J . Phys. Chem. 1993,97, 4335-4343
4335
Zero-Kinetic-Energy (ZEKE) Photoelectron Spectroscopy of pDifluorobenzene via Different Intermediate Vibrational Levels in the SI State Georg Reiser,+Dieter Rieger, Timothy C. Wright,* Klaus MiiUer-Dethlefs,’ and Edward W. Schlag Znrtitut f i r Physikalische und Theoretische Chemie, Technische Universitiit Miinchen, Lichtenbergstrasse 4, W-8046 Garching, Germany Received: November 10, 1992; In Final Form: January 20, 1993
ZEKE (zero-kinetic-energy) photoelectron spectra of p-difluorobenzene (p-DFB) were obtained by two-color 1+1’ photoionization via the S1 Oo, 3I, 6l, 92, 17l, 27l, and 301 vibrational states as intermediate resonances. The ZEKE spectra show substantial activity in transitions to combination bands with totally symmetric modes and a number of transitions which are symmetry forbidden under D2h symmetry. New fundamentals and combination bands of the electronic ground state of the cation are assigned, and improved vibrational frequencies are derived. Ab initio SCF calculations on the SOand S1 states ofp-DFB and the ground ionicstate are presented and discussed in comparison to the experimental results. It is concluded that the geometries of the ground ionic state and the SOstate are of D2h symmetry and that a lowering of symmetry in the SIstate, together with a breakdown of the Born-Oppenheimer approximation, is the most likely cause for the appearance of the “symmetryforbidden” bands.
I. Introduction
Fujii et al.14used two-color multiphoton ionizationto investigate Rydberg series converging to the Do ZB2, ionic ground state. By analysis of these Rydberg states and an extrapolation to n Q), an ionization energy of 73 871 cm-I was derived which agrees perfectly with the ZEKE value’ of 73 872 f 3 cm-I. Also determined were two vibrational frequencies: 837 (US) and 1374 cm-1 (v3). State-of-the-art photoelectron spectra, using resonant twophoton ionizationand time-of-flightanalysisof the photoelectrons, obtained by Sekreta et a1.2show prominent contoursof vibrational bands of thep-DFB cation in the ionic ground state. These timeof-flight photoelectron measurements employed 1+ 1 or 1+ 1’ REMPI and used different vibrational levels of the SIstate as intermediate resonances in order to vary the vibrational activity in the ion. This work represented, until now, the most complete analysis of the vibrational structure of the p-DFB cation in its ground electronic state. Additionally, Fuji and Ito investigated the photoionization efficiency (PIE) out oftheS1 stateusing 1+1’and 1+2’REMPI.Is They observed different threshold behavior for the 1+1’ process compared to the 1+2’ REMPI process. This will be commented on later in the text.
-
In a previous piece of work,’ the ZEKE (zero-kinetic-energy) photoelectron spectrum of p-difluorobenzene ( 1,4-C6H4F2,p DFB), obtained by two-color l+l’ photoionization via the SI 61 vibrational state as the intermediate resonance, was compared with a recent timeof-flight photoelectron (TOF-PE) spectrum by Sekreta et al.z Due to enhanced resolution,the ZEKEspectrum resolved a large number of fundamental and combination bands of the electronic ground state of the cation, which in the TOF-PE spectrum appear ascongested,unresolved peaks. It was previously demonstrated how the combination of PES with resonanceenhanced multiphoton ionization (REMPI-PES or “excited state PES”) allows one to influence the vibrational photoionization propensity by selecting different intermediate vibronic states.2In this work, this idea will be applied to ZEKE measurements. Thep-DFB neutral and its SI -+So transition have been studied extensively in the works of Cvita3 and H ~ l l a sCoveleskie ,~ and Parmenter,4 and Robey and Sch1ag.s More recently, Knight and Kable6analyzed the vibrational structure of the electron-dipoleallowed SI So transition in absorption and single-vibroniclevel fluorescence (SVLF) so that now all vibrational frequencies in the SIstate, with the exception of six high-frequency modes, 11. Experimental Section are known (the knownfrequencies have recently been tabulated).7 Different experimental methods have also been employed on The experimental setup used is the same as the one employed the cation. T h e p D F B cation, like most of the larger molecular by Habenicht et a1.16 The principle of ZEKE spectroscopy is ions, does not fluoresce, and hence most methods of fluorescence based on electron extraction by a delayed electric field pulse and spectroscopy are not applicable. Ab initio calculations from von has been described elsewhere.’7-zo Niessen et a1.8 give an electronic configuration for the outer The object of the measurements presented here was to prepare molecular orbitals of p-DFB of ...(bz,)Z(b~s)2(b~u)2(b~~)~(b~g)zp-DFB in selected vibrational states in SIby absorption of the (a,)’J(b3,)o within the DZh symmetry group. The z axis of a rightfirst photon and then to ionize from these vibrationally selected handed coordinatesystem for the molecular frame passes through states in SIby the second photon. The SI-SO excitation spectra the two fluorines, and the molecule lies in the y z plane. This is and the precise pump energies of the SIvibrational intermediate the so-called Ir convention with the z axis as the rotational axis resonances were obtained by measuring the mass-selected ion of lowest moment of inertia, i.e., coincident with the a axis? currents ( m / e = 114) in one-color (1+1) REMPI experiments. Using this electronic configuration, the transitions observed in In these experiments, the first dye laser was tuned through the the He I and He I1 photoelectron spectralO-l3 have been assigned regionof 530-550 nm, and thelaser output wasfrequencydoubled with reasonable certainty. From these results, it follows that the in a KDP crystal. symmetry species for the electronic ground state for the p-DFB The room-temperaturep-DFB was coexpanded in a skimmed, cation is ZB2,. pulsed jet with argon as the carrier gas. The expansionconditions were optimized for the respective SI-SO vibrational transitions. * Author to whom correspondence should be addressed. To excite SIvibrational states by hot band transitions (here Present address: Department of Chemistry, University of California, 17:, 30!), the expansion conditions were changed to favor higher Berkeley, CA 94720. jet temperatures; this was achieved by decreasing the argon t Royal Society Postdoctoral Fellow.
-
~~
+
0022-3654 I93 12097-4335%04.00/0 0 1993 American Chemical Society
Reiser et al.
4336 The Journal of Physical Chemistry, Vol. 97, No. 17, 1993
I
5
I
1
n zl
0
l
/
/
I
I
100
I
-
0
I
I
l
/
/
I
'
100 [GHzl SO0; transition for 5 K. The
Figure 1. Measured and simulated SI zero point on the energy scale refers to the band origin.
-
backing pressure, (An increase in argon backing pressure led to the disappearance of the ST So hot bands.) A comparison of the 0; transition under "warm" expansion conditions leads to a rotational temperature of about 25 K, whereas for the "cold" expansion conditions 5 K was obtained. A typical rotational contour of the SI+ So transition for 5 K is shown in Figure 1 together with a computed simulation using the known rotational constants4of p D F B in the S I and SOstates. The ZEKE spectra were obtained by pulsed field ionization of Rydberg states (also known as ZEKE-PFI), by applying an extraction field pulse rising to 0.7 V cm-I in 10 ns. Two dye lasers (Lambda Physik FL 3002) were synchronously pumped by an excimer laser (Lambda Physik EMG 1003i MSC). One dye laser was used to pump the SI So vibronic transition and the probelaser was then tuned through theionizationthreshold (except for the 3; intermediate state, see later). No time delay was employed between the two laser pulses. The dye lasers were calibrated against the iodine absorption spectrum.21 For the second laser, an iodine absorption spectrum was measured simultaneously while recording the ZEKE spectra. Several peaks (marked R in the figures) come from one color accidentally hitting a ZEKE excitation together with the intermediateresonance or from Coulombeffects due to resonances in S I ,since the SIstate of p-DFB is about halfway between the Soand the ground state of the cation. (Only the main "resonant" peaks are labeled R in the spectra; all such identified peaks are given in Table 11.) The strong increasein ion production captures some (low-energy) electrons in the ion cloud. These electrons will be extracted by the delayed field pulse and appear at the same time-of-flight as ZEKE electrons. They can be unambigously identified by comparison of the probe laser photon energy with the SI-SO spectrum. The ionizing laser was not attenuated further since this would have led to the disappearance of the weaker transitions in the ZEKE spectra.
-
111. Results
-
Before the ZEKE spectra were measured, the dependence on rotational excitation within the SIstate was investigated. With the pulsed dye lasers employed (bandwidth in the UV 0.3 cm-I), no rotational resolution for the SI -SO transition can be achieved. However, a careful choice of the exciting wavelength can lead to a preferential excitation of either low-energy or higher energy
37020.
37030.
37040.
37050.
cm -1
Figure 2. Do Oo ZEKE peak pumping different positions in the SI 00 band. The corresponding positions 1-5 are indicated in Figure 1.
rotational states in SI; this effect is shown in Figure 2. In these experiments, ZEKE spectra (to the Do Oo level) were measured for different excitation wavelengths within the SI SO 0; vibronic transition. The corresponding excitation wavelengths are marked in Figure 1. For each excitation wavelength, a ZEKE spectrum was measured. It is apparent from Figure 2 that the width of the observed ZEKE band (corresponding to the lowest vibrational state of the p-DFB cation) depends strongly on the rotational excitation in the SIstate. The minimum width (5-cm-1 FWHM) was generally observed for excitation in the center of the SI SOband. This corresponds to excitation in the dip that is seen in Figure 1, and this was the region where pumping was carried out in this work. A simulationof the rotational distribution in SIshows that, in fact, the region where the dip is observed corresponds,as expected, to states with low rotational excitation. For the measurement of the ZEKE spectra out of the vibrational states in SIthat had to be pumped via hot bands; Le., exciting through the 17; and 30; transitions, a similar effect is observed: the warmer jet temperature due to the changed expansion conditions led to a broader rotational distribution pumped in SI, and hence, for these conditions, the width of the ZEKE peaks observed was ca. 20 cm-I. For the ZEKE spectra reported here, different SI SO transitions were pumped: O;, 3:, 6:, 9:, 17:, 27:, and 301 (the vibrations are denoted according to the Mulliken notation).22 Table I gives the energy positions for the investigated vibrational intermediate states of p-DFB. ZEKE Spectravia Different VibrationalIntermediateSlStates. ZEIIE Spectrum from the SI00 Level. The ZEKE spectrum from the vibrationless SIstate is reproduced in Figure 3. The scanning region ranges from the ionization energy to approximately 3000 cm-I above. The width of the ZEKE signal peaks is below 6 cm-1 (FWHM). The majority of the bands observed in this ZEKE spectrum can be assigned to vibrational states of the p-DFB cation. Next to the vertical transition into the vibrationless state of the cation, the spectrum is dominated by transitions into totally symmetric modes and combination bands
.-
-
-
The Journal of Physical Chemistry, Vol. 97, No. 17, 1993 4337
ZEKE Spectroscopy of p-Difluorobenzene TABLE I: Enereies of Transitions for PDFB ~
~~
~
~
hv1lcm-I 36 838.5 38 089.5 37 248.5 38 014 37 240 36 740 36 799
00
3; 6; 9: 21; 171 301
~~
hvz/cm-' (to I.E. at 73 869 cm-l)'
transition
SI-SO
~
Tob/cm-' 36 838.5 38 089.5 37 248.5 38 014 37 240 37 112.5 36 958.5
31 030.5 31 779.5 36 620.5 35 855 36 629 36 756.5 36 910.5
-
Not corrected for the lowering due to the pulsed electric extraction pulse. b Of upper state. pDFB Do
S,
0" 8"
O0
/
5" 4" 8'
I
75600 Total Energy [ an" ] Figure 3. ZEKE spectrum of p-DFB via the SIOo state.
of these. The strongest transitions are the 61,51,4l, and 2l ones and various combinations of two quanta of these. However, the nontotally symmetric modes ujo, ~ 1 7 and , us also appear. These modes are also observed in combination with ag modes. Some transitions observed in the ZEKE spectrum could not be unambiguously identified within the present analysis. The favored assignment, taking into account the possible combination bands, are given in Table 11. ZEKE Spectrum from the SI61 Level. Figure 4 shows the ZEKE spectrum with SI 6l as the resonant intermediate state. For the v6 mode, a progression with four quanta is observed with the maximum intensity for the 62 level. This shift of the FranckCondon (FC) maximum toward higher vibrational excitation in v6 was also observed in the corresponding time-of-flight photoelectron spectrum.2 The spectrum in Figure 4 also mainly shows transitions into symmetricmodes. The most probable assignment taking into account the combination bands is also given in Table 11. ZEKE Spectrum from the SI3l Level. The scanning range for the measurement from SI3I ranges from 970 to 1970 cm-' above the ionizationenergy. Thevertical transition into the 3I vibration of the cation dominates the spectrum as seen in Figure 5. Other transitions were assigned to the totally symmetric modes or combination bands 3I6l, 2l, 52, and 4I6I. A notably strong transition is found for 3I8l. As observed for the SI6l and SIOo ZEKE spectra, the U S vibration seems to play a very special role for the ionization process. Other weak peaks are reproducible, and their assignment is given in Table 11. ZEKESpect"fromtheS1 92Level. For theSl g2intermediate state vibration (see Figure 6), a very strong transition was also observed for the vertical transition into 92. Also, the combination band with the totally symmetric mode v6 is observed with very high intensity. Other transitions into totally symmetric modes are weaker. The vs vibration only occurs as the overtone 82 and as an overtone combination with the modes v6 and v9, Le., as 6 W and 9W. (See Table 11.) ZEKE Spectrum from the SI271 Level. The ZEKE spectrum in Figure 7 was observed when pumping the SI SO 27; transition. Thestrongest transitions observed are the27I vibration
-
in the cation and combinations with the totally symmetric modes v4, v5, and U6. These transitions are all symmetry allowed under D2h symmetry. Notably, we again observe the 'symmetryforbidden" a, vibration us in the combination bands 27I8l and 27W. (See Table 11.) ZEKE Spectrum from the SI17l Level. Figure 8 shows the ZEKE spectrum from the SI 17' vibrational state. This intermediate state had to be pumped via the SI SO 17; hot band. This leads to a significant broadening of the rotational distribution in SI which gives rise to a significant broadening of the observed ZEKE peaks (FWHM = 20 cm-I). Also for this ZEKE spectrum, the main transitions (indicated in Figure 8) are symmetry allowed under D2h symmetry. However, deviations aredemonstrated by theobservation of thevibrationless state Oo (the adiabatic ionization energy, AIE), 172, and combinations with the a, 8l mode: the 8I17l, 82171,and 5181171. (See Table 11.) ZEKE Spectrum from the SI301Level. The ZEKE spectrum measured with the SI301intermediate vibration (Figure 9) was obtained by pumping the SI-SO 30; hot band transition. Most of the observed transitions (which are also summarized in Table 11) can be assigned to symmetry-allowedtransitions. However, again the a, us vibration is observed in combinations 3O18I,30182, and 3016181.
IV. Discussion The most prominent feature of the ZEKE spectra observed here is the strong activity of the ag modes v2+6 (the aBvibration ul has not yet been seen in conventional photoelectron spectra and is, with the exception of the ZEKE spectrum from SI Oo, outside the scanning range employed in the experiments reported here). In particular, the u6 vibration is the most prominent mode observed in the ZEKE spectra. On the basis of the FranckCondon principle, it is expected that the modes excited indicate the geometry change on ionization (although some account of Duschinsky rotationz3 of the normal coordinates within the molecular symmetry group D2h may have to be taken). To be pointed out here is the restricted validity of the Au = 0 propensityrule forp-DFB. This propensityhas previously been observed for the ionization of aromatic molecules from their SI ~tates.2~ The failure of the rule is not so surprising though, as it is only expected to hold when the geometries of the SIand the ionic states are similar (as they are, for example, for Rydberg states and their correspondingions). For the different vibrational excitations in the SIstate, there are some bands in combination with a quantum of mode 6 of similar strength as the dominating Au = 0 transitions (Do 3O16I-SI 301,Do 9261-SI 92,Do 17I6I -SI 17I). For the SI6l intermediate state, the Franck-Condon maximum is observed for the 62 vibration in the cation. This is in agreement with the previously published photoelectron spectrum2 (the stronger appearance of the 2l band in the ZEKE spectrum pumping SI Oo is due to the dye tuning curve). This observation,the shift of the FC maximum toward 62,implies that the geometries of the SIstate and the ionic state differ along this mode so that maximum overlap is achieved for the first overtone in the ion, rather than the fundamental. Within the Born-Oppenheimer approximation (and in the absence of any other coupling), no transitions can be explained for which the symmetry species of the vibrational wave function in the SIstate is different from that in the ion. Table I11 lists those transitions which violate the symmetry restriction. Most prominent are the vibrations us, ~ 1 7 and , ~ 3 0 . The observation of these vibrations will be discussed in the following subsections. Nontotally Symmetric Vibrations. These vibrations are illustrated in Figure 10. The assignment of the V I 7 mode (symmetry species bZg; see Figure loa) in the p-DFB cation rests on the ZEKE spectrum from SI171 as the intermediate state. The vertical transition (which is assigned to Au17 = 0) appears 306 cm-I above the
Reiser et al.
4338 The Journal of Physical Chemistry, Vol. 97, No. 17, 1993 TABLE II: List of ZEKE Transitions of pDFB' SI +So Y+
0" 30' 17' 8' 27l 6' 8'301 6'30' 17' SI ' SI, 8'17l SI ' SI' SI s o
3;
0;
6;
92,
SI
27),
SI ' Si'
8'27l 6'8l ? SI 'Si,
SI +So
6' SI
'SI'
618'30' ?SI ' S o
? ?S,'SO
5'6' 3'8' ?
-
64 2'301 ? SI +-so
719 742
SI +-So
5*301 3l6'
800 -
5l30' 8'17' ? SI ' SI, SI 'SI, 8217'
? SI 'So st 'So
1
? ?
5ll7l 41 8?27l SI
'SI,
6l8' 6'82 SI -so
6'9'
SI 'So SI S 'o ? ? ? 6' 1533
aao*
1024 38054 -
1078 1109 1147' 1163
4'5' 930 37559 -
1073 -
37657 -
-
-
-
1148 37785 1157 -
1195 1260 ? 5l27' 1273' 5'6' 4'30' 27' ? 27'6' 17I3O1 6'17'30' 1307 6'27l 6' 1317 1334 ? 9l17'
4'6' ?
2'6' 526' 4'5'301 ? 5'6l 8292 2'6'301 SI S 'o SI 'So
5'6'30'
? SI S 'o
9' 4'17' SI ' SI' 5'8ll7l 3I3O1 ?
5'8' 4'27' 416' ?
1401' -
1714 1759 -
1816
1815'
1816 38443 38475
1857
-
-
-
37660 -
-
-
2008 2030 2079 21 15 2133" -
-
1596
1582 -
415' ? 2'5'271 2'41301 5'6' 3'4'6' ? I 1 / ? 2'4'17' Q
171
301
1702 37557
37656 -
2245 -
-
2517 2551 2572 39284
+-So
SI 'So
27;
38843
2426 2471 2490
-
9;
-
2427 2472 2487 2511
2303 'So
'So
1955" 1971 1988 2028 2038 2077 2114 2131': 2154
4l5'61 215'/4'63 ? 53 2162 3'4' 5262 3 ~ 5 ~ 8 ~
'So
426' 2I4l
-
37719 -
2397 241 1
SI
-
-
-1 1734 1779 37559
2528 2554 ? 2618 3141301/315161 2654 39723 SI 'So
1374
1533 1559 1590
1715 -
2397 -
SI
'si1
SI S 'o
1639 1678 -
2368
42
SI
1639: 1675' 1693 -
1959: 1989:
6; 1640 1653 1674 -
? 2'9' SI +So ? 6l + 1957 ? SI 'So
?SI'S0 SI
'so
3:
2257 226 1 38881 38906 2302 38966 -
5'6'301 3'6*
5181
3'
+
SI +-So ? 4'27'
6'8'
SI
0:
SI 'So SI 'So
836' 872
-
V+
52 ? 5'27'
SI ' S , '
51 8'301 ? 28' 6'27' 6'17'30'
301
5'8'27l 2'
0' 126 303 359: 439' -
+ -
82 6'17l
17;
2741 2789 2826 2910 2949 2966 3098 3127
39720 2922
Energies of bands in cm-' above LE. and assignment to SI-SO resonances for which the corresponding photon energies are given. -, not identified in scan range. *, observed in ref 2 (not necessarily listed therein). ?, assignment uncertain. **, band energy is seen in combination with Vg.
-
-
ZEKE Spectroscopy of p-Difluorobenzene p-DFB: DO
The Journal of Physical Chemistry, Vol. 97, No. 17, 1993 4339
S, 6 l ?l
p-DFB: Do
I
S, 27,
75000
74000
L
Total Energy [ cm-’] Figure 4. ZEKE spectrum of p-DFB via the SI6’state.
-
P e a
sT
/
-
p D F B Do
I
I
I
74500
74000
75000
75500
Total Energy [ cm“ ]
-
S, 3,
Figure 7. ZEKE spectrum of p-DFB via the SI27I state. p-DFB: Do
l ;3
S, 17’
I
I
.P v)
3’8’
W
\
Y
w
N
7!xioo
75bO
75kM
Total Energy [an-’ ]
-
73500
Figure 5. ZEKE spectrum of p-DFB via the SI 3’ state. p-DFB: Do
74000
7&00
75boo
Total Energy [ c”’]
S, 9‘
-
Figure 8. ZEKE spectrum of p-DFB via the SI17’ state. p-DFB: Do
S,30‘
z.a v)
W Y W
N
30,5, 74600
74koo
75500
7 5 h
1
78000
-’
Total Energy [ cm ] Figure 6. ZEKE spectrum of p-DFB via the SI9*state.
adiabatic ionization energy, i.e., above the vibrationless state. In violation of the symmetry selection rules, the transition into the vibrationlessstate of the cation (of aBsymmetry) is observed with significant intensity. For ZEKE spectra from totally symmetric vibrations in SI, SIOo and 6I, the activity of a vibration with 303 cm-1 is seen which, within the precision of the measurement, can also be assigned to VI% The ~ 3 mode 0 (symmetry species bgu) is characterized by the in-phase movement of the fluorine atoms out of the plane (see Figure 1Oc). This movement explains the low frequency of 129 cm-I as found from the vertical transition from SI 301.ZEKE spectra from SIOo, 3l, and 6l,i.e., of ag symmetry, also show an active ionization with a frequency of 126 cm-I. Table V shows that the next vibration appears at approximately300cm-I. Hence the 301 vibration can be assigned here unambiguously.
74600
30‘2’ 30’4’
’,
/
I
I
75000
76000
Total Energy [ cm” ] Figure 9. ZEKE spectrum of p-DFB via the SI 301state. In the time-of-flight photoelectron spectrum,2 with the SI 8’ intermediate state resonance, the frequency for the mode in the p-DFB cation was measured as 347 cm-I, a frequency that, somewhat surprisingly, was also observed from SIOo. In all the ZEKE spectra reported here, the vibrational activity of a mode with 359 cm-1 is observed. This vibrational frequency must be assigned to the v g mode of symmetry species a, (see Figure lob). SCF ab Initio Computations of the pDFB Cation. To aid in the assignment of the observed vibrations in the p-DFB cation and to check the experimentallyobserved vibrational frequencies, ab initio calculations were performed. The program CADPAC25 was employed at the restricted (open-shell) HartreeFock level,
Reiser et al.
The Journal of Physical Chemistry, Vol. 97, No. 17. 1993
4340
A
TABLE IIk List of Observed Symmetry-Forbidden ZEKE Transitions (for 46). SI +so
01
V+
00 30' 17' 8' 6' 8'30' 172 8'17' 6'17' 8'27l 6'8' 6 ' 17'30' 6'8130' 5'8' 628I 2716117'30' 6217'30' 5'6'30' 5'8'17' 3'30' 5'8'27' 3'8' 3'5'8'
3;
126 303 359 -
-
-
799 -
742
800 872 1195 1307 1401 -
6; 126 302 358 -
-
1502 1734
1237 2572
9:
27; -
-
439 -
-
788 1297 1625
171
301
0
-
-
618 669
-
927 -
1499 -
Energy incm-I. Blankentriesindicate thatthe transition wasoutside the energy range of the scan. -denotes that the band was observed but is symmetry allowed. - denotes that the band is not observed in the spectrum.
TABLE I V Calculated Bond Lengths for pDFB (in A). atom 1-atom 2
CF-F CF-CH CH-CH
CH-H (1
Sn ('AQ)
e x d value (So)*
Dn PB,.)
1.358 1.374 1.381 1.069
1.354(4) 1.388(3) 1.400(3) 1.088(5)
1.313 1.415 1.350 1.069
I
h
CFdenotes a C atom next to an F atom and CH denotes a C atom
next to an H atom. These are gas-phase electron diffraction result^.^'
using the standard 3-21G basis set. For both the electronicground state of the neutral and the electronic ground state of the cation, the geometry optimization leads to D2h symmetry (even with geometry restrictions such that only the planarity of the ring is enforced). The bond lengths are summarized in Table IV and are compared to available experimental values: all bond angles are close to 120°, although it is noted that the CH-C&H angle (see heading of Table IV for notation) increases slightly from 121.2 to 122.4' on ionization. Vibrational frequencieswere also calculated using analytic gradient methods. Calculations for the SI state under the C, symmetry restriction led to a first-order saddle point, as indicated by the presence of one imaginary frequency, suggesting that the geometry of the SI state is not of DZh symmetry and seems not to be planar (the saddle point itself has lost the C2(x) and C2b) axes, although the geometry is not distorted too much from D2h symmetry). Of particular note is that the imaginaryvibration resembles most closely the v g vibration (implying that the SIstate minimum may be found along the v g coordinate); as noted above, this vibration is present in a lot of the ZEKEspectra, supportingthe result of the ab initio calculation. Unfortunately, all attempts to converge the geometry in the lower point group (Cl) failed due to extremely poor convergence in the SCF routines. The result of n 0 n - D ~symmetry ~ for the SIstate has been suggested previously (see next subsection for details). Recent semiempirical calculations26seem to suggest that the SI state geometry was successfully converged under D2h symmetry-completely at variance with the results here. It would seem that further ab initio calculations should be carried out on this state using a larger basis set and including electroncorrelation energy.
Figure 10. Diagrams of the vibrational motion of the symmetry-forbidden fundamentals (a, top) U S ; (b, middle) Y17; (c, bottom) u j o .
In a corresponding way as has already been observed for ab initio calculations of the closely related p-dichlorobenzene (pDCB),27the distance between the fluorine and the CF atom as well as the central C-C bond length is reduced in the cation compared to the neutral. The other (apicial) C-C bond length becomes longer; the C-H bond length remains the same. As for p-DCB, the a-molecular orbital from which the electron is ejected on photoionization shows partially bonding (for apicial) or antibonding (for central) character for the C-C bonds. Table V shows the experimentally determined vibrational frequencies for the p-DFB cation, and as a comparison, the computed values are also given. The computed values were multiplied by a scaling factor of 0.89, which is typically applied to vibrational frequencies at the SCF level. The accuracy of the (scaled) computed frequenciesis typically of the order of 5%. For all modes where they are known, the experimentaltrend, whether the frequency of the cationicvibration increases or not, is predicted correctly by the computed values. (The direct comparison of modes between SOand the ion must be treated with some caution though, as the ionic vibrational motions may be affected significantly by Duschinsky mixing.) Forp-DCB?' a correspondinglygood agreement was seen between scaled SCF values (obtained using a 6-31G basis set) and the experimentalvalues obtained from matrix-isolatedp-DCBradical
The Journal of Physical Chemistry, Vol. 97, No. 17, 1993 4341
ZEKE Spectroscopy of p-Difluorobenzene
TABLE V Measured and Calculatd Frequencies of pDFF3 Normal Modes (in cm-l)’ so
mode 1 2 3 4 5 6 7
symmetry
exptlb
SCFc
a,
3088 1617 1257 1140 860 450 945 422 800 3073 1514 1228 1014 740 928 692 374 3073 1633 1306 1085 348 3085 1617 1285 635 446 838 505 158
3044 1615 1295 1152 833 452 1050 421 881 3029 1394 1155 1043 752 1007 724 392 3042 1525 1235 1078 318 3030 1578 1259 648 448 910 538 164
a,
8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
big blu
b28
b2u
b38
b3u
SI (IBzu) exptlb
... ... 1251 1116 818 410 583 179 588
...
1335 1015 937 666 670 528 274
...
...
1591 1100 352
...
1516 933 558 403 619 438 120
DO(2B2g) exptlb SCFc 3098@) 1640 1375 1148 836 439
...
359 726
... ... *. ... ... ... ..*
303
... ... ... ... ... ... .*. ... ...
430 859d 508e 127
3047 1647 1362 1167 794 434 1078 395 846 3034 1470 1292 943 683 1067 750 326 3045 1470 1235 1096 333 3034 1371 1203 576 416 924 526 132
The SCF values are scaled with a factor of 0.89. As listed in ref 7. This work. Assignment uncertain. e From ref 2.
cations. Additionally, a 3-21G/UHF calculation of the vibrational frequencies of the neutral benzyl radicalZ8(also scaled by a factor of 0.89) gave good agreement with known experimental values. In short, the calculationssupport the experimentalassignments for the ionic frequencies and lead to a D2h structure for the So and ground ionic states. For the SIstate, deviations from D2h symmetry, mainly along the vg coordinate, are indicated. Symmetry Lowering of the S1State. There are a number of studies in the literature that have looked at the possibility of symmetry lowering in theSl stateand/or theionicstateofp-DFB. Firstly, the rotationally resolved absorption spectrum of Cvitag and Holla3concluded that there was no evidence for nonplanarity of the SIstate, while the study from Udagawa et al.29concluded merely that the two geometries must be similar due to the preponderance of totally symmetric modes observed. Nonplanarity was considered, but dismissed, by Catlett et al.30as a passible reason why the ~ 3 mode 0 was so active in IVR (intramolecular vibrational redistribution). Fujii et al.I4 studied the two-photon, two-color MPI spectra of jet-cooled p-DFB. In particular, Rydberg series were analyzed, and it was found that the DO SI transition only resulted in s and d series being observed. It was noted that this implies that there is a retention of the center of symmetry between the SIstate and the ion. Also, it had been previously noted that the one-photon vacuum UV studies on the DO SOtransition31gave rise to a p series as well as a d or f series, thus implying that a center of symmetry is also retained between the ground state and the ion. (In fact, if the center of symmetry is retained, then the second Rydberg series would have to be an f series.) Additionally, since four Rydberg series were found (as opposed to the three d series expected under D2h symmetry),14 it was implied that the symmetry of the Rydberg states was 10wered.I~ The suggestion was that they had C2h symmetry, with the fluorine atoms out-of-plane in opposite directions (thus preserving the center of symmetry). On the other
-
-
hand, Coveleskie and Parmenter4also suggestedthat the SIstate was nonplanar but due to a distortion in the ~ 3 0coordinate (fluorines moved out of plane by equal amounts in the same direction). Knight and Kable? in their extensive study of the SIand So states of p-DFB, considered symmetry lowering of the SIstate as a possible explanation of the appearance of certain D2hsymmetry-forbiddenbands in their spectra. However, it was not deemed possible that this molecular distortion would account for all of their bands: in fact they noted that only the b3, modes would become allowed (with the molecular symmetry lowering to CZh, via an in-plane bend of the fluorine atoms, with the x axis becoming the C2 axis). The recent laser photoelectron study by Reilly et aL2suggested that the symmetry of the ion was reduced along the vg mode. This would give an ion of D2 symmetry; interestingly, this is exactly the mode that corresponds to the imaginary frequency in the ab initio calculation on the SIstate reported earlier in the text. Hence, it seems that the symmetry reduction sought after by Reilly et a1.2 may be present in the SI state, not in the ion. Also, the calculated geometry of the ion (as well as the SOstate) was clearly D2h in this work (in agreement with the ab initio calculationsof Szczepanskiet aI.z7on thep-DCB SOstate and cation); this is also in agreement with the observation of Rydberg p series observed when exciting from the SOstate.31 A lowering of the symmetry of the SI state to D2 (Le., along the Y8 coordinate) still does not explain the appearance of all bands in either fluorescence spectra or the ZEKE spectra reported here: the symmetries of the Y 8 , V17, and ~ 3 vibrations 0 change from aurb ~and , b3u to a, b2, and b3, respectively, on going from the D2h to the D2 point group. Thus, only the appearance of the vibration is explained by this symmetry lowering. If the symmetry lowers even further to C2, C,, or Ci, then at least one of these modes is still symmetry forbidden; lowering to C1 symmetrywould, of course,make all vibrationstotally symmetric. Thus, it would seem that the geometry of the SIstate is not the only factor in the appearance of ‘forbidden” bands, but it would seem probable that the symmetry is lower than DZh. However, loss of the center of symmetry of the S1state would seem to contradict the findings of Fujii et aI.,l4who deduced that the center of symmetry is retained in the Do SItransition due to the nonobservation of a p or f Rydberg series. Maybe the nonobservation of these series by Ito and co-workers14 is due to some other reason; a possible alternative explanation is that the Rydberg series they assign to a d series is in fact an f series. Vibronic Coupling between Electronic States and Coriolis Coupling. It was noted by Knight and Kable6 that vibronic coupling between electronic states was a reasonable explanation of the forbidden and combination bands observed in the SI- S o transition in their spectra. One might speculate about vibronic coupling between the 2B2,@b3, vibronic state-and the ZBlu electronically excited state of the cation. The H 2Blustate is expected = 6 eV above the ionic ground state.” However, this state is not accessibleby a one-electron (“Koopmans”)ionization from the S1 state. This is true for all the ionic states calculated in ref 11; the states that are accessible will have one electron in the a, orbital (unoccupied in the SOstate but singly occupied in the SIstate) and the other electron in an appropriate orbital to obtain the correct symmetry. The symmetries of the coupling electronic state required for each of the forbidden vibrations to become vibronically allowed are Blu, B2urand A, for the V30, V 8 , and v17 modes, respectively. With one electron in the a, orbital, this requires the other electron to be in orbitals of bl,, b2,, and a, symmetry, respectively. The energies of the first two of these states above the Do origin may be estimated using the approximation used by Siegbahn and co-workers32 that the ionization energy of an excited ionic state is approximately equal to the ionization energy of the “unexcited state” plus the corresponding neutral excitation energy. This allows ionization energies of the
-
4342
The Journal of Physical Chemistry, Vol. 97, No. 17, 19513
ionic states with the a, orbital excited to be calculated from the ionization energies given in ref 1J. The lowest unexfited states of the correct symmetry are the A 2B1, state and the I 2B2, state. This allows ionization energies of 5.5 and 12.5 eV to be calculated for the respectiveexcited states. Thereseems to be no state below 26 eV of the correct symmetry to make the Y17 mode vibronically allowed. All of the above energy differences are rather large, so it is expected that this type of vibronic coupling will be relative weak and not contribute to the ZEKE spectra in this work. In any case, vibronic coupling should lead to a strong decrease in vibrational frequency: this is not observed in the ZEKE spectra for the ~ 3 mode, 0 for example, and hence, again it is concluded that vibronic coupling is not responsible for the appearance of this feature. It is possible that the vibronic coupling occurs in the SIstate: such schemes for the SI-SO transition were discussed by Knight and Kable6 and will not be further commented on here. Knight and Kable6 also considered Coriolis coupling as a possible source for the appearance of forbidden bands in the SI SOtransition. However, for the ion, since the most active "allowed" bands are the a, bands, this requires the other interacting vibration to be of b,,, b2g,or b3, symmetry. Hence, it would only be possible for the ~ 1 vibration 7 to be explained by this mechanism. Other types of forbidden bands arise in photoelectron spectra such as the ones which are analogous to the satellite bands in X-ray PES. These are the configuration interaction (CI) bands which occur in vacuum UV PES. These have been described from both an e~perimental,~ and a computational viewpoint34 and will not be further explained here. Suffice to say that they arise by interaction between states of the same symmetry, so for the Y8 vibration, some of the states with an a, outer electron may mix with some of the Koopmans ionic states (which would be directly formed from SO);the CI states could then vibronically couple with the ground state and make vibrations allowed. Vibronic Couplingdue to a Breakdown of the Bom-Oppenheimer Approximation. If thevibronic coupling is strong, then the BornOppenheimer approximation breaks down, the usual photoelectron vibrational selection rules do not apply, and the vibronic wave functions must be considered. This has been briefly considered in recent pieces of work by Okuyama et and Dyke et al.,36 and the arguments will be applied here to p-DFB. Weak Vibronic Coupling. If the vibronic coupling is weak, the Born-Oppenheimer approximation holds and the transition strength, M,is given by
Reiser et al. forbidden. Similarly, this applies for the YE and the v3ovibrations. Lowering the symmetry does not help this situation (as noted above) since lowering to CZh symmetry only makes the V I 7 mode allowed, if they axis becomes the C2 axis. The other modes are disallowed whichever of the Cartesian axes becomes the Cz axis. Lowering to C2symmetry makes the v17 mode allowed (again for they axis as the C2 axis); the ~ 3 mode 0 becomes allowed if the x axis remains as the Cz axis and the mode is allowed whichever of the axes is the C2 axis. Similar arguments apply to other symmetries, except for CIwhere all vibrations are allowed. It is clear that it is unlikely that this is the mechanism for the appearance of all of the above-mentioned bands. Strong Vibronic Coupling. If the coupling is strong, then the separation of the electronic and vibrational motions no longer becomes possible, and vibronic states must be considered. The equation to be looked at is
This implies the following:
+
or
where JIev denote vibronic wave functions. Then, since the p components have symmetries blurbz,, and b3, in the D2h point group, the following may be derived for the Do SItransition (since the symmetry of the S1 state is Bz, and the symmetry of the ion is BZg):
-
Here, it should briefly be noted that the symmetries of s, p, d, and f orbitals in the molecular DZh point group using the I' axis system and keeping the z axis (D2h) as the z axis (D,h)37 are s: ag (sa)
d: ag(Pa); a, f:
(where +e and +e+ are the SIand ionic electronic wave functions, respectively; similarly, +,,, and are the vibrational wave functions; xf represents the ZEKE-electron wave function; p is the electric dipole moment operator in the molecular frame), so both of the following conditions necessarily hold for non-zero transition moment:
+"+
It is the second condition that gives rise to the restriction that only the symmetric modes may be excited in odd quanta and the asymmetric modes are only excited in even quanta (ignoring combination bands). For example, if the S Istate is excited by one quantum of the Y17 mode, then (since the second rule implies I'($vt)@l"($v+)2 a,) b,,@~(+,+) 1ag (4) and this shows that a transition to the (aa) vibrationless state is
bl,(fa); b,,
+ b,, (dr); b2, + b,,
+ b,,
UT); a,
+ b,,
(db) ( f b ) ; b,,
+ b,,
(f4)
Sinceevery symmetry element of the D2h point group is represented in the above list, it follows that by emission of an electron of the correct symmetry (or, more accurately, since ZEKE-PFI is used here, exciting an electron to a Rydberg orbital of the correct symmetry) the overall symmetry condition is met, so any transition will be vibronically allowed. If the YE, ~ 1 7 ,and ~ 3 modes 0 are considered, then this implies the emission of an electron with symmetry blurbz,, or b3, for the vibration, corresponding to a p wave (or appropriate components of an f wave), and the ~ 1 and t'30 modes give rise to electron wave functions with symmetries ag, bl,, or b3g and a,, bluror b2,, respectively. By this argument, all vibrational bands in the ZEKE spectrum may be explained. Of course, the application of the same argument to the SI So transition is not as straightforward, as there is no electron to take into account "symmetry bookkeeping", so symmetry lowering and the other suggestions of Knight and Kable6 must be considered. Of particular interest in this context are photoionization efficiency measurements reported from the SI 00 state.15 These photoionization efficiency measurements were carried out as 1 1' and 1+2'REMPI measurements. For 1+2'photoionization (with SIOo as the resonance), pronounced steps in the PIE curve were observed at 0,359,798,919, and 1197 cm-I above the ionization
-
+
7
ZEKE Spectroscopy of p-Difluorobenzene energy. In contrast to this, these thresholds were much weaker in the 1+ 1' two-photon ionization. In the 1 1' PIE curve, it was claimed that mainly transitions into ag modes were observed, namely, 0 (O:), 444 (6I), 798 (5l), and 1197 (4l), respectively. (Note that these are Fujii and Ito's assignments; vide supra.) These frequencies also correspond to strong peaks in the ZEKE spectrum from SIOo. However, in the ZEKE spectra, which correspond to the 1+1' photoionization, the peaks are clearly assignable to0 (OE), 440 (6l), 800 (61S1),and 1195 (5I8I) cml-l; Le., the last two are of a, symmetry, not of agsymmetry as Fujii and Ito assume. (In fact, Ito and co-workersI4previously assigned a vibration at 837 cm-I to u5 in agreement with the value obtained here. It is not clear why the 798-cm-l vibration was assigned to the v 5 vibration in ref 15.) Fujii and ItolS concluded that the symmetry of the emitted electron is different upon ionization such that the symmetry of the cation is unchanged. (In fact, it was concluded that the 1+1' REMPI must lead to a d electron and the 1+2' REMPI must lead to a p electron; however, the 1+2' REMPI must lead to an f electron (fa, fa, fS, or f4) or a p electron (pu or pa) if the center of symmetry is retained; the 1+1' leads to a d a or a dS electron wave.) The arguments regarding the symmetry change of the electron due to the observation of different vibrations are implicitly assuming a breakdown in the Born-Oppenheimer approximation, Le., a coupling between the departing electron and the vibrational motion. With the new assignments deduced from the ZEKE spectra, however, those conclusions are not fully justified since the assignment of the observed thresholds in the PIE measurements is now different, so the symmetry arguments change. One of the above sections has shown that, in fact, all photoionization transitions may be allowed if the vibronic coupling is strong enough, in which case the symmetry of the outgoing electron (or Rydbergelectron) will differfrom vibronicstate tovibronicstate. Also it remains an open question why the other totally symmetric modes (seen clearly here) are not seen in the 1+2' REMPI spectra,l5 in contrast to the very strong transition into the vibrationless state of the cation; in addition, Oo and 2l (1644 cm-I) were seen in the 1+2' PIE spectrum, both of agsymmetry. It is possible that the influence of the emitted ZEKE electron on the symmetry selection rules has not yet been applied sufficiently (e.g., rotational and nuclear spin selection rules may be important, as has been demonstrated p r e v i o u ~ l y I ~ - ~ ~ ) .
+
V. Conclusions
The Journal of Physical Chemistry, Vol. 97, No. 17, 1993 4343
Acknowledgment. T.G. W. is grateful for the award of a Royal Society Postdoctoral Fellowship under the European Science Exchange Programme. Financial support from the European Community under the Science Program (Grant No. SCl *-CT900462-MD) is gratefully acknowledged. References and Notes (1) Rieger, D.; Reiser, G.; Muller-Dethlefs, K.; Schlag, E. W. J . Phys. Chem. 1992, 96, 12. (2) Sekreta, E.; Visvanathan, K. S.; Reilly, J. P. J . Chem. Phys. 1989, 90, 5349. (3) CvitaS, T.; Hollas, J. M. Molec. Phys. 1970, 18, 793. (4) Coveleskie,R. A.; Parmenter, C. S. J . Molec. Spectrosc. 1981,86,86. (5) Robey, M. J.; Schlag, E. W. Chem. Phys. 1978, 30, 9. (6) Knight, A. E. W.; Kable, S. H. J . Chem. Phys. 1988, 89, 7139. (7) Su, M.-C.; 0, H.-K.; Parmenter, C. S. Chem. Phys. 1991,156,261. (8) von Niessen, W.; Diercksen, G. H. F.; Cederbaum, L. S. Chem. Phys. Lett. 1977, 45, 295. (9) Bunker, P. R. Molecular Symmetry and Spectroscopy; Academic Press: New York, 1979. (10) Potts, A. W.; Price, W. C.; Streets, D. G.; Williams, T. A. Discuss. Faraday SOC.1972, 54, 168. (1 1) Palmer, M. H.; Moyes, W.; Spiers, M.; Ridyard, J. N. A. J . Molec. Struct. 1978, 49, 105. (12) Bieri, G.; Asbrink, L.; von Niessen, W. J. Electron. Spectrosc. Rel. Phenom. 1981, 23, 281. (13) Turner, D. W.; Baker, C.; Baker, A. D.; Brundle, C. R. Molecular Photoelectron Spectroscopy; Wiley Interscience: London, 1970. (14) Fujii, M.; Kakinuma, T.; Mikami, N.; Ito, M. Chem. Phys. Lett. 1986, 127. 297. (15) Fujii, M.; Ito, M. Chem. Lett. 1991, 933. (16) Habenicht, W.; Reiser, G.; Muller-Dethlefs, K.J. Chem. Phys. 1991, 95, 4809. (17) Muller-Dethlefs, K.; Sander, M.;Schlag, E. W. Z . Naturforsch. 1984, 39a, 1089. (18) Muller-Dethlefs, K.; Sander, M.; Schlag, E. W. Chem. Phys. Lett. 1984, 112, 291. (19) Reiser, G.; Habenicht, Muller-Dethlefs, K.; Schlag, E. W. Chem. Phys. Lett. 1988, 152, 119.
(20) Muller-Dethlefs, K.; Schlag, E. W. Annu. Reu. Phys. Chem. 1991, 42, 109. (21) Gerstenkorn, S.; Luc, P. AtlasduSpectred'Absorptiondela Mol8cule d'lode; CNRS 11: Paris, 1978. (22) Mulliken, R. S. J. Chem. Phys. 1955, 23, 1997. (23) (a) Duschinsky, F. Acta Physiochem. V.R.S.S.1937, I , 551. (b) See also: Small, G. J. J. Chem. Phys. 1971, 54, 3300. (24) Song, X.;Wilkerson, C. W.; Lucia, J.; Pauls, S.; Reilly, J. P. Chem. Phys. Left. 1990, 174, 377. (25) Amos, R. D.; Rice, J. E. Cambridge Analytic Derivatives Package (CADPAC) 4.0; Cambridge, 1987. (26) Davidson, E. R.; Elston, H. J.; Parmenter, C. S. Chem. Phys. Lett. 1992, 197, 123. (27) Szczepanski, J.; Personette, W.; Pellow, R.; Chandrasekhar, T. M.; Roser, D.; Cory, M.; Zerner, M.; Vala, M. J . Chem. Phys. 1992, 96, 35. (28) Eiden, G. C.; Weinhold, F.; Weisshaar, J. C. J . Chem. Phys. 1991, 95, 8665. (29) Udagawa, Y.; Ito, M.; Nakakura, S. J . Molec. Spectrosc. 1970,36, 541. (30) Catlett, D. L., Jr.; Holtzclaw, K. W.; Krajnovich, D.; Moss, D. B.;
In this work, the ZEKE spectra ofp-difluorobenzene, recorded via a number of vibrational levels of the SI('BzJ state, have been presented. A number of vibrational frequencies of the groundstate cation have been measured, and these have been compared with values obtained from ab initio calculations. Theobservation of nontotally symmetric vibrational modes of the cation has been discussed, and the favored interpretation is that there is a deviation from DZhsymmetry in the SIstate, together with strong vibronic coupling in the ion (and/or possbly the SI)state, causing a breakdown of the Born-Oppenheimer approximation. The conclusion is supported by the (rather low-level) ab initio calculations where the geometry optimization of the SIstate, restricted to C, symmetry, gave rise to a first-order transition state for the SI state. Analysis of the vibrational wave function of the mode with an imaginary frequency showed that it was predominantly the vs mode. That this mode is seen in many of the ZEKE spectra (as well as previous REMPI-PE spectra) lends support to this conclusion.
89, 1517. (31) Gilbert, R.; Sandorfy, C. Chem. Phys. Lett. 1974, 27, 457. (32) Allan, C. J.; Gelius, U.; Allison, D. A.; Johansson, G.; Siegbahn, H.; Siegbahn, K. J. Electron Spectrosc. Rel. Phenom. 1972173, I , 131. (33) Potts, A. W.; Williams, T. A. J. Electron Spectrosc. Rel. Phenom. 1974, 3, 3. (34) Okuda, M.; Jonathan, N. J . ElectronSpectrosc. Rel. Phenom. 1974, 3, 19. (35) Okuyama, K.; Cockett, M. C. R.; Kimura, K. J . Chem. Phys. 1992, 97, 1649. (36) Dyke, J. M.; Ozeki, H.; Takahashi, M.; Cockett, M. C. R.; Kimura, K. J. Chem. Phys. 1992, 97, 8926. (31) Herzberg, G. Molecular Spectra and Molecular Structure III.
Note Added in Proof After this paper was completed, Jouvet et a1.39 reportdd the threshold ionization spectrum ofp-DFB using the mass-analyzed threshold ionization (MATI) technique.40 where the ions are detected instead of the electrons in a ZEKE-type experiment.
1966. (38) Muller-Dethlefs, K. J . Chem. Phys. 1991, 95, 4821. (39) Jouvet, C.; Dedonder-Lardeux, C.; Martrenchard-Barra, S.; Solgadi, D. Chem. Phys. Lett. 1992, 198, 419. (40) Zhu, L.; Johnson, P. J . Chem. Phys. 1991, 94, 5769. (41) Domenicano, A.; Schultz, G.; Hargittai, I. J. Molec. Struct. 1982, 78, 97.
Parmenter, C. S.; Lawrence, W. D.; Knight, A. E. W. J . Phys. Chem. 1985,
Electronic Structure of Polyatomic Molecules; Van Nostrand: Princeton,
