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lone pairs be very mutually repulsive relative to bonding pairs, but here we have a question not of their absolute repulsion energies but rather the rate of change of these repulsion energies as a function of the degree of eclipsing. This rate of change and consequent effect on molecular geometry has been skillfully examined by Palke and KirtmanVz3 Experimentally, the introduction of oxygens into six-membered rings fails to give unamibiguous support for this idea. For example, Strauss and Pickettz4reported barriers to pseudorotation in trioxane which were actually smaller than those in cyclohexane. This reduction in rotation barriers for the bond pair-lone pair interactions of trioxane relative to the bond pair-bond pair interactions of cyclohexane is consistent with the heirarchy of rotational barriers for ethane, methylamine, and methanol (2.9, 1.9, and 1.1 kcal, respectivelyz5). The larger rotational barrier in cis-hydrogen peroxide (7.0 kcal/moIz6) supports our idea of interactions between Palke, W. E.; Kirtman, B. J . Am. Chem. SOC.1978, 100, 5717. Pickett, H. M.; Strauss, H. L. J . Am. Chem. SOC.1970, 92, 7281. Eliel, E. Conformational Analysis; American Chemical Society: New York, '1965. (26) Hunt, R. H.; Leacock, R. A,; Peters, C. W.; Hecht, K. T. J. Chem. Phys. 1965, 42, 1931.
lone pairs on adjacent oxygens being particularly problematic for rotation to an eclipsed conformation. (Note that this figure corresponds to the eclipsing of two sets of lone pairs. trans-Hydrogen peroxide rotates so as to eclipse two bond pair-lone pair sets and has a smaller 1.1-kcal rotation barrier.) In summary, our theoretical results, though produced in the absence of experimental data on the molecules in question, align relatively intuitively with expectations from analogies with known compounds (cyclohexane, trioxane) whose conformational preferences are well tabulated in the literature. This does not by itself validate our preliminary results produced by single-configuration S C F methods, but we are sufficiently encouraged by this to believe that ascent to higher levels of theory (configuration interaction and coupled cluster) will provide meaningful information regarding structural and energetic predictions for the six-membered oxygen ring. We are currently working on improving our precision in predicting this molecule's energy differences between conformations as well as its exothermicity upon decomposition.
Acknowledgment. This research was supported by the Air Force Office of Scientific Research under Grant AFOSR-87-0182. Registry No. 06,11 1557-60-9.
Chemical Information from Electron-Energy-Loss Near-Edge Structure. Core Hole Effects in the Beryllium and Boron K-Edges in Rhodizite R. Brydson; D. D. Vvedensky,*W. Engel,# H. Sauer,s B. G. Williams,L E. Zeitler,*g and J. M. Thomas*II Department of Physical Chemistry, University of Cambridge, Lensfeld Road, Cambridge CB2 1 EP, U.K.; The Blackett Laboratory, Imperial College, London SW7 2BZ, U.K.; Fritz-Haber-Institut der Max- Planck- Gesellschaft, Faradayweg 4-6, DlOOO Berlin 33 (Dahlem), Germany: International Centre for Insect Physiology and Ecology (ICIPE),P.O. Box 30772, Nairobi, Kenya; and Davy- Faraday Research Laboratory, The Royal Institution, 21 Albemarle Street, London W1X 4BS, U.K. (Received: June 9, 1987; In Final Form: October 28, 1987)
The prospects of being able to retrieve coordination numbers of light elements ( Z < 10) in solids by analyzing the fine structure of near-edge regions of electron-energy-loss peaks corresponding to excitations from core levels are examined with specific reference to boron and beryllium in the mineral rhodizite, the structure of which is already known. Proof that there are both Beo4and BOptetrahedra in this material is obtained from the correspondence of observed and calculated spectra. Successful modeling using real-space multiple scattering calculations is achieved only if core hole effects are included by use of excited absorbing atom potentials. Various approximations to these potentials are investigated, and we conclude that the best are the ( Z + 1 ) excited-state and ( Z + 2) ion approximations. The importance of core hole effects is discussed for elements of low atomic number; and a comparison is drawn with previous work on beryllium carbide, a new calculation being performed for this solid.
Introduction It has recently been re~ognizedl-~ that information of considerable chemical significance can be extracted from electron-energy-loss spectroscopy (EELS) of solids. Such spectral information is obtainable by using transmission electron microscopes that have attached to them an appropriate electron spectrometer. Chemical composition, oxidation states, and, under favorable circumstances, bond distances and the electronic structure of the solids4 can all be extracted from materials of microscopic dimension, provided they are not ultrasusceptible to electron-beam-induced damage. With the recent advent of so-called parallel d e t e ~ t i o ncoupled ,~ with good energy resolution (ca. 0.5 eV), it has been possible to 'University of Cambridge. 1Imperial College. 5 Fritz-Haber-Institut der Max-Planck-Gesellschaft. International Centre for Insect Physiology and Ecology. l1 The Royal Institution.
0022-3654/88/2092-0962$01.50/0
study, among other things, the electron-energy-loss near-edge structure (ELNES) of inner-shell electron excitations.6-8 Here we concentrate, for heuristic purposes, on the ELNES of the beryllium and boron K-edges in the mineral rhodizite, which has hitherto been the subject of detailed structural studies by X-ray (1) Thomas, J. M.; Williams, B. G.; Sparrow, T. G. Acc. Chem. Res. 1985, 18, 324. (2) Colliex, C. In Aduances in Optical and Electron Microscopy; Barer, R., Coslett, V. E., Eds.; Academic: London, 1984; Vol. 9. (3) Egerton, R. F. Electron Energy-Loss Spectroscopy in the Electron Microscope; Plenum: London, 1986. (4) Thomas, J. M.; Sparrow, T. G.; Uppal, M. K.; Williams, B. G. Philos. Trans. R . SOC.London, A 1986, 318, 259. ( 5 ) Shuman, H. Ultramicroscopy 1981, 6, 163. (6) Lindner, Th.; Sauer, H.; Engel, W.; Kambe, K. Phys. Rev. B Condens. Matter 1986, 33, 22. (7) Vvedensky, D. D.; Pendry, J. B. Phys. Reu. Lett. 1985, 54, 2725. (8) Vvedensky, D. D.; Pendry, J. B. Surf. Sci. 1985, 162, 903.
0 1988 American Chemical Society
Core Hole Effects in the Be and B K-Edges in Rhodizite d i f f r a c t i ~ nhigh-resolution ,~ electron microscopy (real-space imaging),1° and multinuclear solid-state, high-resolution NMR." The mineral samples emanated from Madagascar and were made available by the British Museum (Natural History). Their composition was determined by both wet chemicallo and EELSl2 methods. The stoichiometry is best represented by ~~.46Cs0.36Rb0.06Na0.02)~0.90A13 99Be4(B1l.35Be0.55Li0.02)028~ The coordination of both beryllium and boron, each of which is surrounded by four oxygens, is known to be tetrahedral. The central aim of this work is to ascertain whether available theoretical procedures would lead to a computed spectrum for the ELNES of both the B K-edges and Be K-edges that matched the observed spectrum. Under the conditions of small momentum transfer and small sample thickness, the interpretation of such ELNES follows along lines similar to that of X-ray absorption near-edge structure (XANES). Observed near-edge features have been shown to be closely related to the projected density of unoccupied states. More formally, the core edge intensity, Z(E), may be written according to Fermi's Golden Rule as
where P ( E ) is a matrix element overlap factor which describes the coupling between the initial and final states within the dipole selection rule (AI = f l ) and N(E) is the projected density of states with the appropriate ~ymmetry.'~Thus, if P(E) is slowly varying in the energy region of interest, then the ELNES reflects the density of unoccupied states in the conduction band. In reality, this simple single-electron picture may be modified by relaxation of the unexcited electrons in response to the production of a core hole and excited electron-core hole interactions (excitonic eff e c t ~ ) . ' ~However, ~'~ one-electron theory has in some cases been strikingly successful in the interpretation of near-edge structures and X-ray absorption produced by electron-energy-l~ss~~~'~ measurements.I8J9 In previous studies6Vz0we have successfully matched experimentally measured ELNES with the results of real-space multiple scattering calculations performed using the "ICXANES" computer code of Vvedensky et al.*' Briefly, the transition rate of excitation is calculated within the dipole approximation, using essentially an atomic contribution modified by multiple scattering of the excited electron by the surrounding atoms. This approach, while essentially equivalent to a Korringa-Kohn-Rostccker (KKR) band structure calculation, is considerably more flexible, allowing the inclusion of excited atom potentials to account for core hole effects. The scattering properties of the various atoms are described by phase shifts which may be calculated by numerical integration of the Schrodinger equation assuming a muffin tin form for the atomic potentials in the crystal, obtained in the Mattheiss prescription by the superposition of neutral atomic charge densi(9) Pring, A.; Din, V. K.; Jefferson, D. A.; Thomas, J. M. Mineral. Mag. 1986, 50, 163.
(IO) Pring, A,; Thomas, J. M.; Jefferson, D. A. J. Chem. SOC.,Chem. Commun. 1983, 734. ( 1 1) Pring, A. Ph.D. Thesis, University of Cambridge, 1984. Thomas, J. M.; Klinowski, J. Adv. Catal. 1985, 33, 199. (12) Engel, W.; Sauer, H.; Brydson, R.; Williams, B. G.; Zeitler, E.; Thomas, J. M. J. Chem. SOC.,Faraday Trans. 1 , in press. (13) Azaroff, L. V.; Pease, D. M. In X-ray Spectroscopy; Azaroff, L. V., Ed.; McGraw-Hill: New York, 1974. (14) Leapman, R. D.; Grunes, L. A,; Fejes, P. L. Phys. Rev. B Condens. Matter 1982, 26, 614. (15) van der Laan, G.; Zaanen, J.; Sawatzky, G. A.; Karnatak, R.; Esteva, J. M. Phys. Rev. B Condens. Matter 1986, 33, 4253. (16) Grunes, L. A.; Leapman, R. D.; Wilker, C. N.; Hoffmann, R.; Kunz, A. B. Phys. Rev. B Condens. Matter 1982, 25, 7151. (17) Grunes, L. A. Phys. Rev. B Condens. Matter 1983, 27, 211 1. (18) Dobler, U.; Baberschke, K.;Vvedensky, D. D.; Pendry, J. B. SurJ Sci. 1986, 178, 679. (19) Vvedensky, D. D.; Pendry, J. B.; Dobler, U.; Baberschke, K. Phys. Rev. B Condens. Matter 1987, 35, 1156. (20) Brydson, R.; Williams, B. G.; Sauer, H.; Engel, W.; Zeitler, E.; Thomas, J. M. J. Chem. SOC.,Faraday Trans. 1 , in press. (21) Vvedensky, D. D.; Saldin, D. K.; Pendry, J. B. Comput. Phys. Commun. 1986, 40, 421.
The Journal of Physical Chemistry, Vol. 92, No. 4, 1988 963
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Figure 1. (expt) Experimental EELS spectrum of the beryllium K-edge in rhodizite after background subtraction. (a-c) Results of'ICXANES calculations for beryllium tetrahedrally coordinated to a single shell of oxygen atoms. Spectrum a has been calculated by using ground-state potentials. In spectra b and c core hole effects have been included by use of (b) the Z* approximation and (c) the (2 + 1 ) ion approximation. Details are given in the text.
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Figure 2. As for Figure 1 except that a r e hole effects have been included by use of (a) the (2+ 1 ) O approximation, (b) the (2 + 1)* approximation, and (c) the ( Z + 2) ion approximation. Details are given in the text.
ties?2*23 The multiple scattering calculation is performed in real space by dividing the cluster into shells of atoms surrounding the absorbing atom. The multiple scattering is solved within each shell in turn, and the results are combined so as to reassemble the final cluster, use being made of any structural symmetry.
Experimental Section Methods of sample preparation and of recording and processing EELS spectra, including the procedure for deduction of background intensity and discussions of the relative rates of multiple scattering events (as well as such refinements as Bragg scattering followed by edge scattering), have been discussed fully elseBriefly, the parallel recording system, which is described in some detail in ref 12, consists of a silicon intensified target (SIT). (22) Loucks, T. L. Augmented Plane Wave Method Benjamin: New York, 1967. (23) Mattheiss, L. F. Phys. Reu. A 1964, 133, 1399. (24) Brydson, R. D.; Thomas, J. M.; Williams, B. G. J . Chem. Soc., Faraday Trans. 2 1987,%3,147.
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Results and Discussion In an earlier workz0we confirmed the octahedral coordination of aluminum to oxygen in rhodizite by comparing the experimentally measured ELNES with the results of multiple scattering calculations. To do this, we used a cluster consisting of a single shell of oxygen neighbors surrounding an aluminum atom and compared the theoretical results of both octahedral and tetrahedral coordination with experiment. The inclusion of only a single shell of neighbors may be justified by consideration of the following points. The 02-ion is a very strong backscatterer and produces considerably more structure than other species,6 which, in view of the comparatively large unit cell of rhodizite (ca. 7 A cubic) containing many different atoms, would suggest that many of the gross features in the ELNES spectrum are due to the nearestneighbor oxygen shell. It has been shown by Knapp et aLZ5that the transition-metal K-edges of complex oxides essentially reflect the local coordination of the transition-metal atom to oxygen. With this in mind, we set out to model the beryllium and boron K-edges using the “ICXANES” approach. In both Figures 1 and 2 the curve labeled “expt” shows the experimentally measured beryllium K-edge in rhodizite. The results of real-space, multiple scattering calculations obtained with just a single shell of tetrahedrally coordinated oxygen neighbors surrounding a central beryllium atom together with a damping of -2 eV are displayed in Figures 1 and 2, curves a-c. They constitute a variety of approximations for the potential of the absorbing beryllium atom. In all cases matrix element amplitudes and phases were obtained from atomic self-consistent field (SCF) c a l c ~ l a t i o n sand ~ ~a~muffin ~ ~ tin potential imposed on the structure of beryllium oxide B e 0 (which consists of BeO, tetrahedra2*). The exchange parameter, a, was taken to be 0.8 (close to Schwarz’s valuez9). The choice of muffin tin radii (MTR) for the calculations was investigated, and it was found that sufficiently convergent calculations were achieved with radii r(Be) = 1.695 au and r ( 0 ) = 1.395 au. Owing to the arbitrary position of the muffin tin zero, these, and all other, theoretical curves have been aligned to experiment in such a way that the first peaks coincide. In Figure 1, curve a shows the result of using ground-state potentials.26 (We shall call this the Z approximation.) As can p resonance with very be seen, this produces a very broad s little initial structure. The use of a ground-state potential for the central absorbing atom takes no account of the effect of the core hole. One way to do this is to use the so-called Z* approximation, in which an excited electronic configuration is assumed for the absorber. For beryllium, we used the results of an SCF calculation for the configuration Be Is( 1) 2s(2) 2p( l ) , following the prescription of Herman and skill mar^.*^ The ICXANES results are shown Figure 1, curve b. This sharpens up the resonance but still does not provide us with the strong initial peak. Using a Clementi atomic wave functionz6 for the Z + 1 element, but adjusting the occupation number of the appropriate core state and keeping the atomic number 2 the same [Le., in this case B Is( 1) 2s(2) 2p( 1) (and Z = 4)-the so-called (2 + 1) ion approximation], shown in Figure 1, curve c, produces a very similar result to that of the Z* approximation. We also investigated other excited electronic configurations including Slater’s transition-state approximation (in this case Be ls(1.5) 2s(2) 2p(0.5)). However, none of these gave agreement with experiment owing to the fact that the initial peak was always too weak. All the approximations above (Figure 1, curves a-c) have employed the atomic number Z = 4 for the central beryllium absorbing atom in the muffin tin potential calculation. An alternative approach is to increase the number of electrons, and thus the
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(25) Knapp, G. S.; Veal, B. W.; Pan, H. K.; Klippert, T. Solid State Commun. 1982, 44, 1343. (26) Clementi, E.; Roetti, C. Atomic Data and Nuclear Data Tables; Academic: New York, 1974; Vol. 4. (27) Herman, F.;Skillman, S.Atomic Structure Calculations; PrentlceHall: Englewood Cliffs, NJ, 1965. (28) Wyckoff, R. W. G . Crystal Structures; Intersclence: New York, 1960; Vol. 1 (29) Schwarz, K. Phys. Rev. B. Solid State 1972, 5, 2466.
atomic number, for the absorbing atom in the calculation of the potential. This attempts to model both the effective increase in nuclear charge due to the core hole and the screening effect of the excited electron on the other electrons. Thus, in Figure 2, curve a shows the results of using the Clementi atomic wave function for boronz6 (and thus Z = 5 in the muffin tin potential calculation) for the central absorbing atom-the so-called ( Z 1)’ ( ( Z + 1) ground state) approximation. This creates a sharper s p resonance, but again we observe little initial structure. However, this sharp initial peak may be reproduced by using the results of an S C F c a l c ~ l a t i o nfor ~ ~the excited state of the Z 1 element (the ( Z + 1)* approximation). In Figure 2, curve b, we have employed the excited electronic configuration B Is( 1) 2s(2) 2p(2) (and Z = 5) for the beryllium absorber, calculated by using the method of Herman and skill ma^^.^^ The use of the (2 2) ion approximation [Le., the Clementi atomic wave function26for the 2 2 element with an appropriate core electron removed, C ls(1) 2s(2) 2p(2) (and Z = 5) in the potential calculation] for the absorbing atom, shown in Figure 2, curve c, produces a result almost identical with that of the (2 + 1)* approximation. It should be noted that the anomalous shoulder prior to the first peak in our calculations is not present in the experimental data. Furthermore, we are unable to model the peak lying approximately 16 eV from the edge which, as we shall demonstrate, also occurs at the boron K-edge. Thus, we conclude that the initial sharp peak present in the experimental ELNES (Figures 1 and 2 (expt)) may be modeled only if an excited atom potential calculated by using the (2 + 1)* approximation (Figure 2, curve b) [or alternatively the ( Z + 2) approximation (Figure 2, curve c)] is employed. However, since we have included only a single shell of neighbors, and more distant shells could well modify the near edges, an unequivocal confirmation of our conclusion must await a further calculation. The results shown in Figures 1 and 2 are, nevertheless, highly suggestive. The approximation used for our calculations correctly models both the increase in effective nuclear charge due to the presence of a core hole and the screening effect of the excited core electron, especially in the near-edge region. The structure factor further out from the edge is considerably broader than that produced by our calculation with this potential approximation; this extended structure is similar to that obtained by using the (Z 1) ion approximation (Figure 1, curve c), indicating that core hole effects are more predominant close to the edge. Our calculation neglects any energy dependence of the potentials; indeed, it has been shown that the ( Z + 1) ion approximation correctly models the extended energy-loss fine structure (EXELFS) of an edge.30 The only previous attempt to match the ELNES of the Be K-edge with the results of band structure and multiple scattering calculations was performed by Disko et aL3’ in their study of the ELNES of beryllium carbide (BqC). Projected density of states calculations (constructed from a linear combination of atomic orbitals (LCAO)) and initial ICXANES calculations did not successfully model the first sharp peak on the experimental Be K-edge, but agreement was achieved on the C K-edge. Essentially identical results were obtained by Herzig and R e d i t ~ g e rfrom ~~ an augmented plane wave (APW) band structure calculation. However, it was found that if anionicity of Be(+le78),C(-3.56) was assumed, simulated by the addition of a lattice of paint charges to the Coulomb part of the potential obtained from S C F calculations, then reasonable agreement was obtained for the Be K-edge. Photoemission and absorption data for Be0,33together with the fact that Be2C readily hydrolyzes to BeO, suggest that the electronic structure in B e 0 is similar to that in Be,C. Thus, bearing in mind our findings, it seems reasonable to conclude that their agreement in assuming such an ionicity (and more importantly
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(30) Ekardt, W.; Tran Thoai, D. B. SolidState Commun. 1983, 45, 1083. (31) Disko, M. M.; Spence, J. C. H.; Sankey, 0. F.;Saldin, D. Phys. Reo. B: Condens. Matter 1986, 33, 5642. (32) Her& P.; Redinger, J. J . Chem. Phys. 1985, 82, 372 (33) Formicher, V. A. Sou. Phys.-Solid State (Engl Transl.) 1971, 13, 754.
Core Hole Effects in the Be and B K-Edges in Rhodizite
The Journal of Physical Chemistry, Vol. 92, No. 4, 1988 965
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Figure 3. (expt) EELS spectrum of the beryllium K-edge in Be2C as measured by Disko et al.25 Peaks a-e have been indicated. (theory) Results of our ICXANES calculation for beryllium surrounded by six nearest-neighbor shells in Be2C. Core hole effects have been included by use of the (Z+ 1)* approximation; details are given in the text. Features corresponding to peaks a-e in the experimental spectrum have
Figure 4. (expt) Experimental EELS spectrum of the boron K-edge in rhodizite after background subtraction. (theory) Results of the ICXANES calculation for boron tetrahedrally coordinated to a single shell of oxygen atoms. Core hole effects have been included by use of the ( Z + 1)* approximation;details are given in the text. 121
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been marked. allowing for it in this way) is rather fortuitous. Indeed, any muffin tin potential calculation should, to some extent, take any ionicity into account. Clearly, a self-consistent calculation is required, but it has been shown that, as far as XANES is concerned, the non-self-consistent Mattheiss prescriptionZ2gives a sufficiently accurate approximation to a fully self-consistent calculation even in ionic materials such as calcium oxide, Ca0.34935 Furthermore, it is odd that the disagreement lies solely on the Be K-edge, where one would expect such core hole effects to be important due to the very few electrons present on the atom and the fact that any core exciton would be expected to be bound more strongly at the cation sites owing to the reduction in screening. Consequently, examining all the facts, we conclude that the main problem in modeling the Be K-edge lies in the large influence of the core hole. The agreement we obtain for the case of beryllium tetrahedrally coordinated to oxygen indicates that the use of either the ( Z + 1)* or ( Z 2) ion approximation does allow for this to a certain degree. On this note, analogous calculations for the Be K-edge in Be$ are presented in Figure 3. The curve labeled “expt” displays the experimental data of Disko et al.31 for the Be K-edge in Be2C, while the curve labeled “theory” shows the results of our ICXANES calculations. Here we have taken a to be 0.8, r(Be) = 1.7083 au, and r(C) = 1.8464 au in the muffin tin potential calculation. (These values for the muffin tin radii are slightly different from those given in ref 32, and we note that the choice was reasonably critical in order to obtain good agreement.) We have not included any correction for the ionicity. Instead, in the calculated curve we have used the (Z I)* approximation [Le., B ls(1) 2s(2) 2p(2) (and 2 = 5)] for the absorber, obtained from S C F calculation^.^^ We have taken into account six nearestneighbor atomic shells around the beryllium atom and included a damping of -2 eV. It is evident that our calculation correctly models the strong initial peak, a, which is impossible to reproduce if a ground-state electronic configuration is employed for the absorbing beryllium atom (as found by Disko et aL3*). The further features present in the experiment, peaks b-e, also show up in the calculated curve, and these have been indicated. However, it should be noted that these are somewhat misaligned on the energy scale relative to the first peak, a, the peaks all being too close to a by roughly the same amount. This anomaly has also been found on the 0 K-edge in MgO where the ( Z + 1)’ approximation was
+
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(34) Norman, D.; Garg, K. B.; Durham, P. J. SolidSrate Commun. 1985, 56, 895. (35) Wille, L. T.; Durham, P. J.; Sterne, P. A. J . Phys., Colloq. 1986,
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Figure 5. A portion of the experimental boron K-edge in rhodizite, shown in Figure 4 (expt), on an expanded scale. Note the similarity to the initial
structure of the beryllium K-edge (Figure 1 (expt)); further details are given in the text. used to model the effect of the core hole,6 and presumably it is due to neglect of the energy dependence of the potentials. This apart, these results suggest that the initial sharp peak, a, present in the experimental spectrum is due almost entirely to core hole effects. Further evidence for our postulate is available in Figure 4 where the curve labeled “expt” shows the experimentally measured boron K-edge in rhodizite, while the curve labeled “theory” indicates the results of our ICXANES calculations for a single shell of oxygens tetrahedrally coordinated to boron. As before, we have obtained matrix element amplitudes and phases from a muffin tin potential calculation on boron oxide B2O3 (which contains BO4 tetrahedra36). The exchange parameter, a,was again taken to be 0.8. Muffin tin radii were again investigated and were eventually chosen to be r(B) = 1.7000 au and r ( 0 ) = 0.7756 au. As in the case of beryllium, the use of ground-state atomic wave functions resulted in a very broad p resonance with no initial structure. Successful agreement was only obtained if the ( Z 1)* approximation (i.e., C ls(1) 2s(2) 2p(3)-the results of a Herman-Skillman calc~lation,~’ and Z = 6 in the muffin tin potential calculation) was employed for the central absorbing boron atom. As is evident, the theoretical curve reproduces all three major features present in the experiment, indicating the applicability of our procedure. The small preedge peak present in the experimental spectrum has been previously assigned to an excitonic transition within the band gap,20and the ICXANES approach would not be. expected to predict this. We have shown previouslyz0 the correlation between features on both the beryllium and boron K-edges (and also other edges in the EELS spectrum of rhodizite), which is to be expected since the local projected density of unoccupied states is expected to be very similar. Since we are able to model, to some extent, the presence of the feature approximately 16 eV from the boron edge, we must ask who do we
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(36) Berger, S. V. Acta Chem. Scand. 1953, 7, 623
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of excited absorbing atom potentials in real-space multiple scattering calculations. Investigations into the best approximation for these excited potentials in other light-element K-edges, as well as a method for the inclusion of energy-dependent potentials, are currently being performed. It should be noted, however, that while EELS is ideally suited to the measurement of such light-element edges, data of sufficient quality for accurate comparison with theory may be obtained only with the use of an efficient parallel detection system coupled with good energy resolution. The broader significance of this work is that microscopically small regions of a sample are amenable to structural probing by ELNES. This means that the coordination of light elements can be ascertained from minute samples and in localized regions, a feature of potential importance in solid-state chemistry and in the study of devices associated with nanotechnology.
fail in the case of beryllium. At present we are unable to answer this question, although further measurements on minerals containing Be04 tetrahedra are in progress to ascertain whether this is a feature of the nearest-neighbor oxygen shell. The detailed structure of this feature of the B K-edge mentioned above becomes evident if we examine closely the region from approximately 210 to 230 eV. This portion of the spectrum is shown on an expanded scale in Figure 5 and exhibits an edgelike structure with a narrow peak at around 214 eV and a rather broader peak at around 219.5 eV. This is a feature of the B K-edge since core levels of other elements do not exist at this energy. Thus, we must assume that above the main threshold further empty states of p symmetry are available which give rise to a sharp onset. This extended structure resembles the initial structure at the Be K-edge in rhodizite (Figure 1 (expt)), possessing the same splitting and relative intensities of the two peaks. This indicates that an absorber potential similar to the one successfully employed in the case of the Be K-edge should be used to model this extended feature. We therefore conclude that energy-dependent potentials are required for the successful modeling of ELNES spectra measured over a wider energy range. This work reveals the importance of core hole effects in the near-edge structure of light-element K-edges. We present a method for the modeling of such features based on the inclusion
Acknowledgment. We thank Dr. W. Ekardt for helpful discussions concerning this work. We acknowledge with gratitude support from the SERC (for a studentship to R.B.) and the Max-Planck-Gesellschaft for catalyzing the collaboration between the various authors, the Royal Society for a Senior Fellowship (to B.G.W.), and the British Museum for specimens of rhodizite. Registry No. Be, 7440-41-7; B, 7440-42-8; Be,C, 506-66-1; rhodizite, 12230-24-9.
A Low-Temperature (23 K) Study of L-Alanine Riccardo Destro,*+Richard E. Marsh, Arthur Amos Noyes Laboratory of Chemical Physics,$ California Institute of Technology, Pasadena, California 91 125
and Riccardo Bianchit Department of Chemistry, Carnegie- Mellon University, Pittsburgh, Pennsylvania 1521 3 (Received: June 12, 1987)
From a spherical crystal of L-alanine an extensive set (20Mo5 looo) of X-ray diffraction data has been measured at 23 (1) K. No phase transition has been observed on cooling, and the cell parameters of the orthorhomtic crystals (space group P212,2,) are, at the temperature of data collection, a = 5.928 (1) A, b = 12.260 (2) A, c = 5.794 (1) A. The contraction of the cell volume, with respect to the room temperature value, amounts to 2.2%. Intensity data, carefully corrected for scan-truncation losses, have been analyzed with various models. The best fit was reached by interpreting the electron density function in terms of pseudoatoms (multipoles). The analysis of the correlation coefficients has shown that the quality and quantity of the data set allowed a reliable deconvolution of thermal motion from the charge density. Precise and accurate geometry, as well as experimental deformation maps of both charge density and electrostatic potential, has been obtained. Ab initio calculations of atomic populations and group charges for the zwitterionic amino acid have been performed with various basis sets, up to the 6-31G** level. Derived results are compared with those of the multipole analysis of the X-ray diffraction data.
Introduction X-ray diffraction studies, when carried out at room temperature and with normal experimental and refinement techniques, can provide conclusive proof of atom connectivity with interatomic distances accurate to, perhaps, 0.005-0.01 A. The limitations in accuracy usually arise from three sources: (1) At room temperature, crystals of molecular compounds yield a diffraction pattern that dies out rather rapidly, often vanishing in the range 0.6-0.7 in sin O/A, because of smearing effects due to thermal agitation or disorder. (2) Because of this thermal agitation, which may represent a variety of rigid-body or independent-atom modes, it is often Permanent address: Dipartimento di Chimica Fisica ed Elettrochimica, Universitl di Milano, Via Golgi 19, Milano 20133, Italy. *Contribution No. 761 1.
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difficult to estimate true interatomic distances from the time- and space-averaged values that the experiment provides. This is often the most important source of error, for the uncertainty involved in interpreting the patterns of libration may well be considerably larger than the formal errors in atomic position. (3) Scattering by electrons in the valence shells is not adequately represented by the spherically symmetric atom form factors normally used, leading to residual discrepancies between data and model. Effects (1) and (2) can be minimized by cooling the crystal and effect (3) by modelling the outer-shell electrons with appropriate scattering functions. We describe here the results of an extensive and, we believe, an exceptionally careful study of crystals of L-alanine at 23 K. We selected L-alanine (Figure 1) primarily because it is a simple compound which contains a variety of groups: a carboxylate ion in which the two oxygen atoms are involved in very different 0 1988 American Chemical Society
