Symmetry and Bonding Interactions in [Cu 2 Cl 6 ] Complexes

Transcription

1 hys. stat. sol. (a) 913, No. 3, (2002) Symmetry and Bonding Interactions in [Cu 2 Cl 6 ] Comlexes F. E. Atalay 1 ) Science and Art Faculty, Deartment of Physics, İnönü University, 44069, Malatya, Turkey (Received May 1, 2001; acceted Setember 30, 2001) Subject classification: Et; S1.2; S9 Two kinds of magnetic interactions are exerimentally reorted in [Cu 2 Cl 6 ] comlexes, namely ferromagnetic and antiferromagnetic ones. Symmetry related magnetic interactions in these comlexes have been considered. First we defined the local symmetry roerties of the molecule and then we determined symmetry adated molecular orbitals. The bonding orbitals among two Cu atoms in [Cu 2 Cl 6 ] comlexes seem to be s orbitals. However, the structure of these molecules indicates that bonds must exist in these molecules. 1. Introduction KCuCl 3 and TlCuCl 3 crystallize in a monoclinic structure that belongs to the sace grou P2 1 /c [1]. The main feature of this crystal structure is the double chain of edge-sharing octahedra of Cu 2 Cl 6 along the a-axis. All of the octahedra are distorted to the Jahn-Teller effect, and their elongated axes are aligned in the same direction, so that all of the Cu 2+ ions in the double chain are magnetically equivalent to each other. Figure 1 shows the exchange interactions between neighboring Cu 2+ ions in double chains. Magnetic roerties of KCuCl 3 and TlCuCl 3 had been reorted by Shiramura et al. [2]. They suggested that J 1 and J 3 interactions are antiferromagnetic. The nature of J 2 interaction has not been clarified. The exchange interactions in the double chain are described by S ¼ 1/2 in the Heisenberg sin ladder with additional diagonal interchain interaction. In order to investigate the magnetic roerties of KCuCl 3 systems theoretically, molecular orbital aroximation has been considered. It is assumed that based on the definition of molecular magnetic orbitals deending on the symmetry and bonding interactions the J 2 interactions may be redicted. 2. Symmetry Adated Molecular Orbitals of [Cu 2 Cl 6 ] In order to describe the molecular orbitals of the [Cu 2 Cl 6 ] anionic comlex, the local symmetry of the molecules was used. The comlex shows D 2h symmetry. By grou theoretical means from the Fig. 1. Structure of exchange interactions in KCuCl 3 systems 1 ) Corresonding author; Tel.: ; Fax: ; fatalay@inonu.edu.tr # WILEY-VCH Verlag Berlin GmbH, Berlin, /02/ $ 17.50þ.50/0

2 914 F. E. Atalay: Symmetry and Bonding Interactions in [Cu 2 Cl 6 ] Comlexes Fig. 2. Symmetry elements of Cu 2 Cl 6 aroriate valance orbitals of the metal and the ligands symmetry orbitals can be calculated. Illustration of the three sace coordinates and the symmetry elements of [Cu 2 Cl 6 ] are shown in Fig. 2. The two coer atoms in xy lane are bridged by two Cl atoms out of that lane. In addition, two Cl atoms in the xy lane connect each Cu atom. This suggests that the x direction is the bonding direction. First the investigation of the transformation roerties of the various sets of atomic orbitals was erformed. From linear combinations of the orbitals that transform, the irreducible reresentations of the D 2h grou were derived. Finally, the interaction between orbitals of same symmetry secies was included. 3d x 2 y 2, 4s and 4 x,4 y,4 z orbitals of the two coer atoms and 3 x,3 y, 3 z orbitals of two terminal Cl atoms and those of two bridging Cl atoms are considered as valance shell atomic orbitals. 2.1 Atomic orbital symmetries of Cu atoms in [Cu 2 Cl 6 ] If four Cl atoms are neglected and only two atoms are considered in the [Cu 2 Cl 6 ] comlex, it is evident that the two coer 3d x 2 y 2, 4s and 4 x,4 y,4 z orbitals are resembled searately to each other. Considering two coer 3d x 2 y 2 and 4s orbitals, the linear combinations of these orbitals transform as A g and B 3u. If we label coer 3d x 2 y 2 orbitals as 3d x 2 y2(a) and 3d x 2 y2(b) then the correct linear combinations are of the form 1= ffiffiffi 2 3dx 2 y 2ðaÞþ3d x 2 y 2ðbÞ ; ð1aþ 1= ffiffiffi 2 3dx 2 y 2ðaÞ 3d x 2 y 2ðbÞ ð1bþ and similarly linear combinations of two coer 4s orbitals can be written as 1= ffiffiffi 2 ð4sðaþþ4sðbþþ; ð2aþ 1= ffiffiffi 2 ð4sðaþ 4sðbÞÞ: ð2bþ

3 hys. stat. sol. (a) 189, No. 3 (2002) 915 Table 1 Symmetry tyes and symmetry adated linear combinations 4 orbitals of coer symmetry tyes linear combinations 4 orbitals of coer A g 1= ffiffiffi ð4x ðaþþ4 x ðbþþ B 3u 1= ffiffiffi ð4x ðaþ 4 x ðbþþ B 1g 1= ffiffiffi ð4y ðaþþ4 y ðbþþ B 2u 1= ffiffiffi ð4y ðaþ 4 y ðbþþ B 2g 1= ffiffiffi ð4z ðaþþ4 z ðbþþ B 1u 1= ffiffiffi 2 ð4z ðaþ 4 z ðbþþ The A g combination is to be identified as a Cu Cu s-bonding orbital and the B 3u combination corresonds to Cu Cu s antibonding orbital. However, the existence of this strong s metal metal bonding has as reorted a weak ossibility [3]. In fact, the large Cu Cu distance comared with the coer atomic radius, suggests that no direct metal metal interaction is anticiated. Further calculations therefore were erformed considering no direct metal metal interaction. Symmetry adated 4 x,4 y,4 z orbitals of coer were also found as shown in Table The symmetries of Cl 3 orbitals in [Cu 2 Cl 6 ] The four terminal Cl atoms of the [Cu 2 Cl 6 ] comlex considerably consists of 3 orbitals. These orbitals are all equivalent to each other and therefore may be interconverted by the symmetry oerations of the grou, so that one must consider all four together. Symmetry elements and reducible reresentation of the terminal Cl 3 orbitals were found to be A g þ B 1g þ B 2u þ B 3u [4]. Labeling the terminal Cl 3 orbitals as A, B, C and D, symmetry adated linear combinations were calculated as shown in Table 2. The symmetry adated linear combinations of Cl 3 orbitals which were obtained show correct symmetries to interact with some of the coer orbitals. Thus, A g and B 3u combinations interact with coer sd hybrids. B 1g and B 2u symmetries does not show the same symmetry with coer orbitals. The investigation of the interaction between the A g 3 Cl orbitals with neighbouring coer orbitals do not give strong metal metal bonds, and Cu Cu bonding and antibonding configurations can be obtained. There are also B 3u Cu-Cl bonding and antibonding molecular orbitals. But A g and B 3u Cl 3 z atomic orbitals do not contribute to lane bonding. Considering the Cl 3 x,3 y,3 z orbitals out of the xy lane, these two Cl bridging atoms aear to lay a major role in magnetic roerties. We must again consider these two orbitals together. Cl 3 x,3 y,3 z orbitals have B 2g þ B 3u,B 3g þ B 2u and A g þ B 1u reducible grou reresentation, resectively. Symmetry adated linear combinations Table 2 Symmetry tyes and symmetry adated linear combinations of Cl 3 orbitals in lane symmetry tyes A g B 1g B 2u B 3u linear combinations of Cl 3 orbitals in lane 1=2ðA þ B þ C þ DÞ 1=2ðA B þ C DÞ 1=2ðA þ B C DÞ 1=2ðA B C þ DÞ

4 916 F. E. Atalay: Symmetry and Bonding Interactions in [Cu 2 Cl 6 ] Comlexes Table 3 Symmetry tyes and symmetry adated linear combinations of Cl 3 orbitals out of lane symmetry tyes linear combinations Cl 3 orbitals out of lane B 2g 1= ffiffiffi ð3x ðeþþ3 x ðfþþ B 3u 1= ffiffiffi ð3x ðeþ 3 x ðfþþ B 3g 1= ffiffiffi ð3y ðeþþ3 y ðfþþ B 2u 1= ffiffiffi ð3y ðeþ 3 y ðfþþ A g 1= ffiffiffi ð3z ðeþþ3 z ðfþþ B 1u 1= ffiffiffi 2 ð3z ðeþ 3 z ðfþþ of two bridging Cl 3 orbitals are given in Table 3 (which are labeled E and F as shown in Fig. 2). Any imortant interaction involving these bridge Cl orbitals is reasonably exected to be governed by Cu-Cl bonding orbitals of A g symmetry and antibonding orbitals Fig. 3. A g bonding and antibonding molecular orbitals in [CuCl 3 ]

5 hys. stat. sol. (a) 189, No. 3 (2002) 917 Fig. 4. B 3u bonding and antibonding molecular orbitals in [CuCl 3 ] of B 3u symmetry. All interactions between the two bridge Cl orbitals, the four terminal Cl and the two Cuorbitals in the Cu 2 Cl 6 molecule are shown in Figs. 3 and Conclusion It was found that B 3u Cl orbitals of both in lane and out of lane contribute to bonding when bonding interactions are more effective. All bonding orbitals of B 3u symmetry give square lanar structure to Cu 2 Cl 6. But among these bonding orbitals, there are two cases to rovide maximum bonding. The first one is of character which occurs between 3 x,3d x 2 y 2,4s,4 x orbitals in lane and 3 x orbital out of lane as shown in Fig. 4a. In this tye of bonding, the increase of bridging angle out of lane Cl ligand atoms, metal ligand metal bonding will be decreased. The second one occurs between 3 y,3d x 2 y 2,4s,4 x orbitals in lane and 3 x orbital out of lane. We assume that this bonding is most stable, because bonding occurs both in x and y direction (Fig. 4h).

6 918 F. E. Atalay: Symmetry and Bonding Interactions in [Cu 2 Cl 6 ] Comlexes References [1] Y. Fujii, Z. Wang, and R. D. Willett, Inorg. Chem. 34, 2870 (1995). [2] W. Shiramura, K. Takatsu, H. Tanaka, K. Kamishima, M. Takahashi, H. Mitamura, and T. Goto, J. Phys. Soc. Jn , 693 (1998). [3] M. Kato and Y. Muto, Coordin. Chem. Rev. 92, 45 (1988). [4] F. E. Atalay, Ph.D. Thesis, Inonu University Malatya (Turkey) 2000.