J. Phys. Chem. 1994,98, 8761-8764
8761
Third-Order Nonlinear Optical Properties of Soluble Octasubstituted Metallophthalocyanines Maria A. Diaz-Garcia,?Isabelle Ledoux,* Jose A. Duro,S Tomas Torres,f* Fernando AgulM-Mpez,'*?and Joseph Zyss'J Departamento Fisica de Materiales C-IV and Departamento Quimica Orghnica, Universidad Autbnoma de Madrid, 28049 Madrid, Spain, and France Telecom, CNET Paris- B, DEp. d'Electronique Quantique et Moliculaire, 196, Av. Henri Ravera, 92225 Bagneux, France Received: February 17, 1994; In Final Form: April 29, 1994"
The molecular hyperpolarizabilities y(-3w:o,w,o) and y(-2w:o,w,O) of new soluble octasubstituted metal-free phthalocyanine l a (RsPcH2) and metallophthalocyanines lb,c,d (RsPcM, M = Cu2+,Ni2+, Co2+) have been determined by third harmonic generation (THG) and electric field induced second harmonic generation (EFISH) in chloroform solutions. Excitation wavelengths were 1.340 pm for T H G and 1.064 pm for EFISH experiments. Both real and imaginary parts of y have been obtained from the concentration dependence of the harmonic intensities. While no systematic differences between the metal-free and the metallocompounds have been found in the T H G experiments, a marked enhancement in the magnitude of y has been brought about by the metal in the EFISH measurements. Experimental T H G data have been satisfactorily analyzed in terms of a four-level model including two one-photon-allowed levels (corresponding to the Q and B bands) and a one-photon forbidden level placed a t around 0.5 pm from the ground state. The enhancement of y observed in the metallocompounds in the EFISH experiments appeared to be related to o resonance with additional one-photon-forbidden d-d levels associated with the metal, expected in the 1-1.3 hm region.
Introduction Currently, metallophthalocyanines (PcM) and related compounds, such as metallotriazolehemiporphyrazines,are being intensively studied as targets for organic materials with large and fast third-order nonlinear optical (NLO)responses.l-13 These metallomacrocycles are highly conjugated .rr-electron systems whose electronic distribution can be easily modified by incorporation of different metal atoms in the central coordination hole or through peripheral substitution in the macroring either by electron-donating or withdrawing groups. The optical spectra of phthalocyanine^'^ are dominated by two intense bands, the Q band in the visible range (at around 0.670 pm) and the B band in the near ultraviolet region (at around 0.340 pm). They are correlated with AT* transitions in a one-electron level diagram, suchas that reported by Ortiet al.,15througheffectiveHamiltonian calculations. The presence of a metal introduces minor changes in the structure of the spectra, partly due to a change of symmetry from D2h (for the metal-free compound) to either D4h or C4" (for the metallophthalocyanines depending on whether the metal fits or not inside the ring). Moreover, new metal-ligand and ligandmetal charge-transfer bands as well as strongly forbidden metalmetal transitions may appear in the spectra in the near infrared (1-1.3 pm). The third harmonic nonlinear susceptibilities x ( ~of) metallophthalccyanine thin films have been extensively investigated.3~~-~* However, the determination of the molecular hyperpolarizability y is hindered by the lack of a reliable knowledge of the film structure. On the other hand, molecular hyperpolarizabilities y(w:w,--w,w) have been determined for several metallophthalocyanines and naphthalocyanines by means of degenerate fourwave mixing (DFWM).4y6 Moreover, y(-3u:o,u,o) values have been obtained from THG experiments in solution for a number of structurally related compounds, including a silicon-naphthalo~yanine~ and several metallotriaz~lehemiporphyrazines.~~ + Dep. FKsica de Materiales C-IV. 5 0
Dep. Qufmica Orginica. France Tele.com. Abstract published in Advance ACS Abstracts, August 1, 1994.
la (R,PcHJ: M = 2H l b (RaPcCu): M = Cu IC (R,PcNi): M = NI Id (RgPcCo): M = Co
Figure 1. Chemical structure of octasubstituted metallophthalocyanines.
We have recently described the preparation of octasubstituted copper phthalocyanine l b ( R ~ P c C U )(see ' ~ Figure 1) where the nucleophilic centers of its eight amide chains can act cooperatively in cation coordination to promote sandwichlike agreggation in solution. Moreover, phthalocyanine l b (R8PcCu)"shows liquidcrystal behavior at room temperature." Therefore an important feature of phthalocyanines 1, besides their high solubility in apolar organic solvents, is their feasibility to self-organize either in a cofacial oligomeric arrangement by cation-induced aggregation in solution or by formation of discotic mesophases. These characteristics prompted us to undertake a study of the NLO properties of phthalocyanines 1.
0022-3654/94/2098-8761$04.50/0 0 1994 American Chemical Society
8762 The Journal of Physical Chemistry, Vol. 98, No. 35, 1994
Diaz-Garcia et al.
/
.
,
0 05
0
x
100
200
300
400
500
CELL DISPLACEMENT (microns)
600
700
800
Figure 2. THG maker fringes at 1.34 pm for a chloroform solution of RsPcCu (1 X IO-) M): (*) experimental values; (-1 best fit.
In this paper we report on THG and EFISH experiments at respectively 1.340 and 1.064 pm fundamental wavelengths for this series of new octasubstituted metal-free and metallophthalocyanines 1 in chloroform solutions as monomeric ~pecies.1~ From the concentration dependence of the harmonic intensities, both real and imaginary parts of y have been determined. While the THG technique has the advantage of probing exclusivelyelectronic nonlinearities, EFISH experiments may also include some reorientational contribution. Nevertheless, thermal effects are avoided. Experimental Section The compounds were characterized by elemental analysis, I R and UV-visible spectroscopies, fast atom bombardeament (FAB) mass spectrometry, and nuclear magnetic resonance. UV-visible and infrared measurements were carried out respectively on Perkin-Elmer Model Lambda 6 and PU 97 16 Philips spectrometers. FAB-MS spectra were determined on a MAT 900 (Finnigan MAT, GmbH, Bremen) instrument. Proton N M R spectra were recorded with a Bruker WM-200-SY, 200 M H z spectrometer. THG and EFISH experiments have been performed in chloroform solutions, as a function of concentration at respectively 1.340 and 1.064 km fundamental wavelengths. Both are emitted by Q-switched Nd3+:YAGlasers with 60 and 20 ns pulse duration, respectively. A liquid cell with thick windows in the wedge configuration18 was used to obtain the Maker fringe pattern (harmonic intensity variation as a function of liquid cell translation). In the EFISH experiment, the incident beam was also synchronized with a dc field applied to the solution containing the nonlinear molecules. From the concentration dependence of the harmonic signal with respect to that of puresolvent, both real (7') and imaginary (7") parts of the molecular hyperpolarizability y (y = y' + iy") were determined. The method of analysis19JO consists of two steps: first, a least-squares fit of these Maker fringes allowed us to determine the dispersion of the refractive index (real part) and the maximum harmonic intensity for each concentration (in this case it ranged between 2.5 X 1LV and 2 X 10-3 M). The imaginary part of the index is directly measured from the absorption spectra of the solutions. An example of the fitting is given in Figure 2. No appreciable difference was found in the fitted dispersion An = n3, - n, for the solution with respect to the solvent (An = 0.0 162). In the second step, a least-squares fit of the maximum intensity (at fixed cell position) as a function of concentration was performed as illustrated in Figure 3a for THG data and Figure 3b for EFISH data. From these fittings the molecular hyperpolarizability values were finally determined. Compound lb (RsPcCu) was described in detail recently.16 The synthesis17 of the metal-free phthalocyanine la (RsPcH2)
CC-' -1
'
2
'
c
6
8
12
' L
C O N C E N T R A T I O N ( x 1 0-4m o l / l ) Figure 3. Harmonic intensity (maximum amplitude) as a function of concentration: (A) THG at 1.34 pm for RsPcNi and RgPcH2; (B) EFISH at 1.06 pm for RsPcCo and RsPcH2.
and the nickel(I1) complex IC (RsPcNi) was achieved by standard procedures starting from the corresponding 1,Zdicyano derivative. The synthesis of the cobalt(I1) complex (RgPcCo) is described below. Synthesis of 2,3,9,10,16,17,23,24-Octaki~((dioctylamino)carbony1)methoxylphthalocyaninate Cobalt(II), Id. This compound was obtained in three steps starting from 4,Sdibromo1,2-[((dioctylamino)carbonyl)methoxy]benzene (4,5-DBB).I6 (a) 1,2-Dicyano-lJ- [((diocty1amino)carbony1)methoxy] benzene (1,2-DCB). A mixture of 4,5-DBB (5.30 g, 6.38 mmol) and copper(1) cyanide (1.83 g, 20.42 mmol) in D M F (41 mL) is heated at reflux temperatureunder argon for 13 h. After cooling, the mixture is treated with 150 mL of hexane, 75 mL of CH2Cl2 and 150 mL, of NH4OH (30%). The organic phase is treated several times with N H 4 0 H (30%) until the blue color disappears and afterward with water. Pure 1,2-DCB is isolated from the mixture by column chromatography on silica gel (hexane/CHC13/ AcOEt = 3/3/1) and then recrystallized from MeOH to yield 2.15 g (47%) of a white solid, mp 75-77 OC. Anal. Found: C, 72.31; H , 10.19; N, 7.65. Calcd for C44H74N404-0.5H20: C, 72.19; H , 10.37; N, 7.65. I R (cm-l, CHC13) 2920, 2870, 2240 (w, C E N ) , 1660 (s, C=O), 1590,1460, 1430,1370, 1290 (C0-C), 1110 (s, C-0-C). FAB-MS (m-NBA, m / z ) 724 (M + H+),454 [M+-OCN((CH2)7CH3)2]. 'HNMR(CDCl3)0.87, 0.89(12H,t,t,J=6.2Hz,CH3), 1.3(40H,m,CH2), 1.6(8H,
The Journal of Physical Chemistry, Vol. 98, No. 35, 1994 8763
Third-Order Nonlinear Optical Properties 18
TABLE 1: Characteristic Parameters for B and Q Bands (01 and 02 Transitions, Respectively) of Phthalocyanines, Determined from Their Linear Optical Spectra’
h
compd bmaX c rol M I X02max c rO2 l c ~ R ~ P c H ~ 348 5.8 12037 14.6 690 6.7 1300 8.1 R~PcCU 330 1.7 14359 15.6 672 17.9 445 10.5 RsPcNi 285 7.9 10188 16.0 665 18.3 452 10.1 R~PcCO 320 8.8 10684 17.0 668 16.2 632 12.0 kabmaX (nm) is the center of the transition ab, c (X104 dm3 mol-’ cm-I) is the extinction coefficient,rab(cm-l) is the line width, pub (debye) is the transition dipole moment. 200
400
600
800
W A V E L E N G T H (nm)
Figure 4. Optical electronic spectra of R8PcH2 (full line) and RgPcCo (dashed line).
TABLE 2 Third-Order Microscopic Hyperpolarizability7 (XlO-32 esu) of Phthalocyanines from THG and EFiSH Experiments at Respectively 1.340 and 1.064 pm Fundamental Wavelenethsa y’ (x1&32),
compd
esu
ly”l
(~10-9,
esu
ly1
(x10-32),
esu
THG (A = 1.340 pm) m, CHZCHIN),3.2,3.3 (8H, m, m,CHzN),4.88 (4H, s, CH20), R ~ P c H ~ -2.97 3.47 4.57 180 f 49.4 R~PcCU -2.23 180 f 24.4 1.01 2.45 7.11 (2H, s, arom H). I3C NMR (CDC13) 13.9 (CH3), 22.4, -2.51 1.95 3.18 RBPcNi 180 37.8 26.8, 27.3, 28.7, 29.1, 31.6 (CHz), 45.9, 46.8 (CHzN), 66.9 3.06 4.48 R~PcCO -3.28 180 f 43.0 (CHzO), 108.8 (CCN), 115.5 (CN), 118.0 (arom CH), 151.5 (C-0), 165.0 (C=O). EFISH (k = 1.064 pm) -0.21 0.90 0.92 180 f 76.9 (b) 1,3-Diimino-5,6-bis[ ((dioctylamino)carbonyl)methoxy]180 f 35.7 -3.20 2.30 3.94 isoindoline (1,j-DII). NH3 (gas) is bubbled through a suspension -1.54 1.93 2.41 180 f 51.4 of 1.16 g (1.60 mmol) of 1,2-DCB and 30 mg (0.5 mmol) of -3.22 2.99 4.39 180 f 42.9 sodium methoxide in 15 mL of dry MeOH for 15-30 min. y’, y”, IyI and $ are real part, imaginary part, modulus and phase, Afterward the mixture is heated to reflux temperature for 4 h respectively. while keeping gas bubbling. After cooling, the solution is filtered, and the solvent removed. In this way an oily greenish product at around 0.670 pm is observed, similar spectra being observed is obtained in quantitative yield. IR (cm-1, CHC13) 2920,2860, for the other metallocompounds. For Id (R~PcCU)a very weak 1660-1630 (s,C=O), 1460,1420,1060 (s, C-0-C). FAB-MS band at 1.085 pm has also been observed. In all cases monomeric (m-NBA,m/z) 741 (M + H+),471 [M+-OCN((CHZ)~CH~)Z]. species of phthalocyanines are i n v o l ~ e d . ~ ~ JThis ~ . ~fact ~ - ~has ~ FAB-MS (high resolution) Found: 740.6105. Calcd for C44been confirmed even for high concentrations (2 X 10-3 M) of H77N504: 740.6054. IH NMR (MeOH-d4) 0.92 (12H, t, J = compounds la-d by the spectral profile of the Q-band in the 6.7 Hz, CH3), 1.31 (40H, br s, CHZ), 1.6 (8H, m, CH2CHzN), UV-visible spectra and by EPR of compound lb. The most 3.4 (8H, m. CHzN), 4.99 (4H, s, CH20), 7.45 (2H, s, arom H). important features for Band Q bands are listed in Table 1: center lc NMR (MeOH-d4) 14.2 (CH3), 23.4, 27.6, 27.7, 28.2, 29.5, of the transition (A,,,), extinction coefficient (e), line width (I’ 30.1, 32.6 (CHI), 46.9, 47.7 (CHzN), 67.8 (CHzO), 107.7 = fwhm) and the dipole transition moment from the ground state (CC=N), 130.6 (aromCH), 151.4(C-O), 168.2 (C=O), 170.4 (h, calculated by integration of the spectrum). (C=N) . Experimental values of the real y’ and imaginary y” parts of (c) 2,~,9,10,16,17,23,24-0ctakis[((dioctylamino)carbonyl)- y(-3w:w,w,w) and y(-2w:o,w,O), from THG and EFISH data methoxylphthalocyaninate Cobalt(II) (RaPcCo, 14. 1,3-DII respectively are summarized in Table 2. To the best of our (170 mg, 0.23 mmol) and CoC12.6H20 (14.3 mg, 0.06 mmol) in knowledge, no previous EFISH data have been reported. 0.17 mL of 2-(dimethy1amino)ethanol are heated at reflux Our present THG y(-3w:w,o,o) values, measured at 1.340 temperature under argon for 7.5 h. After cooling, the crude pm, are of the same sign (negative) and magnitude as those product is extracted with hexane from a hexane/MeOH/HzO previously obtained for metallophthalocyaninesM and higher than (8/5/3) two-phase system. Then, it is purified by column those reported for the related compounds metallotriazolehemichromatography on silica gel (AcOEt/MeOH = 10/1) and porphyrazines.13 While in these cases4J3 partly-filled d shells washed with CHjCN/HzO (5/1). Finally the green-bluish induced a marked enhancement of y, in the present case no product is dried at 140 O C / l e 3 Torr. The yield is 52 mg (30%), significative effect of metal complexation was observed. mp 132-134 OC. Anal. Found: C, 69.29; H, 10.00; N, 7.36. The situation is different for the EFISH results. Table 2 shows Calcdfor C176Hz96CON16016’5Hz0: c,69.50; H, 10.14;N, 7.37. that y(-2w:w,w,O) for the metal-free molecule l a (RsPcH2) is 1 IR (cm-I, CHC13) 2930, 2860, 1710 (s), 1650 (s, C=O), 1480, order of magnitude lower than its corresponding y(-30:w,w,w) 1420, 1280 (C-0-C), 1140-11 10 (C-0-C). UV-vis I,,,/nm value from THG. On the other hand, the metallocompounds (log c/dm3 mol-1 cm-1) (CHC13) 297 (4.9), 331 (4.8), 385-390 1b-d keep a similar value of y for THG and EFISH. Therefore, (sh), 604 (4.6), 650-655 (sh), 669 (5.2). FAB-MS (NPOE,m/z) a clear effect of the metal is revealed, which becomes highest for 2949 (M+). Id (R~PcCO). Our discussion will deal with effective Hamiltonian (VEH) Results and Discussion calculations.15 The higher lying P and lower lying A* one-electron energy levels are schematically represented in Figure 5 for the Compounds l a 4 are very soluble in apolar organic solvents such as hexane and carbon tetrachloride, among others. Their unsubstituted metal-free phthalocyanine (PcH2). The two solubility in the most polar ones (MeOH, DMF) is slightly lower. componentsoftheQ band are respectively associated to 4a,-6b2,* and 4au+6b3,* transitions. On the other hand, the B band Optical spectra of l a (RsPcHz) and Id (RgPcCo) in chloroform originates from a groupof close-lyingtransitions, the most intense are represented in Figure 4 as an illustration. The spectrum of l a (RsPcH2) displays the typical split Q band in the lower energy being 7bI,+6bzg*, 7b1,+6b3,*, and 3a,+6bzg*. In this scheme, one-photon-forbidden transitions would also be expected: region at 0.698 and 0.661 pm and the B or Soret-band centered at around 0.346 pm. In the case of Id (RgPcCo) a single Q band 4a,+5a,*,8bl,*,9bl,*, approximately in the 400-600 nm region;
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The Journal of Physical Chemistry, Vol.98, No. 35, 1994
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the 5a,* orbital, both having different parity. On the contrary, the B-excited configuration cannot be coupled to the one-photon forbidden level since two electrons should change from the 7bl,5a,* to the 4a,6b2,* orbitals. This immediately justifies that pi3 = 0 (whereas p23 # 0), in agreement with the calculations made with our model. For the EFISH experiments, interpretation of the results may be not simple. On one side, possible molecular reorientational effects may arise through the dielectric anisotropy of the planar phthalocyanines or even due to a small dipolar coupling contribution in the case of the metallocompounds.8 At variance with the THG experiments where the nonlinearity is strongly influenced by the 3w resonance with the B band, the EFISH data are only sensitive to resonance effects at w and 2w. This is similar to the case of the DFWM experiments6 performed at 1.064 pm fundamental wavelength. Therefore, y (EFISH) and y (THG) values for the metal-free phthalocyanine are expected to be different as experimentally found. On the other hand, experimental evidence6 indicates that the transition metal introduces strongly forbidden bands in the 1-1.3 pm region. Then, w resonance with this band would account for the observed metalinduced enhancement of y in the EFISH experiments. However, this resonance effect might not essentially modify the THG data, largely governed by the 3w resonance. In other words, one may foresee that T H G data are less sensitive to the presence of the metal ion than the EFISH ones. This behavior has been roughly confirmed by simulation of the effect of the new metal-associated level on the previous four-level expression for y (THG). Anyhow, additional data to fully clarify the nonlinear behavior of the metallophthalocyanines are now in preparation.
t
-2a, PcHz
Figure 5. Valence effective Hamiltonian (VEH) one-electron energy levels ~ a l c u l a t e dfor ~ ~PcH2.
7bl,-+5a,*,8bl,*,9bl,* between 280 and 305 nm and higher energy transitions from 7bl, and 6blu levels. In principle, both Q and B bands should contribute to y for THG and EFISH experiments. However, a model including only these two levels,in addition to the ground state, is not in accordance with the experiments. On the other hand, as we noted previously, parity-forbidden one-photon transitions are also expected. Therefore, a more elaborated model including, at least, a one-photonforbidden level, should be used. It has been ascertained that a four-level model including the ground state IO), two one-photon-allowed 11) (B band) and 12) (Q band), and a one-photon-forbidden (two-photon-allowed) level 13), may satisfactorily explain the THG data. Quantitative analysis based on four-level expressions derived from Orr and Ward formula^^^^^^ for y were carried out. Hyperpolarizability values were fitted in terms of excitation wavelength, by using the position, line width, and dipole moment associated with the onephoton-forbidden level as fitting parameters. A good agreement was found in all the compounds when this level was placed at around 500 nm, with a line width r23= rOz and dipolar moments p23 = 7.5, 11.5, 7, and 10 D for l a ( R ~ P c H ~l )b, (R~PcCU), IC (RsPcNi), and Id (R~PcCO)respectively and pi3 = 0. In accordance with the one-electron level scheme of Figure 5, this one-photon-forbidden level may be associated to an excited configuration such as 7blu24alu15au*1(ignoring lower occupied levels), located in the 400-600 nm region from the ground state. On the other hand, representative excited configurations for Q and B bands are respectively 7b1,24a,16b2,*1 and 7b1,14a~,26b2,*1. The Q-excited configuration is coupled to the one-photon forbidden state since only one electron changes from the 6b2, to
Acknowledgment. This work was supported by CICYT (Spain) through grants MAT9010317, MAT9310075 and TIC91/0142. We thank Dr. W. Torruellas and Dr. F. Kajzar for useful discussions. References and Notes (1) Nalwa, H. S . Appl. Organomet. Chem. 1991, 5 , 349. (2) Nalwa, H. S. Adu. Mater. 1993, 5 , 341. (3) Ho, Z. Z.; Ju, C. Y.; Heterington 111, W. M. J. Appl. Phys. 1987, 62, 716. (4) Shirk, J. S.; Lindle, J. R.; Bartoli, F. J.; Hoffman, C. A,; Kafafi, Z. H.; Snow, A. W. Appl. Phys. Lett. 1989, 55, 1287. ( 5 ) Wang, N. Q.; Cai, Y. M.; Helfin, J. R.;Garito, A. F. Mol. Crysf. Liq. Crysl. 1990, 189, 39. (6) Shirk, J. S.; Lindle, J. R.; Bartoli, F. J.; Kafafi, Z. H.; Snow, A. W.; Boyle, M. E.; Int. J. Opt. Phys. 1992, 1, 699. (7) Casstevens, M. K.; Sa", M.; Pfleger, J.; Prasad, P. N. J. Chem. Phys. 1990, 92, 2019. (8) Chollet, P. A.; Kajzar, F.; Le Moigne, J. Mol. Eng. 1991, I, 35. (9) Hosoda, M.; Wada, T.; Yamada, A.; Garito, A. F.; Sasabe, H. Jpn. J. Appl. Phys. 1991, 30, 1715. (10) Hosoda, M.; Wada, T.; Yamada, A,; Garito, A. F.; Sasabe, H. Jpn. J. Appl. Phys. 1991, 30, 1486. (11) Grund, A.; Kaltbeitzel, A.; Mathy, A.; Schwarz, R.;Bubeck. C.; Vermehren, P.; Hanack, M. J. Phys. Chem. 1992, 96, 7450. (12) Nalwa, H. S.; Kakuta,A.; Mukoh,A. J. Phys. Chem. 1993,97,1097. (13) Dfaz-Garcia, M. A,; Ledoux, I.; Fernindez-Lizaro, F.; Sastre, A.; Torres, T.; Agull&L6pez, F.; Zyss, J. J. Phys. Chem. 1994, 98, 4495. (14) Leznoff, C. C.; Lever, A. B. P.; Phthalocyanines. Properties and Applications; VCH Publishers: New York, 1989, 1993; Vols. 1-3. (15) Ortf, E.; BrMas, J. L.; Clarke, C. J. Chem. Phys. 1990, 92, 1228. (16) Duro, J. A,; Torres, T. Chem. Ber. 1993, 126, 269. (17) Duro, J. A. Ph. Thesis, Universidad Autdnoma de Madrid, 1993. (18) Kajzar, F.; Messier, J. Reu. Sci. Instrum. 1987, 58, 2081. (19) Kajzar, F.; Ledoux, I.; Zyss, J. Phys. Reu. A 1987, 36, 2210. (20) Kajzar, F. Spring Proc. 1989, 36, 108. (21) Sielcken, 0. E.; van Tilborg, M. M.; Roks, M. F.; Hendriks, R.; Drenth, W.; Nolte, R.J. J. Am. Chem. SOC.1987, 109, 4261. (22) Kobayashi, N.; Lever, A. b. P. J. A m . Chem. Soc,1987, 109, 7433. (23) Ahsen, V.; Yilmazer, E.; Ertas, M.; Bekiroglu, 0. J. Chem. SOC., Dalton Trans. 1988, 401. (24) Orr, B.; Ward, J. F. Mol. Phys. 1971, 20, 531. (25) Ward, J. F. Rev. Mod. Phys. 1985, 37, I .
