN, ORCHARD AND TURNER 119(e) a.o., which leads to a relative lowering of the 6e level and a raising of the 7e levelas shown in fig.2(b). This metal-halogen n-interaction is greatest in the chloride,so that more uniform values of the Mn(CO)5X first IP (from 7e) are observed. Ourinterpretation is also consistent with the trend observed in the 6e-2b2 energy separation(table I), since the stabilization of the 6e level should diminish in the sense C1> Br > I.As a final comment on the Mn(CO), halides, we recall our earlier observationthat the PE spectra are consistent with the electron density on the metal decreasingin the order I>Br>Cl.This correlates with the relative thermal stabilities of thehalides. The non-existence of metal carbonyl fluorides presumably relates to theexcessively high positive charge that would appear on the metal atoms, leading tosubstantial weakening of the metal-carbonyl bond.In terms of our assignment, the methyl compound Mn(CO),CH, is distinguishedfrom its hydride and halide analogues in that the predominantly metal b2 m.0. isof higher energy than the similarly localized e m.0. Also, with the single exceptionof the carbonyl Mn,(CO),, itself, the average IP in region A of the Mn(CO),X PEspectrum is the least of the series Mn(CO),X: this reflects the strong a-donatingpower of the CH3 group compared with that of H and halogen.The markedstabilization of the 6e level relative to 2b2 may in turn be understood in terms ofthe differing interactions of the metal dxz,dyz a.0. and the dxy a.0. with the available x*acceptor orbitals, together with effects due to the mixing of the metal p x , p c andd,,, dyz a.0. The strong a-donor property of the CH3 group should markedlyreduce the electro-negativities of all the metal valence a.0. leading, in particular, toincreased mixing of the 4p and n' orbitals (both a , and e). This effect should lowerthe 6e and 6a, levels relative to 2b2.Thus, even if the direct interaction of the metal4px and 3dx a.0. is not particularly strong in Mn(CO)Q13, a substantial 4px-x*mixing rray be responsible for the reversal of the relative energies of the 6e and 2bzlevels. But the CH3 group also possesses vacant acceptor orbitals which, in termsof a local CfV microsymmetry, are of a , and e symmetry. The latter CH3 orbitalhas n-symmetry with respect to the Mn-C bond, and may mix strongly with metaldxz,drz. Thus, the pronounced stabilization of the mainly metal 6e level may bedue also to back-donation of metal electron density into the n* orbitals of the methylgroup.Turning to the IP data for perfluoro-methyl compound, Mn(CO),CF,, it appearsthat the CF3 group is roughly comparable to iodide in its a-donor strength.ThePE spectrum of Mn(C0),COCF3 suggests, on the other hand, that the perff uoro-acetylgroup is intermediate in behaviour to the CH3 and CF3 groups, both with respect toa-donor and also n-acceptor properties. These conclusions are reasonable on simpleelec tr onegat ivit y grounds.Mn2(CO),o PE SPECTRUMThe average IP in region A of the Mn2(CO)10PE spectrum is lower than thecorresponding average IP for any of the other Mn(CO)SX molecules studied here.This is as expected, since the effective charge on the manganese atom should be leastwhen X = Mn(CO)5. Also, the PE spectrum of Mn,(CO),, in region A differsfrom that of Mn(CO),H in apparently having a third band. This is only partlyresolved from the adjacent PE band so that its relative intensity is difficult to gauge :but the overall intensity ratios in region A are not far from 4 : 2 : 1 (ignoring theshoulder, the intensity ratio would be about 4 : 2.9).A tentative explanation ispossible in the following terms.The molecule Mn2(CO)lo is and therefore of Dqd symmetry, in thesolid phase. The mainly metal 36 m.0. of the Mn(CO), monomer species the120 PHOTOELECTRON SPECTRA OF Mn(CO),Xcorrelate in the manner indicated in table 3. A possible ground electronic configura-tion for the dimer is thus . . . (5e2)4(6e1)4(6e,)4(6a,)2, where the order 6e3>6e,seems probable on overlap grounds, but where the energy of 5e2 relative to the othere-levels is uncertain. Four low energy LP with relative intensities 2 : 2 : 2 : 1, wouldthen be expected.Therefore we assign the shoulder in region A of the Mn,(CO)loPE spectrum to the 6a, level, and the peaks to the three filled e levels : the two lowerlevels are assumed to lie too close in energy to be resolved.We cannot be sure that Mn2(CO)lo is indeed staggered in the vapour phasethough, on simple steric grounds for example, it seems a more probable configurationthan the eclipsed one of D4h symmetry. In the latter case we expect (cf. table 3)a ground electronic configuration such as . . . (2b2,)2((zb,,)2(6e,)4(6e,)4(a,,)2, whenthere should be five low-energy IP with relative intensities 1 : 1 : 2 : 2 : 1. Arationalization of the Mn2(CO)lo PE data for region A would therefore involve theassumption that rather more m.0.were close in energy. This cannot be excludedas a possibility, but it seems less likely than an assignment based on the assumptionof a staggered geometry for Mn2(CO),o.We gratefully acknowledge Clive Baker's advice and assistance with the measure-ment of the photoelectron spectra. Also we thank Turner and Newall, Ltd., fora fellowship (to J. C. G.).Note added in proof; We have re-examined pentacarbonyl-manganese chlorideand have succeeded in obtaining a photo-electron spectrum free of the impuritybands in the low ionization energy region (region A) that were probably due to forma-tion of the dimer [Mn(CO),CI],. The revised figures for the first three photoelectronband maxima are 8*83, 10.46 and 11.08 eV.D. W.Turner, Proc. Roy. Soc. A , 1968, 307, 15.D. W. Turner and D. P. May, J. Chem. Phys., 1966,45,471.R. B. King, J. C. Stokes and T. F. Korenowski, J. Organometal. Chem., 1968, 11,641.W. Hieber and G. Wagner, Z. Naturforsch., 1958, 136,339.W. Hieber and G . Wagner, Annalen, 1958,24,618.W. Beck, W. Hieber and H. Tengler, Chem. Ber., 1961,94, 862.E. W. Abel and G. Wilkinson, J. Chem. SOC., 1959,2,1501.M. I. Bruce, Adv. Organometal. Chem., 1968, 283.G. A. Junk, H. J. Svec and R. J. Angelici, J. Amer. Chem. Soc., 1968,90,5758.lo J. C. Hileman, D. K. Huggins and H. D. Kaesz, Znorg. Chem., 1962, 1,933.l1 E. 0. Brimm, M. A. Lynch and W. J. Sesney, J. Amer. Chem. Soc., 1954,76,3831.l2 D. J. Parker and M. H. B. Stiddard, J. Chem. SOC. A , 1966, 1,695.l 3 D. W. Turner in Physical Methods in Advanced Inorganic Chemistry, ed. H. A. 0. Hill andl4 T. Koopmans, Phybica, 1933, 1, 104.l5 R. E. Watson, Tech. Report no. 12 Solid State and Molecular Theory Group, (Massachusettsl6 P. E. Cade, K. D. Sales and A. C. Wahl, J. Chem. Phys., 1966,44,1973.l7 D. C. Frost, C. A. McDowell and D. A. Vroom, J. Chem. Phys., 1967,46,4255.l8 D. W. Turner, A. D. Baker, C. Baker and C. R. Brundle, Molecular Photoelectron Spectroscopy,l9 H. J. Lempka, T. R. Passmore and W. C. Price, Proc. Roy. Soc. A , 1968,304,53.2o G. Herzberg, Spectra of Diatomic Molecules, (Van Nostrand, New York, 1950) and B. J.21 K. G. Caulton and R. F. Fenske, Znorg. Chem., 1968, 7, 1273.22 J. S. Griffith, The Theory of Transition MetaZ Ions, (Cambridge University Press, 1961), andF. A. Cotton, Chemical Applications of Group Theory, (Interscience, New York, 1963).23 C. K. Jargensen, Orbitals in Atoms and Molecules (Academic Press, London, 1962), chap. 10,and T. M. Dunn, Trans. Faraday Soc., 1961, 57, 1441.24 L. F. Dahl and R. E. Rundle, Acta Cryst., 1963, 16,419.P. Day, (Interscience, London, 1965).Institute of Technology, Cambridge, Massachusetts, 1959).Wiley, 1969 (in press).Ransil, Rev. Mod. Phys., 1960, 32,245

 



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