Electron Spin Resonance Studies of the Triplet State By Colin Thomson DEPARTMENT OF CHEMISTRY UNIVERSITY OF ST ANDREWS ST ANDREWS FIFE SCOTLAND 1 Introduction Electron spin resonance (e.s.r.) spectroscopy has proved to be of immense value to the Chemist in the study of the electronic structure and properties of transition- metal ions1 and free radicalsY2 and one might expect this technique also to be of use in the study of the ground or excited triplet states of molecules. Owing however to experimental difficulties it was 1958 before Hutchison and Mangum3 first detected the naphthalene triplet state by e.s.r. but since that time it has become apparent that e.s.r. can yield very detailed information concerning the electronic structure of the triplet state information which supplements that obtained by conventional spectroscopic techniques.The experimental study of photoexcited triplet states by optical means has been thoroughly reviewed and the present Review is concerned with the study of organic triplet states by e.s.r. Of more recent origin is the study of molecules with a triplet ground state. Such states have considerable importance in organic chemistry and e.s.r. is a valuable tool in their study. The electronic spin interactions within the triplet state are examples of 'weak interaction^'^ and their measurement and theoretical calculation constitute sensitive tests of approximate molecular wave functions. 2 The Phosphorescence of Aromatic Molecules Many aromatic molecules dissolved in rigid glassy solvents at low temperatures exhibit phosphorescence upon irradiation with ultraviolet light.* The lifetime T~ varies from a few milliseconds to ca.30 sec. and this phenomenon was attributed by Lewis and Kasha6 to the radiative decay from the lowest excited triplet state of the molecule (7') to the ground state So. The triplet state is popu- lated via a radiationless transition from the lowest excited singlet state S, into which the molecule reverts following the initial excitation. The situation is sum- marised in Figure 1. The triplet state is paramagnetic as Lewis Calvin and Kasha showed by susceptibility measurements,' and should therefore be detectable by e.s.r. After considerable effort Hutchison and Mangum3 succeeded in observing the naphtha- A. Carrington and H. C. Longuet-Higgins Quart. Rev. 1960 14 427. C . A. Hutchison jun. and B.W. Mangum J . Chem. Phys. 1958,29,952; 1961,34,908. S . K. Lower and M. A. El-Sayed Chem. Rev. 1966 66 199. M. Karplus Rev. Mod. Phys. 1960 32,455. G. N. Lewis and M. Kasha J. Amer. Chem. SOC. 1944,66,2100. a A. Carrington Quart. Rev. 1963,17 67; J. R. Morton Chem. Rev. 1964,64.453. ' G. N. Lewis M. Calvin and M. Kasha J. Chem. Phys 1949,17 804. 45 Electron Shin Resonance Studies of the Triplet State ’s ‘S \ I I i l l 3 r 7; 3 0 Figure 1 Excitation and decay of aromatic triplet states. Dashed lines denote non-radiative processes. Transitions denoted kr and kp are the radiative fluorescence and phosphorescence transitions with typical lifetimes of ca. sec. and several seconds respectively lene triplet in 1958. The interpretation of the e.s.r. observations necessitates an understanding of the quantum mechanical description of the magnetic interac- tions between the two unpaired electrons and an external magnetic field to which we now turn.3 Quantum Mechanical Descriptfon of the Triplet State The triplet-state wave function and energy levels are the eigenfunctions and eigenvalues of the total molecular Hamiltonian operator Jf which can be written as a sum of a spin-independent part So and a spin-dependent part Sg. The usual electronic problem of quantum chemistry is that of finding those wave functions #k,g,m which are simultaneously eigenfunctions of So and of the total spin operator s2 and its component 3,. z=z,+z (1) For a triplet state S = S + S = 1 and m can take the values -l,O,l. In phenomena involving the interaction of the electron and nuclear spins with external electromagnetic fields Sa has to be included with the results that the eigenfunctions +k,g,m are no longer eigenfunctions of S.3 causes mixing be- tween singlets and triplet states and lifts the triplet spin degeneracy and the eigenvalues and eigenfunctions must be found by diagonalisation of the matrix of 2 using the #k,s,m as basis functions. Ss is a sum of two parts the spin-orbit interaction Sa0 and the dipolar spin- spin interaction Zag. These interactions have the explicit form8 H. F. Hameka ‘Advanced Quantum Chemistry’ Addison-Wesley New York 1965. 46 Thomson 2 yeso = c (si. A ~ ) i where (3) and 1 3 In these equations the summation is over all the electrons Hi and Fi are the magnetic and electric field strengths at the position of electron i due both to external fields and to the nuclei and the other symbols have their usual meaning.Since SS 2Po the effect of Zg on the zeroth-order eigenfunctions and energies t,bk,s,m and Ek can be found by perturbation theory if the zeroth order functions $k,s,m are known. In the triplet state the eigenfunctions of So 3$k,s,m can be written as products of a spatial part and the appropriate spin function. The spin functions for a single electron are a and /3 and are eigenfunctions of s with eigenvalues m of +&h and - 8h respectively and of g2 with eigenvalue S(S + 1)h2 - $a2. In the case of two unpaired electrons coupled to give S = 1 the appropriate spin functions are where we have written the value of 2s + 1 as superscript and the m value as subscript. The usual Dirac notation for these states is given on the right-hand side.The three triplet functions with a common spatial part combined with the above spin functions are degenerate in the absence of Zs and correspond to pure spin states. Since the Pauli principle states that the total wave function must be antisymmetric the above symmetric spin functions must be multiplied by an antisymmetric spatial part. The perturbation 2Pso causes a mixing between singlet and triplet states and therefore a relaxation of the selection rules for T -+ So and S1 -+ T transitions.* X, on the other hand doesnot mix singlets and triplets but both Zso a n d x lift the degeneracy of the triplet state. From the point of view of e.s.r. Sss is the most important perturbation* and we henceforth discuss this term alone referring to the small effects of Sso in Section 15C.Although singlets and triplets are mixed by S it is meaningful to describe the states as predominantly singlet or triplet. *This is true for organic triplet states but in other systems such as transition-metal ions spin- orbit effects can be comparable with or greater than spin-spin effects. 47 Electron Spin Resonance Studies of the Triplet State 4 The Effixt of an External Magnetic Field For an atom with spherical symmetry a magnetic field lifts the triplet degeneracy so that the possible energy levels in the absence of Zss and Zso are the eigen- functions and eigenvalues of 2 =gps,< (7) as in the free-radical case but where s can have eigenvalues 0 f l i.e. Transitions between the triplet sub-levels are subject to the selection rule Am = 1 and occur at values of the magnetic field H which satisfied the resonance condition 3 hv =gpHz (9) where Y is the microwave frequency.Therefore resonance occurs at the same field value as for free radicals. The transition corresponding to Am = 2 is strictly forbidden because of the high symmetry. However in the case of mole- cules when Zss is included the reduced symmetry results in quite a different splitting which we shall examine in detail in Section 6. 5 Semi-classical Picture of Spinspin Interaction@ The two unpaired electrons with spin S = 8 each have magnetic moment $ = g/%? and the interaction SSs is equivalent to the classical interaction between two magnetic moments p1 and p2 with interaction energy r12 is the distance between the magnetic moments and 4 is the angle between the direction of the magnetic moments and the vector K2.The angular brackets denote an average over the distribution of the two electrons. For an atom <cos* 4> = &and therefore E, = 0 and the triplet degeneracy remains. In the molecular case we no longer have spherical symmetry but only one or more symmetry axes. In the absence of an external field the interaction energy between the spins will be different in different directions the spin will be coupled to the molecular framework and this is equivalent to quantisation of the spin along the molecular axes due to a local magnetic field within the molecule. This field is of the order of 2000 gauss and the energy levels of the system are then determined by this molecular field. In planar aromatic molecules the z-axis perpendicular to the aromatic plane is always a symmetry axis and may be a three- or six-fold symmetry axis in molecules like coronene.In this case the x and y axes are equivalent and quantisa- tion of spins can occur along the z-axis or in the x-y plane. The former situation will be doubly degenerate since the situations with mz = f l will be physically J. H. van der Waals and M. S. de Groot J. Chim. phys. 1964 1643. 48 Thomson indistinguishable but quantisation in the plane (corresponding to in = 0) will have a different energy. In this case the spin-spin interaction will result in one doubly degenerate level and one single level (Figure 2a). Z mZ t @ \ +* - 1 - f 0.13 cm-l t i I \ - 0 mx=O f- my=O .C mZ=o 0028 0.086 Figure 2 Zero-field splitting of the triplet spin sub-levels by dipolar interaction [Reproduced with permission from J.H. van der Waals and M. S. de Groot J. Chim. phys. 1964 16431 (a) Triphenylene (b) Naphthalene In molecules of lower symmetry one can show that the triplet degeneracy is lifted completely and there are three levels even in zero-field corresponding to quantisation of the spin along one of the three symmetry axes of the molecule (Figure 26).9 One might expect that the e.s.r. signal will give information con- cerning the symmetry of the triplet state. If an external magnetic field H is applied which is small compared with zs8 the spins will still be predominantly coupled to th,e molecular axes but if H is verylarge the spins will be quan- tised along H,. In the usual e.s.r. experiment H = ca. 3000 G and is thus a competition between the molecular axes and the external field for the spin quantisation.The result\is that the triplet energy levels are strongly dependent on the angle between H and the molecular symmetry a~es.39~1~~ For an assembly of randomly oriented molecules there will be a wide range of possible energy levels and the resonance fields will occur over several hundred gauss for transitions at constant microwave frequency. Thus the resonance will be highly anisotropic and the resulting broad lines difficult to detect. This fact was responsible for the earlier failures in the search for triplet state e.s.r. signals. lo C. A. Hutchison jun. Rec. Chem. Progr. 1963,24 105. 49 Electron Spin Resonance Studies of the Trrlplet State 6 Quantum Mechanical Treatment of Triplet State Energy Levels in the Presence of H and Xss In the presence of Zso and an external field the Hamiltonian becomeslo 3 ye = pGo .g . s -+ zss = p ~ . g . s + S . 5 . s (1 1) where since 3 and H are vectors the interaction may be written in tensor form and g and F are the g and spin-spin interaction tensors. However the tensors can always be transformed to an axis system in which they are diagonal. Further- more the g-tensor is usually nearly isotropic and in this case and henceforth we denote its isotropic value by g and the diagonal elements of the tensor by qi in which case 2 = g / G O . S + TxZSz2 + TvYSv2 + TzzSz2 (12) 2 and the terms gpS. H and ZSs are comparable in magnitude. The zero-field splitting of the levels is due to Zss and the splitting depends on the orientation of the spins and on their spatial distribution.The zero-field energy levels and wavefunctions are found by diagonalisation of the matrix of Hss with respect to the zeroth order basis functions 350 35 f 1. It is convenient to rearrange Xss so that spatial and spin parts are separated. This is a straightforward expansion and if the axes are chosen so as to diagonalise the tensor F one can show thatll Since the total wave function is written as a product the principal values of the tensor in the situation where 3 8 s is diagonalised will involve integrals of the antisymmetric spatial part of the wave function with the above co-ordinate operators. Van Vleck and McLachlan12 have shown that the matrix elements of ZSs are equivalent to those of the spin Hamiltonian operator Hs = D(Sz2 - $3') + E(gZ2 - $2) where s, sY and 3 are the components of the total spin = s + 3,.This form is the most useful for describing experimental results since these are the result of transitions between spin levels and the separations between these levels enables one to measure the zero-field splitting (Z.F.S.) parameters D and E.9910 The zero-field splitting of the levels is easily found by use of eqn. (14) with H = 0. In molecules with a three- or six-fold symmetry axis E = 0 and the eigenvalues of 2' = D ( S ~ - gS2) are l1 S. A. Boorstein and M. Gouteman J . Chem. Phys. 1963 39,2443. J. H. van Vleck Rev. Mod. Phys. 1951,23,213; A. D. McLachlan Mol. Phys. 1963,6,441. 50 Thornson in agreement with the semi-classical picture of Section 5. For E # 0 there are off-diagonal elements of iF8 between the basis functions 11 > lo> and I - 1 > and the 3 x 3 matrix is then (16) and there are three non-degenerate levels with El = QD + E E = 60 - E E = -$D (17) -1 This splitting is illustrated in FiguLe 2b.The effect of an external field H is shown in Figure 3 for the c a z of H along two of the three principal axes of the naphthalene molecule. For H parallel to they,-axis the energy-level diagram is shown in heavy lines in Figure 3 and for H parallel to z the energy levels are H (gauss) Figure 3 Energies of the triplet state sub-levels of naphthalene as a function of the external field Ho 2 Heavy lines Ho parallel to y-axis A - Light lines Arrows correspond to e.s.r. transitions with v' = 9650 Mc./sec. Ho parallel to z-axis denoted by the light lines.1° This behaviour is predicted from the above spin Hamiltonian and this accurately describes the experimental results in single crystals.In the limit of very strong fields the wave functions of the states are the pure spin functions but at 3000 G the 11 > and I - 1 > states are strongly mixed. The quantum of radiofrequency energy is indicated in the diagram and it is clear that for am = 1 transitions (the high field region) one obtains two possible transitions at very different resonance fields and these fields are different for each of the three orientations above. Thus the e.s.r. spectrum is highly anisotropic and the exact field strengths depend critically on the angle between H and the molecular axes. 51 Electron Spin Resonance Studies of the Trblet State However in the molecular case van der Waals and de Groot13 have shown that there is a finite probability for observing Am = 2 (low field) transitions with an intensity of ca.1 to 2 % of the Am = 1 transitions and these transitions are much more isotropic than the high-field transitions as is clear from Figure 3. 7 E.S.R. Spectra in Randomly Oriented Samples For glassy samples where the triplets are randomly oriented each triplet state has its molecular axis system at different angles 8 4 to the direction of H (z-direction in the laboratory frame; Figure 4). The energy levels are determined by 8 and 4 and are obtained by expanding the expression for gps . H and dia- gonalising 3 = gps. H + A?, with the triplet basis functions. The general analysis by Kottis and Lefebvre following earlier work by van der Waals can be summarised as follow^.^^^^^ z 4 Figure 4 Reference systems Oxyz in the laboratory OXYZ in the molecule.ON is the inter- section between the xOy and XOY planes OM the projection of Oz in the XOY plane. U is a unitary vector in the XOZ plane along the direction of the oscillating field H is the static magnetic field 01 the angle between the two fields [Reproduced with permission from P. Kottis and R. Lefebvre J . Chem. Phys. 1963,39,393] If we use the basis functions (these are more convenient for reasons of sym- metry) and rewrite l3 J. H. van der Waals and M. S. de Groot Mol. Phys. 1959,2,333; 1960,3,190. l4 Ph. Kottis and R. Lefebvre J. Chem. Phys. 1963,39,393; 1964,41 379. 52 Thornson where X Y and Z are the principal values of the coupling tensor then X = QD + E ; Y = QD- E; z= -#D X + Y + Z = O In this case the energy levels are the solutions of the cubic equation E3 - E[(gflHo)2 - ( X Y + XZ + Yz)] + (g/3H,,)2 [Xsin2 8 cos2 4 + Ysin2 8 sin24 + Zcos2 8] - XYZ = 0 (21) The condition for resonance is that two of the roots be separated by 6 = hv and this condition is x sin2 8 + Y sin2 8 sin2 4 + z cos2 B = XYz(g/3H,)-2 'f 4(XY + XZ + Y2)p f(8 4) = FW, 6) 3-* [(gfiHo)-2 (a2 + XY + XZ + Yz) - 11 [(4g/%f0)~ - S2 - (22) which can be written (23) For a given molecule the solution can be illustrated graphically and is given in Figure 5 for the case of naphthalene3 which has values of X = 0.0197 cm.-l Y = 0-0471 cm.-l 2 = -0.0669 cm.? g = 2-0030.The function F(H, 8) is plotted with these values and if a line parallel to the Ho axis is drawn at an ordinate equal to the value off(8 4) the abscissae give the allowed resonance fields.It is clear that the observed behaviour is predicted by the construction. There are in general three resonance fields for every 8,+; two at high field (Am = 1) and one at low field (&n = 2) and the low-field one is very much less aniso- tropic. The largest value off(8 4) is 2 and thus the largest resonance field possible in the low-field region occurs at H,1 = 1648 for ClOH8 whereas the minimum field Hm occurs when F(H, 6) ceases to be real i.e. H = (2gfl)-1 [62 + 4(XY + xz + Yz)] = (2gB-l [S2 - 4[D2/3 + E 2 ] ] i For Cl&€, the low-field anisotropy is ca. 121 G and a peak can be seen at this value in random samples. The largest signals occur when the resonance field is stationary i.e.dH = 0 where and this occurs (1) when F'(Ho 8) -KO which is the case for H = H, and (2) when df = 0 which is the case for H aIong one of the three principal axes of the molecule. These are the CANONICAL ORIENTATIONS and for these values there are again three possible fields which we label H2H;H; in the Am = 2 region and HZ2H$H and Hz3Hv3 H in the Am = 1 region. 53 I I I _all-------------------------------*-----.-v==.- Figure 5 The function F& 8) for naphthalene at 9279 Mc.lsec. The axis system used by Kottis and Lefebvre has the x and y axes interchanged from those used in Figure 3 [Reproduced with permission from P. Kottis and R. Lefebvre J. Chern. Phys. 1963,39,393] Thomson It has been shown that when one averages the resonance fields over all the molecules the distribution of resonance fields is that shown in Figure 6.14 There are thus maxima (peaks) in random samples at the canonical fields and H, the latter being the most intense.For molecules of higher symmetry Hzl and H,l 1500 ibQ0 woo Figure 6 Distribution of resonance fields in the Amz = 2 region for naphthalene at v = 9219 Mc. /see. [Reproduced with permission from P. Kottis and R. Lefebvre J . Chem. Phys. 1963,39,393] 55 Electron Spin Resonance Studies of the Triplet State merge into a single peak and H disappears hence the structure of the spectra in random samples will enable one to deduce the triplet symmetry. The Am = 1 region gives similar structure from the canonical peaks in random samples and it is possible to relate the resonance peak positions to X Y and Z and hence obtain the Z.F.S.(zero field splitting) parameters in randomly oriented samples. The gross features of the spectra of random samples can also be predicted from the experimental results on single crystals. 8 Experimental Methods in the Study of Triplet States A. Single Crystals,-For the study of oriented triplet states,3J0 the molecule is incorporated into a material with which it will form a substitutional solid solution and a single crystal grown. The concentration of guest molecules should be ca. 10-2-10-3~ (pure crystals of the host do not show phosphorescence owing to rapid exciton transfer effects). If the crystal is a true substitutional solid solution the guest molecules will be in known orientations in the lattice if the crystal structure of the host is known. The crystals are mounted so that they can be rotated about their principal axes or the magnet can be rotated and the crystal heLd fixed.In this way the variation of the resonance with the angle between H and the molecular axes can be determined. Crystals are cooled to 7 7 " ~ and irradiated with ultraviolet light in the singlet absorption band after suitable focusing of the light through ports in the side of the cavity. The characteristic phosphorescence decay time can be measured from the decay of the e.s.r. signal after the radiation is cut off. With mixed crystals energy transfer effects can be studied. The disadvantage is that suitable host crystals for the molecule of interest are difficult to find. B. Rigid Glasses.-The zero-field splitting parameters can fortunately be obtained from the use of random sample^.^,^^ In this technique the molecule is dissolved in a solvent which freezes to a clear transparent glass at 77"~.The most commonly used is ether-isopentane-alcohol (E.P.A.) but many other sol- vents have been described by Smith Smith and M~G1ynn.l~ E.P.A. is relatively stable and easily prepared but most glasses are not stable over a wide tempera- ture range. C. Plastics.-The incorporation of the organic molecule into a plastic16 has the advantage of stability over a wide temperature range and in this case the molecule is dissolved in monomer the polymerisation is carried out and the sample irradiated. Variations in lifetimes and Z.F.S. parameters with temperature can then be determined. D. The Cavity Arrangements.-The observation of the e.s.r. signals in single crystals can be carried out with the conventional e.s.r.system with the radio- F. Smith J. Smith and s. P. McGlynn Rev. Sci. Insfr. 1962 33 1367. l6 C. Thornson J . Chern. Phys. 1964 41 1. 56 Thomson 4 frequency field Hrf perpendicular to H,. This arrangement also can be used to observe the Am 1 transitionsin random samples. However in the special arrangement with H parallel to Ho additional features of the spectra and the canonical peaks at low field are more readily seen and this is to be preferred to the conventional arrangement for studies of = 2 lines in random samples since D and E can be obtained directly. For Hrf perpendicular to H,, low-field measurements give H which is related to D* = (D2 + 3E2)* and D and E cannot be determined separately. The experimental results in single-crystal studies are usually fitted to the spin Hamiltonian so that the experimental and predicted spectra agree.For random samples computer simulation of the spectra is carried out. 9 Experimental Investigations of TripIet States of Aromatic Molecules by E.S.R. The triplet states of aromatic molecules can be divided into two types? In aromatic hydrocarbons the lowest unfilled and highest filled M.O.’s are n-type and the lowest triplet state is always of the (n -v*) type in which an elktron is promoted to an excited T* orbital. With the introduction of heteroatoms with lone pairs there is also the other possibility that the lowest triplet state is an (n 3 n*) type with the electron promoted from a lone-pair non-bonding orbital n on the heteroatom. The nature of the lowest triplet state depends on the molecule; in general (n -T*) states have short (< 0-1 sec.) phosphorescence lifetimes whereas (r 3 n*) have lifetimes > 0.1 sec.Only (n 3 n*) triplet states have been detected by e.s.r. and in this section we consider only this type of triplet. A. E.S.R. of Aromatic Molecules in Single Crystals.-The full power of the e.s.r. method is available for the case of oriented molecules in single crystals and in this case the observed spectra allow one to determine the g-tensor components and those of the spin-spin interaction tensor. The principal values of the latter X,Y,Z are related to D and E (eqn. 20). Despite the limitations discussed above a large number of aromatic molecules have been studied in the four host crystals durene biphenyl fluorene and benzophenone.(i) Aromatic hydrocarbons. The pioneering work of Hutchison and Mangum and subsequent studies by their &t0up,17 remain the classic experiments on oriented triplet states. The results are given in Table 1. Naphthalene and its deuterated derivatives have been the most extensively studied in durene biphenyl and fluorene. The observed spectra in these matrices show that matrix effects on D and E are small. The results accurately fit the spin Hamiltonian and show that the host molecules are well oriented and that spin-spin interaction is the domin- ant perturbation. In the case of naphthalene17 or phenanthrene in biphenyl and pyrene in l7 N. Hirota C. A. Hutchison jun. and P. Palmer J. Chern. Phys. 1964 40 3717; R. W. Brandon R. E. Gerkin and C. A. Hutchison jun.ibid. 1962,37,447. 57 Electron Spin Resonance Studies of the Triplet State Table 1 E.s.r. results in single crystals aromatic compounds Molecule Naphthalene [2H,]Naphthalene Phenanthrene Pyrene Quindxaline Quinoline Isoquinoline Phenoxazine Host crystal Durene Biphenyl Durene Biphenyl Fluorene Durene Durene Durene Biphenyl D/hc (cm.-l) +O-10119 + 0.0994 + 0.0992 1 f0-1010 f0-10043 f00810 f0.0806 &O* 1007 f0-1030 f0-1004 f 0.1247 E/hc (cm.-l) -0.0141 1 -0.0154 - 0.01 548 0.01 34 f0.04658 f0.0182 f0.0182 0.01 82 0.01 62 r0.0117 f0-0119 Ref. 3 10 17 10 17 10 17 18 b a 19 19 48 J. S. Vincent and A. H. Maki J. Chem. Phys. 1963,39,3088; b 0. H. GrifFith J . Phys. Chem. 1965 69 1429. biphenyl,l* four resonance lines (Am = 1) are found for each orientation since in these systems there are two inequivalent lattice sites for the C1& molecules in which the planes of two such molecules are mutually perpendicular.The simple two-line pattern discussed above has so far not been found in practice because of the more common feature of inequivalent lattice sites. In the cases of quinoline and isoquinoline eight peaks are found for each orientation,lg because in this case the principal axes of the molecular spin-spin tensor do not coincide with the durene axes so there are two magnetically inequivalent orientations of quinoline in each of the two lattice sites in durene. The effect of temperature on the D and E values is small but measurable. The decay of the phosphorescence and that of the e.s.r. signal as measured by the lifetimes T~ and T ~ R are found to be exponential and the two sets of values are in good agreement.For instance C,,H in durene has T~~ = 2.1 f 0.1 sec. compared with T~ = 2.6 + 0-2 sec. The substitution of deuterium in the mole- cule increases both T~ and the signal intensity and T~ approaches the true radia- tive lifetime which is often much larger than the observed decay time. The single-crystal results at 7 7 " ~ give only the relative signs of D and E and l8 S. W. Charles P. H. H. Fischer and C. A. McDowell Mul. Phys. 1965 9 517. l9 J. S. Vincent and A. H. Maki J . Chem. Phys. 1965,42 865. 58 Thomson measurements at 4 ' ~ and 1 ' ~ are necessary to obtain the absolute signs.2o These studies have furnished very detailed information and there is hope that other host crystals will be found which will extend the applicability of the method.B. E.S.R. of Aromatic Molecules in Rigid Glasses.-The study of triplets in glasses greatly extended the utikty of the method. The earlier workers observed Am = 2 transitions a,nd with Hrf pqpendicular to H, only Hmin was observed. However the use of Hrf parallel to H does result in characteristic structure in this region from which D and E can be determined. The use of fully deuterated molecules has also helped in detecting these weak peaks since line-broadening is less. The observation of Am = 1 transitions has superseded this work and D and E have now been measured for a large variety of molecules (Table 2). Table 2 E.s.r. results in glasses and plastics aromatic hydrocarbons Molecule Benzene Djhc (cm.-l) E/hc (cm.-l) 0.1 56 0 0.1 59 0 Naphthalene [2H,]Naphthalene Anthracene [2H ,]An t hracene Phenanthrene [2H ,]Phenan t hrene Pyrene 0.10046 - 0.01 536 0.0724 0.0081 - - 0.100 0.047 - I 0.1050 0.046 Chrysene - - 0.095 10.025 [ D*/hc (cm.-l) Ref.0.1 56 13 0.1 59 22 0.1048 13 0.1 049 22 0.1063 16 0.1008 a 0.077 22 0.0737 a 0.1335 22 0.129 23 0.1 29 b 0.1336 16 0.1321 C 0.093 23 0.0929 22 0-1052 22 0.103 b 0-104 23 2o A. W. Hornig and J. S. Hyde Mol. Phys. 1963 6 33. 59 Electron Spin Resonance Studies of the Triplet State Table 2-continued Molecule 1 ,ZBenzanthracene 1,2 :5,6-Dibenzan- thracene 1 ,2-Benzopyrene 3,CBenzopyrene Triphenylene Coronene 1,12-Benzoperylene Biphenyl Terphenyl Fluorene Fluoroant hene Toluene Acenap ht hene Trip t ycene Decacylene 60 D/hc (cm.-l) E/hc (cm.-l) D*/hc (cm.-l) Ref. 0.079 0.090 0.090 - 0.1353 0-1 34 0.1360 0.1 338 0.096 0.097 1 0.0983 0.093 - 0.1092 - - - 0.1075 - - - - - - 0.135 (77°K) 0 0.057 0 0.083 0.100 0.098 0.0758 0.1353 0.1 34 0.1360 0.1338 0.096 0.0971 0.0983 0.093 0.071 8 0- 1 094 0.1 130 0.1111 0.0961 0- 1092 0.1 096 0.1088 0-076 0-08 17 0-171 0.1029 0.1 35 0.057 23 23 23 22 22 13 16 a 13 22 16 b 16 d 22 16 22 d 22 16 b 16 21 16 21 41 Thomson Table %continued Molecule D/hc (cm-l) E/hc (cm.-l) D*/hc (cm.-l) Ref.[ DecacyleneI2- 0.021 0 0.021 41 1,3,5 Triphenyl- benzene 0.111 0 0.1 11 13 [TriphenylbenzeneI2- 0.042 0 0.042 41 a E. Wasserman L. C. Snyder and W. A. Yager J . Chem. Phys. 1964 41 1763 ; b G. von Foerster Z . Nuturforsch. 1963 189,620; M. S. de Groot and J. H. van der Waals Physica 1963 29 1128; d S. Siege1 and H. Judeikis J . Phys.Chem. 1966 70 2201. (i) Aromatic hydrocarbons. The appearance of Am = 2 peaks with Hrf parallel to H reflects the symmetry of the state and in molecules of DBh symmetry two peaks are observed and this has been found for coronene triphenylene and triphenylbenzene (Figure 7)>3 Benzene does not give the two-peak pattern 11 77°K 1646 - V /t 40 I K 1 7 I I I I I I I I I I I I I 1 1500 1550 1600 1650 1400 1450 1500 1550 GAUSS 1492 I Figure 7 AmZ = 2 Transitions in glassy samples [Reproduced with permission from J. H. van der Waals and M. S. de Groot Mol. Phys. 1960 3 1901 (a) Naphthalene (b) Triphenylene showing conclusively that the lowest triplet state no longer has hexagonal symmetry.21 This surprising result had been suggested in early phosphorescence studies and the e.s.r. results showed this fact unequivocally.The spectrum of benzene and the methylbenzenes and the decay times T~~ 21 M. S. de Groot and J. H. van der Waals Mol. Phys. 1963,6,545; M. S . de Groot I. A. M. Hesselmann and J. H. van der Waals ibid. 1965 10,91. 61 Electron Spin Resonance Studies of the Trblet State are very temperature-dependent. These effects have been interpreted in terms of the non-equivalence of the possible conformational isomers and these effects could hardly have been investigated except by e.s.r.21 For those molecules which have been studied in glasses and in single crystals observed values of D and E and D* are in good agreement. The line-widths have been correlated with the carbon-hydrogen ratios and indicate that hyperfine broadening predominates.22 Hyperfine interactions are not usually resolved in glasses.Measurements on the Qm = 1 peaks give D and E directly and have been carried out for a large number of hydrocarbons most recently by Brinen and O r l ~ f f . ~ ~ A typical spectrum (deuteriophenanthrene) is shown in Figure 8. (ii) Aromatic heterocycles and substituted hydro~arbons.~~ Generally speaking (Table l) substituents affect E most and D least but the effects are small and usually can be attributed to increased delocalisation. However no systematic study has yet been reported and correlations with spectroscopic evidence might be fruitful. C. E.S.R. of Aromatic Molecules in Plastics.-The D and E values obtained by this t e c h n i q ~ e ~ ~ ~ ~ are in good agreement with the work in single crystals and glasses; slight differences are believed to be due to a stronger matrix effect than is found in the other matrices.Line-widths are always larger in plastics. D has been studied as a function of temperature for coronene and triphenylene16 but the interpretation given of the slight decrease with T is not unambiguous. The triplet-state lifetimes vary with temperature but also with the nature of host and the previous history of the sample. Further work is needed on these systems. 10 Hyperhe Interactions in Triplet States Additional structural information is obtained from hyperfine splittings which can be observed in single crystals. The origin of hyperfine interactions (h.f.i.) both anisotropic and isotropic is now well understood from studies of radicaIs and has been reviewed.2 The unpaired spins in triplets give rise to h.f.i.in a similar manner but unlike the case of free radicals in solution it is possible to determine the anisotropic h.f.i. if the triplets are oriented. To a very good approximation the isotropic and anisotropic splittings of a proton in an aromatic C,-H band are proportional to the spin density pa on the adjacent carbon 2 where a 18 and y are direction cosines of H with respect to (1) the C-H bond direction (a axis) (2) the normal to the plane (b axis) and (3) the c axis per- 22 B. Smaller J . Chem. Phys. 1962 37 1578. 23 J. S. Brinen and M. K. Orloff J . Chem. Phys. 1966 45 4741; S. Siege1 and H. S. Judeikis J . Phys. Chem. 1966 70 2201. 24 See refs. 16 21 and 22. 25 N. Trublin R. Santus and M. Ptak Comp. rend. 1965 260 1134. 62 Thomson 8 N M N I X I 00 0 cu M I X v) v) 3 Q (3 0 0 9 3 3 ? 3 3 3 3 3 z 3 n c 3 E 63 Electron Spin Resonance Studies of the Triplet State pendicular to a and b.A By and C are the isotropic plus anisotropic h.f.i. per unit spin density on the contiguous carbon atom in the axes a b and c respec- tively. Measurements of the hyperfine splittings give Aa Bu and Ca since the isotropic splitting Ai for C-H is ca. -63 Mc./sec. The results show that Aa = 30 Bu = -61 and Ca = -92 Mc./sec. The spectra can be rationalised in terms of these values. The most detailed measurements have been made on naphthalene deuterionaphthalene and phenanthrene. We can regard the naphthalene molecule as a collection of eight C-H frag- ments (Figure 9) of which 3ere are two types which are structurally inequivalent the a and 18 fragments.If H is applied along the x (long) axis of the molecules -61.5 A -30.0 Figure 9 Hyperfine interactions in naphthalene in terms of the interaction with a and fl C-H fragments [Reproduced with permission from C. A. Hutchison jun. Rec. Chem. Progr. 1963 24 1051 then this direction is parallel to the c axis of the 01 protons (which have the largest spin density on the adjacent carbon atom) but at the same time H, is close to the a axis for the fragments. Since these directions are those for largest h.f.i. for a protons and smallest h.f.i. for fi protons the hyperfine pattern is one of five lines from the four a-protons (aaH) each split into five from the smaller /%splitting (apH). The five-he pattern is observed at 7 7 " ~ bUtgpH is unresolved though some additional structure is observed at 4 " ~ .For H parallel to the z axis dl protons will appear equivalent and only a single broad line is observed. For H parallel to the y axis a single peak with some structure is observed as is predicted from the values of A" BQ and CQ for the protons involved. Detailed analysis of the h.f.i. gives the spin densities on the carbon atoms and these can be correlated with theoretical calculations and the results confirm the symmetry of the triplet state. 64 Thornson No hyperfine structure has been observed for oriented pyrene since here the spin densities are low and there are several similar coupling constants but it has been observed in oriented quinoxaline quinoline and isoquin~line~~ where similar information has been obtained. 11 E.S.R. Spectra of Ground-state Triplets There are a number of interesting molecules26~27~2* which have a triplet ground state (as opposed to the triplet excited state of an aromatic molecule) and in recent years the chemistry of carbenes and nitrenes have shown that derivatives of methylene CH2 and nitrene NH react as though they were in a triplet ground state and this has been confirmed by e.s.r.We define a ground-state triplet as one which gives an e.s.r. spectrum which fits the usual spin Hamiltonian with S = 1 but whose e.s.r. signal is stable at 7 7 " ~ for several hours in contrast to excited states which decay in seconds. The ground-state triplet states of substituted methylenes have been studied both in rigid glasses and in single crystals,29 and are produced by photolysis of the particular precursor diazo-compound at 77 OK i.e.Am = 1 and a m = 2 transitions can be observed although not all possible transitions are always detected. The triplets are stable to ca. 1 3 0 " ~ and in con- trast to aromatic triplets D is usually >Om1 cm.-l. The origin of this large value is discussed in Section 16C. A tabulation of some of the resuIts representing the various types is given in Table 3 and considerable structural information has been obtained. Diphenyl- methylene is almost linear but with mutually perpendicular phenyl rings since E #0.30 Phenylmethylene has been studied but not :CH itself. The e.s.r. results for pentaphenylcyclopentadienyl confirm the prediction of a triplet ground state by molecular orbital theory.31 The derivatives of NH the nitrenes have also been extensively studied and are similar to the methylene~.~~ The observed Z.F.S.correlate with the crr-electron spin densities in phenyl-substituted nitrenes,= since only one of the two r orbitals z6 W. Kirmse 'Carbene Chemistry' Academic Press New York 1964. 27 A. M. Trozzolo R. W. Murray and E. Wassermann J . Amer. Chem. SOC. 1962,84,4990. 28 R. W. Murray A. M. Trozzolo E. Wasserman and R. M. R. Cramer J. Amer. Chem. SOC. 1962 84 3213. ps R. N. Brandon G. L. Closs C. E. Davoust C. A. Hutchison jun. B. E. Kohler and R. Silbey J. Chem. Phys. 1965 43 2006. 30 E. Wasserman A. M. Trozzolo W. A. Yager and R. W. Murray J. Chem. Phys. 1964 40 2408. 81 R. Breslow H. W. Chang and W. A. Yager J . Amer. Chem. SOC. 1963 85 2033. 82 G. Smolinsky E. Wasserman and W. A. Yager J . Amer. Chem. SOC. 1962 84 3220; E.Wasserman G. Smolinsky and W. A. Yager ibid. 1964 86 3166. G. Smolinsky L. C. Snyder and E. Wasserman Rev. Mod. Phys. 1963 35 576. 65 Electron Spin Resonance Studies of the Triplet State Table 3 E.s.r. results for ground-state triplets Molecule Structure Dlhc (cm.-') E/hc (cm.-l) Ref. CARBENES Diphenylmethylene Ph-C-Ph 0.401 0.4050 Phenylmet hylene Ph-C-H 0.518 Perfluoroalkylmethylenes R-CH 0.7 Cy anome t h y lene H-C-CEN 0.889 ./.A H . 1,NaPhthYl- & & 0.4555 methylenes 0.4347 DICARBENES p-Phenylene-bis (phenyl methylene) pht=(=Jt~h - 0.0521 NITRENES Nitrene Cyanoni trene 2-Naphthylnitrene 4-Ni trophenylni trene n-Propylnitrene MISCELLANEOUS Diazomethylene Dicyanomet hylene Fluoren ylidene C ycl open t adien y 1 i dene Indenylidene Propargylene NH 1-86 NCN 1-544 PrLN 1 -607 CNN 1.153 NCCCN 1-002 0.4078 0 0-4089 OrJl 0.3777 H-C-C CH 0.6276 0.01 8 0.01 86 0.024 0.02 0.04 0 0.0202 0.0208 0.002 0 0.002 0 0 0.0034 0.002 0.002 0.0283 0.01 20 0.01 60 0 27 28 a 27 b 37 36 36 C d e 67 67 32 e e f 27 34 34 38 Q R.W. Brandon G . Closs and C. A. Hutchison jun. J. Chem. Phys. 1962 37 1878; E. Wasserman L. Barash and W. A. Yager J . Amer. Chem. SOC. 1965 87 4974; CA. M. Trozzolo R. W. Murray G. Smolinsky W. A. Yager and E. Wassennan J . Amer. Chem. SOC. 1963 85 2526; 6 R. N. Dixon Canad. J . Chem. 1959 37 1171; E. Wasserman L. Barash and W. A. Yager J . Amer. Chem. SOC. 1965 87 2075; f E. Wasserman A. M. Trozzolo W. A. Yager and R. W. Murray J . Chem. Phys. 1964,40,2408. 66 Thomson involved conjugates with the ring. The other 2p7r orbital on the nitrogen is in the molecular plane.A rather different type are the triplets of fluorenylidene (l) cyclopenta- dienylidene (2) and indenylidene (3),= the first of which has also been studied in single crystals. D values of ca. 0.4 cm.-l are observed owing to the occurrence of one un- paired electron in a 2p7~ orbital and the other in a 0 orbital on the same centre. The bonds to the bivalent carbon are bent and this has been found to be the case in the methylene derivatives from 13C studies.35 In the case of naphthyl- methylenes two distinct geometrical isomers are observed from a single diazo- precursor thus confirming the non-linear characterF6 Several more complicated ground-state triplets such as ~yanomethylenes,3~ propargylene derivatives:* the species CNN NCN and NCCCN,39 and several dicarbenes and dinitrenes where the spins are ca.6 A apart,4O have been studied. Finally aromatic hydrocarbons with three- or six-fold symmetry axes may form dinegative ions with triplet ground states and triphenylene and decacyclene dianions are examples of this type with low values of D owing to stronger electron correlation.4l 12 Studies of Energy Transfer Of considerable importance is the use of e.s.r. to study the problems of energy transfer from excited triplet states. This problem has been studied for many years by optical methods but once more additional information is obtained by use of e.s.r. The effect of excitation transfer within the triplet state is typified by the examples of benzene the methylbenzenes and the molecules triptycene and tribenzotriptycene; in the last the three aromatic rings are not conjugated with one another.2f As mentioned in Section 9B (i) the benzene spectrum indicates that the molecule no longer has hexagonal symmetry.This implies that there are two configurations I and I1 with two different bond lengths and different energies in 34E. Wasserman L. Barash A. M. Trozzolo R. W. Murray and W. A. Yager J. Amer. Chem. SOC. 1964,86,2304. 3b E. Wasserman J. Chem. Phys. 1965 42 3739. 36 A. M. Trozzolo E. Wasserman and W. A. Yager J. Amer. Chem. SOC. 1965,87,129. s7 K. A. Bernheim R. J. Kempf P. W. Humer and P. S. Skell J. Chem. Phys. 1964,41,1156. 38 R. A. Bernheim R. J. Kempf J. V. Gramas and P. S. Skell J . Chem. Phys. 1965 43 196. 39 E. Wasserman L. Barash and W. A. Yager J. Amer. Chem. SOC. 1965 87 2075. 40 A. M. Trozzolo R.W. Murray G. Smolinsky W. A. Yager and E. Wasserman J. Amer. Chem. SOC. 1963 85,2526. 41 R. E. Jesse P. Biloen R. Prins J. D. W. van Voorst and G. J. Hoijtink Mol. Phys. 1963 6 633. 67 Electron Spin Resonance Studies of the Triplet State each of which there are two equivalent conformations. Vibrations of the right symmetry can cause the system to interconvert between the Type I conforma- tions via Type 11. A theoretical study substantiates this model.21 The rate of this process compared with characteristic e.s.r. times determines the spectral appear- ance and accounts for the temperature-dependence. For a very fast inter- conversion rate the time-average conformation will have D,* symmetry and in this case one can show that the resonance peak broadens and moves to higher fields as is observed when the temperature is raised.The converse is found for decreasing temperature. The methylbenzenes in which the equivalence of the conformational isomers is destroyed exhibit similar behaviour. Triptycene and tribenzotriptycene21 are similar except now the individual conformations are replaced by excitations in individual n-systems. For rapid excitation transfer once again Dgh symmetry is approached and the observed temperature-dependence gives the rate of transfer of triplet excitation. At ~ O " K the excitation is mainly localised but it is delocalised at 7 7 " ~ . The second triplet state energy-transfer mechanism is intermolecular. This was first observed by Farmer Gardner and McDowell bye.s.r.,42 who showed that the benzophenone triplet transfers energy to a naphthalene molecule giving the triplet of the latter in a rigid glass.No benzophenone triplet resonance is observed since this is an (n 3n*) state. Much more detailed investigations on the mechanism of energy transfer in single crystals have since been carried out by Hutchison's which have shed some light on triplet-transfer and triplet-triplet annihilation processes and have shown that the transfer proceeds via the crystalline host lattice and that complex-formation does not occur. Smaller Avery and R e m k ~ ~ ~ have studied similar problems in glasses of different viscosity and have shown that exchange mechanisms dominate at high 7 but diffusion processes at low 7. Similar work has been done by Siegel and his collaborator^.^^ Finally it has been shown that energy transfer from the triplet state to the solvent produces free radicals at a rate proportional to the rate of decay of the triplet state and it is believed to involve a highly excited triplet state.47 The influence of deuteration of triplet state lifetimes has been extensively studied by Hir~ta.*~ 13 The EIectronic Structure of Triplet States The correlation of the observed Z.F.S.parameters with the molecular electronic structure is perhaps the most important aspect of this work since these weak p2 J. B. Farmer C. L. Gardner and C. A. McDowell J. Chern. Phys. 1961,34 1058. N. Hirota and C. A. Hutchison jun. J . Chem. Phys. 1964 42 2869. 44N. Hirota J . Chem. Phys. 1965 43 3354. O5 B. Smaller E. C. Avery and J. R. Remko J. Chew. Phys. 1965 43 922. authors. 47 B. Smaller Nature 1962 195 593.p8 N. Hirota J. Chem. Phys. 1967 46 1561. S. Siegel and H. Judeikis J. Chem. Phys. 1965 42 3060 and many earlier papers by these 68 Thomson interactions constitute a very sensitive test of the molecular wave fun~tion.~ Since the triplet wave function must have an antisymmetric spatial part this means that the unpaired electrons must occupy different spatial orbitals i.e. they are kept apart by Pauli's principle and approximate wave functions can be used to describe the state with some confidence in this case.49 For a 2Nr-electron aromatic molecule the ground-state wave function can be approximated by the single Slater determinant based upon doubly occupied M.O.'s #1 ...... +NO The lowest triplet state is described in terms of one-electron excitations from configuration being M.O.+i to an antibonding M.O. +k (k = N + 1 ..... 2N) the lowest energy 3@. (N-+ N + 1) = b&&&. . .+N+N+~ I (28) for the state with Mz = +1 (we restrict our discussion to this component). The exact triplet wave function in general will be a superposition of all possible contigurations of the appropriate symmetry i.e. 'y/ = cc Ctk @(i 3 k) i k # i with the dominant term 3@(N 3 N + 1) particularly if the +i are open-shell S.C.F. orbitals.50 More complicated wave functions such as the Unrestricted Hartree-Fock51 functions do not appear to be as useful for evaluating the zero-field splittings. The ground-state triplet states have similar descriptions where however the unpaired electrons may now occupy different orthogonal orbitals on the same centre one of which can conjugate with aromatic rings.It should be emphasised that these orbital descriptions are all approximate but a similar analysis52 holds for exact wave functions in the calculation of Z.F.S. parameters. 14 Theoretical Calculation of D and E The theoretical calculation of D and E involves the evaluation of the expectation value of ZS8 (eqn. 5) with the triplet-state wave function. The evaluation of the spin-spin interaction energy can be shown to give the following expressions for D and E 48 J. C. Slater 'Quantum Theory of Molecules and Solids' McGraw-Hill New York 1963 vol. 1. 61 G. G. Hall and A. T. Amos Adv. Atomic and Mol. Phys. 1965,1,1; A. T. Amos and L. C. Snyder J. Chem. Phys. 1965,43,2146. 62 R. McWeeny J . Chem. Phys. 1961,34,399; R. McWeeny and Y . M i m o Proc. Roy. Soc. 1960 A 259,554; R.McWeeny J. Chem. Phys. 1965,42 1717. C. C. J. Roothaan Rev. Mod. Phys. 1960,32 179. 69 Electron Spin Resonance Studies of the Tr&let State where the expectation value is over the antisymmetric spatial part of the wave function. We shall not go into a detailed discussion of the evaluation of this expectation value in this Review (for further details consult refs. 51 53 54-57) but shall indicate the problems involved and the significance of the results. It is clear from eqn. (29) that the evaluation of D and E will involve knowledge of the coefficients Ci in the configuration interaction description and the integrals involving the particular configurations. The former is a straightforward problem in quantum chemistry and for the latter one can show that these integrals reduce to molecular integrals over M.O.’s of the form {ab cd) = JJa(l)b(2) 6 [c(l)d(2) - ~ ( 2 ) d ( l ) ] d ~ ~ d ~ ~ where the operators 6 are those of eqn.(31). The numerators of the operators measure the anisotropy in the two-electron distribution functions and the de- nominators reflect its overall size. If the M.O.’s are expressed in L.C.A.O. form i.e. 2N a = CaiXi (33) i= 1 then the problem reduces to evaluation of products of the coefficients ai and the atomic integrals (ij kZ) where now i,j,k,Z refer to 2pn atomic orbitals. Until quite recently only approximate values of the latter were available but recent work by Karplus and his co-workers% has furnished accurate values of these integrals. The integrals may involve n atomic orbitals on two three or four centres for ( 7 r - 7 ~ ~ ) states but for methylenes and nitrenes there are also one-centre integrals .15 Comparison of Experimental and Theoretical Values of D and E A. Aromatic Hydrocarbons.-Early work was based on a two-configuration approximation5* to the triplet state with wave function 3YLa = sin e@(N -f N + 1) + cos 8@(N - 1 -+ N + 2) (34) a31. Shavitt and M. Karplus J . Chem. Phys. 1965 43 398; C. W. Kern and M. Karplus ibid. 1965 43 415; M. Godfrey C. W. Kern and M. Karplus ibid. 1965 44 4459. 64 J. H. van der Waals and M. S. de Groot Mol. Phys. 1964 8 301. 6s Y. N. Chiu J . Chem. Phys. 1963 39 2763 2749. 66 C. Thomson Mol. Phys. 1966 11 197. 67 J. S. Brinen and M. K. Orloff J . Chem. Phys. 1966 45 4747. N. S. Ham and K. Ruedenberg J. Chem. Phys. 1956,25 13. 70 Thornson 8 is the mixing parameter determined in ref.58 by energy minimisation but in Goutermann’s earlier it was treated as a parameter and the optimum value found by comparison with experiment. These early calculations used approximate values of the two-centre integrals and Hiickel or Hoffmanso M.O.’s and neglected three- or four-centre integrals. The results in Table 4 Columns 1 and 2 show that the results were satisfactory for the smaller mole- cules. Similar calculations were carried out by chi^.^^ A more serious criticism of this approach is that the best 8 values differ from those values which give the best triplet energy58 and so these calculations do not really test the quality of the triplet wave function. For higher accuracy the triplet-state wave function must be obtained by minimisation of the energy as was shown by van der Waals and de Groot5* and Thom~on.~~ These authors used similar approximations for the integrals but used rather different wave functions.Van der Waals’s calculations and later work by Brinen and Orloff5’ were based on Open Shell S.C.F.-Pariser-Parr-type wave functions including a semi- empirical treatment of the 0 electrons but employing the zero-differential over- lap approximation. Thorn~on~~ on the other hand used Hummel and Ruedenberg’ssl wave func- tions which give very good agreement for triplet-state energy levels. These include overlap between nearest neighbours (T.B. M.) or nearest and next- nearest neighbours (I.R.M.) and employ well-tested methods of evaluating electron repulsion and core integrals. Both sets of calculations used extensive configuration interaction which is necessary for accurate work (Table 4 Columns 3,4; 6,7).This work is currently being extended by use of the accurate integral values of K a r p l ~ s . ~ ~ ~ ~ Agreement with experiment was very good particular improvements being apparent for the peri-condensed molecules. However the importance of the influence of (T electrons54 and more accurate integral values53 need studying in order to obtain values of D and E to within a few per cent. of experimental values. Nevertheless the calculations using properly energy minimised wave functions do appear to constitute a good test of the wave functions used.G3 B. Aromatic Heterocycles and Other Molecules.-Very little work has been carried out on other than hydrocarbons particularly with respect to the use of accurate integrals.Boorstein and G~uterman~~ have carried out similar calcula- tions to those of van der Waals on quinolines and quinoxalines using more accurate (but still not exact) integrals but more work is needed in this area. An estimate of (nlr*)-state Z.F.S. parameters has been made by Sternli~ht.~~ See ref. 11 for bibliography of earlier calculations in this approximation. R. L. Hummel and K. Ruedenberg J . Phys. Chem. 1962 66 2334. 6o R. Hoffman J . Chem. Phys. 1963 39 1397. 62 C. Thomson unpublished work. 6s See however T. J. Dougherty T. Vladimiroff and S. T. Epstein J . Chem. Phys. 1966,45 1803. 64 S. A. Boorstein and M. Gouterman J . Chem. Phys. 1965,42 3070. 66 H. Sternlicht J . Chem. Phys. 1963 38 2316. 71 Table 4 Theoretical values of D and E for some aromatic hydrocarbons 1 2 -3 4 5 6 7 Molecule D E D E D E D E D E D E D E I - - - Benzene (Dab) 0.1519 0 0.1519 0 0-179 0 0.15333 0 - - - - 0.157 - - - Naphthalenet 0.1003 -0.0133 0.0958 -0.0211 0.111 -0.028 0.099 -0-024 0.045 0.005 0.088 -0.011 0-100 -0.011 - - 0.097 -0.022 - - 0.1002 -0.0146 - - Anthracene 0.0727 -0.0148 0.0721 -0.0166 0.076 -0.012 0.071 -0.009 0.034 0.012 0.049 -0.002 0.074 0.001 0.077 -0.011 - - I - - 0.084 -0.041 - - 0.069 0.037 0.080 0.039 Pyrene - - - Phenanthrene 0.0731 0.0269 0.0851 0.0304 0.115 0.056 0-100 0.048 0.063 0-082 0.082 0-059 0.092 0.051 0.116 0.039 1,12-Benzperylene - - - - - - - - - 0.042 0.001 0.063 -0.001 Coronene 0.0522 0 0.0608 0 - - - - - - - - - - - - 0.0546 0 - - - - 0.134 0 Triphenylene 0.0697 0 0.0810 0 - - - - - - - - 0.0693 0 - *Approximations used 1.Reference 1 1 All two-centre integrals included. Single Gaussian approximation in integral evaluation. Two-configuration wave function (eqn. 34) based on Hiickel orbitals. 2. Reference 11 As for 2*but with Hoffmann orbitals. 3. Reference 54 Pariser-Parr approximation in Open-Shell SCF-M.O. calculation including C.I. with all singly and some doubly excited configura- tions; integrals by direct quadrature. 4. References 54 and 57 As for 4 but only singly excited configurations included; semi-empirical adjustment of nearest-neighbour ( X i X j ; X r X j ) to take o-effects into account. 5 . Reference 5 1 Unrestricted Hartree-Fock method; single Gaussian approximations in integral evaluation Pariser-Pam parameters. 6. Reference 56 Ruedenberg TBM wave functions; single Gaussian approximation to integrals; overlap between nearest neighbours.7. Reference 56 As in 6 but wave functions (IRM) included nearest and next-nearest neighbour overlap integrals. ?The values of D and E for naphthalene using Pariser's eight-configuration wave function and accurate values of all two- three- and four-centre dipolar integrals are D = 0.1081 E = -0.0093 (ref. 53). % P Y Thomson C. Ground-state Triplet States.-The calculation of the Z.F.S. parameters in the substituted methylenes and nitrenes has been considered in detail by Higuchi in a series of papers!e These calculations typified by the work on substituted methylenes have shown that the one-centre terms are the most important and for reasonable values of the integrals the calculated D and E are in fair agree- ment with experiment.D and E mainly depend on the spin density at the methy- lene carbon.% The effect of bond angle on D and E shows that the -C- bond is bent.6s The exact explanation of the observed angle must however await more detailed calculations including in-plane a-electrons. Similar calculations on nitrene derivatives have been made?' The use of ab-initio wave functions will be of great importance in this type of work and Loundsburyss has calculated D for NH using one centre ab-initio SCF wave functions with encouraging results. Finally the influence of spin-orbit interaction has been investigated (eqns. 3 and 4) which was neglected in all the above discussion^.^^ This is a second-order effect and it appears likely that for methylenes the contribution to D is ca.10% of the spin-spin interaction. It is expected to be less important in delocalised systems but quantitative calculations are needed. 16 Miscellaneous Remarks The Triplet State in Solution.-Very few studies have been carried out on triplet states in solution since (1) lifetimes are usually too short or (2) the Z.F.S. aniso- tropy results in lines too broad to observe. Recently however Lemaire and his co-workers have described'O some biradicals which give well-resolved triplet state spectra in solution. The molecules consist of two nitroxide radical fragments linked via a saturated chain. The e.s.r. spectra depend on the magnitude of the exchange integral J coupling the two unpaired electrons. For J < nN the spectrum is a triplet charac- teristic of two independent nitroxide groups but for J B aN five lines are observed separated by aN12.Each electron interacts with both nitrogen nuclei. For J = ca. a, line-width alternation occws and Lemaire et al. have described biradicals in which J varies from one extreme to the other. By using liquid 66 J. Higuchi J . Chem. PAYS. 1963 38 1237; 1963 39 1847; 3455; 1964 41 2084. 42 54. *O S. H. Glarum J. Chem. Phys. 1963 39 3141; S. J. Fogel and H. F. Hameka ibid. 1965 42 132. 70 R. M. Dupeyre H. Lemaire and A. Rassat J. Amer. Chem. SOC. 1965,87,3771; R. Briere R. M. Dupeyre H. Lemaire C. Morat A. Rassat and P. Rey Bull. SUC. chim. France 1965 11 3290. J. A. R Coope J. B. Farmer C. L. Gardner and C. A. McDowell J . Chem. Phys. 1965 J. B. Loundsbury J. Chem. Phys. 1965 42 1549. 73 Electron Spin Resonance Studies of the Triplet State crystals,71 where the molecules are partly oriented these workers have been able to observe further splitting of the lines owing to the zero-field splitting in the triplet state.Extensions of this type of work to other systems should be most interesting. Polarised Light Studies.-Oriented triplet states can be produced by use of polarised light and the influence of the polarised light on the canonical peak intensities has given interesting information on the polarisation of the exciting singlet.72 17 Conclusions I have tried to show that e.s.r. has provided a wealth of important information concerning the electronic structure of the triplet state together with information of energy-transfer processes and the factors influencing such processes. The detailed information available emphasise the power of the e.s.r. technique and present the theoretical chemist with data which test the available theories of the electronic structure of such states. I thank Professors D. Kivelson M. A. El-Sayed and Y-N. Chiu for many fruitful discussions on this topic. 'l H. R. Falle G. R. Luckhurst H. Lemaire Y. Marechal A. Rassat P. Rey MoI. Phys. 1966 11 49. 72 M. A. El-Sayed and S. Siegel J . Chem. Phys. 1966,44 1416; M. Lhoste P. Hang and M. Ptak ibid. p. 645 654; G. P. Rabold and L. H. Piette Photochem. und Photobiol. 1966 5 733. 74