Ab initio CI calculation of K shell absorption spectra in transition metal compounds

Chemical Physics 174 (1993) 57-70 bosh-Holland

Ab initio CI calculation of K shell absorption spectra in transition metal compounds G. Fronzoni, P. Decleva and A. Lisini Diparilmento di Scienze Chimrche, Via A. Valerio 38, 34127 Trieste, Italy

Received 29 October 1992; in final form 25 March 1993

The metal 1s excitation spectra of several o~anometallic compounds have been calculated at the ab initio lh-lp CI level, providing for an adequate treatment of relaxation and an accurate choice of the basis set. The results are discussed and compared with our previous theoretical results relative to the 2p metal edge for the same systems, The 1s spectra, probing the metal 4p content of the excited states, can identify the final levels complementary to those determined by the metal 2p-+3d excitations. A complete pattern of the low-lying virtual levels of a particular system can be obtained merging the results relative to the two metal edge spectra ( 1s and 2p) allowing a detailed discussion on the character of the metal-lig~d interaction. The 1s spectra are found to be sensitive to the nature of the ligands and the bonding situation and not dependent on the change of metal atom in series with the same kind of ligands.

1. Introduction

In the recent years there has been a growing interest in the X-ray abso~tion spectroscopy (XAS) because of the progress in the development of the synchrotron radiation sources, which allow the measurement of the spectra more quickly and with better resolution than before and provide ideal conditions for performing poiarized studies in single crystals which give additional information about the symmetry of the final states. The great advantage of XAS is associated with the strongly localized nature of the excitations of the core electrons to bound states and into the continuum, which makes the K and L edge spectra very sensitive to the electronic configuration and to the local geometric environment of the absorbing atom. Therefore the X-ray absorption features have been very useful in providing information about the coordination chemistry and the electronic states of metal centres in a wide range of compounds f l-l 81 and more recently also in the very complex systems, ranging from biological molecules to species adsorbed on metal surfaces and catalytic processes [ 19-271. For first row transition metal complexes XAS is often applied in the metal IS edge region; in fact it is 0301-0104/93/$06.00

experimentally easier to work with hard X-rays since matter is mostly transparent in this energy region. The features in the high energy region above the absorption edge (EXAFS ) [ 28 ] are well described in terms of single scattering process, and are currently employed to extract geometrical informations around the absorbing atom, In the near-edge region (NEXAFS ) the metal K edge spectra show generally more or less marked absorption features just before and at the onset of the main absorption edge, followed by further structures superimposed to continuum absorption. These spectral features can be related to electronic transitions from the 1s metal level to discrete or quasidiscrete final states and their interpretation is more diffrcuit. Here the excited electron feels the full details of the molecular potential (that is multiple scattering effects become very important in a scattering approach) and a simpler interpretation may be afforded by a molecular orbital description in terms of bound or quasi bound excitations into low-lying virtual molecular orbitals. Actually the only ab initio studies of XAS structures in transition metal compounds are those of Bair and Goddard [29 1 and Kosugi and co-workers [ 30,3 11, while a few other attempts have been made on the basis of the rather crude EHT [ 201 or CNDO

0 1993 Elsevier Science Publishers B.V. All tights reserved.

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G. Fronzom et al. /Chemical Physics 174 (1993) 5 7- 70

[ 32 J approaches. Considerable more effort has been applied with the local density multiple scattering approach [ 10, I 5,331, which has the additional advantage of treating both bound and continuum states with the same scheme. The muffin-tin approximation employed is however known to cause a considerable distorsion of the pattern of low-lying levels [ 341. The qualitative MO picture has often been employed to interpret the near edge features. However, convicting assignment of the tine structures observed in the spectra of transition metal compounds have been made [ 8,16- 18,291 and despite the progress in interpretation of the spectra, a more detailed theoretical knowledge of the origin of the spectral features and of their relationship with electronic structures is still necessary for the complete analysis of NEXAFS spectra. In particular the pre-edge absorption features lying a few eV below the K edge are of considerable importance in the assignment of low-lying virtual orbitals. These transitions are common in first row transition metal compounds and their intensity is quite sensitive to the coordination geometry of the metal atom and to the nature of the ligands and the metal-ligand bonding. Generally the pre-edge peak has been assigned to the electronic transition from the metal Is core level to the 3d-like molecular orbitals. In centrosymmetric complexes this transition is only quadrupole allowed and is therefore very weak. When the symmetry is broken the pre-edge absorption becomes dipole allowed, due to the mixing of the 3d and p metal orbitals, and its intensity tends to increase depending on the extent of this mixing [ 20 1. A quantitative understanding of the factors affecting this preedge region requires a detailed and systematic theoretical investigation on the nature of the bound final states of the system. If the interaction with the continuum is weak, also the low-lying resonances above edge can be interpreted employing the discrete states obtained from the finite basis set calculation, as has been done in previous work [ 29-3 1,35,36 1. Such approximation can be further refined in the rigorous framework provided by Stieltjes moment theory [ 37 ] . With the aim of gaining a deeper understanding of the nature of the transitions involved in the near-edge region, and their relationship with the electronic structure of the system, in this paper we present ab initio CI calculations of the near-edge 1s metal exci-

tation spectra of a series of or~nometallic eompounds related by the change of metal atoms and/or the ligands in order to examine possible trends associated with the various factors involved. ‘We have considered first the series of carbonyls Ni(CG )4, Fe(C:0)5 and Cr( COfb, which have the same ligands and different metal atom and we have next analysed the change of ligands from Fe (CO ) s to Fe (Cp ) 2 and from Cr(CO), to Cr(NO)* and CrO&l,. For most of these molecules we have recently obtained theoretical results relative to the absorption spectra at 2p metal edge [ 38,39 I, which have allowed to correlate the calculated spectral features both to the nature of the ligands and to the molecular symmetry and the formal d electron count of the metal atom. The agreement between these theoretical results and the experimental EELS spectra [ 403 has pointed out the adequacy of the ab initio CI scheme employed for the inte~retation of the discrete me-edge features. Therefore we have adopted the same computational scheme also in the case of 1s spectra, as it is not expected that stronger correlations than in the 2p case are active between the closed valence shell and the excited Is electron. The complementary information., because of different transition moments, provided by K-shell spectra, gives a full picture of the low-lying unoccupied levels which is of great relevance to the understanding of the electronic structure and the nature of the metal-ligand bonding in transition metal compounds.

2. Computational details The present calculations have used the same extended basis sets and computational schemes as in the preceding works relative to the 2p excitation spectra on the same molecules [ 38,391. The Ni, Fe and Cr basis sets are the [ 14s9pj sets of Wachters 1411 and the [ 6d] sets of Rappe 1421. The [ 14~9~1 sets have been augmented with one s function (with exponents cy,= 0.346 for Ni, 0.298 for Fe and 0.253 for Cr) and three p functions (the two Wachters’ p functions to describe the 4p orbital and one p function with exponent a,=0.314 for Ni, 0.283 for Fe and 0.244 for Cr). The [ 6d] set has been supplemented with one diffuse d function (cu,=O.O5 for Ni, 0.037 for Fe and 0.031 for Cr). The final metal

G. Fronzoni et al. / Chemical Physics 174 (1993) 5 7- 70

basis set is [ 15s12p7d] contracted to (8s6p4d). The adequacy of these metal basis sets to properly describe the change in metal orbitals in the presence of the core hole has been already pointed out by the previous results. For the Cl atom in Cr02C12 the basis set used is the [ 1 ls7pJ set of Huzinaga [43] contracted to (5s3p), while the first row atoms basis sets are taken from the Huzinaga [ 9s5p] set [ 441 contracted to (3~2~). The general contraction scheme [ 45 ] has been employed leaving uncontracted the most diffuse functions. The relaxation of the valence orbitals after the core excitation has been taken into account by the use of SCF orbitals optimized for the 1s core ionized species. The CI scheme has been mostly limited to the single excitations from the 1s metal orbital in this survey study, as it is not expected that strong correlations are active between the closed valence shell and the excited electron. Furthermore this single excitation scheme has the important advantage of a clearly defined ionization limit which is the energy of the hole state single configuration with respect to which the term values of core excitations are referred. Actually strong relaxation at the metal site, tied to a strong increase in d population (the d orbitals are pulled down in energy by the core hole) could give rise to satellites in the spectra associated with double excitations. In fact such states are claimed to be responsible for an extra band in the 1s absorption spectra of copper complexes [ 29-3 11, although no delinite evidence is available [ 16,18 1. We have tested the adequacy of the 1h-l p CI model by performing more extended calculations on Ni(C0)4 and Cr(C0)6, including 2h-2p excitations in the valence shell both for the ground and the excited states. For the GS a perturbative selection based on the lh-lp reference vector has been employed, keeping a maximum of about 17000 configurations. For the core excited states an additional excitation was allowed from the highest occupied orbitals into the lowest virtuals, again giving a maximum of 2700 configurations in Cr(C0)6. In the present case the inclusion of 2h-2p excitations does not affect considerably the pre-edge spectral pattern obtained at the 1h- 1p CI level, as discussed in the following. The algorithm presently available for the evaluation of transition moments requires the use of a single set of orthogonal orbitals, so we are forced to use

59

ion SCF orbitals also for the CI description of the ground state. Relaxation to ground state has been described again adopting a single excitation ( 1h-lp) CI scheme. The closeness of the energies of the lhlp wavefunction and of the ground state SCF solution assures that the relaxation is well accounted for by this scheme. This is further confirmed by the stability of the results obtained with respect to the use of a 2h-2p CI expansion for the initial state. SCF and CI calculations are performed with the MELDF set of programs [ 461. Oscillator strengths are computed from the CI vectors without further approximations employing both the dipole length and the velocity operators. Agreement between the two is generally satisfactory and only the latter is reported. Electric quadrupole transitions have not been considered because of the smallness of the relative transition moment observed in previous studies. Experimental geometries are employed for all molecules [ 471.

3. Results and discussion Excitation energies (term values) and oscillator strengths for the systems examined are reported in tables l-3 and figs. 1 and 2. Figs. 1 and 2 display only the pre-edge region of the spectrum while transitions up to about 30 eV above threshold are reported in the tables. Figs. 3-5 report the MO interaction diagrams for the molecules considered, which although qualitative have been drawn to incorporate correctly both the information on the occupied levels, obtained from photoelectron spectra [ 48,491, and that on the virtual levels from the core ( Is, 2p) excitation spectra [ 38,391. The present results complete and sharpen the picture already obtained from 2p metal spectra and allow then a full interpretation of the observed spectral pattern and a correlation with the molecular structure and bonding situation. It is worth noting that, insofar as the spectrum is dominated by single particle excitations, and because of the weak coupling with the underlying core hole, the spectral pattern obtained is largely independent of the actual core level involved in the excitation, as is expected on the basis of the equivalent cores approximation (ECA) [ 501. The initial core level then determines which final levels are effectively

G. Fronzoni et al. /Chemical Physics 174 (1993) 5 7- 70

60

Table 1 Term values (eV) and oscillator strengths for metal 1s excitation spectraof Ni(CO).+, Fe(CO)S and Cr(C0)6 Ni(CO).,

WCO),

Fe(CO)5

MO

7-

fx lo4

tot, 1Ill: 14ta 16t, 1stz 1912

3.37 0.25 -9.83 - 14.33 -23.01 -25.36

0.87 1.38 18.63 5.61 1.38 3.48

rr?+d* r*+p* rt*+p*+3d p*+x*+d* p”+tP+d* p*+rt*

MO

7’

fx IO4

1 le’ 13e’ lOa; 1 la;’ 16e’ 12a” 2 17e’ 18e’ 19e’ 13aZ 20e’

2.98 0.52 0.45 -7.39 - 8.87 -9.49 - 10.73 -11.80 - 14.76 -15.11 -22.01

0.22 0.90 0.47 1.15 6.74 2.51 I .22 2.20 10.46 6.09 1.72

n*+3d*+p’ x*+p* tt*+p* rdc+p* n-+p* e+p* p*+rP+d* p*+Z+d* p*+rS+d* p*+x* p*+n*fd*

MO

T

j-x lo4

9t,, lot,”

2.64 0.64 -7.38 -8.81 - 14.60 - 17.44 - 18.18

0.36 1.83 2.25 10.50 24.45 3.36 3.21

1lb” 12t,, 13t,, 14t*, 15k”

x++p* lt*+p* ?t*+p* x*+p* x*-En* rr*+p* rr-+p*

Table 2 Term values feV) and oscillator strengths for metal Is excitation spectra of Ni(CO), and Cr(CO)& calculated at 2h-2p CI level Ni(CQ)e

Wco),

MO

T*)

px lo4

101s 11t*

4.23 0.55

1.26

1.08

x*+d* n*+d*

MO

T”’

fx 104

9t,, lOtI”

3.73 0.97

0.48 2.01

X’+p* rP+p*

‘) The term values are referred to the energy of the 2h-lp CI hole state (ionrzation limit).

probed, because of the non-negli~ble transition moment. So the spectral information obtained from different core levels can be merged to a good approximation to derive a complete pattern of virtual levels for the considered system (or better its equivalent cores species). Let us first discuss qualitatively the single-particle spectrum of the system [ 501. Generally there will be a set of compact, valence-like orbitals, followed by a set of diffuse Rydberg orbitals, mainly located outside the ligands, and then the ionization continuum. In a LCAO description with a finite basis set one obtains a set of low lying discrete states, which give usually a good description of the valence-like states, and possibly of the first few members of the Rydberg series, if the A0 basis contains a sufficient number of diffuse functions. Additional discrete states appear above the ionization limit. While part of these are just an artifact of the calculations, and represent a discretization of the non-resonant continuum, antibonding orbitals deriving from the compact valence A0 orbit-

als are closely associated with shape resonances observed in the cross section. The close connection between shape resonances in photoabsorption and minimal basis set antibonding orbitals have been thoroughly investigated [ 361, and a rigorous calculation of resonances can be afforded by the Stieltjes imaging technique starting from the discrete pseudospectrum [ 371. However, especially if the interaction with the non-r~on~t continuum is rather weak, the high intensity discrete valence transitions above edge may afford a good estimate of the resonant features. As an example we have reported the computed above-edge spectrum of Fe( Cp), in fig. 6, which nicely reproduces the experimental pattern [ 15 1. We have however concentrated attention on the discrete pre-edge transitions, for which an accurate description is expected from the present approach, and discuss only the largest intensity transitions above edge in conjunction with the available experimental data. On the basis of the outlined MO description in a transition metal compound we may expect a set of

G. Fronzoni et al. /Chemical Physics 174 (1993) 57- 70 Table 3 Tern values (eV) and oscillator

strengths

WCP),‘) T

fx

% gal,

1.56 1.54 0.47 -0.02 -0.98 - 5.00 -6.05 -6.92 -8.16 - 10.43 -11.80 - 14.64 - 19.79 -22.87 -28.65

q.a. q.a. q.a. 0.02 0.37 0.10 8.68 1.84 3.44 1.13 2.62 1.03 32.92 25.91 8.70

7a2. 8% %, 8a2, lee,. %. lee,. 1Oa2, 1h 1la2, 1%

spectra of Fe(Cp),,

WNOh

MO

5e2, 7e,.

for metal 1s excitation

a) The q.a. abbreviation

lo4 3d’ s*+d’ ti+d* o*+p* o*+p* rr*+p* lt*+p* rr*+p* x*+p* lt*+p* x*+p* 7f+p* rr*+p* x*+p* x*+p*

and Cr02C12

Cro~Cl~

MO

T

fx lo4

1ot, 11tz 12tz 13t, 14tz 15t, 16t, 17t* 18t2 19tz 20t,

2.22 1.01 0.21 -6.18 - 7.76 -9.93 - 13.78 - 17.58 - 18.59 -22.76 - 26.62

0.24 0.30 0.60 4.80 7.35 6.90 3.90 20.58 5.46 8.70 15.78

denotes quadrupole

Cr(N0)4

61

r*+3d*+p* 3d*+p* rr*+p*+d* p*+z*+d* p*+z*+d* p*+x*+d* p*+r*+d* p*+n*+d* p*+r*+d* p*+rr*+d* p*+rr*+d*

MO

T

fx lo4

llb2 17a,

10.01 7.83 6.77 6.72 2.73 1.25 1.18 1.13 0.59 0.46 0.32 -3.34 - 3.92 -4.38 -7.86 7 12.90 - 15.26 - 19.52 -20.61 -20.94 -21.32 -22.84 -28.83 -29.54

0.05 0.09 5.15 2.29 0.01 0.02 0.07 0.04 0.09 0.17 0.08 4.60 1.81 3.20 4.34 12.11 5.51 1.80 9.36 2.59 2.26 1.94 1.15 6.48

9b, 18a, 19a, 20a, lob, 12b2 1 lb, 21a, 22a, 24a, 12b, 14b2 15b2 16b2 14b, 15b, 16b, 31a, 18b2 19b2 34a, 20bz

3d*+r(Cl, 0) 3d*+r(Cl, 0) 3d*+p*+z(Cl, 0) 3d*+p*+r(Cl, 0) d*+p* p’+r(Cl, 0) p*+rr(Cl, 0) p’+rr(Cl, 0) d’ p*+x(O)+d* d*+rr(Cl) 3d*+p*+x(Cl, 0) 3d*+p*+x(Cl, 0) 3d*+p*+x(Cl, 0) p*+d* p*+x*(Cl, 0) +d* p*+lr(Cl, 0) +d* p*+r*(Cl, 0) +d* p*+n*(Cl, 0) +d* p*+rr*(Cl, 0) +d* p*+n*(Cl, O)+d* p*+x*(Cl, O)+d* p*+x*(Cl,O)+d* p*+x*(Cl, O)+d*

allowed transitions.

bound orbitals, and a complementary set of resonances above edge, mainly originating from metal (3d, 4s 4p) and ligand valence orbitals (o, rr, ti, dc), giving rise to the most intense features of the spectrum, a set of bound Rydberg orbitals, and a residual more or less structureless continuum. Since only the (np) d 11s) transition dipole moment is significantly different from zero (the 1s orbital is so localized that direct transition to ligand orbitals is negligible), Kshell absorption effectively probes the content of 4 (n)p participation in the virtual orbitals. This does not mean that any individual virtual orbital is substantially contributed from metal 4p. Indeed the atomic 4p orbital is very diffuse, it has a large overlap with ligand valence levels and is effectively repelled by the latter. The main 4p contribution lies therefore above threshold, and becomes diluted over several states in the continuum. Let us remark however that

bound and continuum states of ti, symmetry, with metal p participation exist also in centrosymmetric (e.g. octahedral) symmetry, so that even transitions below edge may be obtained without consideration of additional mechanisms, like quadrupole ls-3d transitions or vibronic coupling. The latter are of course an additional possibility and quadrupole contributions have been experimentally evidenced by polarization studies in single crystals [ 12 1. Consider now the results for the carbonyl systems Ni(C0)4, Fe(CO), and Cr(C0)6 (table 1 and fig. 1). The pre-edge features do not vary markedly between the carbonyl spectra of fig. 1, in contrast with the variations observed in the calculated 2p metal spectra of these systems [ 391, suggesting a lower sensitivity of the 1s edge excitation spectra to the change of metal atom in systems with the same type of ligand and to the molecular geometry.

G. Fronzoni et al. /Chemical Physw I 74 (1993) 5 7- 70

62

Ni (CO)4

L

Cr0,C12

Fig. 2. Calculated term values (eV) and oscillator strengths for Cr Is pre-edge excitations in Cr(NO), and CrG&. Calculated lines are convoluted with Gaussians of 0.30 eV fwhm.

Fig. 1. Calculated term values (eV ) and oscillator strengths for Ni, Fe and Cr 1s pre-edge excitattons in Ni(CO),, Fe(CO& and Cr(CO),. Calculated lines are convoluted with Gaussians of 0.30 eV fwhm.

Let us examine first the spectrum ofthe tetrahedral molecule, Ni(CO),: There are two lines below the threshold both associated with transitions into t’; levels, but with different intensity due to the different composition of the relative final states. The MO interaction diagram of fig. 3 allows to correlate the spectral pattern to the theoretical attributions of the final states reported in table 1. The lower energy t$ level ( 10t2) is characterized by a mixture of metal 3d* and ligand 2rcorbitals and is further stabilized by interaction with metal 4p orbital which gives it weak metal p character, responsible for the low intensity calculated for the relative 1s transition. This accounts also for the availability of this level for a 2p-+ 3d transition, which is in fact calculated at a very

similar energy 1381, as expected on the basis of the ECA. The higher energy transition has a stronger intensity due to the larger p character (2x ligand and 4p metal) of this state (the relative transition is instead very weak and almost unobse~able in the corresponding 2p spectrum). It may be remarked that the two levels and the associated transition are not related to the symmetry splitting of a degenerate set of atomic orbitals, like metal 3d in e + tl, but derive from different combinations of metal and ligand orbitals of t2 symmetry, and reflect therefore the detailed bonding situation of this compound. As already discussed the excitation of the is electron into a final state with predominant 4p metal character is predicted above the threshold by the present calculation and corresponds to the higher intensity transition to the 14t2 level (at 9.83 eV). Unfortunately no experimental data are available for this molecule. Two or even three pre-edge transitions have been observed in square planar Ni complexes [ 11, with energy separations larger than in the present case (4% 7.5 eV), which are probably ascribed to the larger

G. Fronzonr et al. /Chemical Physics 174 (1993) 5?- 70

63

60*

(CO)4

Ni(CO)b

Ni

Cr

Cr(N0)4

(NO),

Fig. 3. Molecular orbital diagrams for Ni(CO&, and Cr(NO),.

4P

3d

Fe

Fe(CO)5

(CO)5

(Q-)2

Fe(Q),

Fe2+

Fig. 4. Molecular orbital diagrams for Fe(CO), and Fe(Cp),.

molecular splitting between in plane and out of plane orbitals. Although in the carbonyls considered the preedge structure is rather weak, and the splitting at the

limit of what may be experimentally observable, the situation is most favourable in Ni(CO),, with two well separated transitions of comparable intensity.

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G. Fronzoni et al. /Chemical Physics 174 (199315 7- 70

Fig. 5. Molecular orbital diagram for Cr(COts.

WCPj,

5

25

45

E(eV)

Fig. 6. Calculated term values (eV) and oscillator strengths for Fe 1s excitations in FefCp), up to 30 eV above the threshold. Calcutated lines are convoluted with Gaussians of 5.0 eV fivbm.

In the Fe(CO)S spectrum the low energy transition ( 1 le’ ) at 2.98 eV (term value) shows a noteworthy loss of intensity with respect to the corresponding feature in Ni(CO), while the high energy peak is contributed by two components ( 13e’, 1Oal) due to

the lower DSh symmetry (Fe p orbitals span the e’ and a; symmetries, which are then the only ones available for 1s excitation). The 1le’ level (see MO diagram in fig. 4) is characterized by a large 3d Fe component and only a minor cont~bution from 27t ligand and 4p metal orbitals. This accounts for the low intensity of the first line in the Is spectrum and for the high intensity found for the corresponding 2p-t 1 le’ excitation in the 2p spectrum [ 381. The 13e’ and 1Oa; levels originate from the interaction of the 4p metal levels with the respective counterparts of the 2a ligand orbitals; the a; 4p metal level is also partly mixed with 50 ligand components, with a consequent destabilization with respect to e’* ( 13e’ ) molecular orbital. This rationalizes the a’;* level lying at higher energy than e’* level in line with the attribution reported in table 1, and the gain in intensity of these transitions due to the p character (2~ ligand and 4p metal) of the final states. Also in the case of Fe (CO )5 molecule the higher intensity transitions, which indicate a predominant 4p metal character of the relative final states, are predicted above the threshold by the present calculations. Unfo~unately no high resolution experimental data are available for Fe ( CO)S, and the spectrum reported in ref. [ 2 ] does not show any pre-edge transition, but only a single broad peak, which should encompass the high intensity transitions calculated at 8.9 and 14.8 eV, which we shall briefly discuss in conjunction with the spectrum of Fe( Cp),. Among the vast amount of literature available on complex Fe systems in the solid state, a close comparison may be attempted with the carbonyl Fe porphyrins presented in ref. [ 27 1, which are closed shell systems, because of the strong Fe-CO bonding, with local symmet~ close to C.+ Two preedge features separated by about 2 eV are observed in these systems, matching closely our results for Fe(CO)S. The assignment is interesting, because the higher energy transition is associated with antibonding e* d--A mbital, as is confirmed by polarization studies. Because of two more d electrons in Fe (CO) S and the different symmetry, this is the first transition ( 11e’ ) available here, and the second derives from an additional x* ( 13e’ ) ligand orbital, with minor 3d but higher 4p metal participation. Also separation, & 15 eV, between the pre-edge transition and the first ~ximum is similar to the calculated one, as is the 6 eV splitting of the second maximum (feature C, and

G. Fronzoni et ai. / Chemical Physics I 74 (1993) 5 7- 70

D in the notation of ref. [ 27 ] ). Similar structures may be found also in the spectra of Fe phthalocyanines reported in ref. [ 241. An asymmet~ in the pre-edge peak, su~estive of two separate transitions, has been observed also in high resolution spectra of five-coordinate iron complexes [ 20 1. 3.3. Cr(CO), Finally, let us consider the last member of the carbony1 series Cr( CO)6. The similarity of the pre-edge structure of the Cr(C0)6 spectrum with the preceding ones confirms the experimental observation of similar structures for carbonyl and cyanide complexes [ 51. The first transition (2.64 eV) is relative to a level of pure p character (27~ ligand and 4p metal), 9t,,, at variance with the preceding case and the attribution proposed in the literature [ 5,8]. In the octahedral environment the metal d ( tzg and e,) and p (t*,) orbitals belong to different irreducible representations, and therefore there can be no mixing between 4p and 3d metal orbit&s and the only dipoleallowed final states involve t,, virtual orbitals. In this case 1s and 2p excitations map mutually exclusive parts of the virtual manifold [ 39 ] . The stronger intensity of the transition near the threshold (0.64 eV) is an indication of a stronger metal 4p participation in the relative final state ( lOtI,). In fact, as we can see in the MO interaction diagram of Cr ( CO)6, the 4p unfilled metal level interacts with the respective counterparts of the CO 2n orbitals; it is also partly mixed with 50 ligand component giving rise to a destabilization of the higher lying tTUvirtual level of the diagram (lot,,) which has a larger amount of 4p metal component responsible for the higher intensity of the associated transition with respect to the lower lying tr, level (9t,,). The latter derives from a weaker interaction between the 4p metal and 2%ligand levels and retains a substantial 21~ligand character accounting for the low intensity of the ls+9t,, transition. Higher intensity transitions are predicted above the threshold for Cr(C0)6 as for the two preceding molecules, confirming the presence of important metal 4p contribution in high lying virtual levels. Comparing with the old experimental spectrum reported in ref. [ 5 1, there is indeed a nice agreement between the first two observed structures and the calculated position and

65

intensity of the pre-edge transition (0.64 eV) and the following resonances ( -7.38, -8.81 eV). Even a second low intensity low energy pre-edge transition is apparent in the spectra reported in refs. [ 4,6], which matches reasonably the present calculation, and even better the more correlated results reported below, which increase the energy separation between the two pre-edge transitions. There is instead no sign of a further structure matching the computed one at 14.6 eV, which is likely to interact strongly with the nonresonant continuum, and possibly broadened and pushed to higher energy, contributing to the following broad maximum. In the case of Ni(C0)4 and Cr(C0)6 molecules, we have performed also larger calculations to investigate quantitatively the effect of double excitations in the description of the 1s metal pre-edge features. 2h-2p excitations from valence shell have been included in the CI description both of the ground and the excited states. The 2h-2p CI results are reported in table 2. The most notable difference with the lhIp CI data is the increase of the term values which shifts the spectral pattern away from the threshold increasing by about 1 eV the energy separation between the spectral lines. The variations of the oscillator strengths are of minor entity and therefore the 2h-2p pre-edge spectra of these carbonyl compounds resemble closely those obtained at 1h- 1p CI level, confirming that in these systems strong correlations between the closed valence shell and the 1s excited electron are of minor importance. The simple 1h- 1p CI scheme presently adopted can therefore provide a satisfactory description of the spectra in closed shell transition metal molecules like those considered here. The results of the 1s excitation spectra obtained for the carbonyl systems also reveal that there is only a very small contribution from the 4p metal orbital to the metal-ligand interaction, reflected by the very small fraction of the total intensity associated with the pre-edge 1s+4p transitions, and also by the scarce influence of the change of metal atom in systems with the same type of ligands. In fact the composition of the excited states below the ionization limit is dominated by the n* ligand and/or 3d metal orbitals with possible small contribution of 4p metal orbital participation, which makes possible to observe the transition from 1s metal level. It is interesting to discuss now the variations in the

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G. Fronzoni et al. / ChemicalPhysicsI74 (I 993) 5 7-70

1s pre-edge spectra associated with the change of ligands on the same central atom. In this respect we have examined the Fe(Cp), molecule to compare with Fe(CO),, and Cry and Cr02C12 systems to compare with Cr(CO&. The relative results are reported in table 3 and figs. 2 and 6. 3.4. Fe(C5H5,12 Let us consider first the Is excitation results for Fe (Cp )z. It is well apparent the absence of 1s transitions below the threshold in contrast to the case of 2p excitation spectrum where several transitions are present below the threshold [ 391. However the analysis of the eigenvalues of the relaxed SCF calculation of Fe(Cp), reveals that there are only few virtual states at low energy available for a pre-edge transition. As we can see in the MO interaction diagram of fig. 4 all these states have g symmet~ and the relative dipole allowed transitions from the Is orbital are therefore forbidden. The 5ei,, 9a,, and 5e2, states, predicted below the threshold by our calculations and characterized by a predominant Fe 3d contribution, are however available for quadrupole transitions. Therefore the weak pre-edge structure observed in the experimental spectrum can be associated to quadrupole allowed 1s transitions, according to the interpretation proposed in the work of Ruiz-Lopez et al. [ 151. The first virtual state of correct symmetry available for a 1s dipole allowed transition is the 7e,, level which derives from the interaction between the 4p (e,,) metal level and the lower lying corresponding A ring orbital. Due to the energy separation between these two levels there is only a slight stabilization of the t ligand orbital to the occupied e,, MO and a destabilization of the virtual counterpart 7eiu, with respect to the 4p metal orbital. The latter is pushed towards an energy region where several virtual states are collected whose transitions are observed near the ionization threshold in the 2p excitation spectrum (for example the 2p-+6ez, and 2p-+6e,, transitions have been calculated 0.17 eV below the threshold). The Is-t 7e,, transition is indeed predicted just above the threshold ( -0.02 eV) with a very low intensity due to the essentially ligand character of the final state. This shows that interaction of metal 4p with the ligand o, dc orbitals (not shown in fig. 4) is still very large, so that the excited states with impo~ant

metal 4p contribution are so much destabilized as to be largely pushed at higher energy, as observed in the carbonyl systems. Comparing these calculated high energy transitions with the experimental spectrum [ 15 1, at least at a qualitative level due to the absence of the continuum interactions in our calculation, a nice theoretical reproduction of the two experimental structures (denoted as shoulder B and main peak C) above the threshold is apparent from fig. 6. The main experimental feature C, separated by about 20 eV from the pre-edge structure, can be indeed related to the calculated higher intensity transition at about 20 eV from the threshold (see table 3), while the shoulder B is represented by the group of transitions calculated between 6 and 8 eV below the threshold. Even the weak structure D at higher energy is correctly reproduced. As this is the only high quality spectrum directly comparable to the present results, the agreement is indeed very satisfactory. Also the about 5 eV energy shift between the absorption peak in Fe(CO)s, which lies midway the two structures B and C in Fe( Cp)2, which is clearly seen in the old experimental results [ 2 1, is correctly reproduced by the present calculations (tables 1 and 3 ), considering that the threshold in Fe(CO)S is about 2.8 eV higher than in Fe(Cp), (from the Fe 2p,,, ionization energies reported in ref. [ 5 I ] ), which adds to the c 3 eV term value difference presently computed. Comparing to Fe{ CO), the results of the calculations prove the strong modification of the metalligand interaction, on going from the carbonyl ligands to the ~yclopentadienyl ones, which is also responsible for the notably different spectral patterns obtained for the 2p+ 3d transitions of these systems [ 39,401. Notably both 1s and 2p spectra indicate the push of all virtual levels close to the threshold in ferrocene, which correlates well with the special stability of this class of compounds. Although the role of the 4p Fe shell in the bonding is only of minor importance, however the final excited states to which the 4p levels contribute have a very different nature in the two Fe compounds because of the different interaction between the 3d compounds because of the different interaction between the 3d metal shell and the 2n and 50 ligand CO orbitals in Fe (CO), or x and x* ligand Cp- orbitals in Fe(Cp),, as already discussed in the preceding

G. Fronzoni et al. /Chemical Physics I74 (1993) 5?- 70

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work [ 391 and qualitatively outlined by the interaction diagrams of fig. 4. 3.5. Cr(NO)d Finally let us consider the 1s excitation spectra of Cr (NO), and CrOzClz molecules, reported in table 3 and fig. 2. In the pre-edge region of Cr(N0)4 there are three dipole-allowed transitions into three different tt virtual levels. The first two t$ final states ( 1Ot,, 11t2) essentially derive from the interaction between the 3d tz metal component and the corresponding one of the 21~ligand levels, as we can see from the MO interaction diagram of fig. 3. The presence of the two transitions Is+ lot2 and 1s+ 1It, of comparable intensity in the 1s spectrum indicate a participation also of 4p metal orbital to these excited states, confirming the preceding hypothesis made on the basis of the 2p+3d excitation results [ 38 3. The third line in the spectrum is relative to the 1s transition to 12t, level which derives from a further interaction between d” ligand and 4p metal orbital% The larger mixing of the 4p metal orbital in this final state is pointed out by the larger intensity of the relative transition, with respect to the lower lying structures. So the behaviour is exactly the opposite of that found in 2p absorption, where there is a large, similar intensity in the first two tz final orbitals, and much smaller in the third one. Comparing Cr(CO& with Cr(N0)4 the change from CO to NO ligands strongly m~ifying the metalligand interactions, affects significantly the shape of 1s excitation spectra and can be explained through the aid of the MO interaction diagram of Cr(N0)4 (fig. 3). It is apparent the closeness in energy between the 3d metal shell and the 2x ligand orbitals, which are partially occupied, at variance with the case of 2n orbitals of CO ligand completely unfilled. This situation together with a less relevant interaction with the low lying o levels is responsible for a smaller destabilization of the lower lying virtual levels, available therefore for transitions below the threshold. The very low total intensity calculated for the pre-edge structure in Cr( NO), reveals a notable difference with respect to other tetrahedral Cr compounds for which intense pre-edge features [ 10,2 5 ] are experimentally observed.

This is also the case of Cr02C12 compound which shows a very intense low energy pre-edge feature with respect to the other two Cr compounds here considered. Furthermore it should be noted that the total intensity of the transitions below the threshold is comparable to that above the threshold, in the range of energy presently considered, on the contrary of all preceding cases examined. This is however in line with the expe~mental pattern observed for Cr compounds with metal-oxygen bonding and can be considered therefore a specific probe of the characteristic bonding situation present in CrOzClz due to the high electronegativity of the ligands and to the presence of only filled ligand 7t orbitals. For this reason there is no strong repulsion between the ligand rr* orbitals and the 4p metal one, responsible for the pushing of this orbital above the threshold, which can have therefore a large component available for the transition from the 1s level. This accounts for the relatively high intensity of the transitions into 9b, and 1Sal levels (representing the lowest tZ level in hypothetical tetrahedral representation). As we can see in table 2 these levels have a predominant metal 3d character with some amount of metal and ligand p character, in line with the assignment proposed for the Cr porphyrine compounds [ lo,25 1. In addition, comparing our theoretical results for Cr02C12 with the expe~mental ones for Cr porphyrins, we observe a noteworthy agreement of the energy separation between the intense pre-edge peak and the first intensity maximum above the threshold (about 10 eV ) . The present results can be also compared with the spectra of CrO- and Cr03Cl- reported in ref. [ 7 1, There is a clear evolution of the spectrum in going from the former to the latter, which is closer to Cr02C12. While the strong pre-edge transition stays unaffected, two structures are apparent above threshold in CrO&-, a shoulder at about 12 eV from the pre-edge transition, and a maximum at 20 eV, both nicely reproduced by the present results. A second weak pre-edge transition present in CrO:- instead disappears in CrO,Cl-, and is not found also in the present calculations, although a host of very weak transitions are predicted below the threshold. We can generally conclude that the observed preedge transitions may be interpreted admitting that the

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G. Fronzoni et al. /Chemical Physics 174 (1993) 5 7- 70

low-lying virtual levels are dominated by interactions among the metal 3d and o and x ligand valence orbitals. The metal 4p orbitals have only a minor influence on such levels, and although their mixing is weak, it allows the mapping of such levels by the 1s transitions. The interaction with ligand orbitals is however strong, because of the large overlap. This leaves almost unaffected the ligand orbitals, as lowest levels, but pushes by orthogonality the remaining part of 4p above the threshold. Here most of the total intensity available to the transition is found, because the highly contracted 1s orbital effectively probes only the 4p region closest to the nucleus. Therefore, at variance with the 2p spectra, the most important part of the spectrum lies above the threshold, although the small pre-edge features still convey significant information. The following lower lying virtuals are then higher Rydberg np orbitals, which lie mostly outside the whole molecule, giving rise to transitions of negligible intensity and which are little affected by details of the molecular electronic structure. The rest of the 4p is expected to give strong intensity in the continuum a few eV above threshold, which is indeed observed in most actual spectra, often as pronounced resonances. The present discrete state calculation seems to provide a fair description of such resonances, although a more rigorous approach, along the lines of ref. [ 371, is probably needed for a strict quantitative comparison with experiment. At the same time, the present results indicate the need of gas phase high resolution experimental data, in order to carefully check the predicted pre-edge structures, to arrive at a detailed understanding of XAS spectra in organometallic compounds.

4. Concluding remarks The metal 1s excitation spectra of several organometallic systems have been calculated at the ab initio SCF-CI level and compared with the theoretical spectra relative to the 2p metal edge previously obtained for the same systems. The 1s spectra are dominated by the transition moment to metal 4p final state, thus directly probing the metal 4p content of the unoccupied states. In this respect the 1s edge appears less rich of information than the upper core 2p excitation, in particular as concerns the metal-ligand

bonding interaction. However, since the initial 1s core level probes final levels complementary to those determined by 2p-+3d excitations, the present 1s results can be merged with the 2p ones relative to the considered system, allowing to obtain a complete pattern of the low-lying virtual levels which are very important to discuss the character of the metal-ligand bonding. In this respect qualitative MO interaction diagrams outlined on the basis of both the core excitation results ( 1s and 2p) have proven to be very useful to rationalize the spectral information. The 1s spectra show a notable sensitivity to the nature of the ligands reflecting therefore the different metal-ligand interactions in analogy with the behaviour observed in the 2p metal spectra, in particular as concerns the intensity trend. Instead there is no significant variation of the spectral pattern with the change of metal atom along the series of carbonyl compounds and this could be related to the small contribution of the metal 4p orbital to the metal-ligand interaction. The present ab initio treatment already adopted for the calculations of the 2p excitation spectra, providing for an accurate treatment of the strong relaxation in the response of the core hole formation and an accurate choice of the basis set, appears to be adequate to interpret also the 1s spectra, giving therefore access to a detailed interpretation of the discrete structures in core excitation spectra of a wide range of complex systems.

Acknowledgement Thanks are due to CNR and MURST of Italy for financial support. Free computer time on the CRAY Y-MP/464 of CINECA (Bologna) is gratefully acknowledged.

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