J. Phys. Chem. 1996, 100, 869-872
869
Electronic Structure of CdS Cores in Cd Thiolate Complexes and Clusters V. S. Gurin† Physico-Chemical Research Institute, Belarusian State UniVersity, Leningradskaja str., 14, Minsk, 220080, Belarus ReceiVed: September 19, 1995X
The electronic structure of small clusters forming the inorganic cores in cadmium thiolate complexes is analyzed on the basis of semiempirical quantum chemical calculations. Orbital energies, atom charges, and peculiarities of chemical bond formation are considered for sphalerite lattice fragments CdxSy (x e 20, y e 35). The variation of calculated properties with size is nonmonotonous, but the tendency for band structure formation occurs with increasing size. The HOMO-LUMO energy differences for some structures are close to the experimental observations for the Cd thiolate complexes. Calculations show the major role of tetrahedral coordination in the properties of these structures.
Introduction Studies of some large complexes with many metal atoms are of interest in connection with developments in the field of quantum size semiconductors.1-5 When these complexes contain cores (cages) similar to bulk lattice fragments, they can be considered as intermediate forms between a molecular state and a bulk solid. Many examples of such compounds obtained up to date include Cd, Zn, Cu, Fe, etc. with metal-sulfur bonds.6-18 The inorganic cores of these complexes correspond to the sulfides of these metals, which are one of the two popular semiconductors under investigation for quantum size properties (e.g., CdS, ZnS). The cores in these complexes can have either bulk crystal structure or some different form. In the abovementioned complexes of cadmium and zinc, however, bulklattice fragments dominate; they can form stable compounds. For example, the cores with the contents of Cd10S2020- and Cd20S3530- 12,13,19-22 fully correspond to the sphalerite lattice of CdS with unavoidable distortion at boundaries. Other thiolate complexes also form sphalerite lattices: Cd4S64-, Cd10S1612-, Cd6S44+, etc., but there are also structures with significant deviation from the sphalerite core as in the case of very small complexes.23,24 A theoretical elaboration of small semiconductor clusters with CdS-based structures is a rather complicated problem because of their large sizes and many heavy metal atoms. With usage of the methods of solid state physics, CdS cluster structures were calculated previously25-29 with no relation to the molecular-like structures. In a recent work,30 the author considered some CdS-based clusters with different structures, and molecular-like energy spectrum appeared for clusters with tens of atoms. In the present work we use the semiempirical quantum chemical method to calculate the electronic structure of some of these fragments in order to follow the variation of properties of small semiconductor clusters. The consideration of cadmium sulfide in this context is rather useful since data on their properties are available now, and many clusters and thiolate complexes are identified with a certain number of atoms.6-18 It should be pointed out that semiempirical quantum chemical methods combine the flexibility in the construction of large structures with many heavy atoms with the possibility of performing calculations with a restricted CPU time. We use † X
E-mail:
[email protected]. Abstract published in AdVance ACS Abstracts, December 1, 1995.
0022-3654/96/20100-0869$12.00/0
the extended Hu¨ckel (EH) method that was used successfully for metal complexes,31,32 clusters,33 “cluster-matrix’ systems”,34,35 etc. The more sophisticated (e.g., ab initio) methods for calculations of large clusters like those considered in the present work are practically impossible and may be performed only for the smallest structures containing few atoms. Meanwhile, EH provides the true tendency in qualitative properties of the systems calculated, and the empirical parametrization can give a quantitative description of their properties. Other existing general schemes of electronic structure calculations, e.g., on the basis of effective mass approximation (EMA),1,2,36,37 are used for estimations of size-dependent properties of the clusters (in this number, CdS, ZnS). They can explain and predict successfully properties of particles, including hundreds and thousands of atoms with translational symmetry, but in the case of the smallest clusters (tens of atoms) the applicability of EMA is lost. The molecular orbital (MO) approach developed using quantum chemical methods for the clusters has no such restrictions. Details of Calculations Calculations were performed by means of the EH method with charge and configuration self-consistence.38 The parametrization was made by use of atomic spectroscopy data and thermodynamic values for binding energies of the corresponding chemical bonds (the basis: 4d(Cd), 5s(Cd), 5p(Cd), 3s(S), 3p(S)).39 Off-diagonal matrix elements of the Hamiltonian were determined according to the Wolfsberg-Helmholz formula with constant K ) 1.8 as well as in ref 30. The geometry of the structures calculated are shown in Figure 1. They are the fragments of a CdS sphalerite lattice, including up to 20 cadmium atoms with boundary atoms of different coordination (in the sphalerite lattice the coordination of both types of atoms is the same and equal to four). When these cores are bounded in the thiolate complexes, the dangling sulfur atoms are connected to the organic moeities. Their contribution within the framework of the present calculations is taken into account by the charges of clusters as a whole, and these moeities in reality neutralize the large charges of our clusters. We consider the two cases of the Cd-S interatomic distances: 2.52 Å (equal to that in the bulk sphalerite CdS) and 2.50 Å (determined for the compounds with Cd10S2020- and Cd20S3530cores21). This is also consistent with the interatomic distances in CdS and CdSe particles with sizes in the range 1-10 nm obtained from extended X-ray absorption fine structure studies.40 © 1996 American Chemical Society
870 J. Phys. Chem., Vol. 100, No. 2, 1996
Gurin
TABLE 1: Mulliken Occupation Analysis for Some Clustersa
a
cluster
S
S
Cd4S10 Cd10S20 Cd20S35 Cd4S6 Cd10S16 Cd20S31 Cd6S4 Cd16S13
s1.87p5.84 s1.87p5.84 s1.87p5.84 s1.79p5.59 s1.78p5.61 s1.78p5.61 s1.70p5.24 s1.71p5.30
s1.78p5.63 s1.78p5.61 s1.78p5.63
S s1.73p5.46 s1.73p5.41
s1.73p5.60 s1.73p5.40
s1.79p5.63
S
Cd s0.48p0.72d9.970 s0.48p0.72d9.970 s0.48p0.72d9.970 s0.45p0.50d9.979 s0.49p0.70d9.970 s0.46p0.54d9.973 s0.41p0.32d9.979 s0.41p0.32d9.979
s1.69p5.18
s1.69p5.18
Cd
Cd
s0.49p0.70d9.970 s0.49p0.70d9.970
s0.50p0.68d9.970
s0.46p0.54d9.973 s0.49p0.70d9.970
s0.50p0.68d9.970
s0.50p0.67d9.970
Cd-S interatomic distance is 2.52 Å (bulk value). Data are given only for different atom positions.
TABLE 2: Calculated Charges at Atom Sites (in Units of the Electron Charge), HOMO, LUMO, and Values of Total Electronic Energy for Clusters (Only for Different Atom Positions) cluster
S
S
Cd4S10a Cd4S10b Cd10S20a Cd10S20b Cd20S35a Cd20S35b Cd4S6 Cd10S16 Cd20S31 Cd6S4 Cd16S13
-1.707 -1.703 -1.707 -1.703 -1.707 -1.703 -1.382 -1.384 -1.384 -0.942 -1.005
-1.416 -1.409 -1.135 -1.127 -1.135 -1.127
-1.415 -1.409 -1.415 -1.409
-0.870 -0.861
-1.135 -1.135
-1.414
-0.870
a
S
S
-0.868
Cd +0.830 +0.818 +0.830 +0.817 +0.830 +0.817 +1.073 +1.028 +1.028 +1.295 +1.289
Cd
Cd
+0.839 +0.827 +0.838 +0.826
+0.852 +0.842
+0.840 +0.839
+0.852
+0.864
HOMO, eV
LUMO, eV
Etotal, eV
-12.47 -12.40 -12.33 -12.25 -12.23 -12.15 -12.83 -12.42 -12.27 -12.79 -12.48
+4.34 +4.92 +3.15 +3.59 +2.50 +2.88 -5.64 -5.28 -5.26 -6.54 -7.31
-1903.5 -1903.1 -4168.2 -4167.1 -7745.7 -7743.5 -1430.6 -3694.8 -7272.3 -1551.6 -4416.2
b
Cd-S interatomic distance is 2.52 Å. Cd-S interatomic distance is 2.50 Å.
Figure 2. Schemes of energy levels for the calculated clusters. The vertical arrows show the HOMO-LUMO transitions. Charges in cluster formulas are omitted.
Figure 1. Geometry of the clusters calculated. The scale is different for different clusters. Charges in cluster formulas are omitted.
Results and Discussion The results of the calculations are collected in Tables 1 and 2 and Figure 2 in the form of energy level schemes. Analysis of the occupied MO according to the contribution of different atomic orbitals (AO) indicates the clear dominance of s- and p-orbitals for all the clusters. The significant s- and pcontributions appear for both atoms, and one can speak on the binding due to the hybridized orbitals. The clusters with Td symmetry, Cd4S1012-, Cd10S2020-, and Cd20S3530-, which can be considered as one homological row, have almost identical occupations for the corresponding atoms. This is also reflected on the charge distribution (Table 2). However, the small contribution of cadmium d-orbitals cannot be ignored completely. Contributions of d-orbitals are rather small and are present mainly by the combination of dxy-dxz-dxz, which corresponds to the familiar separation of d-orbitals in tetrahedral
fields. From the data on Mulliken occupation for these clusters in Table 1 we see that clusters without the low-coordinated atoms have less p-occupation both for sulfur and for cadmium atoms. Differences in s- and d-occupations are not significant. It should be emphasized that the present scheme of Cd-S binding in the clusters cannot be reduced fully to some pure classical case of hybridization, although they are closer to such a scheme than nontetrahedral CdS clusters.30 The classical scheme of bond formation known for bulk sphalerite semiconductors is different in the case of the smallest clusters, and some other structures can be formed.23,24 Also, no single coordination center is present. In other words, our cluster cores can be treated as many-center compounds with nonequivalent coordination centers. According to the present calculations, the effect of the interatomic distance variation (in the above-mentioned range 2.50-2.52 Å, in accordance with the experimental findings) upon energy values and charge distribution (Table 2) is rather weak. Hence, possible contraction of the clusters with decreasing size does not contribute significantly to the properties of these structures. Among the data on charge distribution (Table 2) the considerably large values of charges at sulfur atoms reflect their ionic state. This can support the possibility of high chemical activity of these atoms with respect to ion-exchange reactions and fusion to form the larger structures like those in refs 20-22. The nature of the explicit nonuniformity in the charge distribution for sulfur in these clusters consists of the difference of internal
Electronic Structure of CdS Cores and external atoms with various coordination; the charges at the cadmium atoms are closer since their coordination remains tetrahedral in all these structures. In the large cores all cadmium atoms appear to be internal, and their atomic charges are almost the same as those in bulk CdS. The orbital energies calculated for the clusters (Table 2 and Figure 2) indicate the explicit difference in the form of an energy spectrum for small and large clusters. For the smallest ones (Figure 2) the energy spectrum is explicitly molecular-like, although in the case of CdS bulk fragments, Cd4S1012-, one can see the clear tendency for formation of the three energy bands: the lowest s-states (due to s-orbitals of S) in the region near -20 eV, the weakly splitted d-states (due to Cd), and a more extended region (∼-10-15 eV) formed mainly by p(S) and s(Cd). The more pronounced band-like structure occurs for Cd10S2020- and Cd20S3530- (Figure 2). The density of states of these clusters is very similar, and the energy level structure is close to that for the smallest fragment Cd4S1012-. This similarity also concerns charges (Table 2). Values of the HOMO energy regularly increase, and the LUMO energy decrease in this row, but ∆ ) E(HOMO) - E(LUMO) remains large (>14 eV), more than both the band gap of the bulk CdS (Eg ∼ 2.5 eV) and the energy of the maximum in the absorption spectra of Cd10- and Cd20- compounds.3,20-22 It is assumed that this contradiction is provided by the effect of organic moeities upon the energy of the excited (LUMO) level (from the data of Table 2 one sees that the energy of the LUMO changes strongly with the transition between different groups of clusters). An organic group closes the dangling atoms and decreases their charges. Calculation of these more complicated clusters can be the topic of further work. The following row of calculated cores is obtained as a result of deleting the dangling sulfur atoms: (Figure 1) Cd4S64-, Cd10S1612-, and Cd20S3122- and the two-coordinated sulfur ones Cd6S44+ and Cd16S136+ constructed from Cd10S2020- and Cd20S3530-, respectively. The data for these “truncated” cores are given in Table 2. One can conclude that the deletion of the low-coordinated sulfur leads to a noticeable decrease of ∆, and charge distributions become more uniform. For the largest structure from the “truncated” clusters Cd16S136+ ∆ is close to the energy of the maximum in the absorption spectum observed in refs 20-22 for CdS clusters of 10 and 13 Å in size with near numbers of atoms (4.4 and 3.5 eV, respectively). Within the triplets of clusters (Cd4-Cd10-Cd20) the calculated charges are almost same; ∆ decreases in this row, and values of the charges show a decrease of ionity with an increase in the number of atoms in clusters. Thus, the value of the HOMO-LUMO difference has the explicit tendency to decrease both with increasing size and with transition to the structures with higher coordination numbers. The latter factor appears to be more significant than can be explained by the large variations in the conditions of orbital overlapping in the structures of different coordination. The familiar effect of charge carrier confinement that is essential for the interpretation of quantum size properties of semiconductor particles and clusters1,2 also takes place in our clusters. It occurs implicitly in the results of energy level calculations. However, the pure confinement effect cannot be sufficient to explain the large variations of cluster properties. Conclusions Application of the EH method to the calculation of electronic structure and some properties of the inorganic cores in cadmium thiolate complexes allows us to draw the following main conclusions. (i) There is a general trend in the variation of properties of these semiconductor clusters, which form the inorganic cores
J. Phys. Chem., Vol. 100, No. 2, 1996 871 of thiolate complexes. Their electronic structure acquires the band-like character for clusters with more than 10 metal atoms. The HOMO-LUMO difference varies in the direction of the bulk band gap as size increases. (ii) Sphalerite cores of different content form the stable clusters; the experimentally verified existence of them does not contradict the theory. (iii) The chemical bond in the clusters is not reduced to the classical case of sp3-hybridization of the diamond-like semiconductors to which CdS sphalerite belongs. There is the small contribution of d-orbitals. CdS-based clusters can be considered as many-center compounds with a pronounced degree of bond delocalization around the cluster. (iv) Dangling and low-coordinated atoms in the cluster have large charges and can be rather reactive. However, the construction of clusters with a minimum number of dangling atoms is possible (positively charged Cd6S44+ and Cd16S136+ and negatively charged Cd4S64-, Cd10S1612-, and Cd20S3122-). Charges at the internal atoms are very uniform like those in the bulk CdS. (v) The value of the HOMO-LUMO difference for the clusters (without the organic moeities) appears close to the experimentally observed values only for the clusters without the dangling and low-coordinated atoms, particularly Cd6S44+ and Cd16S136+. (vi) The chemical coordination is shown to be more significant in the properties of these clusters rather than the size effect. With four coordination for the maximum number of atoms in the clusters they are similar to CdS particles with the quantum size effect predicted from the EMA approximation, but in the case of clusters with many low-coordinated sulfur and cadmium atoms they are similar to molecules according to the energy spectrum and nonuniform charges. The difference in the coordination with a change of clusters size provides the explicit nonmonotonous variations of their properties. Acknowledgment. The work is partially supported by the Fundamental Research Foundation of Belarus. References and Notes (1) Ba´nyai, L.; Koch, S. W. Semiconductor Quantum Dots; World Scientific: Singapore, 1993. (2) Yoffe, A. D. AdV. Phys. 1993, 42, 173. (3) Wang, Y.; Herron, N. Phys. ReV. B 1990, 42, 7253. (4) Bawendi, M. G.; Steigerwand, M. L.; Brus, L. E. Annu. ReV. Phys. Chem. 1990, 41, 477. (5) Henglein, A. Chem. ReV. 1989, 89, 1861. (6) Dance, I. G. Polyhedron 1986, 5, 1037. (7) Stricker, P. Chem. Commun. 1969, 655. (8) Dean, P. A. W.; Vittal, J. J. J. Chem. Soc., Chem. Commun. 1976, 432. (9) Haberkorn, R. A.; Que, L., Jr.; Gillum, W. O.; Holm, R. H.; Liu, C. S.; Lord, R. C. Inorg. Chem. 1976, 15, 2408. (10) De Brabander, H. F.; Van Poucke, L. C. J. Coord. Chem. 1974, 3, 301. (11) Swayambunathan, V.; Hayes, D.; Schmidt, K. H.; Liao, Y. X.; Meisel, D. J. Am. Chem. Soc. 1990, 112, 3831. (12) Dance, I. G. Aust. J. Chem. 1985, 38, 1745. (13) Dance, I. G.; Choy, A.; Scudder, M. L. J. Am. Chem. Soc. 1985, 106, 6285. (14) Lee, G. S. H.; Craig, D. C.; Ma, I.; Scudder, M. L.; Bailey, T. D.; Dance, I. G. J. Am. Chem. Soc. 1988, 110, 4863. (15) Nosaka, Y.; Shigeno, H.; Ikeuchi, T. J. Phys. Chem. 1995, 99, 8317. (16) Axtell, E. A., III; Liao, J.-H.; Pikramenou, Z.; Park, Y.; Kanatzidis, M. G. J. Am. Chem. Soc. 1993, 115, 12191. (17) Zeng, D.; Hampden-Smith, M. J.; Deusler, E. N. Inorg. Chem. 1994, 33, 5376. (18) Herron, N.; Wang, Y.; Eckert, H. J. Am. Chem. Soc. 1990, 112, 1322.
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