Molecular orbital electronegativities of transition metal fragments: A MO approach based on the transition operator method

Journal of Molecular THEOCHEM Elsevier

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MOLECULAR ORBITAL ELECTRONEGATIVITIES OF TRANSITION METAL FRAGMENTS: A MO APPROACH BASED ON THE TRANSITION OPERATOR METHOD

M. C. BijHM

Institut fiir Organ&he (W. Germany) P. C. SCHMIDT

Chemie der Universittit

D-6900 Heidelberg

and K. D. SEN

Znstitut fiir Physikalische Chemie, Physikalische Darmstadt, D-61 00 Darmstadt (W. Germany) (Received

Heidelberg,

Chemie III, Technische

Hochschule

27 April 1981)

ABSTRACT The molecular orbital electronegativities x of various transition metal fragments have been investigated by means of the “transition operator (TO) method” within a semiempirical INDO Hamiltonian. The calculated electronegativities x(T0) are discussed with respect to the donor and acceptor properties of the studied complexes. It is found that the values x(T0) can be correlated with experimental and theoretical data concerning the nature of the chemical bond in transition metal derivatives. INTRODUCTION

Pauling’s idea of electronegativity, x, [ 1, 21 was quantified by Mulliken [3,4] and Moffitt [ 51 who defined x as Xj,M

= $(Ij

+ Aj)

(1)

where Ij and Aj can be interpreted as the ionization energy and the electron affinity, respectively, of the valence state, j, considered. The original atomic definition of x has been extended to the orbital picture of atoms and molecular fragments leading to the “orbital electronegativity” [ 6, 71, where j in eqn. (1) is the active orbital. The parameters have become a powerful tool to estimate the nature of the chemical bond (ionic vs. covalent) or to study charge reorganizations in molecules. However, coherent, well-defined experimental or theoretical procedures to determine the ~i,~ values were still missing. In most cases, the values of Ij and Aj in eqn. (1) are obtained by means of extrapolation procedures starting from ground-state ionization energies and electron affinities [ 6-101 . Recently, it has been shown in the framework of density functional theory [ 111 that x can be defined by the negative of the chemical potential Xj,M

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x=_

aE

(2)

( aN > v

Based on Slater’s transition-state concept [13], both expressions for x, eqns. (1) and (2), have been combined within the local potential approximation to calculate electronegativities of atomic systems [ 14, 151 . The LCAO Fock operator analogue of Slater’s transition-state model is the “transition operator (TO) method” [ 161, which makes use of fractional occupation numbers [ 171 within the Hartree-Fock formalism. The TO procedure has been applied in various ab initio studies [ 181 and has been successfully used for the determination of ionization energies in transition metal compounds [ 19-241. According to Mulliken’s definition, eqn. (l), the TO approach can also be used to calculate electronegativities. This application of the TO method has been used for the calculation of group electronegativities of Be, B, C, N and 0 containing molecular fragments with different types of bonding partners [ 251. In the present work this new theoretical procedure is used to calculate the electronegativities of transition metal compounds and fragments in order to study the donor and acceptor properties of the chemical groups out of which larger organometallic systems are composed and to investigate the magnitude of the 3d acceptor capability in the corresponding ionic complexes (e.g. MnO: in KMnO,). The fragment approach for transition metal compounds was developed by Hoffmann and co-workers [26, 271 in the approximate extended Hiickel framework. The aim of the present paper is to give a more quantitative description of the bonding capabilities (metal-to-ligand vs. ligand-to-metal charge transfer) of the various fragments of transition metal compounds. THEORY

From Mulliken’s point of view, the ionization energy 1j and the electron affinity Aj have to be determined in order to obtain the electronegativity &,M , see eqn. (1). Using the transition operator (TO) method [ 16,181, Ij and Aj are calculated in the following way. Within the unrestricted Hartree-Fock (UHF) formalism [ 281 it is assumed that the molecule or the molecular fragment has (M + N) electrons, M electrons with spin (Yand N electrons with spin 0. Furthermore it is assumed that the transition-state Fock operators for the calculation of Ij and Aj are given by FF$ (1) = F(l),

- f
II jTo(2)>

(3)

IIjTo (2)>

(4)

and F:;(l)

= F(l)@ + i < jT0(2)

where F(l),y and F(l)0 are the Fock operators for the (M + N) electron system and is the Coulomb-exchange operator for the active

45

orbitalj. It can be seen from eqns. (3) and (4) that F,?‘: represents the transition Fockian for the ionization process for the electron occupying the orbital j, whereas Fl?p” corresponds to the electron attachment into the orbital j. The occupation number of the active orbital nj is l/2. The index j in eqns. (3) and (4) must not be identical. From the solutions of the oneelectron Schrodinger equations ?T(l)iTO(l)

= e;,O i,TO(l)

one obtains

1:”

and A,?’

s = (Y,p according

to the analogue

(5) of Koopmans’

theorem

[291 p = --ETO J

ATo

(6)

J,a

J

=

-EJ?p”

(7)

Since the TO method is used to calculate the one-electron energies, Qp, relaxation effects for the ionization and attachment processes are taken into account in eqns. (6) and (7) [30]. However, correlation effects are not included. From eqns. (6) and (7) one obtains electronegativities x?O, according to Mulliken’s definition eqn. (1) ,r” = + (q” J,M

+ ATo)

(8)

In the present work the SCF equations (5) are solved by an improved semiempirical INDO framework discussed elsewhere [ 311. It has been shown that for the case of vertical ionization potentials, the accuracy of the data deduced from this new INDO Hamiltonian surpasses that of current ab initio calculations (minimal basis and double-zeta basis) [ 19-241 . Therefore, it is expected that the results of our semiempirical MO approach for xj,M are of reliable quality. For both sets of equations (5), s = (Yand s = 0, different occupation schemes have been used in order to find the active orbital j among the occupied and unoccupied one-particle states which 11s the lowest value of lTo or ATo, respectively. Obviously, an Aufbau principle for the J J occupation numbers cannot be used in the SCF iterations up to convergence. Therefore, a criterion of maximum overlap between the iterated MO’s and the MO’s of the foregoing SCF step has been applied for the computational procedure. RESULTS

In Table 1 the numerical results for the electronegativity XT%, eqn. (8), are given for a representative selection of transition metal spe&es with an unbalanced electron configuration and of well known organometallic fragments. Besides $$, the corresponding electronegativities, x_$, of the widely used Pauling scale are listed. These are given by [ 321 eqn. (9). $?

= 0.336

(x;“M -

0.615)

(9)

1

14.47 12.75 12.22 10.18 8.29 7.59 7.79 7.04

6.52 7.92 7.87 8.66 8.04 7.67 8.81 6.13

Quartet Triplet Doublet Doublet Doublet Doublet Doublet Doublet

Doublet Doublet Doublet Triplet Doublet Doublet Singlet Singlet

VC, CrO, MnO, CUCI, NiCl NiBr Ni(C, H5) Ni(C,H,) Ni(N0) -2.41 0.93 -0.16 0.14 1.39 1.42

Ni 3do, NO 50 Co le(3d,,/3dyz) CP(~), Fe 3d,,/3d,, Fe le(3d,z_yz, 3dxy) Mn 2e(3&,, 3d,,) Mn 3d,a Cr la,(3d,z) Cr 3d,2

1.19 0.29

4.85 5.03 5.22 5.98 -1.19 -3.22 -0.72 -0.87

AlTo

0 2Pn (It,) 0 2Pn (It,) 0 2PT (It,) Cl 3pn Cl 3~0, Ni 3do Br 4pn CP (.rr), Ni 3d,,/3dy, A(+), Ni 3d,,

MO type of the j’th cationic transition MO

Cr 2e(3d,,/3dyz) Bz(n*), Cr 2e(3d,~-,~/3dx,)

0 2PT (It,) 0 2P7r (It,) 0 2PT (It,) Cl 3pn Ni 3do, Cl 3pu Ni 3do Ni 3dy,, CP(~) Ni 3d,, A(n*) N0(2n*), Ni 3dn Co 3d,z, CO(n*) Cp(n*) Fe 2e(3d,,, 3d,,) Mn 2e(3d,,, 3d,,) Mn 3d,2

MO type of the j’th anionic transition MO

m

3.02 2.76 2.71 2.49 0.98 0.52 0.98 0.82 0.48 1.27 1.08 1.26 1.37 1.31 1.46

0.87

9.66 8.89 8.72 8.08 3.55 2.19 3.54

3.09 2.06 4.43 3.86 4.40 4.72 4.55 5.00

3.21

xj,P

m xi,M

; i j g k k

a

I

:

a a a b

Ref

aL. E. Sutton (Ed.), Tables of Interatomic Distances and Configuration in Molecules and Ions, Spec. Publ., The Chemical Society, London, 1958, Vol. 11. bR.D. Willett, J. Chem. Phys., 41 (1964) 2293. CI. Hargittai and J. Tremmel, Coord. Chem. Rev., 18 (1976) 257. dK. S. Krasnov, V. S. Timoshinin, T. G. Danilova and S. V. Khandozhko, Moleculyarnie Postoyanie Neorganicheskich Soedinenii, Leningrad, 1966. eL. Hedberg and K. Hedberg, J. Chem. Phys., 53 (1970) 1228. %e have used the structural parameters of the bis(nmethallyl)nickel complex: R. Uttech and H. Dietrich, Z. Kristallogr. Kristallgeom. Kristallphys. Kristallchem., 122 (1965) 60. gRef. 44. hR. K. Bohn and A. Haaland, J. Organomet. Chem., 5 (1966) 470. ‘A. Almenningen, A. Haaland and K. Wahl, J. Chem. Sot. Chem. Commun., (1968) 1027. iA. F. Berndt and R. E. Marsh, Acta Crystallogr., 16(1963) 118. kB. Rees and P. Coppens, Acta Crystallogr., Sect. B, 29 (1973) 2516.

Co(CC), Fe(C,H,) Fe(CC), Mn(CC), Mn(CC), Cr(CG ), Cr(C, Hb)

IiT’

Multiplicity

Compound

Calculated TO ionization potentials (p), electron affinities (A,p), electronegativities according to Mul!iken (x?$ and Pauling (x,?) as obtained by the semiempirical INDO Hamiltonian. The spin multiplicity of the transition metal fragment is g&en in column 2 arid the MO type of the j’th active oneelectron function determining p and A,m is also given

TABLE

%

47

The geometrical parameters for the calculations were taken from the stable components of the fragments as observed by X-ray investigation or electron diffraction, see the final column of Table 1. This choice of geometry does not correspond to the energy minimum for the fragment considered. However, this arrangement of the atoms appears to be adequate for the calculation of x, since we are interested in the bonding mechanisms of real systems. The results for xjTo in Table 1 will be discussed in the next section. In this section the MO character of the transition state j given in columns 4 and 6 of Table 1 will be considered. For those compounds for which the dominant MO contribution to the orbitalj is not identical for ionization and attachment, pronounced effects of reorganization of the electronic charge distribution are found theoretically, In the case of the nickel halides, the active orbital for the Cl fragment has 93.3% Cl 3~0 character for the ionization process whereas the electron attach, ment leads to a TO wave function with 16.6% Cl 3~0 character, while the predominant contribution is the Ni 3do orbital. In the Br fragment, MOj(lj) is of Br 4~0 type (99.7%) whereas MOj(Aj) has 97.3% Ni 3du character. Similar effects of reorganization are obtained for the half-sandwich fragments Ni(C5H5) and Ni(C3H5). For the cyclopentadienyl (Cp) system, 4.8% Ni 3d character is found for the donor function while the acceptor function is localized by 83.5% at the transition metal centre. For the ally1 fragment, the correspondingvalues are 2.3 and 71.1%, respectively. A schematic display of the active orbitals is shown in Fig. 1. The theoretical result, that the lowest donor function for the ally1 fragment is predominantly of ligand type is also verified by photoelectron spectroscopic investigations on bis(n-allyl)z

G Y

N’i

P-i’i

x

TRANSITION FOR THE

TRANSITION 8

STATE

MO

ATTACHMENT

STATE

MO

FOR THE IONIZATION

Fig. 1. Schematic representation of the j’th transition-state orbitals leading to the cationic and anionic states in the half-sandwich compounds Ni(C,H,) and Ni(C,H,).

48

nickel [ 20,331. The donor orbital of the Ni(N0) fragment is the Ni 3do (= 3d,a) function predominantly (92.6%) localized at the 3d centre; the oneelectron acceptor function is a NOT* orbital with negligible Ni 3d participation (3.8%). The carbonyl complexes [COG and Mn(CO),] belong to the molecular point groups CZV and CaV with a vacancy in the axial position. In the Co fragment (dg system), eight Co 3d electrons fill two low-lying E linear combinations. The lower one is of 3d,/3d, character and is stabilized by the equatorial Con* acceptor functions, the upper degenerate Co 3d set (3d,z - Yz/ 3d,,) is destabilized by the equatorial CJdonors. The unpaired Co 3d electron is found in the strongly destabilized 3d2 orbital. In the d7 manganese complex, 3d2 is also singly occupied while two electrons are always placed in the B2 MO (3d,,) and the degenerate E (3d,/3d,) linear combination which are close in energy. The active transition-state orbital in the cobalt complex for ionization is the lower degenerate 3d linear combination (3d,/3d,,) showing the largest rearrangements and the 3&z MO in the Mn pentacarbonyl fragment. In the case of the attachment process, 3dg is the active transitionstate orbital in both carbonyl systems. Once again significant relaxational modifications are predicted in the two transition-state orbitals. In the Mn complex for example, 57.6% Mn 3d2 character is obtained for the orbital wave function determining the cationic transition state, in the anionic counterpart this value is reduced to 18.5%. The valence orbitals of the tricarbonyl derivatives Fe(C0)3, Mn(C0)3 and Cr(CO), have been discussed in large detail in recent years [ 27, 34-361. A graphical representation of the high-lying MO’s of the M(C0)3 fragment in a pyramidal CSV conformation is displayed in Fig. 2. The five 3d functions

M =

Fig. 2. Schematic symmetry.

representation

Cr,Mn,Fe

of the valence

orbitals

of an M(CO),

fragment

with C,,

49

split into two E linear combinations and into an Al orbital. The la, fragment MO is predominantly of 3dz type, the le orbitals are of 3d,z _,,z and 3d,, character. In the d6 Cr(CO), system only these fragment orbitals are occupied. At higher energy the second degenerate 3d MO set is found; the orbitals have large 3d,/3d, amplitudes and the significant destabilization is the result of the e orbitals of the CO ligands. In the Mn tricarbonyl fragment, one electron in the 2e MO set leads to a doublet ground state; in the iron derivative two unpaired electrons occupying the degenerate 2e linear combination result in a triplet state. As shown in Fig. 2, the two high-lying MO’s have large amplitudes in the direction of the uncomplexed positions allowing efficient coupling to additional ligands. The orientation of the 3d lobes within le and 2e is the result of mixing between 3d,2 -g /3d,, and 3d,/3d,, in both degenerate fragment orbitals; le has a non-vanishing 3d,,/3d,, contribution and 2e contains significant 3d,2 - yz / 3d,, admixtures. The transition-state orbital for the attachment process in every case belongs to the degenerate 2e set. For the ionization process, the lowest To value is the result of an electron being ejected from le in the Fe system. DISCUSSION

In this section the results for the electronegativities, xj,r, given in Table 1 are analyzed. The donor and acceptor properties of the compounds in particular are discussed on the basis of the x values and compared with experimental observations. The largest values for $? are found for the compounds VO, , Cr04, MnO, and CuCl,. The values of xiTp0are in the same range (2.5-3.1) as found earlier for OBr, CF3 and BE’, [ 251. This is to be expected since all these compounds have a deficit of electrons. For example, in the case of V04, three additional electrons are necessary for the formation of the singlet ground-state ion V04 3-*, for Cr04, two additional electrons result in a closedshell system. The calculated electronegativities for the five Ni fragments are much smaller. In the halides NiCl and NiBr x?pO(NiBr) is much smaller than $$? (NiCl) indicating the increased donor capability of Br compared to Cl. As a result of the electron-rich Ni centre, the difference in xi’p” for NiCl and NiBr is more pronounced than in the corresponding compounds with active centres belonging to the first period. For example, for Be fragments the values x?pO To (BeBr) = 1.19 have been found [25]. The calculated (BeCl) = 1.43 and xj,r electronegativities for the two half-sandwich fragments Ni( C5H5) and Ni(C3H5) (x = 0.9) illustrate the predominance of the donor properties. Indeed, both Ni systems are electron-donating groups for polynuclear multipledecker sandwiches [ 37, 381. For Ni(CSH5), these donor properties have been used in semiquantitative MO models for triple-decker complexes [39]. For the Ni series given in Table 1, the strongest donor property is

50

found for Ni(N0). From the small value of ~7: (Ni(N0)) = 0.48, a highly ionic character for Ni(N0) in transition met4 systems is expected. This ionicity is found experimentally for (C, H,)Ni(NO) [ 401 as well as theoretically [41,42]. Ab initio [41] and semiempirical [42] calculations show that for the ground state of CpNi(N0) the ionic VB structure Cp-Ni(NOy is much more pronounced than the covalent structure Cp-Ni(N0). This can be rationalized on the basis of the two xjP To values, xjTp (NiNO) = 0.48 and x$o(Cp) = 1.48. Relative to the Ni fragments, the electronegativities of the carbonyl complexes COG and Mn(CO), show enhanced donor capabilities. This is understandable since the carbonyl ligands are electron donors. The values XT; (Co(CO),) and x,Tp”(Mn(CO),) are slightly less than x1:$’ (CH,) = 1.61 [25] and x,?:(H) = 1.52, indicating an electron transfer to the CH3 group or H atom, respectively, in the carbonyl complexes (metal-to-ligand charge transfer) which is found experimentally [43, 441 as well as theoretically [ 26,45-471. The Mn(CO), and COG fragments are important intermediates in various catalytic hydroformylation reactions [48] with Mn(CO)S L and Co(CO),L catalysts. Different possibilities for the electronic structure of the intermediate complexes are discussed in the literature [ 49, 501, Since the calculated values, xj’p , give quantitative indices for donor or acceptor capabilities, the XT: values’for these intermediate complexes may be helpful in the understanding of the corresponding catalytic reactions. The XT%’values for the three M(C0)3 fragments lie between those of typical acceptor fragments (e.g. V04, Cr04) and those of typical donor systems [e.g. Ni(NO), NiBr] , which suggests that these fragments have donor as well as acceptor properties. The sequence $‘O (Cr(CO),) > x,r” (Mn(CO),) > xT” (Fe(CO),) does not accord with the increasing ionization potential for the 3d atoms [ 511 due to the different filling schemes in the tricarbonyl fragments. The calculated values of x,?:, close to 1.2, for the tricarbonyl series indicate significant covalent character in their bonding to organic 71 fragments [e.g., C,H6, CgH5, C4H6, C(CH,),] as a result of a synergic bonding interaction due to metal-to-ligand and ligand-to-metal charge transfer. It is interesting to compare the xF$) values of Mn(CO), and Ni(N0) since both fragments form complexes with the cyclopentadienyl ligand. From the differences between $p” (Ni(N0)) = 0.48 and x,rg (Mn(C0)3) = 1.37, it follows that a strongly ionic interaction is expected for the Ni(N0) complex (see above) while an increase in covalent coupling should be found in the Mn complex. These different binding mechanisms have been found experimentally by photoelectron spectroscopy [ 21, 41,42, 521. CONCLUSIONS

It has been shown that orbital electronegativities, x, calculated by means of the “transition operator” (TO) method can be used as reactivity indices in

51

transition metal compounds. The differences in the values of xTo can be traced back to differences in metal-to-ligand and ligand-to-metal charge transfer. The parameters xTo can also be correlated with experimental quantities such as vibrational frequencies, NMR shifts and vertical ionization potentials. Furthermore, group electronegativities can be calculated for different coordination modes of organometallic fragments in order to study catalytic activities, kinetic stabilities or estimate stereochemical preferences in complexes with different ligands. ACKNOWLEDGEMENTS

We thank the Stiftung Volkswagenwerk (to M.C.B.) and the Alexander von Humboldt Stiftung for support (to K.D.S.). REFERENCES 1 L. Pauling, J. Am. Chem. Sot., 54 (1932) 3570; L. Pauling and D. M. Yost, Proc. Natl. Acad. Sci. USA, 14 (1932) 414. 2 L. Pauling, The Nature of the Chemical Bond, Cornell University Press, Ithaca, New York, 1960. 3 R. S. Mulliken, J. Chem. Phys., 2 (1934) 782; J. Chem. Phys., 3 (1935) 573. 4 R. S. Muihken, J. Chem. Phys., 46 (1949) 497. 5 W. Moffitt, Proc. R. Sot. London, Ser. A, 202 (1950) 534 and 548. 6 J. Hinze, M. A. Whitehead and H. H. Jaffe, J. Am. Chem. Sot., 85 (1963) 148; J. Hinze and H. H. Jaffe, J. Phys. Chem., 67 (1963) 1501. 7 J. Hinze, Top. Cur-r. Chem., 2 (1967) 448. 8 R. P. Iczkowski and J. L. Margrave, J. Am. Chem. Sot., 83 (1961) 3547. 9 R. Ferreira, Trans. Faraday Sot., 59 (1963) 1064; R. Ferreira, Adv. Chem. Phys., 13 (1967) 54. 10 J. E. Huheey, J. Phys. Chem., 69 (1965) 3284; ibid, 70 (1966) 2086. 11 P. Hohenberg and W. Kohn, Phys. Rev. B, 136 (1964) 864. 12 R. G. Parr, R. A. Donnelly, M. Levy and E. Palke, J. Chem. Phys., 68 (1978) 3801. 13 J. C. Slater, J. B. Mann, T. M. Wilson and J. H. Wood, Phys. Rev., 184 (1969) 672; J. C. Slater, Adv. Quantum Chem., 6 (1972) 1. 14 L. J. Bartolotti, S. R. Gadre and R. G. Parr, J. Am. Chem. Sot., 102 (1980) 2945. 15 K. D. Sen, P. C. Schmidt and A. Weiss, Theor. Chim. Acta, 58 (1980) 69. 16 0. Goscinski, B. T. Pickup and G. Purvis, Chem. Phys. Lett., 22 (1973) 167. 17 S. F. Abdulnur, J. Linderberg, Y. Ghrn and P. W. Thulstrup, Phys. Rev. A, 6 (1972) 889. 18 0. Goscinski, M. Hehenberger, B. Roosand P. Siegbahn, Chem. Phys. Lett., 33 (1975) 427; M. Hehenberger, Chem. Phys. Lett., 46 (1977) 117; D. Firsht and B. T. Pickup, Chem. Phys. Lett., 56 (1978) 295. 19 M. C. Bohm, R. Gleiter, F. Delgado-Pena and D. 0. Cowan, Inorg. Chem., 19 (1980) 1081. 20 M. C. Bohm, R. Gleiter and C. D. Batich, Helv. Chim. Acta, 63 (1980) 990. 21 M. C. BGhm and R. Gleiter, Comput. Chem., 1 (1980) 407. 22 M. C. Bijhm and R. Gleiter, Z. Naturforsch., Teil B, 35 (1980) 1028. 23 M. C. Bohm, J. Daub, R. Gleiter, P. Hofmann, M. F. Lappert and K. CfeIe, Chem. Ber., 113 (1980) 3629. 24 M. C. Bohm and R. Gleiter, Chem. Ber., 113 (1980) 3647.

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