J . Phys. Chem. 1987, 91, 4250-4254
4250
phenomena2’which otherwise are difficult to explore with quantum theory. (21) For example: Anderson, A. B.; Mehandru, S. P.; Smialek, J. L J . Electrochem. SOC.1985, 132, 1695.
Acknowledgment. This research has been supported in part by the National Science Foundation through Grant DRM8 114425 to the Research Laboratory at Case Reserve University, and in part by the Chemistry Department.
Comparison of Bonding in First Transition-Metal Series: Diatomic and Bulk Sulfides and Oxides Alfred B. Anderson,* Sung Y. Hong, Chemistry Department, Case Western Reserve University, Cleveland, Ohio 441 06
and J. L. Smialek NASA-Lewis Research Center, Cleveland, Ohio 441 35 (Received: January 27, 1987)
Bond strengths of first transition-metal series diatomic and bulk sulfides and oxides are examined empirically. Diatomic and bulk bond strengths of both the sulfides and the oxides parallel each other in trending across the series, but the sulfide bonds are weaker. These behaviors as well as diatomic bond lengths and stretching force constants are calculated with the atom superposition and electron delocalization molecular orbital (ASED-MO) theory. In this theory binding energies and bond lengths are calculated as the balance of repulsive atom superposition and attractive electron delocalization energies. Within this theory, the trends are explained in terms of variations in these energy components which in turn depend on d electron count, nuclear charge, valence orbital size, and electronegativities.
Introduction Transition-metal sulfides have bonds that are longer and generally weaker than those for the oxides. The sulfide bond lengths are about 0.4 A longer, as expected from the greater S2-ionic radius. A thorough understanding of the differences between metal oxide and metal sulfide bonds is needed in materials science where sulfur is believed to weaken bonding at metal grain boundaries and at metal-oxide and possibly ceramic composite interfaces. The larger size of sulfur atoms and ions may be expected to affect the diffusion mechanism and rate through metals and ceramics to reach interfaces. The purpose of the present quantum chemical study is to explore in detail the reasons for the longer and weaker bonds of transition-metal sulfides compared to the oxides and to extrapolate to bulk oxides and sulfides. In a recent paper we examined bonding in the first transition-metal series diatomic oxides, ScO through ZnO.’ In that study we were able to calculate bond lengths, Re, harmonic stretching force constants, k,, and dissociation energies, De, to good accuracy. We found the bond lengths to be centered around 1.65 A (f0.1 A) with no well-defined trend across the series. Force constants, in contrast, increased from ScO to VO, then decreased to MnO, increased to FeO, then decreased to CuO. In going from ScO to CuO the general trend in k, was down. Bond energies showed a general decrease from ScO to CuO with a dip for MnO between C r O and FeO (Figure 1). Available data2 for the diatomic sulfides are too sparse to establish trends for Re and k,, but for Do data are available which show the same trend as for the oxides (Figure 2). As shown in Figure 3, except for Cu, the oxide bond strengths are greater than the sulfide bond strengths, (1) Anderson, A. B.; Grimes, R. W.; Hong, S. Y . , preceding paper in this issue. ( 2 ) Huber, K. P.;Herzberg, G. Molecular Spectra and Molecular Structure IV. Constants of Diatomic Molecules; Van Nostrand: New York 1979.
0022-3654/87/209 1-4250$01.50/0
and Do for Cr, Mn, Fe, Co, and Ni oxides are grouped together as are the Do for the corresponding sulfides. Parallel trends in bond strengths exist for the bulk oxides and sulfides. We have taken the experimental3 AH values for the reaction W g ) + yM(g)
-
M,O,(s)
(1)
and divided by y X metal coordination number4 to give defined single bond strengths. These are graphed for M2+,M3+, and M4+ in octahedral or approximately octahedral coordinations in Figure 1. It may be seen that these bulk single bond strengths follow trends similar to but smoother than the trend in diatomic bond strengths. A step up in metal oxidation state increases the bulk single bond strength by about 0.5 eV. The oxides of Cu and Zn are tetrahedrally coordinated and the single bond strengths are about 0.5 eV stronger. The bulk sulfides (Figure 2) show similar behavior to the oxides, but the single bond strengths are about 0.3 eV weaker in those cases where comparisons are possible. For M2+ in octahedral coordinations the MO bulk single bond strengths for Mn, Fe, Co, and Ni average 1.59 f 0.01 eV and for the same sulfides the average is 1.26 0.03 eV. From left to right in the transition series there are changes in certain physical properties of the metal atoms which will play a role in our calculations and analysis. These are (i) d electron count (Sc is 3d’4s2 and Zn is 3dI04sZ),(ii) nuclear charge (Sc is 21 and Zn is 30), (iii) valence orbital size (Sc 3d, 4s, and 4p orbitals are the largest and most diffuse and Cu orbitals are the smallest and least diffuse), and (iv) electronegativity, which determines bond (3) Oxide data from: CRC Handbook of Chemistry and Physics, Hodgman, C. D., Ed.; Chemical Rubber Co.: Cleveland, OH, 1962, and Shatynski, S. R. Oxid. Met. 1977, 1 1 , 307. Sulfide data from: Mills, K. C. Thermodynamic Data for Inorganic Sulphides, Selenides, and Tellurides; Butterworth’s: London, 1974, and Tuenge, R. T.; Laabs, F.: Franzen, H. F. J. Chem. Phys. 1976,65, 2400. (4) Wyckoff, R. W. G. Crystal1 Structures; Interscience: New York, 1960.
0 1987 American Chemical Society
The Journal of Physical Chemistry, Vol. 91, No. 16, 1987 4251
Bonding in First Transition-Metal Series 71 *--.,.,/Diatomic
oxides
61
.':-----.-.-.--. . 4 Octahedral '* M3 \:*.:
M2*
1
't
,/' l
1
L
Sc Ti V Cr h4 Fe Co Ni Cu Zn
Figure 1. Experimental energies per bond for diatomic and bulk transition-metal oxides. Data taken from ref 2 and 3 .
+:-.+ -.-.-.\.Octahedral'
;;hT ;eM I* Sc Ti V Cr Mn Fe Co Ni Cu Zn
~
F i g u r e 2. Experimental energies per bond for diatomic and bulk transition-metal sulfides. Data taken from ref 2 and 4.
ionicity. These physical properties are included in our molecular orbital treatment.
Theoretical Method We use the atom superposition and electron delocalization molecular orbital (ASED-MO) theory in this ~ t u d y . ] , ~The ,~ method was thoroughly discussed previously;'*6it is necessary to give only a brief outline of it here. This theory is based on the partitioning of a molecule's electronic charge density function, p , into rigid free atom parts, pa, which center on the nuclei and follow them perfectly as atoms come together to form a molecule, and a nonperfectly following or bond charge density pnpf: atoms
= C
Pa
a
+ Pnpf
The electrostatic force on one of the nuclei (say, nucleus b) may be integrated as two atoms come together to form a molecule. The force on nucleus b that is due to pa and nucleus a is repulsive because the nuclear repulsion component of this force increases more rapidly than the attractive force of pa due to penetration of the Pb charge cloud. The force on nucleus b due to pb is zero. Hence, as the force on nucleus b that is caused by atom a is integrated, a repulsive energy, ER,is obtained. The pnpfdensity will cause an attractive force on nucleus b and so its integral is an attractive energy, Enpf The molecular binding energy curve, E, is then the sum of the two nonzero component^:^ E = ER
+ Enpf
(3)
Since pnpfis not a known function, Enpfcannot be obtained from an integral of the force it causes on a nucleus. Nevertheless, the electron delocalization energy can be well approximated by a molecular orbital delocalization energy in most instanced
E
1
1
1
l
7
+ (VSIP),b]Si;b
exp(-0.13R)
(7)
where s , , ~is the overlap integral for orbital i on center a and orbital j on center b and R is the distance between nuclei a and b.
E .-. ,
P
1
Figure 3. Experimental diatomic transition-metal sulfide bond strengths as a function of the corresponding diatomic oxide bond strengths. Data taken from ref 2.
HLlab= -1.125[(VSIP),"
21
l
2 3 4 5 6 Oxide De (eV)
ER
+ AEMO
(4)
where AEMOis the total one-electron molecular orbital energy minus the total one-electron atomic orbital energies. The appropriate one-electron Hamiltonian is a function of experimentally measured valence state ionization potentials (VSIP), valence Slater atomic orbital overlap integrals, and internuclear distances. It resembles the extended Huckel Hamiltonian Hi? = -(VSIP),"
( 5 ) Anderson, A. B. J . Chem. Phys. 1974, 60, 2477. (6) Anderson, A. B. J . Chem. Phys. 1975, 62, 1187.
(5)
For heteronuclear bonds there are two equivalent ways of evaluating E by using eq 3, either by integrating the force on nucleus a or by integrating the force on nucleus b; the ER and Enpfcomponents are different, but their sum is the same. When the EMoapproximation to Enpfis used, better results are often obtained when ERis calculated by using the nucleus of the more electropositive element and the charge density function of the more electronegative element. This was done for the oxides in ref 1 and will be done for the sulfides in this paper. The VSIP come from the compilation of Lotz' in the case of metal 3d and 4s and sulfur 3s and 3p, and for metal 4p VSIP assignments are made using the lowest 4s to 4p excitation energy in Moore's* compilation. The single-!: 3s and 3p Slater exponents for sulfur are from Clementi and Raimondig and metal double-{ 3d exponents are from Richardson et al.IO The metal single-{ 4s exponents are shifted from those in ref 10, and the 4p exponents are assigned values 0.3 au smaller than the 4s values. These assignments of 4s and 4p exponents are required to yield reasonable calculations of electronic structures for metal diatomic molecules." A rudimentary form of charge self-consistency is achieved in ASED-MO calculations by increasing the VSIP for the electropositive element and decreasing the VSIP for the electronegative element until the charges on the cation and anion correspond to the percent ionic character predicted on the basis of the Pauling electronegativity difference. For the oxides the same fixed shift in oxygen 2s and 2p VSIP was used because ESCA indicates charges of 02-anions are relatively constant in various metal oxides. The same is assumed for S2-for which shifts are smaller, and a zero shift in the 3s and 3p VSIP values is chosen. Anions gain charge and expand, which is handled in ASED-MO calculations by decreasing the Slater exponents. For the oxide molecules decreases of 0.2, 0.3,0.4, and 0.5 au in the 0 2s and 2p exponents were tried, and the 0.3 au decrease was a good average choice for the series. For the diatomic metal sulfides, decreases in 3s and 3p exponents of 0.0, 0.1, and 0.2 au were tried and the 0.1 au decrease was found to be an excellent choice for the series. The metal VSIP were shifted in 0.1 au steps until the charge separation at the predicted Re was as close as possible to that predicted from the Pauling electronegativity difference. Final parameters used are in Table I.
Results The sensitivity of Re, k,, and Do predictions to 0.1 au changes in S 2s a n d 2 p exponents are calculated to be 5-10%. The 0.1 au decrease from tabulated values produces good average results, (7) Lotz, W. J . Opt. SOC.A m . 1970, 60, 206. (8) Moore, C. E. Atomic Energy Leuels; NBS Circ. No. 467; National Bureau of Standards, U S . Government Printing Office: Washington, DC, 1958. (9) Clementi, E.; Raimondi, D. L. J . Chem. Phys. 1963, 38, 2686. (10) Richardson, J. W.; Nieuwpoort, W. C.; Powell, R. R.; Edgell, W. F. J . Chem. Phys. 1962, 36, 1057. (11) Anderson, A. B. J . Chem. Phys. 1977, 66, 5108.
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TABLE I: Parameters Used in the 4s atom 1P sc 7.24 TI 7.62 \ 7.84 Cr 8.17 8.63 Mn Fe 9.17 9.26 co 8.34 &I 9.93 cu 11.69 Zn S 20.20" 3s IP and 3s {.
Calculations: Ionization Potentials, IP (eV); Slater Orbital Exponents, { (au); Linear Coefficients, c 4P 3d
s' 1.45 1.50 1.55 1.60 1.65 1.70 1.75 1 .so 1.85 1.90 2.022"
c
1P 5.26 5.65 5.8 I 6.04 6.35 6.74 6.33 5.15 6.14 7.68
IP 8.7 8.8 9.1 9.65 10.2 10.3 10.4 10.7 12.6 13.5
1.15 1.20 1.25 1.30 1.35 1.40 1.45 1S O
1.55 1.60
10.36'
Cl
.rl
0.3794 0.4206 0.4558 0.4876 0.5139 0.5366 0.5551 0.5683 0.5819 0.5951
4.35 4.55 4.75 4.95 5.15 5.35 5.55 5.75 5.95 6.15
c2 0.8 186 0.7839 0.751 6 0.7205 0.6929 0.6678 0.6461 0.6292 0.6 120 0.5951
.r2
1.30 I .40 1S O 1.60 1.70 1 .80 1.90 2.00 2.10 2.20
1.727'
3p IP and 3p {.
TABLE 11: Calculated Metal Atom Valence Ionization Potential Shifts, AIPMrBond Lengths, Re, Force Constants, k,, and Bond Dissociation Energies, D o for Diatomic Sulfides" molecule scs TiS
vs CrS MnS FeS cos NiS cus ZnS
state
AIPM,eV 22 0.7 3A 0.8 1.1 ~ ~ 2 1 1.4 [S4b 1.2 [91 [54h I .3 1.4 ~~21' 0.7 [3z1h 2.2 2T [I2lh 2.3
exptl
Re, 8, 2.02 2.03 2.03 2.08 2.13 2.10 2.13 2.22 2.25 2.12
total E 5.30 5.17 5.37 4.16 3.29 3.98 3.60 2.29 2.06 3.84
2.08
[2.051]
Do,eV
k,, mdyn/A density eq 4.93 4.92 5.15 4.24 3.48 4.18 3.76 2.53 2.26 4.38
exptl 3.52 [3.52] 4.49 2.86
2.15
MoSoc
M+Sd
6.61 6.38 5.86 4.33 3.1 1 3.41 2.96 3.62 2.44 2.21
4.95 4.82 4.60 3.62 2.45 3.35 3.00
exptl 4.9, 4.7, 4.62 3.3, 2.8, 3.3, 3.39 3s3 2.S0 2.0*
"Experimental values are from ref 2; uncertain experimental values are in brackets. Do determined by using k , from total energy calculations. *Assumed. 'Dissociation to Mo with no 4s electrons except for Zn, which is s2, and Cu and Ni, which are s'. dDissociation to M+ with no 4s electrons, except for Zn+, which is s'
,
,
#
I
!
1
1
Sc Ti V Cr Mn Fe Co NI Cu Zn
Figure 4. Predicted and experimental (ref 2) diatomic transition-metal sulfide bond lengths, Re. Point in parentheses is uncertain.
lr
I ,
#
#
I
Sc TI V Cr Mn Fe Co Ni Cu Zn
all of which are tabulated in Table 11. Predictions for bond lengths are in Figure 4. Only one reliable experimental value, for Tis, is available; the value for CuS is uncertain as indicated by parentheses in the figure. The trend in predictions parallels the one predicted for oxides from ref 1. More experimental force constant data are available and they may be compared with our predictions in Figure 5. Predictions using the Poisson equation for force constant^,'^^^^^^'^'^
kc = 4*ZMpS(&)
(8)
where ZMis the metal nuclear charge and ps is the sulfur atomic density, are nearly the same, which was also the case for the oxides. The experimental value for the Tis force constant is, according to ref 2, uncertain. The predicted ScS force constant is high compared to the experimental value, and predicted CrS, MnS, and CuS values are within 15% of experiment. Bond energies are calculated as the difference between the calculated molecular energies and the energies of sulfur and metal in states whose orbitals correlate with the molecular orbitals. Molecular states have been assigned only for ScS (22),T i s (3A), and CuS (%). These correspond to high-spin occupations, just as for the oxides, and, because of the small splitting of the d orbital levels (see Figure 6 ) , high spin has been assumed in our calculations for all the sulfides. For the early transition-metal sulfides through FeS the S 3p orbital levels lie beneath the metal d levels. (12) Anderson, A. B.; Parr, R. G. J . Chem. Phys. 1970, 53, 3375. Anderson, A. B.; Parr, R. G. Chem. Phys. Lett. 1971, 10, 293. Anderson, A. B.; Parr, R . G . Theor. Chim. Acta 1972, 26, 301. Anderson, A. B. J . Mol.
Spectrosc 1972, 44, 41 1.
Figure 5. Predicted and experimental (ref 2) diatomic transition-metal sulfide bond stretching force constants, k,. Point in parentheses is uncertain. Dashed line connect points predicted by using eq 8; solid line connects force constants predicted by using the total energy.
On dissociation, the and u2 levels become S 3p and the u3 level, which holds one electron, becomes metal 3d. These molecules would then dissociate to 3p6 S2- and d" M2+. Because such highly charged ions would not form, we take 3p5 S- and 4s0 M+ states in the dissociation limit and calculate the ion energies by summing over the filled valence orbitals using the molecular VSIP values. This yields accurate Dopredictions for ScS-FeS as is shown in Figure 7. Cobalt has a 3d VSIP 0.1 eV greater than for Fe and 0.04 eV greater than for S 3p, so it is reasonable to calculate Do for COS in the same way as for FeS, and the results of the calculation are accurate and they are comparably accurate when dissociation is to neutral 4s03d9and 4s13d8Co too. For ZnS the occupied molecular orbitals correlate with ground-state 3p4 S and 3d1°4s2 Zn atoms and the predicted Do,shown in Figure 7, is calculated this way, agreeing well with experiment. When it is assumed that NiS and CuS dissociate to neutral 3p4 S and 4s1d9 Ni and 4s'dI0 Cu atoms, predicted Doare close to experiment. For CuS this corresponds to assigning one of the electrons in the doubly occupied u3 orbital to S and the other to Cu. For NiS it corresponds to doing this and promoting one of the Ni d electrons to S 3p. Such assignments are admittedly empirical but lead to accurate bond strength predictions. Dissociation products for NiO, CuO, and ZnO, which are shown in Figure 7 and are discussed below, have also been calculated in this way in the present study.
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The Journal of Physical Chemistry, Vol. 91, No. 16, 1987
atom orbitals and more rapid stabilization as the bonds form. This is especially true for M 3d-S 3p, 0 2p ?r overlaps and M 4s-S 3s, 0 2s u overlaps as shown in Figure 12. All of the other u overlaps are greater for S at distances greater than -2.1 A, but they cross the 0 overlaps between 1.6 and 2.1 8, because the diffuse sulfur orbitals begin to substantially overlap metal d orbital lobes of both signs. Within the sulfide group the magnitudes of all overlap integrals decrease to the right across the transition-metal series; Figure 13 shows representative calculated results. Conclusions
R
6,
Figure 13. Calculated valence overlap integrals between S and Sc, Fe, and Zn as functions of internuclear distance.
As shown in Figure 9, the sums of covalent stabilizations and destabilizations of all kinds for the oxides and sulfides from Sc to Zn show roughly the same values. Except for nickel, where the 3d94s' dissociation product is assumed, and zinc, where there is no charge-transfer stabilization, the charge-transfer stabilizations for the oxides are significantly greater than for the sulfides and clearly the differences in these values cause the differences between total bond energies for the oxides and sulfides. These predicted De values are shown in Figure 10 along with the experimentally determined values. In these predictions the largest deviation from the parallel trend is for NiO. Why are the covalent stabilizations, both the components and their sum, and the ER repulsion energies nearly the same for each metal oxide and sulfide pair? We have plotted ER, EMO,and the total energy for the oxide and sulfide diatoms of Sc, Fe, and Zn in Figure 11 to find out. ER for the sulfides rises much sooner than E R for the oxides and reaches a value of about 1 eV at an internuclear separation of about 2.1 A in each case. This distance is approximately the equilibrium bond length. For the oxides ER values of 1 eV are reached at about 1.65 A, corresponding to approximate Re values. The EM0 energies become negative (stable) more rapidly for the sulfides. The increase in ER as the bonds form is more rapid for the sulfides than for the oxides because the sulfur valence orbitals are more diffuse so that the metal nuclei penetrate the sulfur density sooner. This greater orbital size is also responsible for larger overlap with the metal
We have developed a picture of bonding in the first transition-metal series diatomic oxides and sulfides. Bond lengths are a balance of forces, one due to atom repulsion which is dependent on the shape of the valence S and 0 electronic charge density functions and the other due to attraction of the nuclei for the electron delocalization bond charge cloud. The repulsive force increases more rapidly for the sulfides as the bonds form because the more diffuse S valence electron density shields the S nucleus less. In effect, this makes the S atom larger than the 0 atom, contributing to its larger empirically defined radius. The attractive force, approximated as a valence electron molecular orbital delocalization energy, is greater for the sulfides but equilibrium occurs at -0.4 A longer bond distances than for the oxides because of the rapid increase in the repulsive energy. At equilibrium the attractive and repulsive energy components are remarkably similar for the sulfides and oxides and the differences in bond strengths are due to differences in the metal to chalcogen charge-transfer energy. Empirically defined bulk oxide and sulfide bond strengths appear, on the basis of available data, to parallel the trend for the diatomics, but with scaled down values. The zig-zagging of the diatomic oxide and sulfide bond strengths from Cr to Ni is smoothed out in the bulk. The main deviation occurs for MnO and MnS for which the high-spin occupation of the u4 orbital causes bond weakening. Possibly in the bulk the corresponding orbital is empty, being antibonding and shifted up further in energy by the additional ligands, and this is why the bulk bond strengths do not deviate at Mn. The parallelism of diatomic and bulk bond strengths across the series suggests the same forces discussed above can be used to describe the bulk bonding. There will again be a competition between ER and EMo, only this time there are several ER contributions per 0 or S atom. The band orbital stabilizations will be greater for a given nearest-neighbor distance in the bulk because of the multiplicity of neighbors. However, the total pairwise repulsion energy is sufficiently strong that the bulk bonds are several electronvolts weak and several tenths of an angstrom longer than the diatomic bonds.
Acknowledgment. This research was supported by NASA Grant NAG3-688 from the Lewis Research Center, Cleveland, OH.
