J. Phys. Chem. 1991, 95, 5422-5426
5422
A18 and by the use of eqs AI and A8 (and the corresponding equations with x, y , and z permuted), we find
iD = zp"~,(-y) R~(TW) ~,(cd)
('419)
Since Euler angles give a unique parametrization of an orthogonal matrix we may conclude that
&*:
Y - 7 6 - n - 6
(A201
19-9 In the same manner by eq A1 1,
i$,(*)
= (23)iD
(A211
= qmstR,(y')R y ( W R,(d) whence (23) :
p9-
Y x + 6
(A221
n-9
The effect of the other generator (123) on the Euler angles follows from eq A10, and the effect of the other symmetry operations by group multiplication. The results are summarized in Table I.
Note finally that there is freedom in representing the effect of the symmetries on the Euler angles. For instance, (23) may alternatively be given as (cf. eqs A22, A7, and A8), RAT) Ry(*+G) RA.lr-cp) = RAT) Ry(*) Ry(b) RA-d = RAY) RA*) Ry(*) Ry(-G) RA-d =
R,(*+Y) Ry(*-9) RA-d (A23) The last possibility is given in Table I. Table I1 follows from Table I by writing Dg,{01,~2,~3)*a d"u1d2m4~2)d""u3 (A241 and the use of the well-known properties of the Wigner d funct i o n ~ .Furthermore, ~ we define for all group elements in PI(D,*) a corresponding operator by
h ( R , b , c p , ~ , B , a= ) WP'lR,b,v,r,B,al) (A23 In ref 2 we gave the linear combinations of basis functions adapted to PI(C,). Those adapted to PI(D3*)are easily obtained by the following relations ( E + 8*)IA1) = IAl') ( E - 8*)1A1) = IAT) (B+ %*)(A2)= IA;) ( E - E*)IAz) = [AI") ( E + 8')IE) IE') ( E - 8')IE) = E") (A26) Registry No. Ar, 7440-37-1; NH,,7664-41-7.
Resonances In Valence Shell Photolonlzatlons of Cyanogen. Photoelectron Angular Dktrlbutlon Parameters of the g2&, A2Ef, B2E:, and Ionlzatlons up to a Photon Energy of 28.5 eV
C2n,
Jagen Kreile, Heinz-Meter Kurland, Werner Seibel, and Armin Scbweig* Fachbereich Physikalische Chemie, Universitdt Marburg, Hans- Meenvein-Strasse, 3550 Marburg, Germany (Received: December 13, 1990)
Photoelectron angular distribution parameters for the first four valence shell photoionizations of cyanogen, for the first one also vibrationally resolved, have been measured by using synchrotron radiation. Compared to earlier measurements, the present ones refer to an extended energy range (14.3-28.5 eV) and are more accurate and precise. Resonance features are discussed with regard to former experimental and theoretical findings and, in particular, to contradictory theoretical results. Thus, our measurements provide evidence for the presence of a ru shape resonance in the A2Z+ ionization, only predicted by a former frozen core Hartree-Fock calculation, and a strong r8 shape resonance in the B2Z{ionization, only supported by our multiple-scaitering Xa calculations. In addition, our measurements reveal a distinct minimum around a photon energy of s 2 0 eV in the A2Z: distribution vs photon energy curve which was not discernible in earlier experimental data.
Introduction High-resolution angle-resolved photoelectron spectroscopy coupled with a variable-energy photon source allows detailed studies to be made on the photoelectron dynamics of molecules incorporating such phenomena as shape resonances and autoionization proces~es.I-~Both types of phenomena give rise to distinct features in molecular photoionization such as rapid variations in photoelectron angular distributions, enhancements in cross sections, and non-Franck-Condon effects in vibrationally resolved Precise measurements of the photoelectron angular distribution parameters for ionizations of molecules as
a function of the photon energy provide a sensitive probe for the identification of shape resonances and autoionizations. Detailed comparisons of experimental and theoretical results are valuable in characterizing the nature of these phenomena. Several studies on the photoionization of cyanogen (ethaneboth experimentalH and theoretical,4'-9 dinitrile, N=C-N), have been made before. Based on partial photoionization cross section and photoelectron angular distribution parameter calcu(4) Kreile, J.; Schweig, A.; Thiel, W. Chem. Phys. Left. 1983, 100, 351. (5) Parr, A. C.; Holland, D. M. P.; Ederer, D. L.; Dehmer, J. L. Int. J. Mass Spectrom. Ion Phys. 1983, 46, 285.
(6) Holland, D. M.P.; Parr, A. C.; Ederer, D. L.; West, J. B.; Dehmer,
(1) Dehmer, J. L.; Dill, D.; Parr, A. C. In Phorophysics and Photochemistry in the Vacuum Ultraviolet; McGlynn, S.,Huebner, R.. Us.D. ; Reidel: Dordrecht, Holland, 1984; p 341. (2) McKoy, V.;Carlson, T. A.; Lucchese, R. R. J. Phys. Chem. 1984,88, 3 188. (3) Madden, R. P.; Parr, A. C. Appl. Opr. 1982, 21, 179.
OO22-3654/91 /2095-5422$02.50/0
J. L. Int. J. Mass Spectrom. Ion Phys. 1983, 52, 195. (7) Kreile, J.; Schweig, A,; Thiel, W. Chem. Phys. Lett. 1984, 108, 259. (8) Lynch, D. L.; McKoy. V.; Lucchese, R. R. In Symposium on Resonances in Electron-MoleculeScattering, van der Waals Complexes and Reactiuc Chemical Dynamics; Truhlar, D. G., Ed.;ACS Symposium Series 263;
American Chemical Society: Washington, DC, 1984; p 89. (9) Lynch, D. L.; Dixit, S. N.; McKoy, V. J. Chem. P h p . 1986,845504,
0 199 1 American Chemical Society
The Journal of Physical Chemistry, Vol. 95, No. 14, 1991 5423
Valence Shell Photoionizations of Cyanogen lations for the g211g, A22:, B2Z:, and C211, ionizations using a mixed LCAO (linear combination of atomic orbitals)/MS Xa MO (multiple-scattering X a molecular orbital) meth~d,'.~.'~ several shape resonances were predicted to occur in these hotoionizations. The presence of a a, shape resonance in the f 2 Z : ionization was verified by determining vibrationally resolved angular distribution parameters using Ne I, He I, and Ne I1 line sources.' Angular distribution parameters (or @ values) for the first four photoionizations were measured with synchrotron radiation up to a photon energy of 24 eV.576 Photoionization cross sections and @ parameters 5 a function of the photon energy were recalculated for the fC2 A22:, and B2Z: ionizations employing the FCHF (frozen core artree-Fock) method.**9Interestingly, the FCHF and LCAO/MS X a MO results are not only quite different in some energy ranges but, even more seriously, also exhibit differences in the number and nature of the shape resonances predicted. Thus, in the energy range considered in the present study the LCAO/MS X a MO calculations indicate the presence of a strong r shape resonance in the B22: ionization, which does not result hom the FCHF calculations; on the other hand, the FCHF method provides evidence for the occurrence of a r, shape resonance in the A2Z: ionization, which is not derived from the LCAO/MS X a MO calculations. Since the experimental data4v6available were not sufficient9 to clarify the situation, we undertook a set of new measurements of the asymmetry parameters (including vibrationally resolved data for the ft211, ionization) using synchrotron radiation. The data are more accurate and precise than the previous ones and refer to an extended range of photon energies (14.3-28.5 eV). The results su est the presence of both a strong r8shape resonance in the B2E, 88 ionization (as indicated by the L_CAO/MS X a MO method) and a ru shape resonance in the A22: ionization (as obtained in the FCHF calculations). In addition, our measurements reveal a distinct minimum around a photon energy of -20 eV in the A221@ vs photon energy curve which was not discemible in earlier experimental datanc6 Other photoelectron spectroscopic work on cyanogen includes the He I"S2 and He III3 photoelectron spectra, the photoionization and the yield curve,14the electron impact energy loss spectr~m,'~ Penning ionization spectrum.I6
'I
NzC - C=N', Epho,=21.00eV. 0'. 19 1'
7:1200
t
nt;
Experimental Section The monochromator, apparatus, data aquisition, data analysis, and correction procedures are described in detail elsewhereI7and are only briefly reviewed here. Measurements of the photoelectron angular distributions were carried out at the synchrotron radiation source BESSY (Berliner Elektronen-Speicherring Gesellschaft fur Synchrotronstrahlung mbH). The elliptically polarized synchrotron radiation was dispersed by a 2-mSeya Namioka monochromator at beamline 43.12. Two gratings with 610 lines/mm (AI/MgF2 coated, ruled) and 1200 lines/mm (Pt coated, holographic) were used to cover the photon energy (Epbt)ranges up to 21 eV and above 21 eV, respectively. For all measurements the monochromator entrance slit was set to 375 pm. The exit slit was set to 250 pm up to 26.5 eV photon energy and opened to 375 pm above 26.5 eV in order to increase the electron signal. Angle-resolved photoelectron spectra of cyanogen were measured in the photon energy range from 14.3 to 28.5 eV, using an angle-resolving photoelectron spectrometer equipped with an ~
~ _ _ _ _ _
(IO) Thicl, W. Chem. Phys. 1981, 57, 227 and references therein.
(11) Baker, C.; Turner, D. W. Proc. R. Soc. London 1968, A308, 19. (12) Turner, D. W.; Baker, C.; Baker, A. D.; Brundle, C. R. Molecular Phororlecrmn Spectroscopy; Wiley-Interscience: London, 1970. (13) Asbrink, L.; von Niesscn, W.; B i d , G. J . Electron Spectrosc. Relat. Phemm. 1980,21,93. (14) Dikler, V. H.; Liston, S. K. J. Chem. Phys. 1967, 47, 4548. (15) g d h , C.; Asbrink, L.; Lindholm, E. Chem. Phys. 1978, 27, 169. (16) rmak, V.; Ycncha, A. J. J . Electron Specrrosc. Relat. Phenom. 1976,4109. (17) b i l e , J.; Kurland, H.-D.; Seibel, W.; Schweig, A. Submitted for
publication.
13
16
15
16
17
IE / eV Figure 1. Background-corrected and smoothed photoelectron spcctrum of cyanogen recorded with synchrotron radiation at E-, = 21 cV and
e/ = 1910.
electrostatic 150' spherical sector analyzer rotatable in a plane perpendicular to the photon beam direction. Operating the analyzer in the constant-energy mode with a preselected pass energy of 1 eV, we found that the resolution of the spectrometer is mainly given by the energy resolution of the monochromator. The full width ?t half-maximum (fwhm) of the first vibrational member of the X2ngphotoelectron band was between 100 and 150 meV in the lower and 100 and 130 meV in the higher energy range. The photoelectron spectrum of cyanogen including the first four ionizations was recorded in the ionization energy range from 12.7 to 16.9 eV comprising 640 data points so that the energy difference between two adjacent data channels was less than 7 meV. At each photon energy, spectra were measured at six different angular positions of the electron analyzer (between 191' and 395', i.e., over an angular range of 2049 relative to the plane of the storage ring. For partial compensation of any drifts, the measurements were carried out in several consecutive series, scanning the angles in each series. In order to correct the electron count rates for the decrease in photon intensity during the sampling proccss, the relative photon intensity was monitored with a gold photocathode mounted behind the ionization region. The sample gas pressure in the spectrometer chamber was held constant at 5.5 X lC3 Pa. The degree of linear polarization P of the monochromatized synchrotron radiation as a function of the photon energy was derived from measurements of the electron angular distributions from selected ionizations of rare gases (Kr+ 2P,/2for EPb I 25 eV, He* 2S1/2for Epbot> 25 eV) with well-known angular distribution parameters. For the range of photon energies applied, P adopted values between 0.96 and 0.99 with an uncertainty of 0.015. j3 and the azimuthal angle X (denoting the rotation of the polarization ellipse with respect to the storage ring plane) were determined from a weighted least-squares fit of the angular distribution f ~ n c t i o n ' ' -to ~ ~the photoelectron intensities (taken as the sum of the corrected a u n t rates in all relevant data channels of a discrete band) measured at different emission angles. Recording of the photoelectron intensities at six different angles over the wide angular range of 204' is very helpful in avoiding systematic errors in @ caused by an eventual noncoincidence of the beam axis of the ionizing radiation and the mechanic rotation axis of the electron analyzer (due to insufficient spectrometer adjustment with respect to the beam axis or changes of the beam position during the measurements). The errors associated with the j3 data represent the combined uncertainties in the least-squares fit and degree of polarization. For all measurements the rotational angle X was found to be in the range of f2'. Cyanogen was supplied by AGA Edelgas GmbH, 98.5% pure, and was used without further purification. (18) Samson, J. A. R.; Gardner, J. L. J . Opr. Soc. Am. 1972, 62, 856. (19) Samson, J. A. R.; Starace, A. F. J . Phys. 1975, B8, 1806.
5424 The Journal of Physical Chemistry, Vol. 95, No. 14, 1991 0
2
c
6
Yo
12
Kreile et al.
05 -
16
f2ngv 1 = 2
NC-CmN'
B
v1.l
13
15
17
19
21 23 Ephol 1 eV
25
27
0.5
-
-5
-
29
Figure 2. Photoelectron angular distribution parameters for the k211 ion state of cyanogen w photon and photalectron energies. ~xperimentaf results (vibrationally averaged): (0)present work (x) rcf 6. Theontical results: (-) LCAO/MS Xa MO method,' (---) FCHF method?
Results .nd Discussion The relevant part of the cyanogen photoelectron spectrum along with the assignment of bands1IJ2 is shown in Figure 1. The vertical ionization energies for the g2 A2Z+, B2Z:, and C2n, ionizations are 13.36, 14.49, 14.86, a 2 1 5 . 4 1 eV.1LJ2The ionization into the g2n,state leads to a well-resolved strong vibrational progression with a spacing of 0.26 eV, which has been ascribed to the m N in-phase stretching mode u1 (where Y, is the nth normal mode of vibration).I1J2 The measured angular distribution parameters together with the calculated LCAO/MS Xa M e and the FCHF 6 functions9 available (Le., 6 as a function of the photoelectron energy Efin or the photon energy E-) are shown in F i i e s 2 and 4-6. (Note that a data point without an error bar means that the error associated with the corresponding p value is smaller than the height of the data symbol depicted,) The measured data for the R2ng and C211, ion states (Figures 2 and 6) are the vibrationally averaged 6 parameters and for the A2Zz and B2Z: states (Figures 4 and 5 ) the ones of the dominant uI = 0 transition. Figure 3 exhibits the experimental 6 curves for the three lowest vibrational levels (Le., for uI = 0, 1, and 2) of the g2n,ion state. The vibrationally unresolved 6 ( ~ 2) forithe pho~ toionization into the g211,state determined in the present work exhibits a small dip at Eun = 1.9 eV and drops to a p r o n o u n 4 minimum at E b 3.4 eV, and after going through another weak at first, then, between dip at 4.9 e ~the, 6 curve 6.6 and 1 1.6 eV, has a continuously decreasing rise, and finally, above 11.6 eV, rises quickly again. Whereas both theoretical 6 curves agree well up to 3.6 eV, the curves are totally different steeply beyond this energy. The LCAO/MS xa MO 6 maximum at 8.6 e ~which , increases to a broad and is not confinned by the experiments. neFCHF curverises, more or less smoothly with energy. The distinct structure between 2.6 and 5.6 eV in the experimental 6 curve is not reprodud by both sorts of calculations. The vibrationally resolved 6 curves (Figure 3) for the three lowest vibrational levels of the g2n,ion state exhibit strong structures 19 e ~ ne . most variations up to Ein the u1 = 0 6 curveare one saddle point (at 15 e ~ and ) ) the u1 = 1 and two minima (at Epha 16.5 and 17.8 e ~ and 2 0 cuww three minima (at E* = 15.3, 16.8, 18.3 eV and at Epb 16, 17, 18.8 eV, respectnely). Within an uncertainty of f0.3 eV (i.e., the energy difference between two adjacent data points) these structures appear in all three vibrationally resolved 6 curves at the same electron energies, Eun= 1.8, 3.1, and 4.7 eV, respectively. Above Em = 19 eV, the u, = 0 and 1 6 values behave similarly. They increase more or less monotonically, up to the end of the energy scale, without prominent structures, but with a significantly reduced slope between Epha= 21.5 and 24.5
X
v1.0 0.5
-
0.0
14
16
18
20
22 Ephol
2L eV
26
28
Figure 3. Vibrationally resolved photoelectron angular distribution parameters for the uI = 0, l, and 2 levels of the g2&ion state of cyanogen VS Photon energy. Experimental results: ( 0 )PrMnt work, ( 0 )ref 4, ref
In contrast, the = Bcurve has a less pronounced minimum at Epb. = 22.3 eV and appears to decrease above 27.5 eV. We structures observed in all three vi~ascribe~ the aforementioned ~ 6 curves between Epbol = l 5 and l6 eV (at brationally == 1.8 eV) and 17.8 and 18.8 eV (at Eh a 4.7 eV) to autoionizing Rydberg levels giving rise to marked peak series in the photoionization yield curve at corresponding energies.I4 The in 3.1these e v ) three belone to a prominent between and=broad 16.* and 17 eV (at feature buch broader than the autoionization peaks) and corresponds to a bump in the photoionization yield curve, with a maXiIllUm at E 16.9 eV.I4 Although the theoretical CI'OSSsection curves4* exhibit no peak enhancement in the vicinity of this energy*the corresponding eigenphase sums derived from both the LCAO/MS Xa MO and the FCHF calculations provide evidence for a strong shape resonance in the u, continuum of the R 2 q ion (at Eiin e 3.8 and 2.5 eV, respectively)?~~The lack of for the uu a peak in the LCAo/MS Xa Mo cross-section channel is due to the nodal behavior of the initial- and final-state wave functions leading to extensive cancellations in the corresponding transition moments.' An improvement of these wave fu~ctionswill likely diminish these cancellationsand, thus, produce an apparent resonance effect in the g211 cross section. The corresponding Q shape resonance in the f211 ionization of the isoelectronic c m & y l e n e (2-Foppnitrile, was 'leafly Out from LCAo/MS Xa Mo ca1cu1ations'*20 and experimentally Observed at EM,= 4.2 eVqMIn conclusion,
P"
(20)
press.
Kreile, J.; Kurland, H.-D.; Seibel, W.;Schweig, A. Chrm. Phys., in
The Journal of Physical Chemistry, Vol. 95, No. 14, 1991 5425
Valence Shell Photoionizations of Cyanogen Ekin
aV
. . 2. . L. . 6. . 8 . . 10.
0
12 I
.
0
1L .
'4
L
2
€kin 6
sv
8
10
12
I
t
t
r
13
15
'-13 17
19
21 23 Ephol / eV
25
27
Figure 4. Photoelectron angular distribution parameters for the h l ion state of cyanogen vs photon and photoelectron energies. Experimental results for oI = 0: ( 0 )present work; (0)ref 4, (X) ref 6. Theoretical results: (-) LCAO/MS X a MO method,' (---) FCHF method? r
2
4
6
a
10
12
1L 1
,
15
17
19
21 23 Ephol 1 eV
25
27
29
Figure 6. Photoelectron angular distribution parameters for the &'I,, ion state of cyanogen vs photon and photoelectron energies. Experimental results (vibrationally averaged): ( 0 )present work, (0)ref 4, (X) ref 6. Theoretical results: (-) LCAO/MS Xa MO method!
for Cyanogen
Theoretical resonance a Present experimental resonance energy. energy derived from the LCAO/MS Xa MO eigenphase sum!*7 'Theoretical resonance energy derived from the FCHF eigenphase sumsg FCHF calculation not available.
1 \ I7 ' 13
17
TABLE I: Experhatrl .ad Theoretical Shpe Rcsonraee hergiea
Ekin / C V 0
15
29
19
21 Ephcl
23 eV
25
27
29
Flgwe 5. Photoelmron angular distribution parameters for the 8%: ion
state of cyanogen vs photon and photoelectron energies. Experimental results for o1 = 0: ( 0 )present work, (0)ref 4, (X) ref 6. Theoretical results: (-) LCAO/MS Xa MO method,' (- -) FCHF method?
-
there is some evidence that the structure between Ephot= 16.5 and 17 eV (at Ekin= 3.1 eV), which is observed in all three vibrationally resolved j3 curves, is due to a low-energy u, shape resonance. The experimental j3 curve for the dominant ul = 0 member of the A2Z: ionization (Figure 4) rapidly falls down from threshold to a prominent minimum at ELin= 2.3 eV, rises again up to 4.8 eV, runs through a marked dip located around 6 eV, and falls, above 7.5 eV, through a weak local maximum at 9.5 eV to a very broad minimum at 12.5 eV. We assign the lower energy minimum in the experimental curve to the u, shape resonance predicted, by both the LCAO/MS Xa MO and the FCHF calculations, to = 3.8'1' and 2.5 eV? respectively. Both theoretical appear at ELin curves qualitatively reflect the present experimental #? curve below 4.5 eV. The dip in the experimental curve located at ELin= 6 eV, however, is not reproduced by the theoretical curves. For this reason and due to the presence of three small peaks in the photoionization yield curve between Epba= 20 and 20.7 eV,I4 this dip is probably due to autoionization. Whereas both theoretical /3 curves possess distinct minima at Eun* 9.0 eV (LCAO/MS X a MO) and at 17.5 eV (FCHF? very broad and flat, out of the range of Figure 4), only the FCHF method provides suffizient evidence for the presence of a ru shape resonance in the A2Z: ionization. It is the broad minimum in the experimental curve at ELin= 12.5 eV that indicates the Occurrence of the ru shape resonance, despite the fact that the calculated resonance energy
is significantly higher than the experimental one. The experimental #? curve for the ul = 0 member of the B2Z: ionization (Figure 5) falls steeply, above threshold, down to two = 2.9 and 4.9 eV. A further broad and marked minima at ELdn very flat minimum occurs at 7.9 eV, after which the cuwe slightly rises exhibiting some oscillatory behavior. The FCHF curve levels down from threshold through a very broad and shallow dip located around 2.6 eV and then smoothly increased without displaying any distinct structures. The behavior of the LCAO/MS X a MO curve is completely different. After running through a sharp and pronounced minimum, it steeply rises, from -0.1 to almost 1.5 within 5 eV, to a broad maximum. The distinct minimum is due to a strong 7r8 shape resonance predicted to appear at Eb = 3.0 eV.49' In the experimental j3 curve the sharp lower energy minimum at 2.9 eV reflects this shape resonance. However, the strength of the resonance is exaggerated by the LCAO/MS X a MO calculations. Below 15 eV, the results of the FCHF calcul a t i o n ~did ~ not give unequivocal evidence of a shape resonance in the B2Z: ionization. The second marked minimum in the experimental #? curve at EL,, = 4.9 eV is probably due to autoionization. This assignment is supported by the presence of two small peaks between Em = 19.5 and 20 eV in the photoionization yield curve, following a series of strong peaks ascribed to autoionizing Rydberg levels." The measured, vibrationally unresolved, #? parameters for the & ionization I , (Figure 6) exhibit no distinct resonance structure. Thus, after a steep rise up to Ekin= 3.5 eV the /3 curve proceads with a continuously diminishing slope and adopts, above 9.5 eV, an almost constant value. Beyond Eh = 2.5 eV the calculated LCAO/MS X a MO curve crosely parallels the experimental curve. The minimum in the theoretical #? curve is due to the rI shape resonance predicted to appear at ELin= 3.0 eV.4' The experiments bear no evidence for this resonance. Unfortunately, FCHF results are not available. Table I summarizes the present results regarding shape resonances in the first four photoionizations of cyanogen for E- =
5426
J. Phys. Chem. 1991,95, 5426-5431
14.3-28.5 eV. A m i n i p m in each of the three vibrationally resolved B curves for the X2& ion state together with the resonance behavior of the eigenphase sum for the u, continuum are good arguments for the presence of a u, shape resonance in this ionization. Two pronounced minima in the experimental /3 curve bear evidence of both the uu shape resonance (predicted by both the LCAO/MS Xa M04v7and the FCHF approaches9) and a T , shape resonance (predicted only by the FCHF calculations9) in the A%: ionization. The f i t minimum in the experimental 822: @ curve is assigned to a 7r shape resonance as suggested by LCAO/MS X a MO calc~~ations,4*~ but not so by the FCHF results? In general, our preceding line sources data4 agree well with the present synchrotron results. Above Eldn= 2 eV, the synchrotron data of refs 5 and 6 and our corresponding data are in fair agreement. At lower electron energies, however, the /3 values of refs 5 and 6 are appreciably different from th_e present ones; especially the steep rise of the fl values for the A22: and B2Z: ionizations immediately above threshold do not appear to be realistic. Due to the high precision of our B values, structural features in the corresponding curves are now more distinct-than in the preceding counterparts. Thus, for example, in our A2Zl /3 curve, a minimum at Ekin= 6.0 eV is clearly seen which was not recognized in the earlier plots because of the strong variations of the 6 values around this energya6 The dismpancies between the LCAO/MS Xa MO and FCHF approaches appear to be more pronounced then previously found for other systems (e.g., Nz2Iand C02=). On the whole, the FCHF calculations reproduce the experimental B values, for the first three photoionizations, slightly better than the LCAO/MS X a MO results. On the other hand, the LCAO/MS X a MO /3 curve for the C2n,ionization agrees very well with the measured curve (21) Lucchese, R. R.; Ram,G.; McKoy, V. Phys. RN. 1982, A25,2572. (22) Lucchesc, R. R.; McKoy, V. Phys. Reo. 1982, A26, 1406.
above Eldn = 2.5 eV. Even if we consider that both theoretical methods do not include autoionization, the calculated curves deviate more from the experimental ones than desired. Therefore, improved theories of molecular photoionization would be timely and helpful.
Conclusions Based on high-precision angular distribution parameters for the first four photoionizations of cyanogen which were determined by using the synchrotron radiation source BESSY, the following conclusions were drawn: (1) there is a distinct minimum in the AZZ: /3 curve (angular distribution parameters vs photoelectron or photon energy) which was not recognized in the earlier res~lts;~6 (2) LCAO/MS Xa and frozen core Hartree-Fock9 results are at variance in predicting shape resonances for the first three ionizations; (3) our_experiments provide evidence for a xushape resonance in the AZZ: ionization which was predicted by the FCHF a p p r ~ a c hbut , ~ not so by the LCAO/MS X a MO me(4) on the other hand, our experimental data indicate a rg shape resonance in the ionization as computed in the but not so in the FCHF a p LCAO/MS X a MO roach;^ ( 5 ) experimental features in the vibrationally resolved XZngB curves as well as both theoretical methods4l9suggest that the a, shape resonance, which is well _characterized(experimentallf16 and _ t h e o r e t i ~ a l l yfor ~ ~ the ~ ~ ~AZZ: ) ionization, manifests also in the XZngionization; (6) finally, no experimental support coulg be found that the ugshape resonance plays also a role in the Czn, ionization, as suggested by the LCAO/MS X a MO calcuIation~.4-~ Acknowledgment. This work was supported by the Bundesminister fur Forschung und Technologie (Project No. 05 349 FA IO and 05 449 FAB). The calculations were carried out at the Hochschulrechenzentrum der Universitlt Marburg. We thank the staff of BESSY for their help. Registry NO. N d - - N , 460-19-5.
Polarlzatlon Mechanisms and Properties of Substltuted Ferrocenes. A Comparatlve Study J. Waite* and M.G.Papadopoulos* National Hellenic Research Foundation, Vas. Constantinou 48, Athens, GR- 116 35, Greece (Received: July 11, 1990; In Final Form: February 5, 1991)
The polarizability, a,and second hyperpolarizability, y, of some ferrocene derivatives are determined by using an optimized semiempirical approach. The bonding in ferrocene has been investigated through the study of the above polarization properties. The results from the ferrocene derivatives have been correlated with the corresponding substituted benzenes. Scales have been presented, where the derivatives are classified according to their polarization properties. The effect of delocalized T electrons, charge transfer, and geometry variations on a and y are commented upon. Selected results of various other properties (e.g., the first hyperpolarizability)are used to demonstrate that some mechanisms (e.g., charge transfer) and changes in geometry may have widely different effects on the molecular properties. Common trends and patterns of behavior are recognized and discussed. The reported results are in good agreement with the experimentally determined ones.
Introduction The polarizability and hyperpolarizabilities of ferrocene, (CIH5)2Fe (fer-H), and its derivatives (fer-X) have been the subject of some recent studies.'-3 Organometallics, in more
general terms, have recently attracted the interest of those who search for novel and efficient nonlinear optical material^.^-^ Thus the selection of ferrocene was natural, taking into account that, first, it may be considered as a model complex of the type (C5H&M, where M is a transition metal6 and, second, the de-
( I ) Ohoral, S.; Samoc. M.; Prasad, P.N.;Tufariello. J. J. J . Phys. Chem. 1990, 94, 2847. ( 2 ) Winter, G. S.; Oliver, S.N.;Rush, J. D. Opt. Commun. 1988,69,45. ( 3 ) Green, M. L. H.; Marda, S.R.;T h o m p n , M. E.;Bandy, J. A,; Bloor, D.; Kolinsky, P. V.; Jones, R.J. Nature 1987, 330, 360.
( 4 ) (a) Tam, w.; Calabrese, J. C. Chem. Phys. Lett. 1988,144,79. (b) Tam, W.; Eaton. D. F.; Calabresc. J. C.; Williams. I. D.;Wang, Y.Anderson, A. G. Materials 1989, 1, 128. (5) Waite, J.; Papadopoulos, M.G. Z . Naturforseh. 1987, 42A, 749.
0022-3654/91/2095-5426$02.50/0
0 1991 American Chemical Society
