- Email: [email protected]
Theoretical investigation of EPR and molecular orbital coefficient parameters for [Cu(hsm)2(sac)2] complex
Chemical Physics Letters 505 (2011) 154–156
Contents lists available at ScienceDirect
Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Theoretical investigation of EPR and molecular orbital coefficient parameters for [Cu(hsm)2(sac)2] complex Emel Kalfaog˘lu, Bünyamin Karabulut ⇑ Department of Physics, Faculty of Arts and Sciences, Ondokuz Mayis University, Kurupelit, 55139 Samsun, Turkey
a r t i c l e
i n f o
Article history: Received 18 January 2011 In final form 15 February 2011 Available online 18 February 2011
a b s t r a c t In this study, the molecular orbital coefficients and the spin Hamiltonian parameters of bis(histaminesaccharinate) copper(II) complex, [Cu(hsm)2(sac)2], are calculated theoretically. Two d–d transition spectra and four EPR parameters g k ; g ? ; Ak ; A? for the Cu(II) complex are calculated by using crystal-field theory. The calculated values are in good agreement with the experimental values. The g and A parameters have indicated that the paramagnetic centre is axially symmetric. Having the relations of g k > g ? > g e and Ak > A? for Cu2+ ions, it can be concluded that Cu2+ ions are located in distorted octahedral sites (D4h) elongated along the z-axis and that the ground state of the paramagnetic electron is dx2 y2 (2B1g state). Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction
2. Theoretical formulas and calculation
The electron paramagnetic resonance (EPR) technique may yield useful information about the immediate environment of paramagnetic centers in crystals [1–3]. Optical absorption studies can provide the crystal field parameters and structure of energy levels of the transition-metal or rare-earth ions [4–6]. The EPR and optical absorption techniques provide information about the electronic structure, oxidation state, site symmetry and the bonding nature of the impurity ions. Histamine (hsm), 1H-imidazole-4-ethanamine, is a biologically important molecule and commonly present in the tissues of living organisms. In histamine and anti-histamine activity, an important role is played by the transition metal ions such as Co(II), Ni(II) and especially Cu(II) in the formation of metal complexes [7]. Bulut et al. observed the optical absorption and EPR spectrum and calculated EPR and molecular orbital parameters of [Cu(hsm)2(sac)2]. Figure 1 shows the molecular structure of title complex, with atom labeling scheme as given in Ref. [7]. The Cu2+ ion is hexa-coordinated by four nitrogens of two bidentate histamine ligands composing the equatorial plane and by two monodentate saccharinato ligands occupying the axial positions, adopting an elongated octahedral geometry [7]. Therefore, the coordination geometry of Cu2+ ions in [Cu(hsm)2(sac)2] complex belongs to the D4h point group. In this study, the spin Hamiltonian parameters and optical d–d transitions are calculated based on the crystal field theory. The molecular orbital coefficients are also obtained by using these results [8–12]. The calculated results are correlated with experimental ones in a comparative manner.
The free Cu2+ ion has 3d9 configuration or 3d1 in hole configuration. It has the ground state 2D since the orbital degeneracy is removed in the lower state when the Cu2+ ion is subjected to a tetragonal or an orthorhombic crystalline field. For a 3d9 ion in tetragonal crystal-field, the Hamiltonian including the electron– electron repulsion, spin–orbit interaction, and the crystal-field potential is given by [8–12],
H ¼ He þ Hso ðfÞ þ Hcf ðDq ; Ds ; Dt Þ where
He ¼
X
E-mail address: [email protected] (B. Karabulut). 0009-2614/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2011.02.038
"
i
Hso ¼ HCF ¼
X i X
! # 2 X e2 h Ze þ r2i ri 2m r ij i>j
ð2Þ
f d ‘i si
ð3Þ
Bkq C kq ðiÞ
ð4Þ
k;q;i
where Bkq is the crystal field parameters and Ckq is ½4p=ð2k þ 1Þ 12 Y kq , with Ykq denoting the spherical harmonics [9– 12]. The crystal-field interaction term can be written as
HCF ¼ B44 ðC 44 þ C 44 Þ þ B40 C 40 þ B20 C 20
ð5Þ
The energy level differences between the excited state 2Eg, 2B2g, A1g and ground state 2B1g are given by
2
E1 ¼ Eð2 B1g Þ ! Eð2 A1g Þ ¼ 4Ds þ 5Dt 2
⇑ Corresponding author. Fax: +90 3624576081.
ð1Þ
2
ð6Þ
E2 ¼ Eð B1g Þ ! Eð B2g Þ ¼ 10Dq
ð7Þ
E3 ¼ Eð2 B1g Þ ! Eð2 Eg Þ ¼ 10Dq þ 3Ds 5Dt
ð8Þ
E. Kalfaog˘lu, B. Karabulut / Chemical Physics Letters 505 (2011) 154–156
155
Figure 1. Structre of the [Cu(hsm)2(sac)2] crystal.
Table 1 d–d Transitions (cm1), EPR parameters g and A (cm1) for [Cu(hsm)2(sac)2] crystal.
B1g ? B2g B1g ? Eg g// g\ A// A\
Calculated
Observed
13 480 16 586 2.228 2.050 187 34
13 513 16 155 2.228 2.052 192 24
In terms of the equivalence between the spin-Hamiltonian and the Zeeman interaction, the expressions of the g factors can be written as [10],
1 1 g z ¼ g k ¼ 2 e; N2 Lz þ 2:0023Sz e; 2 2 1 2 1 g x ¼ 2 e; N Lx þ 2:0023Sx e; 2 2 1 2 1 g y ¼ 2 e; N Ly þ 2:0023Sy e; 2 2
ð9Þ ð10Þ ð11Þ
in which ^Lj ðx; y; zÞ and Sj are the operators of orbit and spin angular momentums, respectively. The forms for the Cu2+ hyperfine constant A are given by [10]
4 3 Ak ¼ K þ P N2 þ ðg k g e Þ þ ðg ? g e Þ 7 7 2 2 11 ðg g e Þ A? ¼ K þ P N þ 7 14 ?
ð12Þ ð13Þ
with ge = 2.0023, k N2 0.68 and P = gegnbebnhr3i = 400 104 cm1 which is the nuclear hyperfine constant of the Cu nuclei [10]. K is the core polarization constant of the transition metal ions. In addition, R 2.029 Å, h 93° and j = 0.32 for the [Cu(hsm)2(sac)2] crystal. The calculated optical absorption bands and spin Hamiltonian parameters are compared with experimental values in Table 1. It is known from group theory that the molecular orbitals of Cu2+ ion have the form [13–15]
1 2
WðB1g Þ ¼ aðdx2 y2 Þ a0 ðr1 r2 þ r3 r4 Þ 1 2 1 0 WðEg Þ ¼ bðdxz Þ pffiffiffi b ðp1 p3 Þ 2 1 0 ı WðEg Þ ¼ bðdyz Þ pffiffiffi b ðp2 p4 Þ 2 1 WðB2g Þ ¼ b1 ðdxy Þ b01 ðp1 p2 þ p3 p4 Þ 2
WðA1g Þ ¼ a1 ðdz2 Þ a01 ðr1 þ r2 þ r3 þ r4 Þ
ð14Þ ð15Þ ð16Þ ð17Þ ð18Þ
The ground state of the copper complex is 2B1g, with the unpaired electron in the nondegenerate B1g molecular orbital (Figure 2) as given in Ref. [15]. Accordingly, Eqs. (14)–(18) shows the various states in order of decreasing energy. The B1g and A1g molecular orbitals account for the r bonding, the eg orbital for the out-ofplane p bonding, and the B2g orbital for the in-plane p bonding [13]. The covalency parameter a2 for the in-plane r bonding is evaluated from the expression [15–17]
Figure 2. Energy levels of Cu2+ complexes with (a) r bonding and (b) p bonding.
E. Kalfaog˘lu, B. Karabulut / Chemical Physics Letters 505 (2011) 154–156
156
Table 2 Molecular orbital coefficients for [Cu(hsm)2(sac)2] crystal.
a
2
b21 b2
Calculated
Observed
0.75 0.61
0.75 0.61
0.64
0.64
A 3 a ¼ k þ ðg k g e Þ þ ðg ? g e Þ þ 0:04 7 P " # 4ka2 b21 g k ¼ 2:0023 1 B1g ! B2g " # ka2 b2 g ? ¼ 2:0023 1 B1g ! Eg 2
be completely covalent. The values of the calculated parameters a2, b21 and b2 indicate that the in-plane r bonding, in-plane p bonding and out-of-plane p bonding are significantly covalent in nature as given in Table 2. 4. Conclusions
ð19Þ ð20Þ ð21Þ
Using the Eqs. (19)–(21), we obtained the results as shown in Table 2. It is seen that the theoretical values are in good agreement with the experimental values. 3. Results and discussion The calculated g and A parameters have indicated that the paramagnetic centre is axially symmetric as given in Table 1. Table 1 also shows that the g values are in the order of g k > g ? > g e and Ak > A? . It can be concluded that Cu2+ ions are located in distorted octahedral sites (D4h) elongated along the z-axis [7] and that the ground state of the paramagnetic electron is dx2 y2 (2B1g state). The value of c = Dgk/Dg\ = |(ge gk)/(ge g\)| is a measure of tetragonal distortion in the coordination environment of Cu2+ ion. c is calculated to be 4.54. The parameters a2, b21 and b2 can be taken as a measure of the in-plane r bonding, in-plane p bonding and out-of-plane p bonding between the d orbital of central metal ion and the p orbitals of the ligands. If a2 = 1, the bond would be completely ionic. If the overlapping integral is very small and a2 = 0.5, the bond could
The EPR and optical absorption spectra of the [Cu(hsm)2(sac)2] crystal are calculated by using the crystal-field theory. The detailed study shows that the octahedral site occupied by the Cu2+ ion is slightly distorted to tetragonal symmetry (Table 2). The molecular orbital coefficients (a2 and (b21 ) are evaluated. These values indicate that the in-plane p bonding is significantly ionic and the in-plane r bonding is nearly covalent. References [1] H. Kalkan, F. Koksal, Solid State Commun. 103 (1997) 137–140. [2] R. Bıyık, R. Tapramaz, O.Z. Yesilel, Spectrochim. Acta, Part A 68 (2007) 394– 398. [3] R. Tapramaz, B. Karabulut, F. Köksal, J. Phys. Chem. Solids 61 (2000) 1367– 1372. [4] R. Bıyık, Physica B 404 (2009) 3483–3486. [5] B. Karabulut, R. Tapramaz, A. Karadag˘, Appl. Magn. Reson. 35 (2008) 239–245. [6] B. Karabulut, A. Tufan, Spectrochim. Acta, Part A 69 (2008) 642–646. _ Bulut, I. _ Uçar, B. Karabulut, A. Bulut, J. Mol. Struct. 834–836 (2007) 276–283. [7] I. [8] A. Abragam, B. Bleaney, Electron Paramagnetic Resonance of Transition Ions, Clerendon Press, Oxford, 1970. [9] P.C. Poole Jr., A.F. Horacio, The Theory of Magnetic Resonance, John Wiley and Sans, Canada, 1972 (p. 452). [10] P. Huang, H. Ping, M.G. Zhao, J. Phys. Chem. Solids 64 (2003) 523–525. [11] F. Wang, W.C. Zheng, H. Lv, Spectrochim. Acta, Part A 71 (2008) 513–515. [12] E. Kalfaog˘lu, B. Karabulut, Balkan Phys. Lett. 16 (2009) 1–6. [13] T.F. Yen, Electron Spin Resonance of Metal Complexes, Plenum Press, New York, 1969. [14] F.A. Cotton, 1971. Chemical Applications of Group Theory, Cambridge, John Wiley and Sans, Canada (1972), P. 386. [15] D. Kivelson, R.J. Neiman, J. Chem. Phys. 35 (1961) 149–155. [16] B.R. McGarvey, J. Am. Chem. Soc. 60 (1956) 71–76. [17] B.R. McGarvey, J. Chem. Phys. 71 (1967) 51–67.
Contents lists available at ScienceDirect
Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Theoretical investigation of EPR and molecular orbital coefficient parameters for [Cu(hsm)2(sac)2] complex Emel Kalfaog˘lu, Bünyamin Karabulut ⇑ Department of Physics, Faculty of Arts and Sciences, Ondokuz Mayis University, Kurupelit, 55139 Samsun, Turkey
a r t i c l e
i n f o
Article history: Received 18 January 2011 In final form 15 February 2011 Available online 18 February 2011
a b s t r a c t In this study, the molecular orbital coefficients and the spin Hamiltonian parameters of bis(histaminesaccharinate) copper(II) complex, [Cu(hsm)2(sac)2], are calculated theoretically. Two d–d transition spectra and four EPR parameters g k ; g ? ; Ak ; A? for the Cu(II) complex are calculated by using crystal-field theory. The calculated values are in good agreement with the experimental values. The g and A parameters have indicated that the paramagnetic centre is axially symmetric. Having the relations of g k > g ? > g e and Ak > A? for Cu2+ ions, it can be concluded that Cu2+ ions are located in distorted octahedral sites (D4h) elongated along the z-axis and that the ground state of the paramagnetic electron is dx2 y2 (2B1g state). Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction
2. Theoretical formulas and calculation
The electron paramagnetic resonance (EPR) technique may yield useful information about the immediate environment of paramagnetic centers in crystals [1–3]. Optical absorption studies can provide the crystal field parameters and structure of energy levels of the transition-metal or rare-earth ions [4–6]. The EPR and optical absorption techniques provide information about the electronic structure, oxidation state, site symmetry and the bonding nature of the impurity ions. Histamine (hsm), 1H-imidazole-4-ethanamine, is a biologically important molecule and commonly present in the tissues of living organisms. In histamine and anti-histamine activity, an important role is played by the transition metal ions such as Co(II), Ni(II) and especially Cu(II) in the formation of metal complexes [7]. Bulut et al. observed the optical absorption and EPR spectrum and calculated EPR and molecular orbital parameters of [Cu(hsm)2(sac)2]. Figure 1 shows the molecular structure of title complex, with atom labeling scheme as given in Ref. [7]. The Cu2+ ion is hexa-coordinated by four nitrogens of two bidentate histamine ligands composing the equatorial plane and by two monodentate saccharinato ligands occupying the axial positions, adopting an elongated octahedral geometry [7]. Therefore, the coordination geometry of Cu2+ ions in [Cu(hsm)2(sac)2] complex belongs to the D4h point group. In this study, the spin Hamiltonian parameters and optical d–d transitions are calculated based on the crystal field theory. The molecular orbital coefficients are also obtained by using these results [8–12]. The calculated results are correlated with experimental ones in a comparative manner.
The free Cu2+ ion has 3d9 configuration or 3d1 in hole configuration. It has the ground state 2D since the orbital degeneracy is removed in the lower state when the Cu2+ ion is subjected to a tetragonal or an orthorhombic crystalline field. For a 3d9 ion in tetragonal crystal-field, the Hamiltonian including the electron– electron repulsion, spin–orbit interaction, and the crystal-field potential is given by [8–12],
H ¼ He þ Hso ðfÞ þ Hcf ðDq ; Ds ; Dt Þ where
He ¼
X
E-mail address: [email protected] (B. Karabulut). 0009-2614/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2011.02.038
"
i
Hso ¼ HCF ¼
X i X
! # 2 X e2 h Ze þ r2i ri 2m r ij i>j
ð2Þ
f d ‘i si
ð3Þ
Bkq C kq ðiÞ
ð4Þ
k;q;i
where Bkq is the crystal field parameters and Ckq is ½4p=ð2k þ 1Þ 12 Y kq , with Ykq denoting the spherical harmonics [9– 12]. The crystal-field interaction term can be written as
HCF ¼ B44 ðC 44 þ C 44 Þ þ B40 C 40 þ B20 C 20
ð5Þ
The energy level differences between the excited state 2Eg, 2B2g, A1g and ground state 2B1g are given by
2
E1 ¼ Eð2 B1g Þ ! Eð2 A1g Þ ¼ 4Ds þ 5Dt 2
⇑ Corresponding author. Fax: +90 3624576081.
ð1Þ
2
ð6Þ
E2 ¼ Eð B1g Þ ! Eð B2g Þ ¼ 10Dq
ð7Þ
E3 ¼ Eð2 B1g Þ ! Eð2 Eg Þ ¼ 10Dq þ 3Ds 5Dt
ð8Þ
E. Kalfaog˘lu, B. Karabulut / Chemical Physics Letters 505 (2011) 154–156
155
Figure 1. Structre of the [Cu(hsm)2(sac)2] crystal.
Table 1 d–d Transitions (cm1), EPR parameters g and A (cm1) for [Cu(hsm)2(sac)2] crystal.
B1g ? B2g B1g ? Eg g// g\ A// A\
Calculated
Observed
13 480 16 586 2.228 2.050 187 34
13 513 16 155 2.228 2.052 192 24
In terms of the equivalence between the spin-Hamiltonian and the Zeeman interaction, the expressions of the g factors can be written as [10],
1 1 g z ¼ g k ¼ 2 e; N2 Lz þ 2:0023Sz e; 2 2 1 2 1 g x ¼ 2 e; N Lx þ 2:0023Sx e; 2 2 1 2 1 g y ¼ 2 e; N Ly þ 2:0023Sy e; 2 2
ð9Þ ð10Þ ð11Þ
in which ^Lj ðx; y; zÞ and Sj are the operators of orbit and spin angular momentums, respectively. The forms for the Cu2+ hyperfine constant A are given by [10]
4 3 Ak ¼ K þ P N2 þ ðg k g e Þ þ ðg ? g e Þ 7 7 2 2 11 ðg g e Þ A? ¼ K þ P N þ 7 14 ?
ð12Þ ð13Þ
with ge = 2.0023, k N2 0.68 and P = gegnbebnhr3i = 400 104 cm1 which is the nuclear hyperfine constant of the Cu nuclei [10]. K is the core polarization constant of the transition metal ions. In addition, R 2.029 Å, h 93° and j = 0.32 for the [Cu(hsm)2(sac)2] crystal. The calculated optical absorption bands and spin Hamiltonian parameters are compared with experimental values in Table 1. It is known from group theory that the molecular orbitals of Cu2+ ion have the form [13–15]
1 2
WðB1g Þ ¼ aðdx2 y2 Þ a0 ðr1 r2 þ r3 r4 Þ 1 2 1 0 WðEg Þ ¼ bðdxz Þ pffiffiffi b ðp1 p3 Þ 2 1 0 ı WðEg Þ ¼ bðdyz Þ pffiffiffi b ðp2 p4 Þ 2 1 WðB2g Þ ¼ b1 ðdxy Þ b01 ðp1 p2 þ p3 p4 Þ 2
WðA1g Þ ¼ a1 ðdz2 Þ a01 ðr1 þ r2 þ r3 þ r4 Þ
ð14Þ ð15Þ ð16Þ ð17Þ ð18Þ
The ground state of the copper complex is 2B1g, with the unpaired electron in the nondegenerate B1g molecular orbital (Figure 2) as given in Ref. [15]. Accordingly, Eqs. (14)–(18) shows the various states in order of decreasing energy. The B1g and A1g molecular orbitals account for the r bonding, the eg orbital for the out-ofplane p bonding, and the B2g orbital for the in-plane p bonding [13]. The covalency parameter a2 for the in-plane r bonding is evaluated from the expression [15–17]
Figure 2. Energy levels of Cu2+ complexes with (a) r bonding and (b) p bonding.
E. Kalfaog˘lu, B. Karabulut / Chemical Physics Letters 505 (2011) 154–156
156
Table 2 Molecular orbital coefficients for [Cu(hsm)2(sac)2] crystal.
a
2
b21 b2
Calculated
Observed
0.75 0.61
0.75 0.61
0.64
0.64
A 3 a ¼ k þ ðg k g e Þ þ ðg ? g e Þ þ 0:04 7 P " # 4ka2 b21 g k ¼ 2:0023 1 B1g ! B2g " # ka2 b2 g ? ¼ 2:0023 1 B1g ! Eg 2
be completely covalent. The values of the calculated parameters a2, b21 and b2 indicate that the in-plane r bonding, in-plane p bonding and out-of-plane p bonding are significantly covalent in nature as given in Table 2. 4. Conclusions
ð19Þ ð20Þ ð21Þ
Using the Eqs. (19)–(21), we obtained the results as shown in Table 2. It is seen that the theoretical values are in good agreement with the experimental values. 3. Results and discussion The calculated g and A parameters have indicated that the paramagnetic centre is axially symmetric as given in Table 1. Table 1 also shows that the g values are in the order of g k > g ? > g e and Ak > A? . It can be concluded that Cu2+ ions are located in distorted octahedral sites (D4h) elongated along the z-axis [7] and that the ground state of the paramagnetic electron is dx2 y2 (2B1g state). The value of c = Dgk/Dg\ = |(ge gk)/(ge g\)| is a measure of tetragonal distortion in the coordination environment of Cu2+ ion. c is calculated to be 4.54. The parameters a2, b21 and b2 can be taken as a measure of the in-plane r bonding, in-plane p bonding and out-of-plane p bonding between the d orbital of central metal ion and the p orbitals of the ligands. If a2 = 1, the bond would be completely ionic. If the overlapping integral is very small and a2 = 0.5, the bond could
The EPR and optical absorption spectra of the [Cu(hsm)2(sac)2] crystal are calculated by using the crystal-field theory. The detailed study shows that the octahedral site occupied by the Cu2+ ion is slightly distorted to tetragonal symmetry (Table 2). The molecular orbital coefficients (a2 and (b21 ) are evaluated. These values indicate that the in-plane p bonding is significantly ionic and the in-plane r bonding is nearly covalent. References [1] H. Kalkan, F. Koksal, Solid State Commun. 103 (1997) 137–140. [2] R. Bıyık, R. Tapramaz, O.Z. Yesilel, Spectrochim. Acta, Part A 68 (2007) 394– 398. [3] R. Tapramaz, B. Karabulut, F. Köksal, J. Phys. Chem. Solids 61 (2000) 1367– 1372. [4] R. Bıyık, Physica B 404 (2009) 3483–3486. [5] B. Karabulut, R. Tapramaz, A. Karadag˘, Appl. Magn. Reson. 35 (2008) 239–245. [6] B. Karabulut, A. Tufan, Spectrochim. Acta, Part A 69 (2008) 642–646. _ Bulut, I. _ Uçar, B. Karabulut, A. Bulut, J. Mol. Struct. 834–836 (2007) 276–283. [7] I. [8] A. Abragam, B. Bleaney, Electron Paramagnetic Resonance of Transition Ions, Clerendon Press, Oxford, 1970. [9] P.C. Poole Jr., A.F. Horacio, The Theory of Magnetic Resonance, John Wiley and Sans, Canada, 1972 (p. 452). [10] P. Huang, H. Ping, M.G. Zhao, J. Phys. Chem. Solids 64 (2003) 523–525. [11] F. Wang, W.C. Zheng, H. Lv, Spectrochim. Acta, Part A 71 (2008) 513–515. [12] E. Kalfaog˘lu, B. Karabulut, Balkan Phys. Lett. 16 (2009) 1–6. [13] T.F. Yen, Electron Spin Resonance of Metal Complexes, Plenum Press, New York, 1969. [14] F.A. Cotton, 1971. Chemical Applications of Group Theory, Cambridge, John Wiley and Sans, Canada (1972), P. 386. [15] D. Kivelson, R.J. Neiman, J. Chem. Phys. 35 (1961) 149–155. [16] B.R. McGarvey, J. Am. Chem. Soc. 60 (1956) 71–76. [17] B.R. McGarvey, J. Chem. Phys. 71 (1967) 51–67.