- Email: [email protected]
An SCF Xα scattered-wave calculation for ferrocene
CHEMICALPHYSICSLETTERS
Volume 24, number 2
AN SCF Xcr SCATTERED-WAVE
15 January 1974
CALCULATION
FOR FERROCENET
N. RijSCH *and K.H. JOHNSON Department of Metalhcrgy and Materils Science, bIassachtssetts Institute of Tec~molog?i. Cam bridge. Massachusetts 02139, USA Received 28 September 1973
An SCF Xa SW calculation using overlapping spheres has been carried out for ferrocene. The agreement with the o&rved op.&al absorption spectrur& both for d-d transitionsand charge-transferexcitations. is excellent. The calculated ~oonizatioxi spectrum ames well with experimental measurements,leading,however, to a different interpreiation for the two lowest ionization potentials. The level ordering for the highest occupied orhitals in ferrocene and the lowest unoccupied orbital is found to be: e&n-Cp) < e,u(n-Cp) < e,$3d) < aIg(3d) < eTg(3d).
The electronic structure of ferrocene, Fe(CSH5)2, has been the subject of many theoretical and experimentai investigations. The basic features are now considered to be well understood, as can be seen from the
orbital calculations using Wolfsberg-Helmholz-type approximations [6-8] yield this level sequence, whereas the results of the SCF LCAO calculations [4,5, iO] are not consistent with these experimental findings. On
_However, none of the nucalculations [4-l 0] has been successful in explaining all the experimental facts as provided by optical absorption measurements [l l-161, electron spin resonance data [ 171 and photoelectron spectroscopy [18,19]. The most controversial issue is the level ordering of the highest occupied molecular orbitals alg and ezg which are assumed to be primarily localized Fe 3d-like states. Using intensity arguments, the level ordering alg < ezg has been inferred from the photoelectron spectrum [IS, 191. The first ab initio SCF LCAO calculation resulted in ionization potentials which agree with the above assignment [IO]. This ordering was also obtained in earlier simplified SCF LCAO treatments [4,5] _It contradicts, however, the level sequence concluded from the interpretation of the visible optical absorption spectrum which assigns this part of the spectrum to the three allowed d-d transitions 115, 16) and yields the ordering ezg < alg < I$. Molecular-
the other hand, the poor quantitative agreement of the Wolfsberg-Helmholz energy levels with the photoelectron and optical absorption data does not allow a decisive conclusion. We report here the results of a molecular-orbital calculation for ferrocene using the SCF Xa scattered-wave method [20-221. With the transition-state procedure [20,22] , this method permits a unified treatment of ground-state properties, ionization spectra and optical excitations_ T’he molecule was assumed to have an eclipsed (Dsh) conformation in accord with the results of an electron-diffraction study of ferrocene in the vapor phase [23,24] . However, in order to facilitate comparisons with earlier molecular-orbital calculations, we have adopted the notation of the point group Dsd corresponding to the staggered configuration found in the solid state. An SCF Xcr SW calculation for ferrocene with Dsd symmetry yielded virtually identical orbital energies to the one with D5h symmetry. The bond lengths were taken to be Fe-C = 2.106 A, C-C c- 1.43 A., and C-H = 1.12 A [23] _The CsH5, cydopentadienyl
reviews of this work [l-3]
mkrous molecular-orbital
L t Research sponsored by the Air Force Office of Scientific Jksearch, United States Air Forci (AFSC), under Contract No. F44620-69-c-o054. * Permanent address: Lehrstuhl fir Theoretische Chemie der TeclinischenUniversittt Miinchen,D-8 Munich,West GernkUlY.
(Cp), ring Wasassumed to be planar. Space was parti; tioned as usual. in the SCF X& SW method [22]; intro-
d&&touching atomic spheres and an outer sphere surrounding the motecule: However, in order to achieve 179:
.;.
..
: ;
..
..
:
-:
.
,.
-.
‘.
‘.‘..
;.
__’
.,
,_ .:
. ._.
‘.
.-. :
.:.-
_; :.
. ..-
Volume 24, number 2
CHEMICALPHYSICS LETTERS
a better description of the Cp rings as weIJ as of their interaction with the iron atom, the carbon spheres were enlarged to overlap with each other and with the iron and hydrogen spheres, respectively_ This procedure has significantly improved the results for molecules like ethylene, benzene, and carbon monoxide 12.51 and Zeise’s anion [26] , and has been fully justified theoretically [27]. The various sphere radii used were: rye = 2.6287 au, rc = 1.55 au, rH = 0.7653 au, and rout = 6.2471 au. The carbon sphere radius is identical to that employed in an earlier overlapping-sphere calculation for benzene [25]. The XLYexchange parameters used for the component atoms were: cr, = 0.7533 I, aH = 0.77725 (the same values used in the calculation for benzene [25] ), and aFe = 0.7 115 1 (from the table provided by Schwarz [28] )_ Outside the atomic spheres a weighted average of the atomic values was used, a = 0.76272. The Fe Is, 2s, and 2p orbitals and the C Is orbitals were initially treated in the “frozen-core” approximation. Releasing the cores after self-consistency in the valence orbitals was attained resulted in shifts of only 0.001 Ry in the valence energy levels. The calculation for the ground-state orbitals offerrocene converged to -C0.001 Ry in 25 iterations, requiring 20 min of CPU time on an IBM 370/l 63 computer. The valence orbital energies are shown in fig. 1, which includes also the energies for the first few unoccupied levels. In the same figure we compare these energies with the SCF Xcy atomic-orbital energies of iron and the molecular-orbital energies as obtained from a SCF Xa SW calculation for the Cp moiety. The latter energies are labeled by the corresponding representations of the D,, point group. The total energy offerrocene was calculated to be Etot = -3297.774 Ry and the virial ratio -Ekin/Etot = 1 .0012. The charge distributions and energies of the SCF Xo! SW orbit& are consistent with the usual description of the chemical bonding in ferrocene Cl-31 _The fact that the two Cp rings exist very much as separate entities in fetiocene is reflected by the energy pairing of those orbit& which are 1aFgely nonbonaing with respect to the Fe atom, e.g. (2eZ9, 2eZu) and (3e%. 3eZu) (cf. Eg. 1). The orbit& associated with the strongest bonding of the n-Cp‘electrons to the Fe atom are 4e,,, 7al,, 6e,,, and Ba,. This is reflected by the corresponding fractions of orbital charge found inside the’Fe sphere, which are 0.30,0.16,0.09, and 0.09, respectively. In the 4elg orbital it is the Fe 3d electrons
15 January 1974 Fe
Fe (C.&J2
I--,7eh
0.0
C5H5
/
----Ie$
-0.2
5e,,-
t
I
9%
-0.4
re;
36
10 0 PE. -0.6
3e;
7. ”
yy3e;
-0.8 5.3 2U-
;;:
6% *=zu- -
G -1.0 2
-I
2e 20
_’
3c; 2e;
-
1.2
-
1.4
-
1.6
4ekI_
ze;
2ego
-
5%
2a,’
t 40&-
- t.8 i
Fig. I. The SCF Xa SW electronic energiesof ferrocene. The levelsare labeled according to the irredudble representations of the point group Dsd. Also shown for comparison are the
SCF Xa energies of the free iron atom and the CSHS moiety. which are responsible for the bonding, whereas the 7alg orbital primarily involves the participation of the Fe 4s electrons. The 6el,, and 6a2, orbit& are 4p-like with respect to the Fe atom. The two highest occupied orbit& 8alg and 4eZg are essentially localized Fe 3d orbitaIs. The corresponding orbital charge fractions in the Fe sphere are 0.87 and 0.82, respectively, indicating that the 8alp orbital is more spatially localized with respect to the Fe nucleus t&an is the 4eZg orbital. This is consistent with the fact that the 8alg orbital is an almost purely nonbonding Fe 3d state, while the 4eZg orbital is slightly bonding wi’& respect to the Cp rings. This difference in the relative Iocalization of the 8aI, and 4ezg orbit& must be taken into consideration when interpreting the pho-
toelectron spectrum of fenocene [IS, 191 on the basis of intensities (see discussion below). Our calculated value of 0.82 for the 4eZg orbital charge fraction is consistent with the square of the value 0.9 1 estimated by Prins 1371 for the coefficient of the Fe 3d atomic orbital on the basis of ESR measurements for the ferricenium ion Fe(CS HS)i.
. . ..’
40;
4s
180 :.
20;
4w
--,5e2,
:-
15 January 1974
CHEhIICAL PHYSICS LETTERS
Volume 24, number 2
The lowest unoccupied
level 5erB (or Se;J
state orbital relaxation tends to be small for most molecules, whereas for ionizing (photoelectron) excitations the relaxation is large. This is true also for the ferrocene molecule. The ground electronic state of ferrocene is the sin: glet 1 A1,(4eQ4 @a#. The one-electron transition 8ar, + 52,, yields excited singlet and triplet states of symmetries * EJ8 and 3E,,, whereas I&,, 3E rgr r E29, and 3E$ multrplets are associated with the 4eZe --f 5e,g transit&. These are all d-d transitions since thk initial-state and final-state orbitals are principally Fe 3dlike. The singlet-singlet transitions, which are spin-allowed, are responsible for the most intense optical absorption observed for ferrocene in the visible part of the spectrum [ 11, 15,16]. Very weak optical absorption in the same spectral range is associated with the spin-forbidden, singlet-triplet excitations [ll, 16]The SCF Xa SW transition-state procedure provides a good approximation to an appropriate average of multiplet energies associated with a given electronic configuration [20] . The calculated 8alg -+ 5era and 4ezg 7 5erg transition energies may therefore be compared wrth averages of the corresponding measured optical absorption energies. These comparisons have been made in table 1 for the optical data measured by Sohn et al. [ 15, 161. Both a straight arithmetic average and a weighted average of the experimental data (weighted according to multiplicity) [20] have been compared with the theoretical orbital transition energies. The quantitative agree-
also cor-
responds principally to an Fe 3d-like orbital, except that it is significantly antibonding with respect to the Cp rings. It is the antibonding partner of the 4elg orbital, which we have shown is responsible for the strongest bonding between the n-Cp electrons and the Fe 3d electrons_ This antibonding character is further reflected by the position of the 5el level relative to the Fe 3d atomic energy Ievei (see Plg. I) and by the orbital charge fractions, which are 0.64 for the Fe sphere, O-24 for the C spheres, 0.11 for the interatomic region, and 0.0 I for the extramolecular region. The remaining empty levels shown in fig. 1 have the following characteristics. The 9alg level corresponds mainly to an Fe 4s-like orbital which is antibonding with respect to the Cp rings. The Sezg level is largely associated with an* -Cp orbital, but with significant Fe 3d antibonding character_ The 7eru level corresponds
r
to a diffuse antibonding Fe 4p-like orbital, and the 4e2,
level belongs to a pure .n* -Cp orbital. We consider next the energies of electronic
excita-
tions in ferrocene. These are calculated in the SCF Xo! SW method by the “transition-state” procedure [20,
221. The transition-state energies, calculated self-consistently for each excitation of interest, automatically include the approximate effects of orbital relaxation usualIy neglected in the application of Koopmans’ theorem to molecular-orbital theory. For internal (optical) excitations, it has been shown [22] that the transition-
Table 1 Comparison of d-d transition energies(3 X 10” cm-‘) calculated by the SCF Xa SW method with experimental optical data for
fenacene in the visible part of the spectrum Multiplet
Experiment a)
Average experimental transition energy
weightedb)‘
arithm.
SCF Xa SW
Orbital
transition energy
transition
at&g a%,
21.8
18.9
19.6
20.4
20.5
8alg
b’%g l&g b3Elg
30.8 24.0 22.4
23.1
24.5
25.2
k2g -
3&g
20.9
a)Refs. [15,16].
‘) Weightedaccording to multiplicity.
+
5e ‘g
%lg
Table 2
izatjon spectrum of ferrocene, as measured by He(I) spectroscopy fl8, 19]_ This has been carried out in table 3, where we compare the orbital ionization potentials calculated by the SCF Xa SW transition-state procedure with the energies of all the bands in the photoelectron spectrum which have been resolved experimentally [l&19]_ Included for comphotoelectron
Comparison of orbital transition energies (G X IO3 cm-‘) calculated by the.SCF Xru SW method with experimental optical charge-transfer energies in the LJVpart of the spectrum Orbital tWsition
Type of
SCF Xa SW transition energy
E?cpesimenC)
transition
6elo - 5elg
L-+ hi
36.5
37.7
%g++%u
hI-+L M-+L L- Iv1
39.2 43.9
41.0
4e2g+
+=2U
6% - 9alg 6elU - 5ezg 5elu + 5elg 3e2,
-+ Selg
6a2u -, Setg
L - LhP
47.1 50.1
L-+&l
53.9
L,-+ hi
55.1 55.5
L 4 1LI
1.5 January 1974
CHEMICAL PHYSICS LETTERS
Volume 24, number 2
are ionization potentials determined in a recent
parison
ab initio SCF LCAO calculation [lo] by taking differences between the total energy of the Ferrocene molecule and the total energies of the ferricenium ion in various electronic configurations. Ionization potentials obtained by applying Koopmans’ theorem to the SCF LCAO orbital energies [ 10) are also included. Some of the photoemission bands correspond to individual OPbitai levels, whereas others correspond to narrow bands of levels. For example. the band whose maximum is at 12.2 eV [I 8] is associated with photoemission from the group of closely spaced leveIs 5el,, 3el,, 3e,, 3eZg, and 6a2u, which we have shown belong primarily to Cp &and orbitals. As mentioned earlier, the level ordering of the highest occupied orbitals 8atg and 4eZg has been the most CORtroversial issue in the electronic structure of ferrocene. The level ordering gal, < 4e2, has been inferred from the photoelectron spectrum [ 18, 191, using the argument that the photoemission peak of greater integrated intensity should be associated with the orbital of greater occupancy- However, this would be true onIy if the spatial localization and nodal character of each of the two orbit& were identical- We have indicated earlier that the essentially nonbonding 8a,,(3d) orbital is more Iocalized within the Fe sphere than is the somewhat bonding 4e2,(3d) orbital. Moreover, the 8alg orbital has a small amount of Fe C-like character, which is allowed by symmetry. It has been well established [29] that the intensity of photoemission from a given orbital level depends critically on the sjze or extent of the orbital and on the number of its nodal surfaces, as a function of incident photon energy or wavelength- These differences in relative spatial localization and nodal character offer a possible explanation of why the 8al, orbital (rather than the 4eZg orbital) can be assigned to the more intense of the first two closely spaced photoemission peaks of ferrocene [i&19]. The orbital ordering 4ezg < Sal, is, of course, essential for interpreting the d-d optical absorption spectrum of ferrocene [15, 161 (cf. table I). This ordering has also been asslimed
42.8 47.5 49.5
51.6
a) Energies of optical absorption peaks, ref.[ 121. b, Some charge transfer because of antibonding Fe 3d content.
ment between theory and experiment is excellent for both averages, providing firm support for the orbital ordering eZg(3d) < a I 9(3d) < e&(3d). The strongest optical absorption in ferrocene occurs in the ultraviolet part of the spectrum [I 2, 13, 161 and may be interpreted largely in terms of charge-transfer excitations. For example, we interpret an absorption edge centered at 37 700 cm-l [ 121 to be associated with the onset of 6e lu (rr-Cp) + 5ele(3d) “Iigand-tometal” (L-+ M) charge-transfer transitions. On the other hand, optical absorption peaks at 41000 and 42800cm-1 [12] are most likely associated with the “metal-to-ligand” (M + L) transitions 8a,,(3d) + +,(lr*-Cp) and 4e&3d) + 4e2,,(n*-‘Cp), respectively. The most intense absorption band has its maximum at 5 1 600 cm-l [ 123 and is probably due to charge-transfer transitions from the band of closely spaced &and-like levels ,Selu(u-Cp), 3ezu(u-Cp), and 6az,(n-Cp) to the Fe-like level Se1 (3d). A summary of our complete interpretation 0 f the W optical spectrum of ferrocene is given in table 2. No attempt has been made to calculate multiplet averages as in table I, but rather to correlate the principal optical absorption peaks 1121 wiih individual (or groups of) orbital transitions. Finally, we can provide antiterpretation of the ion182 .
..‘.
._.
-.‘. _,:
, ‘. .: i.
..^:.:.,:.
_.
._
_.
__
..
.-
‘-
_
Volume 24. number 2
CHEMICAL PHYSICS LETTERS Table 3
Comparison of the ionization potentials (in eV) of ferrocene calculated
by the SCF Xa SW rransition-stare
procedure
and
SCF LCAO method with those measured experimentally He(I) photoelectron spectroscopy Orbit&
SCF XcxSW
Harttee-Fock
transition-state
SCF LCAO
procedure
method
3ezg
11.5 11.6 11.6 11.7
6a2u
11.7
7a1g
12.8
5elu 3e1g 3e2,
Esperiment
10.1”) w5.qb) 6.858’)
7.9 8.5 9.3 9.7
by
(6.88)d)
8.3
(14.4)
7.234
(7.23)
11.1
(I 1.7)
8.715
(8.72)
11.’
(11.9)
9.38
(9.39)
15 January 1974
trast to the results of a recent ab initio SCF LCAO calcuktion [IO] (requiring considerably more computer time), where the calculated ionization potentials are in poor quantitative agreement with experiment (cf. table 3), and where no analysis of optical spectra was provided. Applications of SCF Xor SW method to other organometallic systems, including Zeise’s anion Pt(C2H4)Cl, [26], Ziegler-Natta-type titanium-olefin complexes of catalytic importance [30], and iron porphyrins [3 I ] . will be reported in future publications. One of us (N.R.) is gratefui to the Deutsche Forschungsgemeinschaft for financial support.
References (11.3)
12.2
15.5
(16.0)
11) bi. Rosenblum, Chemistry of the iron group metallocenes (Wiley-Interscience, New York. 1965). [2] D.A. Brown, in: Transition metal chemistry, Vol. 3, ed. R.L. Cnrlin (Dekkcr, dination
f&g
14.2 14.6
2e2u
16.0
2e2
16.1
5a2u
g
New York,
1966).
\ 3 ] C.J. Ballhsusen and H.B. Gray, in: chemistry,
(13.0)
13.6
(13.461
16.4
(16.5)
‘) Ref. [ 10 J, difference of total ene&ies of molecule and ion. b) Ref. [lOI _Koo mans’theorem result. d Ref. [19]. ‘) Ref. 118). in the interpretation
of photoelectron spectra for similar metallocenes based on Mn and Cr [18, 193 _To settle this issue more quantitatively. work is now in progress on calculating the intensities of optical and photoelectron spectra on the basis of the SCF Xa! SW transition-state theory [20] _ In conclusion, we have shown that the SCF Xcu SW method with overIapping spheres is capable of providing an accurate picture of the chemical bonding of ferrocene and a reasonable interpretation of the measured optical and photoelectron spectra. The calculated d-d and charge-transfer transitions are in agree_ment with experiment to a half an electron volt or better (cf. tables 1 and Z), while the ionization potentials have been calculated to an accuracy of approximate!y one electron volt or better (cf. table 3). This is in marked con-
of the coorVol. I,ed. A.E. Mnrtell (Vnn
compounds,
Nostrand-Reinhold, New York, 1971). 141 E.hl. Shustorovich and MI. Dyatkina, DokL Akad. Nauk SSSR 128 (1959) 1234; Zh. Strukt. Khim. 1 (1960) 109. 151 J.P. Dshl and C.J. Ballhausen. Kgl. Danske Videnskab. Selskab blat. Fys. hledd. 33 (1961) No. 5. 161 R.D. Fischer,Theoret. Chim. Acta 1 (1963) 418. [71 A.T. Armstrong, D.G. Carroll and S.P. hlcGlynn, J. Chem. Phys. 47 (1967) 1104. [Sl J.H. Schachtschneider, R. Prins and P. Ros, Inorg. Chim. Acta 1 (1967) 462. [9] 1.H. Hillier and R.hI. Canadine, Discussions Faraday Sot. 47 (1969) 27. [ 101 M. Coutiere, J. Demuynck and A. Veillard, Theoret. Chim. Acts 27 (1972) 281. [ 111 D.R. Scott and R.S. Becker, J. Organometal. Chem. 4 (1965) 409. [ 12) A.T. Armstrong, F. Smith, E. Elder and S.P. McGlynn, I. Chem. Phys. 46 (1967) 4321. [ 131 J-3. Smith and B. Meyer, J. Chem. Phys. 48 (1968) 5436. [ 14 ] P.B. Stephenson and W.E. Winterrowd, J. Chem. Phys. 52 (1970) 3308. [15] Y.S. Sohn, D.N. Hendrickson, j.H. Smith and H.B. Gray, Chem. Phys. Letters 6 (1970) 499. t 161 Y.S. Sohn, D.N. Hendrickson and H.B. Gray, J. Am. Chem. sot. 93 (1971) 3603. [17] R. Prim, Mol. Phys. 19 (19701603. [ 1S] J-W_Rabalais. LO. Werme. T. Bergmark, L. Karlsson, M. Hussain and K. Siegbahn, J. Chem. Phys. 57 (1972) 1185. [ 191 S. Evans, M.L.H. Green, B. Jewitt, A.F. Orchard and C.F.
PygaII, I. Chem. Sot. Faraday II 68 (1972) 1847. 1201 J.C. Slater and K.H. Johnson, Phys. Rev. BS (1972) 844. f83
.., -..
; ‘. .
_.._ ,... i
;.,
..
.,.I
‘.
:: ,
.
-‘, .._ ‘.
..
_,;:.: ,.
._.’
.. _.
,_
:
. ..,
:
.._
:.:
., _ .:
L, .:-
_
.~
y_ .,-
1“
_
:: : :
..
-_ :-‘:
i
”
.
.. .
Volume 24, number 2
CHEMICAL PHYSICS LETTERS
1211 K.H. Johnson and F.C. Smith Jr.. Phys. Rev_ BS (1972) 831. [22] K.H. Johnson in: Advances in q;lantum chemistry, Vol. 7, ed. P--O. LSwdin (Academic Press, New York, 1973) p.143. 1231 R.K. Bahn and A. Haaland, J. Organometal. Chem. 5 (1966) 470. [24] G.J. Palenik, Inorg. Chem. 9 (1970) 2424. 1251 N. RGsch, W.G. Klemperer and K.H. Johnson, Chem. Phys. Letters 23 (1973) 149.
IS January 1974
[26] N. Riisch, R.P. Messmer and K-H. Johnson, I. Am. Chem. Sot.. submitted for publication [27] K.H. Johnson, to be published. (281 K. Schwarz, Phys. Rev. BS (1972) 2466. [29] W.C. Price, A.W. Potts and D-G. Streets, in: Electron spectroscopy, ed. D.A. Shirley (North-Holland, Amsterdam, 1972) p. 187. 1301 N. RBsch and K.H. Johnson, to be published. [3 I ] K.H. Johnson, in: Biomedical physics and biomaterials science, ed. H.E. Stanley (M.I.T. Press, Cambridge, 1972) p. 85.
Volume 24, number 2
AN SCF Xcr SCATTERED-WAVE
15 January 1974
CALCULATION
FOR FERROCENET
N. RijSCH *and K.H. JOHNSON Department of Metalhcrgy and Materils Science, bIassachtssetts Institute of Tec~molog?i. Cam bridge. Massachusetts 02139, USA Received 28 September 1973
An SCF Xa SW calculation using overlapping spheres has been carried out for ferrocene. The agreement with the o&rved op.&al absorption spectrur& both for d-d transitionsand charge-transferexcitations. is excellent. The calculated ~oonizatioxi spectrum ames well with experimental measurements,leading,however, to a different interpreiation for the two lowest ionization potentials. The level ordering for the highest occupied orhitals in ferrocene and the lowest unoccupied orbital is found to be: e&n-Cp) < e,u(n-Cp) < e,$3d) < aIg(3d) < eTg(3d).
The electronic structure of ferrocene, Fe(CSH5)2, has been the subject of many theoretical and experimentai investigations. The basic features are now considered to be well understood, as can be seen from the
orbital calculations using Wolfsberg-Helmholz-type approximations [6-8] yield this level sequence, whereas the results of the SCF LCAO calculations [4,5, iO] are not consistent with these experimental findings. On
_However, none of the nucalculations [4-l 0] has been successful in explaining all the experimental facts as provided by optical absorption measurements [l l-161, electron spin resonance data [ 171 and photoelectron spectroscopy [18,19]. The most controversial issue is the level ordering of the highest occupied molecular orbitals alg and ezg which are assumed to be primarily localized Fe 3d-like states. Using intensity arguments, the level ordering alg < ezg has been inferred from the photoelectron spectrum [IS, 191. The first ab initio SCF LCAO calculation resulted in ionization potentials which agree with the above assignment [IO]. This ordering was also obtained in earlier simplified SCF LCAO treatments [4,5] _It contradicts, however, the level sequence concluded from the interpretation of the visible optical absorption spectrum which assigns this part of the spectrum to the three allowed d-d transitions 115, 16) and yields the ordering ezg < alg < I$. Molecular-
the other hand, the poor quantitative agreement of the Wolfsberg-Helmholz energy levels with the photoelectron and optical absorption data does not allow a decisive conclusion. We report here the results of a molecular-orbital calculation for ferrocene using the SCF Xa scattered-wave method [20-221. With the transition-state procedure [20,22] , this method permits a unified treatment of ground-state properties, ionization spectra and optical excitations_ T’he molecule was assumed to have an eclipsed (Dsh) conformation in accord with the results of an electron-diffraction study of ferrocene in the vapor phase [23,24] . However, in order to facilitate comparisons with earlier molecular-orbital calculations, we have adopted the notation of the point group Dsd corresponding to the staggered configuration found in the solid state. An SCF Xcr SW calculation for ferrocene with Dsd symmetry yielded virtually identical orbital energies to the one with D5h symmetry. The bond lengths were taken to be Fe-C = 2.106 A, C-C c- 1.43 A., and C-H = 1.12 A [23] _The CsH5, cydopentadienyl
reviews of this work [l-3]
mkrous molecular-orbital
L t Research sponsored by the Air Force Office of Scientific Jksearch, United States Air Forci (AFSC), under Contract No. F44620-69-c-o054. * Permanent address: Lehrstuhl fir Theoretische Chemie der TeclinischenUniversittt Miinchen,D-8 Munich,West GernkUlY.
(Cp), ring Wasassumed to be planar. Space was parti; tioned as usual. in the SCF X& SW method [22]; intro-
d&&touching atomic spheres and an outer sphere surrounding the motecule: However, in order to achieve 179:
.;.
..
: ;
..
..
:
-:
.
,.
-.
‘.
‘.‘..
;.
__’
.,
,_ .:
. ._.
‘.
.-. :
.:.-
_; :.
. ..-
Volume 24, number 2
CHEMICALPHYSICS LETTERS
a better description of the Cp rings as weIJ as of their interaction with the iron atom, the carbon spheres were enlarged to overlap with each other and with the iron and hydrogen spheres, respectively_ This procedure has significantly improved the results for molecules like ethylene, benzene, and carbon monoxide 12.51 and Zeise’s anion [26] , and has been fully justified theoretically [27]. The various sphere radii used were: rye = 2.6287 au, rc = 1.55 au, rH = 0.7653 au, and rout = 6.2471 au. The carbon sphere radius is identical to that employed in an earlier overlapping-sphere calculation for benzene [25]. The XLYexchange parameters used for the component atoms were: cr, = 0.7533 I, aH = 0.77725 (the same values used in the calculation for benzene [25] ), and aFe = 0.7 115 1 (from the table provided by Schwarz [28] )_ Outside the atomic spheres a weighted average of the atomic values was used, a = 0.76272. The Fe Is, 2s, and 2p orbitals and the C Is orbitals were initially treated in the “frozen-core” approximation. Releasing the cores after self-consistency in the valence orbitals was attained resulted in shifts of only 0.001 Ry in the valence energy levels. The calculation for the ground-state orbitals offerrocene converged to -C0.001 Ry in 25 iterations, requiring 20 min of CPU time on an IBM 370/l 63 computer. The valence orbital energies are shown in fig. 1, which includes also the energies for the first few unoccupied levels. In the same figure we compare these energies with the SCF Xcy atomic-orbital energies of iron and the molecular-orbital energies as obtained from a SCF Xa SW calculation for the Cp moiety. The latter energies are labeled by the corresponding representations of the D,, point group. The total energy offerrocene was calculated to be Etot = -3297.774 Ry and the virial ratio -Ekin/Etot = 1 .0012. The charge distributions and energies of the SCF Xo! SW orbit& are consistent with the usual description of the chemical bonding in ferrocene Cl-31 _The fact that the two Cp rings exist very much as separate entities in fetiocene is reflected by the energy pairing of those orbit& which are 1aFgely nonbonaing with respect to the Fe atom, e.g. (2eZ9, 2eZu) and (3e%. 3eZu) (cf. Eg. 1). The orbit& associated with the strongest bonding of the n-Cp‘electrons to the Fe atom are 4e,,, 7al,, 6e,,, and Ba,. This is reflected by the corresponding fractions of orbital charge found inside the’Fe sphere, which are 0.30,0.16,0.09, and 0.09, respectively. In the 4elg orbital it is the Fe 3d electrons
15 January 1974 Fe
Fe (C.&J2
I--,7eh
0.0
C5H5
/
----Ie$
-0.2
5e,,-
t
I
9%
-0.4
re;
36
10 0 PE. -0.6
3e;
7. ”
yy3e;
-0.8 5.3 2U-
;;:
6% *=zu- -
G -1.0 2
-I
2e 20
_’
3c; 2e;
-
1.2
-
1.4
-
1.6
4ekI_
ze;
2ego
-
5%
2a,’
t 40&-
- t.8 i
Fig. I. The SCF Xa SW electronic energiesof ferrocene. The levelsare labeled according to the irredudble representations of the point group Dsd. Also shown for comparison are the
SCF Xa energies of the free iron atom and the CSHS moiety. which are responsible for the bonding, whereas the 7alg orbital primarily involves the participation of the Fe 4s electrons. The 6el,, and 6a2, orbit& are 4p-like with respect to the Fe atom. The two highest occupied orbit& 8alg and 4eZg are essentially localized Fe 3d orbitaIs. The corresponding orbital charge fractions in the Fe sphere are 0.87 and 0.82, respectively, indicating that the 8alp orbital is more spatially localized with respect to the Fe nucleus t&an is the 4eZg orbital. This is consistent with the fact that the 8alg orbital is an almost purely nonbonding Fe 3d state, while the 4eZg orbital is slightly bonding wi’& respect to the Cp rings. This difference in the relative Iocalization of the 8aI, and 4ezg orbit& must be taken into consideration when interpreting the pho-
toelectron spectrum of fenocene [IS, 191 on the basis of intensities (see discussion below). Our calculated value of 0.82 for the 4eZg orbital charge fraction is consistent with the square of the value 0.9 1 estimated by Prins 1371 for the coefficient of the Fe 3d atomic orbital on the basis of ESR measurements for the ferricenium ion Fe(CS HS)i.
. . ..’
40;
4s
180 :.
20;
4w
--,5e2,
:-
15 January 1974
CHEhIICAL PHYSICS LETTERS
Volume 24, number 2
The lowest unoccupied
level 5erB (or Se;J
state orbital relaxation tends to be small for most molecules, whereas for ionizing (photoelectron) excitations the relaxation is large. This is true also for the ferrocene molecule. The ground electronic state of ferrocene is the sin: glet 1 A1,(4eQ4 @a#. The one-electron transition 8ar, + 52,, yields excited singlet and triplet states of symmetries * EJ8 and 3E,,, whereas I&,, 3E rgr r E29, and 3E$ multrplets are associated with the 4eZe --f 5e,g transit&. These are all d-d transitions since thk initial-state and final-state orbitals are principally Fe 3dlike. The singlet-singlet transitions, which are spin-allowed, are responsible for the most intense optical absorption observed for ferrocene in the visible part of the spectrum [ 11, 15,16]. Very weak optical absorption in the same spectral range is associated with the spin-forbidden, singlet-triplet excitations [ll, 16]The SCF Xa SW transition-state procedure provides a good approximation to an appropriate average of multiplet energies associated with a given electronic configuration [20] . The calculated 8alg -+ 5era and 4ezg 7 5erg transition energies may therefore be compared wrth averages of the corresponding measured optical absorption energies. These comparisons have been made in table 1 for the optical data measured by Sohn et al. [ 15, 161. Both a straight arithmetic average and a weighted average of the experimental data (weighted according to multiplicity) [20] have been compared with the theoretical orbital transition energies. The quantitative agree-
also cor-
responds principally to an Fe 3d-like orbital, except that it is significantly antibonding with respect to the Cp rings. It is the antibonding partner of the 4elg orbital, which we have shown is responsible for the strongest bonding between the n-Cp electrons and the Fe 3d electrons_ This antibonding character is further reflected by the position of the 5el level relative to the Fe 3d atomic energy Ievei (see Plg. I) and by the orbital charge fractions, which are 0.64 for the Fe sphere, O-24 for the C spheres, 0.11 for the interatomic region, and 0.0 I for the extramolecular region. The remaining empty levels shown in fig. 1 have the following characteristics. The 9alg level corresponds mainly to an Fe 4s-like orbital which is antibonding with respect to the Cp rings. The Sezg level is largely associated with an* -Cp orbital, but with significant Fe 3d antibonding character_ The 7eru level corresponds
r
to a diffuse antibonding Fe 4p-like orbital, and the 4e2,
level belongs to a pure .n* -Cp orbital. We consider next the energies of electronic
excita-
tions in ferrocene. These are calculated in the SCF Xo! SW method by the “transition-state” procedure [20,
221. The transition-state energies, calculated self-consistently for each excitation of interest, automatically include the approximate effects of orbital relaxation usualIy neglected in the application of Koopmans’ theorem to molecular-orbital theory. For internal (optical) excitations, it has been shown [22] that the transition-
Table 1 Comparison of d-d transition energies(3 X 10” cm-‘) calculated by the SCF Xa SW method with experimental optical data for
fenacene in the visible part of the spectrum Multiplet
Experiment a)
Average experimental transition energy
weightedb)‘
arithm.
SCF Xa SW
Orbital
transition energy
transition
at&g a%,
21.8
18.9
19.6
20.4
20.5
8alg
b’%g l&g b3Elg
30.8 24.0 22.4
23.1
24.5
25.2
k2g -
3&g
20.9
a)Refs. [15,16].
‘) Weightedaccording to multiplicity.
+
5e ‘g
%lg
Table 2
izatjon spectrum of ferrocene, as measured by He(I) spectroscopy fl8, 19]_ This has been carried out in table 3, where we compare the orbital ionization potentials calculated by the SCF Xa SW transition-state procedure with the energies of all the bands in the photoelectron spectrum which have been resolved experimentally [l&19]_ Included for comphotoelectron
Comparison of orbital transition energies (G X IO3 cm-‘) calculated by the.SCF Xru SW method with experimental optical charge-transfer energies in the LJVpart of the spectrum Orbital tWsition
Type of
SCF Xa SW transition energy
E?cpesimenC)
transition
6elo - 5elg
L-+ hi
36.5
37.7
%g++%u
hI-+L M-+L L- Iv1
39.2 43.9
41.0
4e2g+
+=2U
6% - 9alg 6elU - 5ezg 5elu + 5elg 3e2,
-+ Selg
6a2u -, Setg
L - LhP
47.1 50.1
L-+&l
53.9
L,-+ hi
55.1 55.5
L 4 1LI
1.5 January 1974
CHEMICAL PHYSICS LETTERS
Volume 24, number 2
are ionization potentials determined in a recent
parison
ab initio SCF LCAO calculation [lo] by taking differences between the total energy of the Ferrocene molecule and the total energies of the ferricenium ion in various electronic configurations. Ionization potentials obtained by applying Koopmans’ theorem to the SCF LCAO orbital energies [ 10) are also included. Some of the photoemission bands correspond to individual OPbitai levels, whereas others correspond to narrow bands of levels. For example. the band whose maximum is at 12.2 eV [I 8] is associated with photoemission from the group of closely spaced leveIs 5el,, 3el,, 3e,, 3eZg, and 6a2u, which we have shown belong primarily to Cp &and orbitals. As mentioned earlier, the level ordering of the highest occupied orbitals 8atg and 4eZg has been the most CORtroversial issue in the electronic structure of ferrocene. The level ordering gal, < 4e2, has been inferred from the photoelectron spectrum [ 18, 191, using the argument that the photoemission peak of greater integrated intensity should be associated with the orbital of greater occupancy- However, this would be true onIy if the spatial localization and nodal character of each of the two orbit& were identical- We have indicated earlier that the essentially nonbonding 8a,,(3d) orbital is more Iocalized within the Fe sphere than is the somewhat bonding 4e2,(3d) orbital. Moreover, the 8alg orbital has a small amount of Fe C-like character, which is allowed by symmetry. It has been well established [29] that the intensity of photoemission from a given orbital level depends critically on the sjze or extent of the orbital and on the number of its nodal surfaces, as a function of incident photon energy or wavelength- These differences in relative spatial localization and nodal character offer a possible explanation of why the 8al, orbital (rather than the 4eZg orbital) can be assigned to the more intense of the first two closely spaced photoemission peaks of ferrocene [i&19]. The orbital ordering 4ezg < Sal, is, of course, essential for interpreting the d-d optical absorption spectrum of ferrocene [15, 161 (cf. table I). This ordering has also been asslimed
42.8 47.5 49.5
51.6
a) Energies of optical absorption peaks, ref.[ 121. b, Some charge transfer because of antibonding Fe 3d content.
ment between theory and experiment is excellent for both averages, providing firm support for the orbital ordering eZg(3d) < a I 9(3d) < e&(3d). The strongest optical absorption in ferrocene occurs in the ultraviolet part of the spectrum [I 2, 13, 161 and may be interpreted largely in terms of charge-transfer excitations. For example, we interpret an absorption edge centered at 37 700 cm-l [ 121 to be associated with the onset of 6e lu (rr-Cp) + 5ele(3d) “Iigand-tometal” (L-+ M) charge-transfer transitions. On the other hand, optical absorption peaks at 41000 and 42800cm-1 [12] are most likely associated with the “metal-to-ligand” (M + L) transitions 8a,,(3d) + +,(lr*-Cp) and 4e&3d) + 4e2,,(n*-‘Cp), respectively. The most intense absorption band has its maximum at 5 1 600 cm-l [ 123 and is probably due to charge-transfer transitions from the band of closely spaced &and-like levels ,Selu(u-Cp), 3ezu(u-Cp), and 6az,(n-Cp) to the Fe-like level Se1 (3d). A summary of our complete interpretation 0 f the W optical spectrum of ferrocene is given in table 2. No attempt has been made to calculate multiplet averages as in table I, but rather to correlate the principal optical absorption peaks 1121 wiih individual (or groups of) orbital transitions. Finally, we can provide antiterpretation of the ion182 .
..‘.
._.
-.‘. _,:
, ‘. .: i.
..^:.:.,:.
_.
._
_.
__
..
.-
‘-
_
Volume 24. number 2
CHEMICAL PHYSICS LETTERS Table 3
Comparison of the ionization potentials (in eV) of ferrocene calculated
by the SCF Xa SW rransition-stare
procedure
and
SCF LCAO method with those measured experimentally He(I) photoelectron spectroscopy Orbit&
SCF XcxSW
Harttee-Fock
transition-state
SCF LCAO
procedure
method
3ezg
11.5 11.6 11.6 11.7
6a2u
11.7
7a1g
12.8
5elu 3e1g 3e2,
Esperiment
10.1”) w5.qb) 6.858’)
7.9 8.5 9.3 9.7
by
(6.88)d)
8.3
(14.4)
7.234
(7.23)
11.1
(I 1.7)
8.715
(8.72)
11.’
(11.9)
9.38
(9.39)
15 January 1974
trast to the results of a recent ab initio SCF LCAO calcuktion [IO] (requiring considerably more computer time), where the calculated ionization potentials are in poor quantitative agreement with experiment (cf. table 3), and where no analysis of optical spectra was provided. Applications of SCF Xor SW method to other organometallic systems, including Zeise’s anion Pt(C2H4)Cl, [26], Ziegler-Natta-type titanium-olefin complexes of catalytic importance [30], and iron porphyrins [3 I ] . will be reported in future publications. One of us (N.R.) is gratefui to the Deutsche Forschungsgemeinschaft for financial support.
References (11.3)
12.2
15.5
(16.0)
11) bi. Rosenblum, Chemistry of the iron group metallocenes (Wiley-Interscience, New York. 1965). [2] D.A. Brown, in: Transition metal chemistry, Vol. 3, ed. R.L. Cnrlin (Dekkcr, dination
f&g
14.2 14.6
2e2u
16.0
2e2
16.1
5a2u
g
New York,
1966).
\ 3 ] C.J. Ballhsusen and H.B. Gray, in: chemistry,
(13.0)
13.6
(13.461
16.4
(16.5)
‘) Ref. [ 10 J, difference of total ene&ies of molecule and ion. b) Ref. [lOI _Koo mans’theorem result. d Ref. [19]. ‘) Ref. 118). in the interpretation
of photoelectron spectra for similar metallocenes based on Mn and Cr [18, 193 _To settle this issue more quantitatively. work is now in progress on calculating the intensities of optical and photoelectron spectra on the basis of the SCF Xa! SW transition-state theory [20] _ In conclusion, we have shown that the SCF Xcu SW method with overIapping spheres is capable of providing an accurate picture of the chemical bonding of ferrocene and a reasonable interpretation of the measured optical and photoelectron spectra. The calculated d-d and charge-transfer transitions are in agree_ment with experiment to a half an electron volt or better (cf. tables 1 and Z), while the ionization potentials have been calculated to an accuracy of approximate!y one electron volt or better (cf. table 3). This is in marked con-
of the coorVol. I,ed. A.E. Mnrtell (Vnn
compounds,
Nostrand-Reinhold, New York, 1971). 141 E.hl. Shustorovich and MI. Dyatkina, DokL Akad. Nauk SSSR 128 (1959) 1234; Zh. Strukt. Khim. 1 (1960) 109. 151 J.P. Dshl and C.J. Ballhausen. Kgl. Danske Videnskab. Selskab blat. Fys. hledd. 33 (1961) No. 5. 161 R.D. Fischer,Theoret. Chim. Acta 1 (1963) 418. [71 A.T. Armstrong, D.G. Carroll and S.P. hlcGlynn, J. Chem. Phys. 47 (1967) 1104. [Sl J.H. Schachtschneider, R. Prins and P. Ros, Inorg. Chim. Acta 1 (1967) 462. [9] 1.H. Hillier and R.hI. Canadine, Discussions Faraday Sot. 47 (1969) 27. [ 101 M. Coutiere, J. Demuynck and A. Veillard, Theoret. Chim. Acts 27 (1972) 281. [ 111 D.R. Scott and R.S. Becker, J. Organometal. Chem. 4 (1965) 409. [ 12) A.T. Armstrong, F. Smith, E. Elder and S.P. McGlynn, I. Chem. Phys. 46 (1967) 4321. [ 131 J-3. Smith and B. Meyer, J. Chem. Phys. 48 (1968) 5436. [ 14 ] P.B. Stephenson and W.E. Winterrowd, J. Chem. Phys. 52 (1970) 3308. [15] Y.S. Sohn, D.N. Hendrickson, j.H. Smith and H.B. Gray, Chem. Phys. Letters 6 (1970) 499. t 161 Y.S. Sohn, D.N. Hendrickson and H.B. Gray, J. Am. Chem. sot. 93 (1971) 3603. [17] R. Prim, Mol. Phys. 19 (19701603. [ 1S] J-W_Rabalais. LO. Werme. T. Bergmark, L. Karlsson, M. Hussain and K. Siegbahn, J. Chem. Phys. 57 (1972) 1185. [ 191 S. Evans, M.L.H. Green, B. Jewitt, A.F. Orchard and C.F.
PygaII, I. Chem. Sot. Faraday II 68 (1972) 1847. 1201 J.C. Slater and K.H. Johnson, Phys. Rev. BS (1972) 844. f83
.., -..
; ‘. .
_.._ ,... i
;.,
..
.,.I
‘.
:: ,
.
-‘, .._ ‘.
..
_,;:.: ,.
._.’
.. _.
,_
:
. ..,
:
.._
:.:
., _ .:
L, .:-
_
.~
y_ .,-
1“
_
:: : :
..
-_ :-‘:
i
”
.
.. .
Volume 24, number 2
CHEMICAL PHYSICS LETTERS
1211 K.H. Johnson and F.C. Smith Jr.. Phys. Rev_ BS (1972) 831. [22] K.H. Johnson in: Advances in q;lantum chemistry, Vol. 7, ed. P--O. LSwdin (Academic Press, New York, 1973) p.143. 1231 R.K. Bahn and A. Haaland, J. Organometal. Chem. 5 (1966) 470. [24] G.J. Palenik, Inorg. Chem. 9 (1970) 2424. 1251 N. RGsch, W.G. Klemperer and K.H. Johnson, Chem. Phys. Letters 23 (1973) 149.
IS January 1974
[26] N. Riisch, R.P. Messmer and K-H. Johnson, I. Am. Chem. Sot.. submitted for publication [27] K.H. Johnson, to be published. (281 K. Schwarz, Phys. Rev. BS (1972) 2466. [29] W.C. Price, A.W. Potts and D-G. Streets, in: Electron spectroscopy, ed. D.A. Shirley (North-Holland, Amsterdam, 1972) p. 187. 1301 N. RBsch and K.H. Johnson, to be published. [3 I ] K.H. Johnson, in: Biomedical physics and biomaterials science, ed. H.E. Stanley (M.I.T. Press, Cambridge, 1972) p. 85.