8496
J. Phys. Chem. 1995,99, 8496-8503
Theoretical Investigation of the NEXAFS Spectra of Acrylonitrile near the Carbon and the Nitrogen K-Edge Immanuel Wilhelmy Lehrstuhl fur Theoretische Chemie, Technische Universitat Miinchen, 0-85747 Garching, Germany
Carine Laffon? Hans-Ulrich Ehrke, and Wilfried Wurth Physik Department E20, Technische Universitat Miinchen, 0-85747 Garching, Germany
Notker Riisch" Lehrstuhl f i r Theoretische Chemie, Technische Universitat Miinchen, 0-85747 Garching, Germany Received: December I , 1994; In Final Form: March IO, 1995@
The polarization-dependent NEXAFS spectra at the C 1s and the N 1s edges of acrylonitrile, CHzCHCN, have been investigated theoretically by means of density functional methods. Discrete absorption lines were calculated by using the transition-state approximation within both the LCGTO-DF method and the MS-Xa technique. The continuum part was studied by the recently developed LDKL-DF method and compared to CMS-Xa calculations. The results were found in excellent agreement with experimental data for an acrylonitrile multilayer on a metal substrate, confirming the experimentally derived adsorption geometry and spectral assignments. The analysis of the continuum wave functions and eigenchannels provides additional insight into the photoabsorption and photoionization final states. Moreover, the present calculations suggest that nearly all peaks above the ionization potential are of one-electron character, reflecting the three dominating shape resonances.
I. Introduction NEXAFS spectra of molecules built from first-row atoms show a variety of discrete X-ray absorption lines and continuum resonances.' The former are often caused by excitations into molecular orbitals of antibonding n character, whereas the latter mainly correspond to resonant states of antibonding u character. The resonance states are usually associated with a "building block" of the investigated molecule, i.e., with one of its (quasidiatomic) fragments.' On the basis of an estimate of the "building block" that dominates the underlying resonance state, spectral features may be assigned by their energetic position and by their dependence on the polarization direction of the light, which provides insight into the orientation of the molecule relative to the polarization vect0r.l In the case of a molecule adsorbed at a surface, this polarization dependence may also yield information on the orientation of the molecule relative to the substrate. Furthermore, resonances of u character show a dependence on the length of the associated This is of importance because the adsorption process may alter the character of individual bonds; consequently, shifts of high-lying continuum resonances relative to their positions for the corresponding gas phase or physisorbed species may be related to chemisorption effects.2 The present theoretical investigation focuses on the NEXAFS spectrum of acrylonitrile, CH2=CH-C=N. So far the most common theoretical tool for the interpretation of NEXAFS spectra has been the continuum multiple scattering (CMS) X a method.'^^.^ This method crucially relies on the muffin-tin form of the local effective potential, which for molecules, especially for planar ones like acrylonitrile, implies
* Author to whom correspondence
should be addressed. ' Permanent address: LURE, Centre Universitaire de Paris-Sud, Bat. 209d. 91405 Orsay Cedex, France. Abstract published in Advance ACS Abstracts, M a y 1, 1995. @
a rather severe approximation that has been relegated from molecular ground-state density functional (DF) calculations quite some time Recently, the LDKL-DF method has been i n t r o d ~ c e d , ' ~ which -'~ is able to yield electronic continuum wave functions for a local potential without any shape approximation. It is one of the goals of the present study to demonstrate the power of the LDKL approach by comparing the LDKL-DF method and the familiar CMS-Xa procedure for a molecule, which presents a challenge to both theoretical procedures. In the following, we will first describe the salient features of the LDKL-DF m e t h ~ d ' ~and . ' ~ its ground-state analogue, the linear combination of Gaussian-type orbitals density functional (LCGTO-DF) meth~d.'.~The latter technique will be used to estimate the discrete excitation energies and their contribution to the NEXAFS spectra. Then we will present the theoretical results for the photoabsorption of acrylonitrile near the C 1s and the N 1s K-edge and compare them to recent experimental results for the photoabsorption of a multilayer of a~rylonitrile.'~ The discussion of the LCGTO-DF and LDKL results is intended to illustrate how these theoretical tools may be used to analyze the resonant states, Le., the bound molecular orbital final states and the eigenchannel continuum states, thus enhancing our understanding of the molecular photoionization process. A comparison of the LDKL-DF results to those obtained with the MS-Xa and CMS-Xa methods shows that both computational strategies reach similar conclusions, although the agreement with the experimental resonance energies is better for the LDKLDF method.
11. Methods The LCGTO-DF (linear combination of Gaussian-type orbitals density functional) method's8 determines the electronic structure using the Kohn-Sham approach to density functional
QQ22-3654/95/2Q99-8496$Q9.QO/O0 1995 American Chemical Society
NEXAFS Spectra of Acrylonitrile theory. All present calculations have been performed in the local density approximation (LDA) or its generalization, the local spin-density approximation (LSDA),l5.l6 by using a standard parametrization of the LDA exchange-correlation energy functional.17 In the LCGTO approach, the Kohn-Sham molecular orbitals as well as the electronic charge density and the exchange correlation potential are expanded employing Gaussian-type functions (GTO's). The Kohn-Sham equations are then solved self-consistently. It is the local form of the effective one-electron potential which affords a significant reduction of the required computational effort for the determination of both the ground-state and the continuum wave functions. Although excitation energies are not directly accessible in the DF approach, they may be estimated by Slater's transitionstate techniqueL8where the occupation of the initial orbital is decreased by half an electron and the occupation of the final orbital is concomitantly increased. The Slater-Jan& theoremI8,l9relates the difference between the Kohn-Sham transition-state eigenvalues, in a good approximation that includes relaxational shifts, to the energy difference of the configurations under consideration. The corresponding photoionization cross section may be simulated by convoluting the discrete spectrum with a Gaussian curve weighted according to the various oscillator strengths. An asymptotically corrected transition-state potential provides a suitable model for the determination of the continuum wave functions of a core level photoionization process, as we have previously ~ h 0 w n . IThis ~ local one-electron potential is obtained by reducing the occupation of the initial state by half an electron. Hence, the Kohn-Sham eigenvalue of the corresponding core level directly fumishes an approximation to the ionization potential.I8 In the LCGTO approach the continuum wave functions may be obtained by the LDKL technique (logarithmic derivative Kohn-Lobatto).'O.' This method is based on the logarithmic-derivative Kohn variational principle20 and draws much of its efficiency from the use of a flexible basis set that combines both atom-centered Gaussian functions well-known from ground-state calculations and single-center Lobatto shape functions necessary for a complete description of ondulatory continuum wave functions. The LDKL technique starts with a partitioning of space into a finite reaction volume Vwhere a local effective potential applies and an exterior region in which a purely Coulombic form of the potential is assumed. For computational convenience this finite volume is chosen as a sphere of radius S. The solution of the Schrodinger equation within the finite volume is obtained by the logarithmic derivative version of the Kohn variational principle,20.21which may be based on the following functional:"
The index Vof the matrix element indicates integration over the molecular volume only. The LDK variational principle is implemented in an algebraic form by using the following ansatz for a scattering wave function of energy E within the sphere:
The first part of yj; comprises the long-range contribution, written as a partial-wave expansion, and the second, short-range part is expanded as a linear combination of GTO's X A centered ~ on the various atomic positions A." In eq 2 Yrm,(S2)denotes a
J. Phys. Chem., Vol. 99, No. 21, 1995 8497 spherical harmonic and &JT) the corresponding radial function, which, in tum,is constructed as an energy-dependent linear combination of Lobatto polynomials. I These polynomials are closely related to the nodes of a Gauss-Lobatto quadrature and ensure a highly efficient computational procedure which allows for a rapid evaluation of the various matrix elements. A complete set of linearly independent solutions is generated by requiring that only one angular momentum component, Ylm, contributes at the boundary of all GTO's having decayed sufficiently. We collect the linearly independent scattering solutions yjk in a row vector Yin and similarly write for the corresponding wave functions in the exterior region, i.e., for r 2 S,22
Here, F and G are diagonal matrices containing the familiar regular and irregular Coulomb waves23and Y is a row vector of the relevant spherical harmonics. The factor-k"= (n2E/2)-L'4 ensures normalization to the energy scale. The real matrices A and B are determined by matching the solutions Yinand their derivatives across the surface of the molecular V to Y O u t . Once the continuum wave functions are calculated for a given asymptotic kinetic energy of the photoelectron, the photoionization cross section is obtained from the proper transition dipole matrix elements.",'2 The matching matrices A and B contain all relevant scattering information and may be used to determine the K matrix:
K = BA-I
(4)
The K-matrix normalized solutions
reflect the coupling between different angular momenta due to the nonspherical molecular potential. The diagonalization of the real and symmetric K-matrix leads to an altemate set of linearly independent, degenerate scattering solutions. In the case of a resonance, these so-called eigenchannel solutions are known to provide the most direct representation of quasi-bound shape resonant state^.^^,^^ Depending on the maximum angular momentum used for the expansion of the wave function, there may be a large number of eigenchannels. Nevertheless, a partitioning of the photoionization cross section at resonance into eigenchannel contributions is helpful for identifying those eigenchannels which mainly support the resonant wave function. From the viewpoint of the present work, the electronic structure description underlying the MS-Xa method is very similar to that of the LCGTO-DF method. The X a approximation to the exchange-correlation energy functional implies only a small difference compared to the local density approximation used in the present LCGTO-DF calculation^.^^^^ Much more significant is the difference resulting from the use of the multiple scattering techniques:' which, on the other hand, is essential for the computational efficiency of the MS-Xa ground state method and of its continuum analogue, the CMS-Xa techn i q ~ e . ~The . ~ underlying muffin-tin approximation to the local effective potential allows for the treatment of "large" systems, albeit at the expense of a reduced accuracy, which may be significant for certain systems28 In the following we will discuss some effects of the potential approximation in comparison with the more precise LDKL-DF method and we will
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demonstrate that the muffin-tin shape approximation is no longer needed to treat molecular systems of current interest.
TABLE 1: Comparison of Experimental and Calculated Inner-Shell Ionization Potentials (IPS,in eV) of Acrylonitrile“
111. Computational Details
theory
Formally, acrylonitrile may be obtained from ethylene by substituting a hydrogen by a cyano group, CN. The molecule
\
,G
,c,= cc\
H
4
H
experimentb IP A
basis 1 IP A
basis 2 IP A
MS-Xa IP A
CH IS 289.8
N
H
core level
I’
x
is planar (point group CJ. The conjugation of the z-electrons shortens the length of the formal single bond between the vinyl group, CzCH-, and th? C-N fragment significantly. This bond has a length of 1.43 A, whereas the single bond in ethene is 1.54 A.29 The lengths of the C-C double bond and the C-N triple bond are 1.339 and 1.164 respectively, and thus almost equal to the bond lengths of the molecules representing the corresponding fragments, ethylene (RCC= 1.339 AZ9)and hydrogen cyanide (RCN= 1.156 A). This comparison also identifies two of the species that are invoked by the “building blocks” principle. For all calculations, the experimentally determined geometry was used.30 Acrylonitrile contains three nonequivalent carbon atoms, which we will label as CH, CC, and CN by reference to neighboring atoms that provide a unique identification. The z-axis is chosen normal to the molecular plane (x,y). The ionization potentials of the 1s edges were calculated by using GTO basis set 1 (C, 13s/8p/5d; N, 13s/8p/5d; and H, 7s/3p). This basis set was also used for the representation of the photoionization initial core level orbital and as an additional multicenter part of the expansion of the continuum wave function. For C and N, basis set 1 is a combination of standard 13s/8p sets;3’ the two d-type polarization exponents3*have been augmented by three additional exponents according to a geometrical series, for carbon starting at 0.133 767 with a progression of 2.1530 and for nitrogen starting at 0.187 65 with a progression of 2.1956. The 6s set used for hydrogen3’ has been augmented by one diffuse exponent (0.031 313). The p set of rep3 was also enriched by one diffuse exponent (0.044 643). The ionization potentials thus obtained were compared to values obtained with a more flexible set of s-exponents for carbon and nitrogen, GTO basis set 2 (C, 15s/ 8p/2d; N, 15s/8p/2d; and H, 6s/2p). The two additional s-exponents were obtained by first taking the geometrical mean of the two largest exponents and by geometrically extrapolating the two largest exponents of the thus enlarged sets. In basis set 2 standard basis sets were used for hydrogen and for all polarization function^.^^^^^ To retain maximum flexibility the GTO basis sets were applied entirely uncontracted. For the LDKL single-center variational basis set, we used a Gauss-Lobatto quadrature of order M = 50 and partial-wave angular momenta up to 1 = 7. The part of the single-center basis set originating from Lobatto nodes located within a distance of 4.6 au from the center of mass of the molecule (coordinate origin and center of the spherical reaction volume Y) was excluded from the variational ansatz. The spherical molecular volume was centered at the center of charge of the nuclear framework and the radius was chosen as S = 35 au. The asymptotic correction of the monopole terms of the singlecenter expansion of the molecular potential12 started at a radius R, (defined with respect to the coordinate origin) which depends on the core hole site according to a multipole threshold of lo-*
289.15 289.15 291.01 Cc IS 290.7 +0.9 290.10 f0.95 290.11 +0.96 292.00 +0.99 CN IS 291.4 +0.7 290.27 f 0 . 1 7 290.31 +0.20 293.52 +1.52 N 1s 403.3 402.39 402.42 402.91 a Theoretical results are shown for the LCGTO-DF method (basis sets 1 and 2, see text) as well as for the MS-Xa method. The spacings A of the ionization potentials of the three inequivalent carbon atoms are also shown. Reference 14.
au. For the various localized core hole situations the corresponding values of this multiple radius R, were 18.0 au (CH, CC), 10.7 au (CN), and 9.8 au (N). Components of maximum angular momenta up to 1, = 14 were included in the singlecenter expansion of the effective one-electron potential. To obtain photon energies from the asymptotic kinetic energy, we used the calculated transition-state ionization potentials (basis set 1, Table 1). For the MS-Xa calculations a value of a = 0.7 was used for the exchange correlation potential scaling. The radius of the outer sphere was Rout= 5.91 au. The radii of the atomic muffin= 1.42 au, &,&) = 1.40 au, Rin(C~) tin spheres were Rin(C~) = 1.34 au, Ri,(N) = 1.41 au, and Rin(H) = 1.04 au. Within the atomic spheres the partial wave expansion of the bound states was limited to li, = 2 (continuum states, li, = 4) and in the outer sphere to lout = 4 (continuum states, lout= 6). For the CMS-Xa calculations the photon energy was calculated by using the MS-Xu transition state ionization potentials (see Table 1).
IV. Results A. Ionization Potentials. The ionization potentials of the C 1s and the N 1s level have been determined employing the LCGTO-DF transition-state technique as well as the approach where both initial- and final-state total energies are being calculated (ASCF). Both types of calculation were carried out for the spin-polarized version of the method. In Table 1 the transition-state results are compared to transition-state results from a MS-Xa calculation and to the experimental ionization potentials determined from XPS measurement^.'^ The transition-state energies of the LCGTO-DF calculations agree quite well with experiment with deviations less than 1 eV, whereas the ASCF values are up to about 1.4 eV lower in energy. Thus the assumptions of the Slater-Jan& theorem’s,’9 are only approximately fulfilled. It is worth noting that the ASCF calculations gave nearly the same splitting of the ionization potentials as the transition method, the values differing by only 0.01 eV. The transition-state energies of the two computational procedures, LCGTO-DF and MS-Xa, differ by about 1.8 eV for the three C 1s levels but are rather close for the N 1s level. However, for the assignment of the experimental ionization spectrum the ordering and spacing of the three C 1s ionization potentials is more important than their absolute values. Both computational methods reproduce the splitting of about 0.9 eV between the CH 1s and the CC 1s ionization potentials very well. However, the difference between the CC 1s and the CN 1s ionization potentials, experimentally 0.7 eV, is significantly underestimated by the LCGTO-DF method, both by the transition state and the ASCF procedure. On the other hand, a splitting of 1.52 eV has been calculated by using MS-Xa method; this, however, represents a significant overestimation.
J. Phys. Chem., Vol. 99, No. 21, 1995 8499
N E W S Spectra of Acrylonitrile
280
282
284
286
288
290
Photon Energy [eVl Figure 1. Discrete absorption spectrum of acrylonitrile near the C 1s edge. Upper panel: LCGTO-DF results. Lower panel: MS-Xa results. The solid line indicates final-state symmetry a", the dashed line symmetry a'. The spectra were obtained from the calculated oscillator strengths by convolution with a 0.3-eV FWHM Gaussian. To explore possible basis-set effects on these LCGTO-DF results, transition-state calculations have been performed by using the more flexible basis set 2. Nevertheless, both absolute ionization potentials and their splitting remained almost unchanged compared to the results of basis set 1. To some extent the differential shifts between theoretical and experimental ionization potentials may also be due to the different physical environment: all calculations apply to an isolated gas-phase molecule in contrast to the experimental situation where a supported multilayer (50 monolayers) has been studied.14 This environment may cause shifts of the ionization potentials by about 1-2 eV due to extramolecular relaxation, i.e., polarization of the surrounding molecules. In any case, as we will be employing a transition-state potential for modeling the final states of the core-level ionization processes, we will also be using the corresponding calculated ionization potentials when determining the continuum photoionization spectrum with the LDKL method. B. Discrete Photoionization Spectrum. The discrete photoabsorption spectrum was obtained by carrying out a series of LCGTO transition-state calculations to determine the excitation energies and the corresponding oscillator strength. This was done for each significant transition, using each C 1s level and the N 1s level as initial states. The photoionization cross section was generated from the discrete line spectrum by convoluting the line spectrum with a Gaussian of FWHM 0.3 eV, which corresponds to the experimental resolution. The resulting LCGTO-DF photoabsorption spectrum near the C 1s edge is given in Figure 1; the transitions are numbered separately for each initial state, e.g., 'H refers to the lowest lying transition originating from the atom CH 1s initial state. The various peak positions and the corresponding final-state symmetry are collected in Table 2 and compared to the experimental data.I4 We notice a consistent underestimation of the experimental excitation energies by about 2.5-3 eV, reminiscent of similar effects for the ionization potentials. However, the experimental level spacing is reproduced quite satisfactorily and the assignment of the experimental spectrum given previou~ly'~ is largely c o n f i i e d by the present results. Nevertheless, some differences are to be noted. Due to the vibrational envelope of the 1~ transition, the corresponding spectral structure overlaps the IC transition, which thus cannot be resolved in the experimental spectrum. Although the vibrational progression cannot be
TABLE 2: Experimental and Theoretically Predicted Transition Energies hv (in eV) of the Discrete Absorption Spectrum of Acrylonitrile photon energy, eV experimentb LCGTO-DF CMS-Xu final Peak state hv A hv A hv A C 1s 'H 3a") 284.5 281.86 282.33 'C 3a" 282.79 +0.93 283.52 +1.19 'N 3a" 286.5 +2.0 283.53 f0.74 285.36 +1.84 2N 13a' 287.2 f0.7 284.17 f0.64 286.20 +0.84 2H 15a' 286.95 f 2 . 7 8 287.36 f0.41 287.72 +1.52 3N 4a"} 290.0 f2.8 287.88 f0.52 286.72 -1.00 'C 4a" 4C 15a' 288.08 f0.92 394.75 N l s 1 3a" 398.7 395.59 2 13a' 399.6 +0.9 396.58 f0.99 395.83 +1.08 3 4a" 402.0 +2.4 399.76 f3.18 397.39 +1.56 Also shown is the energy difference A with respect to the nearest lower lying transition. The peaks are labeled separately for each initial state, e.g., 'Hrefers to the lowest lying transition originating from the atom CH 1s initial state. Reference 14.
13a'
15a'
Figure 2. Contour plots of the discrete final states of acrylonitrile. The final states of symmetry a' have been plotted in the molecular plane: those of symmetry a" are plotted in a parallel plane separated by 0.5 au. The contour values used are f0.003 162 8, fO.01 and f0.03 1 627 8 and fO.1. Localization of the core hole: 3a", 4a", and 15a', CC; 13a', CN. As the contour plots for other core hole sites revealed, the final state is rather insensitive to the atom on which the core hole is localized.
computed by using these techniques, the calculated spectral features are very close to the experimental ones, showing the dominance of the transitions 1~ and lc. Furthermore the excitations CC 15a' and CH 15a' (labeled 4c and 28 in Figure 1) may be identified with the broad peak in the spectrum at normal incidence (at energies close to the peaks labeled 3' and 3" in ref14. The additional excitations of lower intensity below the peaks 4c and 2H, respectively, arise from transitions to the orbital 14a'. Their intensity is, due to their Rydberglike character, comparatively small and thus they will not be considered in the further discussion. Before discussing some details of the spectrum, it is helpful to inspect the character of the four occumng final-state levels (Figure 2 ) . The contour plot clearly reveals the in-plane x*(CcN) character of level 13a'; nevertheless, it is delocalized over the whole molecule. The orbitals 3a" and 4a" are also delocalized; they may be thought of as representing the bonding and antibonding combinations of the out-of-plane x*(C&) and x*(C") orbitals. The shape of these orbitals is rather insensitive to the location of the core hole, therefore only those contour plots for the transition states CC-O.~and cN-0'5 are
-
-.
Wilhelmy et al.
8500 J. Phys. Chem., Vol. 99, No. 21, 1995 -" I
I
Binding Energy [eV]
Peak Intensity [Mbl 0 10 20
13a'
} 3a"
394
396
398
400
402
Photon Energy [eVl Figure 3. Discrete absorption spectrum of acrylonitrile near the N 1s edge. Upper panel: LCGTO-DF results. Lower panel: MS-Xa results. The solid line indicates final-state symmetry la", the dashed line symmetry a'. The spectra were obtained from the calculated oscillator strengths by convolution with a 0.3 eV FWHM Gaussian. shown. The high-lying level 15a' is more difficult to interpret but bears some resemblance to the 2b3,(CH*) orbital of the ethylene fragment.34 Most noticeable in the calculated spectrum is the decreasing intensity of the transitions l ~lc,, and IN,which share a common final state, 3 8 . Furthermore, the spacing of the first two peaks is essentially the same as that of the corresponding ionization potentials, whereas the spacing between the IC and 1~ peaks is 0.56 eV larger than those of the corresponding ionization potentials. Both observations may be rationalized by invoking the notion that a core level excitation takes a local probe of the final-state level and thus the corresponding intensity is correlated with the localization of the final state in the vicinity of that nucleus. Inspection of Figure 2 reveals that the orbital 3a" is almost equally strongly localized near the nuclei CH and CC. Thus the final state provides an equal screening to the corresponding core holes and, at the same time, experiences a comparable attractive interaction into the potential well set up by the core hole. The two corresponding excitation energies are affected by both mechanisms to a similar degree and their splitting remains unchanged. On the other hand, the final-state screening and the attraction due to the core hole is less pronounced for the 1~ excitation, as the final-state orbital 3aff is localized to a smaller degree near this nucleus CN. Thus, relative to the first two processes, the excitation energy increases, as does the energy spacing between the IC and 1~ excitations. This situation is highlighted in Figure 4 where all excitations are referenced to their common initial-state ionization energy. Comparing the energy splitting between the experimental CH and CC 1s ionization potentials, 1.6 eV, and the corresponding measured excitation energies 1~ and l ~2.0 , eV, one observes that the calculated values exhibit a rather similar increase, from 1.13 to 1.68 eV. The argument advanced so far may be tested by applying it to the pair of excitations which share the final orbital 4 8 . This level is somewhat more localized near the nucleus CNthan near the nucleus CC. (Unfortunately, it is not possible to quantify this localization difference by a clear evidence from a Mulliken population analysis of the final states due to the uncontracted and diffuse nature of the orbital basis set.) Consequently, the final-state screening effect and the potential attraction reduce the excitation energy for the process 3~ compared to that of
Figure 4. Schematic representation fo the calculated (LCGTO-DF) discrete photoionisation spectrum of acrylonitrile: transition energies (displayed with respect to the initial-state ionization energies), intensities. and final-state orbitals. the transition 3~ and the intensity relationship is reversed compared to the transitions l c and 1~ (see Figure 4). For N 1s ionization, three significant peaks have been found experimentally below the ionization threshold (Figure 3). These peaks are associated with the same final states as those of the C 1s spectrum, namely, 3a", 13a', and 4a". The calculated spectrum, including its polarization dependence and intensity pattern, is very similar to that of the transitions l ~2N,, and 3s. Also the energy spacing is very similar as may be expected, with small variations being due to differences in the final-state localization and the resulting relaxation effects (Table 2 ) . The difference in the excitation energies 1 and 3,4.2 eV, is calculated somewhat larger than that of the excitations 1~ and 3N, 3.81 eV. The corresponding experimental numbers are 3.1 and 3.5 eV, respe~tive1y.l~ The MS-Xa results for the C 1s ionization (see Figure 1, lower panel) are very similar to those obtained with the LCGTODF method. The spectrum was calculated by using a simplified transition-state procedure: the occupation of the final state by half an electron and thus the corresponding screening effects were neglected. In this way, the full spectrum was obtained from a single transition-state calculation for each initial core level. A significant difference to the LCGTO-DF results is a series of Rydberg-like peaks near the ionization threshold. Peaks l ~lc, , and 1~ appear in the same order as measured and as in the LCGTO-DF results; they also show the same qualitative intensity pattern for the different core hole localizations. The energy spacing between the excitations 3N and 2s is smaller and the peaks 3~ and 3c are interchanged on the energy scale. As their intensity ratio is quite similar to the LCGTO-DF results, this finding is at variance with the rationalization discussed above, which related the intensity to the final-state localization. At present it remains open whether this inconsistent pattern is a consequence of the muffin-tin approximation to the potential. As already noted, the MS-Xa calculation yields a large variety of peaks near the continuum edge, including one similar to the pronounced 15a' peak of CH excitation in the LCGTO-DF calculation. These excitations may involve Rydberg-like final states which cannot be reproduced by the present version of the LCGTO-DF method since the molecule remains neutral within the transition-state scheme and therefore the LDA potential shows the wrong asymptotic b e h a ~ i 0 r . lWithin ~ the MS-Xa method this problem may be overcome by invoking the so-called Latter tail c ~ r r e c t i o nwhich , ~ ~ enforces the correct asymptotic Coulomb form of the potential for the remaining ion. For the same reason, the peaks observed in the N 1s spectrum near 401 eV may be attributed to transitions into
NEXAFS Spectra of Acrylonitrile
J. Phys. Chem., Vol. 99, No. 21, 1995 8501
A
Photon Energy [eV] Figure 5. Photoionization cross section for carbon 1s ionization of acrylonitrile: contributions of the three individual carbon atoms and their sum, yielding the total gas-phase photoionization cross section above the carbon K-edge. Upper panel: LDKL results. Lower panel: CMS-Xu calculations. Rydberg-like states. Apart from that, the MS-Xu absorption spectrum is very similar to the LCGTO-DF results (see Figure 3) as judged by the intensity pattern and the energy spacings. However, as can be seen from Table 2, the asymmetric spacing between the peaks is better reproduced within the LCGTO-DF calculation. C. Continuum Photoionization Spectrum. In discussing the continuum spectrum of acrylonitrile, we will start with the theoretical results, as shape resonances are much more pronounced in the calculated spectra and thus easier to identify and to characterize. Furthermore, our independent-particle picture excludes all many-electron effects and therefore no “contamination” of the photoabsorption cross section by shake effects will take place. Figure 5 (upper panel) gives the calculated total gas-phase photoionization cross section for acrylonitrile, obtained by the LDKL method. The spectrum shows three pronounced resonances, labeled A, B, and C. All of these resonances belong to the final state symmetry a’ and thus are only observed for a polarization of the light parallel to the molecular plane (x,y). This is in line with the experimental findings: at normal incidence, the spectrum shows three broad resonances approximately at the energies 295,300, and 308 eV.7.8 Although there may be some contributions from many-electron excitations, this seems to be in good agreement with the theoretically predicted features. As revealed by the individual calculated cross sections for each carbon atom, all of the resonances are observed for CC Is ionization. Resonances A and B contribute only to the CH 1s cross section and resonances B and C to the CN 1s cross section. To get further insight into the properties of the continuum states, we present eigenchannel contour plots of the K-matrixnormalized a’ final states for CC ionization in Figure 6. The final states for CH and CN ionization are very similar. Due to the low symmetry of the molecule and the high partial-wave angular momentum, 1=7, the final-state symmetry a’ gives rise to 36 eigenchannels out of which typically three to four contribute significantly to the cross section near a resonance. In Figure 6 we display only one of these prominent channels per final state, namely, the one dominating the cross section. As Figure 6 reveals, resonance A at a photon energy of about 292 eV shows pronounced a*(C&) character; on the other carbon atoms JC*(CHCC) admixtures are found. Therefore this
C Figure 6. Eigenchannel contour plots for the continuum states of CC 1s photoionization of acrylonitrile. Only the eigenchannel with the dominant contribution to the photoionization cross section at the resonance photon energy is shown. On the top of each panel, the label of the resonance (see Figure 5) and the corresponding photon energy are given. TABLE 3: Asymptotic Kinetic Energy (in eV) of the Resonances of the Continuum Spectra As Calculated by the LDKL Method (see Figure 5 9 asvmDtotic kinetic enerw. eV initial state resonance A resonance B resonance C 2.89 7.08 C” 1s 1.36 6.06 18.51 cc 1s CN 1s 5.83 15.79 N 1s 2.09 6.66 17.49 experimentb 4.3 9.3 17.3 For comparison we also give the values of experimental spectral features with reference to the CC 1s ionization potential, as for this initial state all three shape resonances are observed. resonance can be observed over the whole molecule. For CN ionization this final state is very close to or below the continuum edge, as can be seen from Figure 5 . Resonance B at about 296 eV shows a significant o* (CHCC)contribution and is observed above all carbon K-edges. For this resonance we also observe p character on CN and N. As expected, the highest lying resonance C reveals a*(C”) character. The corresponding part of this wave function on the rest of the molecule is difficult to interpret within the MO picture but exhibits a*(CcCp~)character on the neighboring carbon atoms. This is in line with the presence of this resonance for CC ionization. Table 3 summarizes the asymptotic kinetic energies of the photoelectrons for the observed resonances. The positions of the resonances have been estimated by a spline interpolation of that partial cross section, which shows the corresponding resonance most prominently. As can be seen from Table 3,
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8502 J. Phys. Chem., Vol. 99, No. 21, 1995 I
2
c.
0.0 1.5
I
c
1
I
h
v1
0.0 1 400
'
.
405
.
410
415
420
425
430
I
Photon Energy [eVl Figure 7. Partial and total photoionization cross section of acrylonitrile near the nitrogen K-edge for the different polarization directions of the light. Component x and y correspond to normal incidence of the light with respect to the molecular plane. At grazing incidence there is also a significant contribution of the z component to the cross section. For the labeling A, B, and C of the continuum resonances, see the text and Figure 5 . The total gas-phase photoionization cross section is given as a solid line. Upper panel: LDKL results. Lower panel: CMS-Xa calculations.
resonance C exhibits a very large final-state shift for CN 1s ionization with respect to the CC 1s ionization. Correspondingly, the resonance height is much stronger on CN (Figure 5). This correlation, namely, a lowering of the final-state energy with increasing oscillator strength, is quite analogous to the effects observed for the 3a" and 4a" final states in the discrete photoabsorption spectrum. As is evident from the discussion above and from inspection of the asymptotic kinetic energies given in Table 3, the energy of the continuum resonances qualitatively correlates with the length of the bonds on which the o* character is observed. However, for acrylonitrile it is not possible to establish a mathematical relation between bond length and o* resonance p o ~ i t i o n ,because ~ , ~ the various core hole sites result in different final-state energies (Table 3) and thus there is no unique kinetic energy which may be assigned to the individual o*-type shape resonances. Tuming to the CMS-Xa results (lower panel of Figure 5 ) , we find two pronounced resonances. Because of their energetic position and strength on the three carbon atoms, these peaks clearly correspond to the resonances labeled B and C. As often within CMS-Xu calculations, the cross section is overestimated with respect to the background.' The resonance energies are calculated about 1 eV below the values predicted by the LDKL method. However, there is only a slight indication for resonance A just above the CH edge. Thus in the CMS-Xa method the corresponding final state may have dropped below the ionization potential. Indeed, as Figure 1 reveals, the discrete spectrum contains a pronounced peak just below threshold at 289.8 eV photon energy, which bears a significant O*(CCCN)character besides some admixtures of Rydberg-like states. The CMS-Xa method thus is able to provide a qualitative picture of the occurring resonances, but the more sophisticated LDKL method furnishes a much better agreement with the experimental spectrum and thus substantially facilitates the interpretation of the experimental photoabsorption spectrum. Concerning the N 1s spectrum, the two theoretical methods yield very similar results (see Figure 7). Again there are three resonances which show the typical o* character on the energetically associated bonds. The fact that all resonances are observed
on the terminating nitrogen atom provides the most convincing argument for the delocalized character of the final states. As eigenchannel contour plots reveal, the characters of the final states are indeed quite similar to those of the corresponding states of C 1s ionization, which are shown in Figure 6. For the N 1s spectrum the CMS-Xa cross section is very similar to the LDKL result except for the much more isolated character of resonance C. Furthermore, this resonance appears near 416 eV, shifted 4 eV downward with respect to the LDKL spectrum, which places the resonance at 420 eV and thus much closer to the experiment (423 eV). The cross section arising from the polarization direction normal to the molecular plane, z, is nearly structureless (Figure 6). This is also the case for C 1s ionization and is in line with the experimentally found enhancement of the shape resonances observable at normal in~idence.'~
V. Conclusions The present theoretical work has demonstrated that nearly all features observed within the NEXAFS spectra of the acrylonitrile multilayer can be identified with one-electron excitations. The spectral features below the continuum edge have clear equivalents in transitions into unoccupied molecular orbitals as shown by both density functional methods employed, LCGTO-DF and MS-Xa. These bound states are delocalized over the whole molecule, as are the continuum resonant states. The latter are accessible via the K-matrix eigenchannels obtained by the LDKL-DF method. Nevertheless, for each of the three shape resonances a significant o* character is associated with one of the various individual intramolecular bonds. The energy of the final state correlates qualitatively with the length of the bond on which the o* character is located, just as predicted by numerous model^.^.^ Nevertheless, each continuum state is obviously delocalized over the molecular frame and thus the "building block" picture is not strictly appropriate for the interpretation of the continuum spectrum of acrylonitrile. It is noteworthy that the photoexcitation final states as well as the shape resonant continuum final states (observable from more than one of the nonequivalent carbon atoms) show a clear correlation between the absorption intensity and the energy position of the final state: a large absorption intensity correlates with a downward energy shift of the final state, reflecting the attractive potential of the individual core hole and the local contribution of the final-state wave function. The discrete part of the spectrum as calculated with the MSX a method agrees surprisingly well with experiment. However, especially the continuum part of the spectrum is much better reproduced by the LCGTOLDKL-DF method, which is not affected by the known drawbacks of the muffin-tin approximation to the potential.
Acknowledgment. We thank Markus Mayer for his assistance during the preparation of the manuscript. The work of I.W. and N.R. has been supported by the Deutsche Forschungsgemeinschaft and by the Fonds der Chemischen Industrie. References and Notes ( 1 ) Stohr, J. NEXAFS Spectroscopy;Springer: New York, 1992. (2) Stohr, J.; Stette, F.; Johnson, A. L. Phys. Rev. Lett. 1984,53, 1684. (3) Sette, F.; Stohr, J.; Hitchcock, A. P. J . Chem. Phys. 1984,81,4906. ( 4 ) Sheehy, J.; Gill, T. J.; Winstead, C. L.; Farren, R. E.; Langhoff, P. W. J . Chem. Phys. 1989, 91, 1796. ( 5 ) Dill, D.; Dehmer. J. L. J . Chem. Phys. 1974, 61, 692. (6) Davenport, J. W. Int. J . Quant. Chem. 1977, S11, 89. (7) Dunlap, B. I.; Connolly, J. W. D.; Sabin, J. R. J . Chem. Phjs. 1979, 71, 4993.
NEXAFS Spectra of Acrylonitrile (8) (9) (10) (11) (12)
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