Huckel Theory and Photoelectron Spectroscopy Ellak I. v m Nagy-Felsobuki University of Newcastle. Newcastle. N.S.W. 2308, Australia Huckel molecular orbital (HMO) theory (1,2) is taught in most sophomore chemistry classes in Australia as it demonstrates the role of a computational theory in chemistry. I t is used to rationalize the electronic structure in T systems (3), aromaticity (4). concerted reactions (5,6), simplificationsin symmetry (7),and the shape of simple orbitals (8).More recently, it was reported that HMO could he used as a platform for an extension to molecular vibrational theory (9). I t is not sur~risinathat there are a numher of HMO computer programs.reporied in the literature (10-13). The use of HMO in giving insight into thesuhtleelectronic interactions characterized by ultraviolet photoelectron spectroscopy (UPS) is not new hut is testimony of itscontinued relevice to another body of experimentalists, namely the photoelectron spectroscopists. For example, Heilhronner and co-workers (14) and, moreover, Bock and co-workers (15, 16) have made extensive use of HMO theory in the interpretation of photoelectron (PE) spectra. As UPS experiments have been reported in this Journal over a numher of years (16-20), it seems timely to report examples puhlished from our own laboratory of the applicahility of HMO theory in this field. HMO Theory and Photoelectron Spectroscopy HMO theory has been adequately descrihed in many hooks and articles, some of which have been listed here (19). In its most simplified form HMO assumes that a and T electronic systems do not interact, and so the Hamiltonian can he separated into two parts, each describing the energetics of each system. For the r system, HMO assumes that it is sufficient to use a minimum set of valence p-type basis functions (one per atom). Hence, all r-type electronic processes are descrihed in terms of the energies of the molecular orhitals (6). For example, within HMO ansatz the ith r ionization potential (IP) based on Koopmans's approximation (21) is given by Equation 1ties HMO theory to the W S experiment, since for closed-shell molecules, according to Koopmans's approximation, UPS involves the ejection of electrons from the molecular orhitals of the target gas by photons of sufficient energy (e.g., He(1) radiation 21.21 or He(I1) radiation 40.81 eV) (1620). Equation 1is usually a "good" approximation since the correlation error (i.e., an electron-electron error) is roughly cancelled hy the relaxation error (i.e., a shielding error); the former is usually negative since the ion possess fewer electrons than the parent molecule, whereas the latter is usually positive since the parent MO's are assumed to he the optimum MO's for the ion (when in fact due to the fewer electrons the optimum MO's for the ion would be more contracted). Figure 1 describes diagrammatically Koopmans's description of ionization. The UPS experiment is governed by the Einstein relationship, KE, = hu - IP,
(2)
where K E is the kinetic energy of the electron of ionization energy IP ejected by radiation of frequency u.
FREE ELECTRON ENERGY
-
(Ic
IONIZATION LIMIT
_____
- - -
o %+P-
o
0
ac+ 0.EZP
0 0
e
ac+l.6Zp
%+2P-
ETHYLENE
LINEAR SUROIENE
Figwe 1. Kmpmans's description of ionllatlon for Wlene and linear butadiene within the HMO framework.
The variation of the photoelectron hand intensities with incident photon energy (especially using He(1) and He(I1) radiation) is a well-established aid in spectral assignment of molecules containing first and second row atoms. Investigations by Peel and co-workers (22) have demonstrated that a "good" approximation to the photoionization cross section (or hand intensity) of a MO (aMO)is given by qM"=
Cc,'.:" +
(3)
i>k
i
Using the HMO approximation eq 3 becomes giMO
= Ccj;qo
(4)
where C's are the HMO coefficients and the of0 are the atomic photoionization cross section. For a spectrometer with a 90' collection angle, the aAOare given by The aj(KE) and @,(KE) (the asymmetry parameter) are functions of the ejected photoelectron's kinetic energy. For first-row atoms use can he made of Manson's (23) tabulated values. Figure 2 graphically illustrates the theoretical atomic cross section data a,(KE) and asymmetry parameter (3 as a function of the ejected electron's kinetic energy (23). I t is clear that, under He(1) conditions, ionization from avalence MO composed primarily of a halogen 3p or 4p A 0 would result in a more intense hand than ionization from a valence MO composed ~rimarilvfrom carbon 2~ or nitroeen 2~ AO's. Thus the ~~O'coeft'iciknts not only giie a descr&tio; of the MO's in terms of AO's but also vield informatim about the variations in spectral intensities-of PE hands. HMO Interpretation of the Energetic Shms In the UPS of Mono-Subslituted Haloamlnes Figures 3 (a-d) are the PE spectra of mono-substituted chloro- and hromo-amines that have been puhlished elsewhere (22,24-26). The spectra have been assigned using allVolume 66 Number 10 October 1989
821
electron and pseudopotential MO (PPMO) methods as well as from information gleaned from their infrared and Raman spectra. We shall concentrate on only the three lowest IP bands. Figure 4 gives a diagrammatic representation of the interaction of the N 2~ A 0 with the haloeen valence no A 0 to yield the three h&hest occupied ~ i j ' s which , reLonahly accountsfor the first three hands. Due co the intensitvof the second hand i t is reasonable t o assume that this band represents ionization from a MO composed primarily of halogen np A 0 character (see Fig. 2) that can only he shifted from the atomic IP value (mean of spin-orbital split I P S ) via an indue to the lower intensity of ductive mechanism. the first and third bands a resonance mechanism needs to be invoked to understand a MO that contains a sizable N ZD as well as halogen np coefficient. By invoking a parallelogram model, the size of all the inductive and resonance mechanisms can be deduced using HMO theory. That is, according to HMO,
to -ax since this is just the coulombic self-energy (i.e., the energrequired to ibnize an electron from a noGbonded p AO). From the characteristic equation we have two equations (one for each root) and two unknowns (aNand 8) and so we can derive,
ow ever,
Using Koopmans's approximation the 6's (or the roots of the secular determinant) must be equal to the negative of the first (I,) and third (I3)IP's. The second IP ( I d must be equal
Figure 2. (a) Total sass saction reduced to per elecbon pair of Me np atomic orbitals ot C. N. F. CI, and Has a functlon of theenergy of the ejected elechon. (b) Angular asymmeby parameter 0 far mep elecbons of C, N. F. CI, and H as a function of the energy ot Uw ejected elecbon.
822
Journal of Chemical Education
Figwe 3. He(l) phdDelecbon specbum of (a) NHsCI.(b) NH2Br. (c)CYNHCI. and (d) CH.NHBr.
The inductive effect on the nitrogen lone pair in the suhstituted m i n e s is given by where INis the first ionization potential of the parent amine. On the &her hand, the inductive effect on t h i halogen lone pair (ix) in the substituted m i n e is given by where Ix is the mean of the IP's of the atomic P spin-orbit split states. Using a parallelogram construction the two resonance effects, r~ and rx, are defined by
section for each MO using Manson's atomic cross-section data (23). Tahle 1 highlights the experimental IPS,HMO parameters. inductive and resonance narameters of the mono-suhstithed haloamines gleaned From the experimental data. Figure 5 gives the various inductive and resonance mechanisms in diagrammatic form. The HMO PE (aJB,) . . . .. values for hutadiene based on the first two 1P's are (-7.531-2.43) eV respectively (14,lS). For NHzCI, NHzBr, CH?NHBr, and CH2NHCI the ratio beTable 1.
Experimental HMO Parameters for Mono-SubstHuted Amlnes' (All Energlea In ev)
Assuming that there exists a linear relationship between the atomic charge and the relative shift of r u with ~ respect to the parent molecule, we can define the nitrogen atomic charge by 4 N = -(ON
+ IN)IIN
(11)
Similarly for the halogen atomic charge we get sx = -(ax + Zx)IZx = (I2- Ix)lZx
(12)
Using the simple MO representations, ~,.. C&%)
. 52.63
56.75
38.73
33.46
SWf refs 20. 22-24fcnauignmant and UPS detalla.
(13) *3 = C21d~ + C214~ the HMO solutions in terms of the experimental IP's are
with the percentage contribution of 100C2. These coefficients can be used to determine the photoionization cross
Figure 4. lmerectlm ot Um np orbitals of mono-substituted haloamlnes based m a simple overlap criteria of the approximate T symmehies.
-
Figure 5. Canparlsansof t b mrelatiom of the mnpsubstitutedhaloarnlnes. k each the lndvctlve shifts are labelled as I and the resonance shins are labelled as r. (a) Mono-chloroamlne and methyl chinoamlne. (b) Mondr* rnoamlne and methyl bromoarnine.
Volume 66
Number 10 October 1989
823
tween the @/Avalues (i.e., Kvalues) are 0.58,0.51,0.41, and 0.52, respectively. Notwithstanding the differences in the electronegativities (see below) these K values are in good agreement with the accepted Kc-cl and KGB, values of 0.4 and 0.3, respectively (2). For NHzC1, NHzBr, CH3NHBr, and CH3NHCl the h~ values are 1.89, 1.68, 1.20, and 1.26, respectively, which is in excellent agreement with the typical h~ value of 1.5 (2). Both inductive shifts, i~ and ix, follow the Allred electronegativity (27) order: C (2.55) < Br (2.96) < N (3.04) < C1 (3.16). For instance, because the electronegativity of CI > Br, it would he anticipated that i~ for NHlCI would he greater than i~ for NH?Br and a similar trend for the methvl ~-~ deriva~ ~ -- ~ tives. Furthermore, due to the fact that the methyl group is an electron-releasing substituent, i t would he expected that i~ for NHzC1 would be larger than that for CH3NHC1, but, because the electronegativity of N a Br, the shift of iN for NHzBr would he expected to he less than that of CH3NHBr. Furthermore, analogous qualitative arnuments can be made to rationalize the relative magnitude o f the resonance parameter r ~hut , in terms of the coulombic self-ener~v,aN. .. The atomic charges ( q and ~ qx) also follow trends in the electronegativity as well as reflect the electron releasing nature of the methyl substituent. However, it should be pointed out that sophisticated PPMO calculations yield atomic charees that are sienificantlv different in maenitude from those reported in ~ a i l 1. e ~ o r k x a m ~ lfor e , NHzBr and CHsNHBr PPMO(25.28) calculates (awlon,) ..- . .-.. to be (-0.369 el-0.134 e) and (-0.211 el-0.173 e), respectively. The calculated percentage charader of nitrogen and halogen of the first and third MO (see eq 14 and Table 1) are in reasonable agreement with the more sophisticated PPMO calculations (28). For example, for NHzCl and CH3NHC1the (HMOIPPMO) nitrogen characters of highest occupied MO are (47%/38%)and (67%151%),respectively. Using Manson's data and the Huckel MO coefficients the He(I)/He(II) cross-section hand ratios can be calculated. The least squares regression fits t o a and B are ~
~
~
.-
~-
~~~~~
where KE is the kinetic energy of the ejected electron. Usinr eas 4. 5. and 15 and the HMO coefficients leads to the ~ei1)iHei11j cross-section ratios given in Table 2 for NH&l and CH2NHCI (for which data is available). For comparative purposes the experimental and the I'I'MO ratios (usinn ea 3 and the PPMO coefficienW are also w e n in this table: While the absolute calculated photoionization cross sections are in poor agreement with experiment, the calculated ratios indicate that the percentage character of the NHXI MO'n reasonahlv describe the variations of the second hand whencomparedio the first and third hands. It is alsosatisiyine to note that the HMO model fairs well in com~arisonto t h i PPMO modeland, moreover, in comparison wkhrespect to experiment. For CH3NHC1the HMO model is in much poorer agree-
824
Journal of Chemical Education
Table 2.
Bard
Experimental and Calculated Relatlve Photoel&mn Band Intenslllesa E ~ P
He(1)
Hs(i1)
Ratio Hell)
1.31 0.72 0.97
1.88 0.10 1.02
0.70 7.20 0.95
PPMO
He(ll)
Ratlo He(l)
1.22 0.73 1.05
0.64 1.27 1.24
HMO He(ll)
Ratio
0.92 1.32 0.76
0.63 1.42 0.71
NHICI 1 2 3
-
0.78 0.93 1.29
0.58 1.88 0.54
-
ment with ex~erimentand with the PPMO model. Nevertheless, the v&t variation of the photoionization cross section of the first hand when c o m ~ a r e dwith the second and third hands is well reproduced. Conclusion The HMO theory continues t o be of relevance today even though for electron-sparse systems i t has been replaced by more sophisticated MO theories (where the drive for the latter is aimed a t achieving numerical precision and accuracy). However, HMO theory will continually be used as a valuable "insight" tool in many areas of spectrscopy and chemistry, justifying completely its pedagogical value in sophmore courses. Acknowledgment I wish to thank M.-T. Wisniowski for preparing all the figures. I also wish t o acknowledge the helpful suggestions of the referee (regarding Fig. 1) and the many discussions with J. B. Peel and F. Carnovale. Literature Cited 1. Gilde, H.-G. J. Chem. E d u . L912,49,24. 2, streitwieruer,A . Infmdulion to Moleeulor Orbital Theory lor O~gonicChemists; Wiley: NeaYork, 1961. 3. Fox. M.A.: Matsen, F. A. J. Chem. Edur. 1985,62,367-573. 4. Schsad. L. J.: Heru, B. A.J. Chem. Educ. 1974,51,MO-M3. 5 Shen, K. J. C k m . Educ. 1913,50.23&242. 6. Dalton, J. C.;Friedrich, L. E. J. Chem.Educ. 1375,52,721-724. 7. Phelsn,N.F.:Orchin,M.J.Chsm.Edur. 1966,43,511-575. 8. McB~ide,J. J.Cham.Educ. 1914.51.471. 9. Keeports.0. J . C h m . E d u . 1986,63,753-756. 10. Rhales, W.G.:Brown,L.J. Chem.Educ. 1914,51,595. 11. Fitzpatrick, N. J. J . Chom. Educ. 1974.51.643. 12. Murgieh, J. J. Chem. Edur. 1917,54,421. 13. Peake. B. M.; Grauwoeljer, R. J. Cham. E d u . 1981.58.692. 14. Hoffman", B.: Heilbmnner, E.; Gleiter, R. J Am. Chrm. Sm. 1910,92,706707. Chem. 1913,12.73P751. 15. Bmk,H.;Ramasy,B.G.Agnelu. 16. Bock, H.: Mallere, P. D. J. Chom.Educ. 1974,51,50%414. 17. Ellison. F. D.;White. M.G.J.Chem. Educ. 1976.53.430-436. 18. Aldor.I.;Yin,L.L.;Tsange,T.;Coyle,G.J.J.Chem.Edue. 1984,61,157-?MI 19. Surer, S.J. J. Chem. Educ. 1982,59,81"815. 20. Peel. J. B.; von Nsm-Felsobuki. E. I. J. Chem. Educ. 1987.64.463465. 21. Rahalais, J. W.Pn'nciple8 of Ullmviolal PhatoelecfmnSpectraacopy;Wiley: London, 1977. 22. Livetf,M.K.:Nsm-Feleobuki.E.I.:Pel.J. 8.;Wlllett.G.D.Inorg. Chem. 1918.17, 1fA&1612. 23. Manson, S. T.J.Elect. Spectrosc. Rolof. Phan. 1973,2,48244. 24. Naw-Fe1sobuki.E. I.;Pecl,J.B.: Wiett,G. 0.J . Elect.Spectrmc.Relot.Phen.1978, 13.17-25. 25. Csmnville, F.; Negy-Felaobuki. E. I.; Peel, J. 8.; Willett, G. D. J. Elect. Speclraae. firlor I'hm 1978, 14. 163 173 26 %a\-Fc1mhuki.E.1:Pccl.J B.J. C. S Famd 111978.71. 19E 1934 27 A.1nd.A I. .I 1nr.r; N ~ r lChem I K 1 . 1 7 . 2 i S 2 2 1 Zd vun N W R1xb"kl.F I Phl>'lhcs,s. I a'lhkiln,"en,l,. lSRn
