- Email: [email protected]
Theoretical examination of optical and EPR spectra for Cu2+ ion in K2PdCl4 crystal
Journal of Physics and Chemistry of Solids 64 (2003) 523–525 www.elsevier.com/locate/jpcs
Technical note
Theoretical examination of optical and EPR spectra for Cu2þ ion in K2PdCl4 crystal P. Huang*, Hu Ping, M.G. Zhao Department of Information Sciences, Institute of Solid State Physics, Sichuan Normal University, Chengdu 610068, People’s Republic of China Received 7 February 2002; revised 16 April 2002; accepted 26 April 2002
Abstract In this work, two d –d transition spectra and four EPR parameters gk, g’, Ak, A’ of K2PdCl4/Cu2þ are uniformly interpreted based on Zhao’s crystal-field model. The calculation result is in good agreement with the experiment findings. The ligand spinorbit coupling is neglected on the calculation, which is consistent with the ab initio result by Hillier et al. [J. Am. Chem. Soc. 98 (1976) 95] q 2002 Elsevier Science Ltd. All rights reserved. Keywords: D. Crystal and ligand field; D. Electron paramagnetic resonance
1. Introduction
where
The crystal K2PdCl4 belongs to the space group D14h (P4/mmm ) with one formula unit per unit cell [1]. The structure consists of square-planar PdCl22 ions stacked above each 4 other along the four fold axis. In K2PdCl4/Cu2þ crystal, the Cu2þ ion enters the Pd2þ site in the form of a square-planar CuCl22 4 complex, as shown in Fig. 1. Cassicy and Hitchman [2], and Chow et al. [3] observed the optical and EPR spectrum, respectively. Aramburu and Moreno [4] have fitted the EPR parameters g and A of K2PdCl4/Cu2þ within a molecular orbital (MO) scheme. In this work, we study g-, Afactors and optical d–d transitions based on Zhao’s crystalfield model with two adjustable parameters. The results calculated are consistent with experimental findings.
He ¼
X
" 2
i
HSO ¼
X
H ¼ He þ HSO þ HCF * Corresponding author. E-mail address: [email protected] (P. Huang).
ð1Þ
ð2Þ
z d l i si ;
ð3Þ
Bkq CqðkÞ ðiÞ
ð4Þ
i
HCF ¼
X k;q;i
All symbols appearing in Eqs. (2)– (4) have their usual meanings. Following the point charge-dipole model containing an average covalence, the crystal field parameters are given by [5– 9] " ! # 5mk eq 5m’ 3 1þ =R5’ þ 4 1 þ =R5k kr 4 l0 N 2 Dq ¼ 2 42 qR’ qRk
2. Theoretical formulas The Hamiltonian including the electron –electron repulsion, the spin-orbit interaction, and the crystal-field potential is given by
# ! X e2 "2 Ze þ 72i 2 ri 2m i.j rij
"
!
#
ð5Þ
3mk 3m’ =R3k kr 2 l0 N 2 =R3’ 2 1 þ qR’ qRk 6eq 5m’ Dt ¼ 2 1þ cos 2w=R5’ kr 4 l0 N 2 qR’ 5
DS ¼ 2
2eq 7
1þ
where q and m denote the effective charge and the electric dipole moment of ligand Cl2, respectively, q ¼ e for Cl2, N, the average covalent reduction factor, R, the bond length
0022-3697/03/$ - see front matter q 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 0 2 2 - 3 6 9 7 ( 0 2 ) 0 0 2 7 7 - 9
524
P. Huang et al. / Journal of Physics and Chemistry of Solids 64 (2003) 523–525 Table 1 d–d transitions (cm21), EPR parameters g and A (cm21) for K2PdCl4/Cu2þ Calculated B1g ! 2Bg
2
2
B1g ! 2B2g
gk g’ Ak A’ a b
Fig. 1. Stereostructure of the CuCl22 4 complex.
of Cu2þ – Cl2, and krn l0 , the expectation value of r n . Diagonalizing the Hamiltonian matrix, we can obtain the 22 energy levels and its eigenvectors. For the CuCl P 4 (D4h ) ion, the ground state E1 can be written as l1l ¼ 10 i¼1 ai fi ; where fi is the basis function. By means of the equivalence between the spin Hamiltonian and Zeeman interaction [10 – 12], the following expressions of g-factors are obtained:
1 1
gz ¼ gk ¼ 2 1;
N 2 Lz þ 2:0023Sz
1; ðCDPÞ ð6Þ 2 2
1
1 ðCDPÞ ð7Þ gx ¼ 2 1;
N 2 Lx þ 2:0023Sx
1; 2 2 2
1
1 ðCDPÞ ð8Þ gy ¼ 2 1;
N 2 Ly þ 2:0023Sy
1; 2 2 2 where l1; ^ 12 l are the diagonalized wavefunctions of ground states, Lx, Ly, and Lz the operators of the orbit angular momentum, Sx, Sy, and Sz the operators of the spin angular momentum. CDP denotes the complete diagonalization procedure. According to the work of Ref. [12], the forms for the Cu2þ hyperfine constant A are given by
4 3 Ak ¼ 2K þ P 2N 2 ð9Þ þ Dgk þ Dg’ 7 7 11 2 2 Dg’ þ N ð10Þ A’ ¼ 2K þ P 14 7
15513 16192 12460 12511 2.239 2.042 2172.8 £ 1024 242.4 £ 1024
Observeda
14300b; 14625a 12500b; 12480a 2.2326 ^ 0.0002a 2.049 ^ 0.002a 2(163.6 ^ 0.5) £ 1024a 2 (34.5 ^ 0.6) £ 1024a
Ref. [2]. Ref. [3].
the electric dipole moment m are known. Using the double zeta-orbital of the Cu2þ ion proposed by Zhao et al., we have [5,11]
z0 ¼ 940 cm21 ;
z ¼ N 2 z0 ;
kr 2 l0 ¼ 3:11 a:u:;
kr 4 l0 ¼ 44:80 a:u:; P ¼ ge gN be bN kr 23 l0 ¼ 400 £ 1024 cm21 where P is the hyperfine constant of the Cu nuclei. In w¼ addition, for the K2PdCl4/Cu2þ crystal, R ¼ 2:265 A; and 908; and K ¼ 128 £ 1024 cm21 : Taking m ¼ 0:32e A; N ¼ 0:80; neglecting the contribution of the ligand SO coupling, using Eqs. (5) – (10) and diagonalizing the complete energy matrix (10 £ 10) we obtained the result as shown in Table 1. It can be seen easily from Table 1 that the theoretical values are in good agreement with the experimental data.
4. Summary and discussion
with Dgk ¼ gk 2 2:0023; Dg’ ¼ g’ 2 2:0023; and P ¼ 2be bN k1=r 3 l is a nuclear hyperfine constant, K the core polarization constant.
Diagonalizing the Hamiltonian matrix, we calculated the d – d transition, EPR parameters g- and A-tensors of K2PdCl4/Cu2þ with the aid of the approximate double zeta d-orbital model. In our calculation, the number of parameters is reduced to two, i.e. only the average covalence reduction factor N and the dipole moment m remained. In Table 1, a comparison with the experimental data is rather satisfactory, showing that Zhao’s two parameters crystalfield model is reasonable. From Table 1, it can be seen that the effect of ligand to g- and A-factors can be neglected, which is consistent with the ab initio result for Co2þ – 4Cl2 by Hillier et al. [13].
3. Calculation
References
The crystal-field parameters can be calculated from the structure data provided that the expectation values kr n l and
[1] Wyckoff (Eds.), Crystal Structure, vol. 3, Interscience, New York, 1965, pp. 72, see also vol. 1, p. 272.
P. Huang et al. / Journal of Physics and Chemistry of Solids 64 (2003) 523–525 [2] P. Cassicy, M.A. Hitchman, J. Chem. Soc., Chem. Commun. (1975) 837. [3] C. Chow, K. Chang, R.D. Willett, J. Chem. Phys. 59 (1973) 2629. [4] J.A. Aramburu, M. Moreno, J. Chem. Phys. 83 (12) (1985) 6071. [5] M.G. Zhao, Acta Chim. Sinica 37 (1979) 241. [6] M.G. Zhao, J.A. Xu, G.R. Bai, H.S. Xie, Phys. Rev. B 27 (1983) 1516. [7] M.G. Zhao, M.L. Du, Phys. Rev. B 28 (1983) 6481.
[8] [9] [10] [11]
525
M.G. Zhao, G.R. Bai, H.C. Jin, J. Phys. C 15 (1982) 5959. M.G. Zhao, Y.F. Zhang, IEEE Trans. Magn. M19 (1982) 1972. M.G. Zhao, J. Chem. Phys. 109 (1998) 8003. M.G. Zhao, Theory of Crystal-Field and Electron Paramagnetic Resonance, Science Press, Beijing, 1991, p. 269. [12] B. Bleaney, K.D. Bowers, M.H.L. Pryce, Proc. R. Soc. Lond. A228 (1955) 1645. [13] I.H. Hillier, J. Kendrick, F.E. Mabbs, C.D. Garaner, J. Am. Chem. Soc. 98 (1976) 95.
Technical note
Theoretical examination of optical and EPR spectra for Cu2þ ion in K2PdCl4 crystal P. Huang*, Hu Ping, M.G. Zhao Department of Information Sciences, Institute of Solid State Physics, Sichuan Normal University, Chengdu 610068, People’s Republic of China Received 7 February 2002; revised 16 April 2002; accepted 26 April 2002
Abstract In this work, two d –d transition spectra and four EPR parameters gk, g’, Ak, A’ of K2PdCl4/Cu2þ are uniformly interpreted based on Zhao’s crystal-field model. The calculation result is in good agreement with the experiment findings. The ligand spinorbit coupling is neglected on the calculation, which is consistent with the ab initio result by Hillier et al. [J. Am. Chem. Soc. 98 (1976) 95] q 2002 Elsevier Science Ltd. All rights reserved. Keywords: D. Crystal and ligand field; D. Electron paramagnetic resonance
1. Introduction
where
The crystal K2PdCl4 belongs to the space group D14h (P4/mmm ) with one formula unit per unit cell [1]. The structure consists of square-planar PdCl22 ions stacked above each 4 other along the four fold axis. In K2PdCl4/Cu2þ crystal, the Cu2þ ion enters the Pd2þ site in the form of a square-planar CuCl22 4 complex, as shown in Fig. 1. Cassicy and Hitchman [2], and Chow et al. [3] observed the optical and EPR spectrum, respectively. Aramburu and Moreno [4] have fitted the EPR parameters g and A of K2PdCl4/Cu2þ within a molecular orbital (MO) scheme. In this work, we study g-, Afactors and optical d–d transitions based on Zhao’s crystalfield model with two adjustable parameters. The results calculated are consistent with experimental findings.
He ¼
X
" 2
i
HSO ¼
X
H ¼ He þ HSO þ HCF * Corresponding author. E-mail address: [email protected] (P. Huang).
ð1Þ
ð2Þ
z d l i si ;
ð3Þ
Bkq CqðkÞ ðiÞ
ð4Þ
i
HCF ¼
X k;q;i
All symbols appearing in Eqs. (2)– (4) have their usual meanings. Following the point charge-dipole model containing an average covalence, the crystal field parameters are given by [5– 9] " ! # 5mk eq 5m’ 3 1þ =R5’ þ 4 1 þ =R5k kr 4 l0 N 2 Dq ¼ 2 42 qR’ qRk
2. Theoretical formulas The Hamiltonian including the electron –electron repulsion, the spin-orbit interaction, and the crystal-field potential is given by
# ! X e2 "2 Ze þ 72i 2 ri 2m i.j rij
"
!
#
ð5Þ
3mk 3m’ =R3k kr 2 l0 N 2 =R3’ 2 1 þ qR’ qRk 6eq 5m’ Dt ¼ 2 1þ cos 2w=R5’ kr 4 l0 N 2 qR’ 5
DS ¼ 2
2eq 7
1þ
where q and m denote the effective charge and the electric dipole moment of ligand Cl2, respectively, q ¼ e for Cl2, N, the average covalent reduction factor, R, the bond length
0022-3697/03/$ - see front matter q 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 0 2 2 - 3 6 9 7 ( 0 2 ) 0 0 2 7 7 - 9
524
P. Huang et al. / Journal of Physics and Chemistry of Solids 64 (2003) 523–525 Table 1 d–d transitions (cm21), EPR parameters g and A (cm21) for K2PdCl4/Cu2þ Calculated B1g ! 2Bg
2
2
B1g ! 2B2g
gk g’ Ak A’ a b
Fig. 1. Stereostructure of the CuCl22 4 complex.
of Cu2þ – Cl2, and krn l0 , the expectation value of r n . Diagonalizing the Hamiltonian matrix, we can obtain the 22 energy levels and its eigenvectors. For the CuCl P 4 (D4h ) ion, the ground state E1 can be written as l1l ¼ 10 i¼1 ai fi ; where fi is the basis function. By means of the equivalence between the spin Hamiltonian and Zeeman interaction [10 – 12], the following expressions of g-factors are obtained:
1 1
gz ¼ gk ¼ 2 1;
N 2 Lz þ 2:0023Sz
1; ðCDPÞ ð6Þ 2 2
1
1 ðCDPÞ ð7Þ gx ¼ 2 1;
N 2 Lx þ 2:0023Sx
1; 2 2 2
1
1 ðCDPÞ ð8Þ gy ¼ 2 1;
N 2 Ly þ 2:0023Sy
1; 2 2 2 where l1; ^ 12 l are the diagonalized wavefunctions of ground states, Lx, Ly, and Lz the operators of the orbit angular momentum, Sx, Sy, and Sz the operators of the spin angular momentum. CDP denotes the complete diagonalization procedure. According to the work of Ref. [12], the forms for the Cu2þ hyperfine constant A are given by
4 3 Ak ¼ 2K þ P 2N 2 ð9Þ þ Dgk þ Dg’ 7 7 11 2 2 Dg’ þ N ð10Þ A’ ¼ 2K þ P 14 7
15513 16192 12460 12511 2.239 2.042 2172.8 £ 1024 242.4 £ 1024
Observeda
14300b; 14625a 12500b; 12480a 2.2326 ^ 0.0002a 2.049 ^ 0.002a 2(163.6 ^ 0.5) £ 1024a 2 (34.5 ^ 0.6) £ 1024a
Ref. [2]. Ref. [3].
the electric dipole moment m are known. Using the double zeta-orbital of the Cu2þ ion proposed by Zhao et al., we have [5,11]
z0 ¼ 940 cm21 ;
z ¼ N 2 z0 ;
kr 2 l0 ¼ 3:11 a:u:;
kr 4 l0 ¼ 44:80 a:u:; P ¼ ge gN be bN kr 23 l0 ¼ 400 £ 1024 cm21 where P is the hyperfine constant of the Cu nuclei. In w¼ addition, for the K2PdCl4/Cu2þ crystal, R ¼ 2:265 A; and 908; and K ¼ 128 £ 1024 cm21 : Taking m ¼ 0:32e A; N ¼ 0:80; neglecting the contribution of the ligand SO coupling, using Eqs. (5) – (10) and diagonalizing the complete energy matrix (10 £ 10) we obtained the result as shown in Table 1. It can be seen easily from Table 1 that the theoretical values are in good agreement with the experimental data.
4. Summary and discussion
with Dgk ¼ gk 2 2:0023; Dg’ ¼ g’ 2 2:0023; and P ¼ 2be bN k1=r 3 l is a nuclear hyperfine constant, K the core polarization constant.
Diagonalizing the Hamiltonian matrix, we calculated the d – d transition, EPR parameters g- and A-tensors of K2PdCl4/Cu2þ with the aid of the approximate double zeta d-orbital model. In our calculation, the number of parameters is reduced to two, i.e. only the average covalence reduction factor N and the dipole moment m remained. In Table 1, a comparison with the experimental data is rather satisfactory, showing that Zhao’s two parameters crystalfield model is reasonable. From Table 1, it can be seen that the effect of ligand to g- and A-factors can be neglected, which is consistent with the ab initio result for Co2þ – 4Cl2 by Hillier et al. [13].
3. Calculation
References
The crystal-field parameters can be calculated from the structure data provided that the expectation values kr n l and
[1] Wyckoff (Eds.), Crystal Structure, vol. 3, Interscience, New York, 1965, pp. 72, see also vol. 1, p. 272.
P. Huang et al. / Journal of Physics and Chemistry of Solids 64 (2003) 523–525 [2] P. Cassicy, M.A. Hitchman, J. Chem. Soc., Chem. Commun. (1975) 837. [3] C. Chow, K. Chang, R.D. Willett, J. Chem. Phys. 59 (1973) 2629. [4] J.A. Aramburu, M. Moreno, J. Chem. Phys. 83 (12) (1985) 6071. [5] M.G. Zhao, Acta Chim. Sinica 37 (1979) 241. [6] M.G. Zhao, J.A. Xu, G.R. Bai, H.S. Xie, Phys. Rev. B 27 (1983) 1516. [7] M.G. Zhao, M.L. Du, Phys. Rev. B 28 (1983) 6481.
[8] [9] [10] [11]
525
M.G. Zhao, G.R. Bai, H.C. Jin, J. Phys. C 15 (1982) 5959. M.G. Zhao, Y.F. Zhang, IEEE Trans. Magn. M19 (1982) 1972. M.G. Zhao, J. Chem. Phys. 109 (1998) 8003. M.G. Zhao, Theory of Crystal-Field and Electron Paramagnetic Resonance, Science Press, Beijing, 1991, p. 269. [12] B. Bleaney, K.D. Bowers, M.H.L. Pryce, Proc. R. Soc. Lond. A228 (1955) 1645. [13] I.H. Hillier, J. Kendrick, F.E. Mabbs, C.D. Garaner, J. Am. Chem. Soc. 98 (1976) 95.