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A study of bonding effect between the metal—metal in the transition metal cluster
Journal of Molecular Structure (Theochem), 151 (1987) 19-27 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands
A STUDY OF BONDING EFFECT BETWEEN THE TRANSITION METAL CLUSTER
THE METAL-METAL
IN
LI JUNQIAN Department
of Chemistry, Fuzhou
University, Fujian (China)
CHENG WENDAN Fujian Institute of Research on the Structure of Matter, Academia Sinica, Fujian (China) (Received 18 August 1986)
ABSTRACT The reduced Mulliken overlap population P,, 1was found to be a suitable indicator of the bonding strength between the metal-metal in the transition metal cluster compound in this paper. It was found that Pmm 1 can be the concentrated expression of the relation between the bonding strength and factors, such as the d-electron number of the metal atom, the nature of the bridge group and the ligand, according to the EHMO calculations and experimental results of the electron absorption spectra for compounds of the transition metal cluster. INTRODUCTION
The study of bonding effects between the metal-metal in the transition metal cluster compounds has been an active and important subject for more than fifteen years. Recently, some authors [l-4] have shown that the bonding strength depends on the electron distribution between the metal-metal, and that this interaction of the metal-metal is affected by the distance of the inter-atoms, the d-electron number of the metal atom and the nature of the bridge group and the ligand. With the definition of the Mulliken population, the reduced overlap population (ROP) is the concentrated expression of the latter factors. Increase in the ROP corresponds to charge flowing into the interatomic region, and is indicative of improved bonding or weakened repulsion. Some typical compounds of the transitional metal cluster were calculated in terms of the EHMO’s and their electron absorption spectra were measured. It was found that the metal-metal ROP adequately describes the relationship between the bonding effect and the bond length, ligand and bridge radical electronegativity as well as the d-electron number of the metal atom, and can correspond to the transitional energies of the transition metal d-electron as seen from the agreement between the theoretical and experimental results in spite of it being a simple model at present.
0166-1280/87/$03.50
o 1987 Elsevier Science Publishers B.V.
20 THEROPANDBONDINGEFFECTBETWEENMETAL-METALINTHECLUSTER COMPOUND From the simple molecular orbital theory, occupied molecular orbtials are expressed
the sum of energies over all the
where J/, is an (Y MO and n, is the electron number on the (YMO. In the EHMO’s the reduced energy matrix element (REME) em*’ is written
where Hij = b$i IHl$ji>and both di and $j are the metal atomic orbit&. Following the Wolfsherg-Helmholz approximation, the REME emm’ can be written e mm' -
C nacaiC&j
(3)
&I.a
If the average 6 is used instead of (Hii + Hjj), the emm’ becomes (4) The metal-metal
ROP P,,*
can be partitioned
into
where cw,-MO is composed of the metal atomic orbitals that contribute predominantly to the occupied MO and q-MO is composed of all the AO’s in the transition metal cluster compound. If Ca, iI, C’ylj, in the ROP partition PI can be regarded as constant C in the cluster compound with the same metal atoms, then PI only change with the overlap integral Si,jl. The term Cali,. C&, which represents the charge distribution between the two metal atoms in a,-MO, are influenced by the nature of the metal, bridge and ligand atoms. If Ca, i,. CL, j2 gives a greater contribution to the partition P2 than Sil j2 , it will be probable that an unusual relation between the bond length and bonding strength will exist. The metal-metal ROP, Pm,,,‘, in some cluster compounds have been calculated by the improved EHMO program [ 51 and listed in Table 1. It is shown that the indicator Pm, 1 of the metal bonding effect in the cluster compounds can correspond to the REME emm’ and the magnetic properties, but the bond length is not so. We discuss the relation between ROP and metal-metal bonding factors individually in the following.
21 TABLE 1 P mm No.
andemmof
some clusters emm (eV)
Cluster
R mm (a
rmm (A)
pmm
1
Mo,G,(SG,NC,H,&
2.562
2.58
0.1077
-2.4293
2
Mo,S,G,(SG,NC,H,),
2.804
2.58
0.1524
-2.8369
3
(Cu( CH,COO),H,O),
2.640
2.34
0.0364
-0.6227
(Cr(CH,COO),H,O), (Mo10J4+ (Mo,S,Y+ (Mo,OCl,)‘+ (Mo,O,Cl$+ (Mo,S,CX,)~+ MdCG),, RedCO),,
2.640 2.468 2.813 2.560 2.560 2.617 2.923 3.020
2.34 2.58 2.58 2.58 2.58 2.58 2.34 2.56
0.5700 0.3151 0.1612 0.3411 0.1536 0.1695 0.1819 0.1033
-9.8056 -8.5211 -3.9279 -9.4631 -3.8668 -4.0102 -4.4150 -1.4435
4 5 6 7 8 9 10 11
Magnetism Diamagnetism (x = 1.54 x 10-a cgs) Diamagnetism (x = 1.18 x lo-* cgs) Paramagnetism (p = 1.413 M) Diamagnetism As above As above As above As above As above As above As above
THE SMALLER ELECTRONEGATIVE DIFFERENCE BETWEEN THE METAL AND BRIDGE ATOM, THE GREATER ROP
Clusters 1 and 2 differ only in the bridge radical [6]. From their diamagnetic properties [7] and the REME emm’ in Table 1, it is found that the MO-MO bond is stronger in cluster 2 than in cluster 1, although the MO-MO distance is longer in cluster 2 than in cluster 1. The reasons for the unusual relationship between the bond strength and bond length are why C,* i,. C%jz gives a greater contribution to the partition P2 than the overlap intergral than si2j,9 and why the partition PI gives a smaller contribution to the P,,f the partition P2 in formula (5). As a result, the metal-metal ROP variations will follow Pz. If Ca, i2.Ca2j2 attempts to give a large contribution to the ROP, then C!,*i, . C& must have a large value in the bonding MO. To meet this condition, the electronegative differences (ED) between the metal and bridge atom have to be as small as possible. Generally, the bridge atom electronegativity is larger than the metal’s, and the more electronegative atom has a lower energy AO. When the metal atomic orbital and bridge one interact, the lower energy orbital mixes with the higher energy one in a bonding way while the higher energy orbital mixes with the lower energy one in an antibonding way. If the ED is small between the metal and bridge atom, then the orbital energy difference will be small also. This means that the metal A0 can give a greater contribution to the bonding MO, and a smaller contribution to the antibonding MO in the small ED than in the large ED. These conclusions are proved by the calculated results. The bonding effect changes with the partition ROP PO because P, gives the greatest contribution to the ROP Pm,1 . P, in Table 2 should belong to
22 TABLE 2 Metal-metal
reduced overlap population
ROP
PO
p,
PS
P mm
Cluster 1 Cluster 2
0.1000 0.1502
0.0032 0.0071
0.0046 0.0035
0.1077 0.1524
0.101 0
2
I
I
I
I
4
6
8
IO
I
-emm (eV)
Fig. 1. The relation between P,,(R,,)
and e,,.
P1 in eqn. (5). The sulphur atom electronegativity (2.58) is closer to the molybdenum’s (2.16) than the oxygen atom electronegativity (3.14). Therefore, the MO-MO bond is stronger in cluster 2 than in cluster 1 according to the results in Table 1. It still remains that the ED influences the trend of the bonding effect for the three metal atom cluster compounds 5-9 [8-111. (See Table 1 and Fig. 1.) THE METAL-METAL
ROP RELATED TO THE d-ELECTRONIC
NUMBER
Cluster compound 3 has the same conformation as cluster compound 4 [12, 131. It seems that the metal-metal bond strength in compound 3 is similar to that in compound 4 by the numerical values of the bond length R mm’ and the covalence radii addivity rmm1 in Table 1. In fact, the Cu-Cu bond strength in compound 3 is far weaker than the Cr-Cr bond strength in compound 4 [ 141. The reason why the Cu-Cu bond strength is different from the Cr-Cr bond strength in compound 4 is that the Cu ion has more d electrons in compound 3, so that the d-electron of the Cu ion can occupy the antibonding MO. Either the overlap intergral Sij or charge distribution CaiCaj is negative in the antibonding MO. As a result, the metal-metal ROP
23
reduces when it sums to all the occupied metal-metal bond strength becomes weak. THE METAL-METAL
MO’s in compound
3, and the
ROP RELATED TO THE LIGAND RADICAL
The observed diamagnetism of MIJ~(CO),~ and Rez(CO)lo [12] without bridging carbonyl groups is direct evidence that the metal-metal bonds are present, although the differences between the distance R,, and the coof the metal-metal are very large in these comvalence radii addivity r,, pounds. The existence of the M-M bonds are explained with difficulty by the classical valence bond theory, but we will be convinced of their existence by the Mulliken population analysis. The d-pn bonding orbitals between the metal and carbonyl groups from each fragment can be made to be a symmetry adapted linear combination with the other one in compounds 10 and 11. There are large charge distributions in the metal-metal region. The metal-metal ROP P,,‘, which is an indicator of the bond strength, are still large even though the interatomic orbital overlap may be small. THE CORRESPONDING RELATION BETWEEN THE METAL-METAL THE ELECTRON ABSORPTION SPECTRA
ROP AND
It is known that electronic absorption spectra can give information about the d-d electronic transition and electronic charge transference. The spectral measurement of the d-d electron transition gives the extent of the metalmetal interaction. It is known that both the experimental results and theoretical analyses are proved in the transition metal cluster compounds. Table 3 gives the MO values of the neighbourhood frontier orbitals in (Mo204C14(H20)2)2- and cis-(Mo204(SCN)$ [15, 161. It will be seen from this that the d orbitals of the molybdenum atom are predominant in this region, and they mostly contribute to the metal-metal bond. Therefore, the MO of the neighbourhood frontier orbtials determines the properties of the d-d transition in the electron absorption spectrum. The metal-metal interaction in the cluster compounds without the bridge groups and IT bonds can be simply treated in terms of the method developed [17]. If each metal atom uses six valence orbitals to form metal-ligand bonds, then three d orbitals are left to form the metal-metal bonds with the other one for core conformation (1). -'
\io,X,i / /I
1\y/h;02
The homonuclear
(x, Y = 0, S)
dimetal
$i = Ci(@i, +, &,), i = 1, 2, 3
(1)
core MO is written
(6)
24 TABLE 3 MO and energy level of two Mo( V) dimeric complex Complex
MO
Wo,O,CW,O),Y-
ag
-13.04 -12.67a -12.31* -12.04 -11.75 -11.62 -11.54
4 a, %
bu
b,
bu cis-( Mo,O,( SCN)J4-
Energy (eV)
a, b, aa a, a2 b, b,
-8.23 --8.13* -7.92a -7.75 -7.50 -7.45 -7.43
Main component
of the MO in frontier region
xy( 0.367) xz(yz)( 0.150) xz(xy)( 0.532) xz(yz)( 0.684) xz(yz)( 0.490) xz(yz)( 0.430) xy( 0.71) xy( 0.472) x2(0.155) x2(0.385) x2( 0.344) x2(0.357) ~~(0.380) XY(O.599)
og(O.138) O,n(O.l37) op(o.319) O;( 0.225) Of( 0.269) Or(O.148) Og( 0.203)
@( 0.144) q(O.269) a( 0.318)
yz(O.155) yz(O.385) y.z(O.344) yz(O.357) ~~(0.380)
Oi( 0.151) Oj;( 0.343) Ot(0.277) Ol( 0.241) 0,“(0.261)
Og(0.391) q(0.395) og( 0.249)
*HOMO or LUMO.
The energy levels, Ei, ET, of the homonuclear core MOs, $i, JIT, are written E.=Q t
+
l+si'
Pi
E*=a-bi i
i=LW
l_siy
and the total core MO energy difference AE are expressed AE = ~ (ET -Ei) $._= 1
x
t i=l
(2a - 2Ei) =E,,’
(8)
where OIi,/Ii, Si, are individually called an atomic integral (Coulomb integral), resonance integral and overlap integral, respectively. Equation (8) shows that AE approachs the metal bonding energy Em,‘. If the average AEi is used instead of AEi in eqn. (8), the calculated AEi in the core MO method approachs the metal-metal reduced energy emm’ in the EHMO’s. It has been found [15, 181 that the core (Mo204)*+ played an important role in determining electronic spectra of the di-p-oxo-di-Mo compounds, and proved that the d-d transition absorption spectra [ 19, 201 related to the level difference (E” -- Ei) of the MO in dimeric compounds. Therefore, the data from the electron spectra measurement can indicate the trends between the metalmetal bonding interaction in the cluster compounds. The above method must be improved for the dimeric compounds with the 71 bonds or bridge groups. Such as conformaton (l), the double bridge dimetal compound, it may be that the two monomeric metal compounds link together by the bridge groups. According to the classical electrostatic
25
interaction model, the interaction energy between the charge 2, atom M and the charge 2, at the atom x or y is written
at the metal
I.7= %m:
(9)
in each monomeric metal compound. It is understood that the charge of atom x is perturbed in the interaction of the two monomeric metal compounds and its charge shift AZ,,, then formula (9) is expressed as v’
=
'&(zb
+
Rmb
A&J = (&II + A&n)&, = zidb Rmb Rmb
It is assumed that the value A(Z,Z,) and the distance Rmb are unchanged in formula (10). It shows that the metal atomic charge is changed from 2, to Zk, as the dimeric compound with the bridge groups is formed. The potential matrix element depends only on the charge 2; of the metal atom when the compound conformation is fixed. Therefore, a single electronic orbital energy is Ej = ($#qJ/j>
= czh,
(11)
The parameter 2; (or f) is regulated for the dimeric compounds of core conformation (l),according to the data of Table 4 from the electronic spectra TABLE 4 The experimental data and calculated value of the UV spectra for some P( 0) or P(S) two metal atomic cluster Cluster
R mm (A)
Spectra lines (nm)
(QH),[Mo,O,(C,O,),(H,O),l (PyW~ lMo,O,(C,O,),(H,O), 1 Na, Dfo,O,Wc~s), 1
492
Na,[Mo,O,(S-hit),]
2.560 2.565 2.569 2.552
[Mo,O,( R-pdta), I*-
2.533
Na, Pfo,O,S,(S-CYS), I
2.820 2.820
Na, [Mo,O,S,(S-hit),]
Na,P%O,S,(EDTA)l Na, lMo,W,(R-pdta),
1
[Mo,O,S(R-pdta),]‘[Mo,O,S(S-cys), I’[Mo,O,S(S-hit),]‘-
2.800 2.810 2.656
476 474 (478 481 (472
400 394 383 400 387 393
468 451 (469 468 476 (469
380 365 387 347 350 381
446 465 463 (463
387
303 303 310 303 300)a 298 290)8
311
277 276 280)a 279 279 270)a
318 328 313 321
285 283 280)a
298 321 308
aThe calculated value of ref. 21. _
26 TABLE 5 Theoretical value of metal bond strength of some clusters Cluster
R mm (A)
Ef - Ei (nm)
(QH),[Mo,O,(C,O,),(H,0), 1 (P,H), IMo,O,(C,O,),(H,O), 1 Na, [Mo,G,(S-cys), 1
2.560 2.565 2.576 2.552 2.533 2.820 2.820 2.800 2.810
478 478 478 476 472 469 469 469 469
Na,[Mo,O,(s-hit),] [ Mo,O,(R-pdta), I’Na, [Mo,G,S,(S-cys), I Na,[Mo,O,S,(S-hit),] N%[Mo,G,S,(EDTA)I Na, [Mo,G,S,(R-pdta),
1
300 300 300 300 290 280 280 270 270
AEi (eV) 1243 1243 1243 1243 1168 1116 1116 1033 1033
2.559 2.559 2.559 2.559 2.639 2.711 2.711 2.790 2.790
TABLE 6 A Ei and EHMO calculated values No.
Cluster
R mm (A)
pmm
1 2 3 4 5 6
[Mo,G,(S-cys), I” [M~,G,S,(S-~Y~),I’MozG,(SG,NC,H,& Mo,G,S,(SG,NC,H,), (Mo,G.J+ (Mo,G,S,)”
2.576 2.820 2.562 2.804 2.550 2.814
0.1462 0.1632 0.1077 0.1524 0.1721 0.2172
e mm (eV -2.7023 -2.7482 -2.4293 -2.8639 -4.8534 -5.4573
measurement
with cc(O) and p(S) dimeric metal compounds,
x=y=o, x = 0, y = s, x=y=s,
f = 1.8; { = 1.7; 5 = 1.6.
AEi (eV) 2.559 2.711 2.559 2.790 2.559 2.790
and listed [21] :
When these { values are regarded as metal atomic charge, we can use eqn. (8) to calculate L??i for the dimeric compounds with the bond or bridge groups. The level difference (Ei* - Ei) and the average AEi are obtained using& parameter 5, given in Table 5 [21]. Table 6 shows that the metal average AEi from formula (8) in the core model corresponds to both the ROP Pmm and the REME emm from the EHMO’s in the dimeric metal compounds. It may well be that AEi is also an indicator for the metal-metal bonding strength. ACKNOWLEDGEMENT
The authors gratefully acknowledge encouraging discussion on their work by Professor Q.-E. Zhang, director of the Chemical Department, Xia Men University, Fujian.
27 REFERENCES 1 Boon Keng Teo, M. B. Haii, F. Fenske and L. F. Dahl, Inorg. Chem., 14 (1975) 3103. 2 R. H. Summerville and R. Hoffmann, J. Am. Chem. Sot., 98 (1976) 7240. 3 R. Mason and D. M. P. Mingos, J. Organomet. Chem., 50 (1973) 53. 4 B. E. Bursten, F. A. Cotton, M. B. Hail and R. C. Najjar, Inorg. Chem., 21 (1980) 302. 5 Liao Daiwei, Zhou Taijin and Wang Yingui, KIA DA KE JI, 2 (1983) 7. 6 M. G. B. Drew and A. Kay, J. Chem. Sot. A, (1971) 1851. 7 Liu Hanqin, Hong Maochun, Jiang Fengying, Yang Wenhuo and Zhan Kun, J. Struct. Chem., 2 (1983) 1. 8 A. Bino, F. A. Cotton and Z. Dori, J. Am. Chem. Sot., 100 (1978) 5252. 9P. J. Vergamini, H. Vahrenkamp, L. F. Dahl, J. Am. Chem. Sot., 93 (1971) 6237. 10 Avi Bino, F. A. Cotton and Zvi Dori, Inorg. Chem. Acta, 33 (1979) L133. 11 Huang Jinling, Shang Maoyu, Huang Jianguan, Zhuang Honghui, Lu Shaofang and Lu Jisxi, J. Struct. Chem., 1(1982) 1. 12 L. F. Dahl and R. E. Rundle, Acta Crystallogr., 16 (1963) 419. 13 J. N. Van Niekerk, F. R. L. Schoening and J. F. De wet, Acta Crystallogr., 6 (1953) 501. 14 J. Lewis, Pure Appl. Chem., 10 (1965) 11. 15 B. J. Trzebiatowska, M. F. Rudolf, L. Natkaniec and H. Sabat, Inorg. Chem., 13 (1974) 617. 16 Li Junqian, Cheng Wendan and Wang Yingui, J. Struct. Chem., to be publsihed. 17 F. A. Cotton and T. E. Haas, Inorg. Chem., 3 (1964) 10. 18 D. H. Brown, P. G. Perkinsand J. T. Stewart, J. Chem. Sot. Dalton Trans., (1972) 1105. 19A. Muller, R. Jostes, W. Jaegermann and G. Bhattacharyya, Inorg. Chem. Acta, 41 (1980) 259. 20 Li Junqian, Zheng An and Huang Jinling, Mol. Sci. Chem. Invest., 2 (1984) 183. 21 Li Junqian and Yang Rong Sheng, J. Fuzhou Univ., 4 (1985) 84.
A STUDY OF BONDING EFFECT BETWEEN THE TRANSITION METAL CLUSTER
THE METAL-METAL
IN
LI JUNQIAN Department
of Chemistry, Fuzhou
University, Fujian (China)
CHENG WENDAN Fujian Institute of Research on the Structure of Matter, Academia Sinica, Fujian (China) (Received 18 August 1986)
ABSTRACT The reduced Mulliken overlap population P,, 1was found to be a suitable indicator of the bonding strength between the metal-metal in the transition metal cluster compound in this paper. It was found that Pmm 1 can be the concentrated expression of the relation between the bonding strength and factors, such as the d-electron number of the metal atom, the nature of the bridge group and the ligand, according to the EHMO calculations and experimental results of the electron absorption spectra for compounds of the transition metal cluster. INTRODUCTION
The study of bonding effects between the metal-metal in the transition metal cluster compounds has been an active and important subject for more than fifteen years. Recently, some authors [l-4] have shown that the bonding strength depends on the electron distribution between the metal-metal, and that this interaction of the metal-metal is affected by the distance of the inter-atoms, the d-electron number of the metal atom and the nature of the bridge group and the ligand. With the definition of the Mulliken population, the reduced overlap population (ROP) is the concentrated expression of the latter factors. Increase in the ROP corresponds to charge flowing into the interatomic region, and is indicative of improved bonding or weakened repulsion. Some typical compounds of the transitional metal cluster were calculated in terms of the EHMO’s and their electron absorption spectra were measured. It was found that the metal-metal ROP adequately describes the relationship between the bonding effect and the bond length, ligand and bridge radical electronegativity as well as the d-electron number of the metal atom, and can correspond to the transitional energies of the transition metal d-electron as seen from the agreement between the theoretical and experimental results in spite of it being a simple model at present.
0166-1280/87/$03.50
o 1987 Elsevier Science Publishers B.V.
20 THEROPANDBONDINGEFFECTBETWEENMETAL-METALINTHECLUSTER COMPOUND From the simple molecular orbital theory, occupied molecular orbtials are expressed
the sum of energies over all the
where J/, is an (Y MO and n, is the electron number on the (YMO. In the EHMO’s the reduced energy matrix element (REME) em*’ is written
where Hij = b$i IHl$ji>and both di and $j are the metal atomic orbit&. Following the Wolfsherg-Helmholz approximation, the REME emm’ can be written e mm' -
C nacaiC&j
(3)
&I.a
If the average 6 is used instead of (Hii + Hjj), the emm’ becomes (4) The metal-metal
ROP P,,*
can be partitioned
into
where cw,-MO is composed of the metal atomic orbitals that contribute predominantly to the occupied MO and q-MO is composed of all the AO’s in the transition metal cluster compound. If Ca, iI, C’ylj, in the ROP partition PI can be regarded as constant C in the cluster compound with the same metal atoms, then PI only change with the overlap integral Si,jl. The term Cali,. C&, which represents the charge distribution between the two metal atoms in a,-MO, are influenced by the nature of the metal, bridge and ligand atoms. If Ca, i,. CL, j2 gives a greater contribution to the partition P2 than Sil j2 , it will be probable that an unusual relation between the bond length and bonding strength will exist. The metal-metal ROP, Pm,,,‘, in some cluster compounds have been calculated by the improved EHMO program [ 51 and listed in Table 1. It is shown that the indicator Pm, 1 of the metal bonding effect in the cluster compounds can correspond to the REME emm’ and the magnetic properties, but the bond length is not so. We discuss the relation between ROP and metal-metal bonding factors individually in the following.
21 TABLE 1 P mm No.
andemmof
some clusters emm (eV)
Cluster
R mm (a
rmm (A)
pmm
1
Mo,G,(SG,NC,H,&
2.562
2.58
0.1077
-2.4293
2
Mo,S,G,(SG,NC,H,),
2.804
2.58
0.1524
-2.8369
3
(Cu( CH,COO),H,O),
2.640
2.34
0.0364
-0.6227
(Cr(CH,COO),H,O), (Mo10J4+ (Mo,S,Y+ (Mo,OCl,)‘+ (Mo,O,Cl$+ (Mo,S,CX,)~+ MdCG),, RedCO),,
2.640 2.468 2.813 2.560 2.560 2.617 2.923 3.020
2.34 2.58 2.58 2.58 2.58 2.58 2.34 2.56
0.5700 0.3151 0.1612 0.3411 0.1536 0.1695 0.1819 0.1033
-9.8056 -8.5211 -3.9279 -9.4631 -3.8668 -4.0102 -4.4150 -1.4435
4 5 6 7 8 9 10 11
Magnetism Diamagnetism (x = 1.54 x 10-a cgs) Diamagnetism (x = 1.18 x lo-* cgs) Paramagnetism (p = 1.413 M) Diamagnetism As above As above As above As above As above As above As above
THE SMALLER ELECTRONEGATIVE DIFFERENCE BETWEEN THE METAL AND BRIDGE ATOM, THE GREATER ROP
Clusters 1 and 2 differ only in the bridge radical [6]. From their diamagnetic properties [7] and the REME emm’ in Table 1, it is found that the MO-MO bond is stronger in cluster 2 than in cluster 1, although the MO-MO distance is longer in cluster 2 than in cluster 1. The reasons for the unusual relationship between the bond strength and bond length are why C,* i,. C%jz gives a greater contribution to the partition P2 than the overlap intergral than si2j,9 and why the partition PI gives a smaller contribution to the P,,f the partition P2 in formula (5). As a result, the metal-metal ROP variations will follow Pz. If Ca, i2.Ca2j2 attempts to give a large contribution to the ROP, then C!,*i, . C& must have a large value in the bonding MO. To meet this condition, the electronegative differences (ED) between the metal and bridge atom have to be as small as possible. Generally, the bridge atom electronegativity is larger than the metal’s, and the more electronegative atom has a lower energy AO. When the metal atomic orbital and bridge one interact, the lower energy orbital mixes with the higher energy one in a bonding way while the higher energy orbital mixes with the lower energy one in an antibonding way. If the ED is small between the metal and bridge atom, then the orbital energy difference will be small also. This means that the metal A0 can give a greater contribution to the bonding MO, and a smaller contribution to the antibonding MO in the small ED than in the large ED. These conclusions are proved by the calculated results. The bonding effect changes with the partition ROP PO because P, gives the greatest contribution to the ROP Pm,1 . P, in Table 2 should belong to
22 TABLE 2 Metal-metal
reduced overlap population
ROP
PO
p,
PS
P mm
Cluster 1 Cluster 2
0.1000 0.1502
0.0032 0.0071
0.0046 0.0035
0.1077 0.1524
0.101 0
2
I
I
I
I
4
6
8
IO
I
-emm (eV)
Fig. 1. The relation between P,,(R,,)
and e,,.
P1 in eqn. (5). The sulphur atom electronegativity (2.58) is closer to the molybdenum’s (2.16) than the oxygen atom electronegativity (3.14). Therefore, the MO-MO bond is stronger in cluster 2 than in cluster 1 according to the results in Table 1. It still remains that the ED influences the trend of the bonding effect for the three metal atom cluster compounds 5-9 [8-111. (See Table 1 and Fig. 1.) THE METAL-METAL
ROP RELATED TO THE d-ELECTRONIC
NUMBER
Cluster compound 3 has the same conformation as cluster compound 4 [12, 131. It seems that the metal-metal bond strength in compound 3 is similar to that in compound 4 by the numerical values of the bond length R mm’ and the covalence radii addivity rmm1 in Table 1. In fact, the Cu-Cu bond strength in compound 3 is far weaker than the Cr-Cr bond strength in compound 4 [ 141. The reason why the Cu-Cu bond strength is different from the Cr-Cr bond strength in compound 4 is that the Cu ion has more d electrons in compound 3, so that the d-electron of the Cu ion can occupy the antibonding MO. Either the overlap intergral Sij or charge distribution CaiCaj is negative in the antibonding MO. As a result, the metal-metal ROP
23
reduces when it sums to all the occupied metal-metal bond strength becomes weak. THE METAL-METAL
MO’s in compound
3, and the
ROP RELATED TO THE LIGAND RADICAL
The observed diamagnetism of MIJ~(CO),~ and Rez(CO)lo [12] without bridging carbonyl groups is direct evidence that the metal-metal bonds are present, although the differences between the distance R,, and the coof the metal-metal are very large in these comvalence radii addivity r,, pounds. The existence of the M-M bonds are explained with difficulty by the classical valence bond theory, but we will be convinced of their existence by the Mulliken population analysis. The d-pn bonding orbitals between the metal and carbonyl groups from each fragment can be made to be a symmetry adapted linear combination with the other one in compounds 10 and 11. There are large charge distributions in the metal-metal region. The metal-metal ROP P,,‘, which is an indicator of the bond strength, are still large even though the interatomic orbital overlap may be small. THE CORRESPONDING RELATION BETWEEN THE METAL-METAL THE ELECTRON ABSORPTION SPECTRA
ROP AND
It is known that electronic absorption spectra can give information about the d-d electronic transition and electronic charge transference. The spectral measurement of the d-d electron transition gives the extent of the metalmetal interaction. It is known that both the experimental results and theoretical analyses are proved in the transition metal cluster compounds. Table 3 gives the MO values of the neighbourhood frontier orbitals in (Mo204C14(H20)2)2- and cis-(Mo204(SCN)$ [15, 161. It will be seen from this that the d orbitals of the molybdenum atom are predominant in this region, and they mostly contribute to the metal-metal bond. Therefore, the MO of the neighbourhood frontier orbtials determines the properties of the d-d transition in the electron absorption spectrum. The metal-metal interaction in the cluster compounds without the bridge groups and IT bonds can be simply treated in terms of the method developed [17]. If each metal atom uses six valence orbitals to form metal-ligand bonds, then three d orbitals are left to form the metal-metal bonds with the other one for core conformation (1). -'
\io,X,i / /I
1\y/h;02
The homonuclear
(x, Y = 0, S)
dimetal
$i = Ci(@i, +, &,), i = 1, 2, 3
(1)
core MO is written
(6)
24 TABLE 3 MO and energy level of two Mo( V) dimeric complex Complex
MO
Wo,O,CW,O),Y-
ag
-13.04 -12.67a -12.31* -12.04 -11.75 -11.62 -11.54
4 a, %
bu
b,
bu cis-( Mo,O,( SCN)J4-
Energy (eV)
a, b, aa a, a2 b, b,
-8.23 --8.13* -7.92a -7.75 -7.50 -7.45 -7.43
Main component
of the MO in frontier region
xy( 0.367) xz(yz)( 0.150) xz(xy)( 0.532) xz(yz)( 0.684) xz(yz)( 0.490) xz(yz)( 0.430) xy( 0.71) xy( 0.472) x2(0.155) x2(0.385) x2( 0.344) x2(0.357) ~~(0.380) XY(O.599)
og(O.138) O,n(O.l37) op(o.319) O;( 0.225) Of( 0.269) Or(O.148) Og( 0.203)
@( 0.144) q(O.269) a( 0.318)
yz(O.155) yz(O.385) y.z(O.344) yz(O.357) ~~(0.380)
Oi( 0.151) Oj;( 0.343) Ot(0.277) Ol( 0.241) 0,“(0.261)
Og(0.391) q(0.395) og( 0.249)
*HOMO or LUMO.
The energy levels, Ei, ET, of the homonuclear core MOs, $i, JIT, are written E.=Q t
+
l+si'
Pi
E*=a-bi i
i=LW
l_siy
and the total core MO energy difference AE are expressed AE = ~ (ET -Ei) $._= 1
x
t i=l
(2a - 2Ei) =E,,’
(8)
where OIi,/Ii, Si, are individually called an atomic integral (Coulomb integral), resonance integral and overlap integral, respectively. Equation (8) shows that AE approachs the metal bonding energy Em,‘. If the average AEi is used instead of AEi in eqn. (8), the calculated AEi in the core MO method approachs the metal-metal reduced energy emm’ in the EHMO’s. It has been found [15, 181 that the core (Mo204)*+ played an important role in determining electronic spectra of the di-p-oxo-di-Mo compounds, and proved that the d-d transition absorption spectra [ 19, 201 related to the level difference (E” -- Ei) of the MO in dimeric compounds. Therefore, the data from the electron spectra measurement can indicate the trends between the metalmetal bonding interaction in the cluster compounds. The above method must be improved for the dimeric compounds with the 71 bonds or bridge groups. Such as conformaton (l), the double bridge dimetal compound, it may be that the two monomeric metal compounds link together by the bridge groups. According to the classical electrostatic
25
interaction model, the interaction energy between the charge 2, atom M and the charge 2, at the atom x or y is written
at the metal
I.7= %m:
(9)
in each monomeric metal compound. It is understood that the charge of atom x is perturbed in the interaction of the two monomeric metal compounds and its charge shift AZ,,, then formula (9) is expressed as v’
=
'&(zb
+
Rmb
A&J = (&II + A&n)&, = zidb Rmb Rmb
It is assumed that the value A(Z,Z,) and the distance Rmb are unchanged in formula (10). It shows that the metal atomic charge is changed from 2, to Zk, as the dimeric compound with the bridge groups is formed. The potential matrix element depends only on the charge 2; of the metal atom when the compound conformation is fixed. Therefore, a single electronic orbital energy is Ej = ($#qJ/j>
= czh,
(11)
The parameter 2; (or f) is regulated for the dimeric compounds of core conformation (l),according to the data of Table 4 from the electronic spectra TABLE 4 The experimental data and calculated value of the UV spectra for some P( 0) or P(S) two metal atomic cluster Cluster
R mm (A)
Spectra lines (nm)
(QH),[Mo,O,(C,O,),(H,O),l (PyW~ lMo,O,(C,O,),(H,O), 1 Na, Dfo,O,Wc~s), 1
492
Na,[Mo,O,(S-hit),]
2.560 2.565 2.569 2.552
[Mo,O,( R-pdta), I*-
2.533
Na, Pfo,O,S,(S-CYS), I
2.820 2.820
Na, [Mo,O,S,(S-hit),]
Na,P%O,S,(EDTA)l Na, lMo,W,(R-pdta),
1
[Mo,O,S(R-pdta),]‘[Mo,O,S(S-cys), I’[Mo,O,S(S-hit),]‘-
2.800 2.810 2.656
476 474 (478 481 (472
400 394 383 400 387 393
468 451 (469 468 476 (469
380 365 387 347 350 381
446 465 463 (463
387
303 303 310 303 300)a 298 290)8
311
277 276 280)a 279 279 270)a
318 328 313 321
285 283 280)a
298 321 308
aThe calculated value of ref. 21. _
26 TABLE 5 Theoretical value of metal bond strength of some clusters Cluster
R mm (A)
Ef - Ei (nm)
(QH),[Mo,O,(C,O,),(H,0), 1 (P,H), IMo,O,(C,O,),(H,O), 1 Na, [Mo,G,(S-cys), 1
2.560 2.565 2.576 2.552 2.533 2.820 2.820 2.800 2.810
478 478 478 476 472 469 469 469 469
Na,[Mo,O,(s-hit),] [ Mo,O,(R-pdta), I’Na, [Mo,G,S,(S-cys), I Na,[Mo,O,S,(S-hit),] N%[Mo,G,S,(EDTA)I Na, [Mo,G,S,(R-pdta),
1
300 300 300 300 290 280 280 270 270
AEi (eV) 1243 1243 1243 1243 1168 1116 1116 1033 1033
2.559 2.559 2.559 2.559 2.639 2.711 2.711 2.790 2.790
TABLE 6 A Ei and EHMO calculated values No.
Cluster
R mm (A)
pmm
1 2 3 4 5 6
[Mo,G,(S-cys), I” [M~,G,S,(S-~Y~),I’MozG,(SG,NC,H,& Mo,G,S,(SG,NC,H,), (Mo,G.J+ (Mo,G,S,)”
2.576 2.820 2.562 2.804 2.550 2.814
0.1462 0.1632 0.1077 0.1524 0.1721 0.2172
e mm (eV -2.7023 -2.7482 -2.4293 -2.8639 -4.8534 -5.4573
measurement
with cc(O) and p(S) dimeric metal compounds,
x=y=o, x = 0, y = s, x=y=s,
f = 1.8; { = 1.7; 5 = 1.6.
AEi (eV) 2.559 2.711 2.559 2.790 2.559 2.790
and listed [21] :
When these { values are regarded as metal atomic charge, we can use eqn. (8) to calculate L??i for the dimeric compounds with the bond or bridge groups. The level difference (Ei* - Ei) and the average AEi are obtained using& parameter 5, given in Table 5 [21]. Table 6 shows that the metal average AEi from formula (8) in the core model corresponds to both the ROP Pmm and the REME emm from the EHMO’s in the dimeric metal compounds. It may well be that AEi is also an indicator for the metal-metal bonding strength. ACKNOWLEDGEMENT
The authors gratefully acknowledge encouraging discussion on their work by Professor Q.-E. Zhang, director of the Chemical Department, Xia Men University, Fujian.
27 REFERENCES 1 Boon Keng Teo, M. B. Haii, F. Fenske and L. F. Dahl, Inorg. Chem., 14 (1975) 3103. 2 R. H. Summerville and R. Hoffmann, J. Am. Chem. Sot., 98 (1976) 7240. 3 R. Mason and D. M. P. Mingos, J. Organomet. Chem., 50 (1973) 53. 4 B. E. Bursten, F. A. Cotton, M. B. Hail and R. C. Najjar, Inorg. Chem., 21 (1980) 302. 5 Liao Daiwei, Zhou Taijin and Wang Yingui, KIA DA KE JI, 2 (1983) 7. 6 M. G. B. Drew and A. Kay, J. Chem. Sot. A, (1971) 1851. 7 Liu Hanqin, Hong Maochun, Jiang Fengying, Yang Wenhuo and Zhan Kun, J. Struct. Chem., 2 (1983) 1. 8 A. Bino, F. A. Cotton and Z. Dori, J. Am. Chem. Sot., 100 (1978) 5252. 9P. J. Vergamini, H. Vahrenkamp, L. F. Dahl, J. Am. Chem. Sot., 93 (1971) 6237. 10 Avi Bino, F. A. Cotton and Zvi Dori, Inorg. Chem. Acta, 33 (1979) L133. 11 Huang Jinling, Shang Maoyu, Huang Jianguan, Zhuang Honghui, Lu Shaofang and Lu Jisxi, J. Struct. Chem., 1(1982) 1. 12 L. F. Dahl and R. E. Rundle, Acta Crystallogr., 16 (1963) 419. 13 J. N. Van Niekerk, F. R. L. Schoening and J. F. De wet, Acta Crystallogr., 6 (1953) 501. 14 J. Lewis, Pure Appl. Chem., 10 (1965) 11. 15 B. J. Trzebiatowska, M. F. Rudolf, L. Natkaniec and H. Sabat, Inorg. Chem., 13 (1974) 617. 16 Li Junqian, Cheng Wendan and Wang Yingui, J. Struct. Chem., to be publsihed. 17 F. A. Cotton and T. E. Haas, Inorg. Chem., 3 (1964) 10. 18 D. H. Brown, P. G. Perkinsand J. T. Stewart, J. Chem. Sot. Dalton Trans., (1972) 1105. 19A. Muller, R. Jostes, W. Jaegermann and G. Bhattacharyya, Inorg. Chem. Acta, 41 (1980) 259. 20 Li Junqian, Zheng An and Huang Jinling, Mol. Sci. Chem. Invest., 2 (1984) 183. 21 Li Junqian and Yang Rong Sheng, J. Fuzhou Univ., 4 (1985) 84.