IJCRR - 4(22), November, 2012
Pages: 12-28
Date of Publication: 24-Nov-2012
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ELECTRON SPIN RESONANCE, NUCLEAR QUADRUPOLE RESONANCE, REFLECTANCE AND MAGNETIC PARAMETERS OF COBALT (II) AND NICKEL (II) COMPLEXES USING DENSITY FUNCTIONAL THEORY
Author: Harminder Singh, A.K. Bhardwaj, M.L. Sehgal, Susheel K. Mittal
Category: General Sciences
Abstract:Density Functional Theory was used to calculate and correlate 14 ESR, NQR, Reflectance and Magnetic parameters of 20 Co+2 and Ni+2 complexes such as [CoX4]2- (X = F, Cl , Br ,I), [Co(OH2)4]2+, [Co(NCO)4]2-, [CoX6]4- (X = F, Cl), [NiX4]2- (X = Cl ,Br, I, NCO), [NiX6]4- (X=F, Cl ,Br, I) [Ni(H2O)6]2+, [Ni(NH3)6]2+, [Ni(CH3NH2)6]2+, [Ni(NH3)4(NCS)2]. All computations were carried out in the gas phase using ADF2010.02 by applying Single Point, LDA, Default , Spin Orbit, Unrestricted, None, Collinear commands using DZ or TPZ basis sets. The complexes were optimized to obtain two ESR (g11, g22, g33, giso, a11, a22, a33, Aten) and three NQR parameters [?, q11, q22, q33, NQCC]. Two Reflectance parameters [?complex, % covalent character] were calculated from giso. In addition, five magnetic [?soc, ?t, ?net, t2g electron delocalization and its constant k] and two more ESR [H^, ΔE hf] parameters were calculated by combining the ESR and Reflectance data. We verified the Laplace equation using the NQR data. The delocalization parameter (k) and the reflectance parameter called Nephelauxetic ratio (?35) were found to have almost the same values as both determine the covalence in complexes. The calculated values of parameters were found in agreement with their reported values.
Keywords: DFT, ESR, NQR, Reflectance, Magnetism, Nephelauxetic ratio, delocalization parameter
Full Text:
INTRODUCTION
Effective Spin Hamiltonian (H^) is a mathematical expression that determines energy of an ESR transitions when an ESR active metal ion is surrounded by ligands in a definite geometry. It depends upon a number of ESR parameters [anisotropic and isotropic splitting factors (g11,g 22, g33, g iso), hyperfine coupling constants( a11,a22 ,a33 ,Aten)], NQR parameters [electric field gradient or efg (q11,q22,q33), Nuclear Quadrupole Coupling Constant(Q)]* , total electronic spin (S), Bohr Magneton of both the electron (?e) and the nucleus (?n), nuclear spin * Q or e Q is the nuclear quadrupole moment. q Or e q is the electric field gradient and product of these quantities (e Q× e q= e2Qq) is nuclear quadrupole coupling constant (Q). quantum number (I), gn (nuclear magnetic ratio) and nature of surrounding nuclei having quadrupole moments(I?1). No doubt, ESR studies on some biologically important(1-2) Co+2 and catalytically(3) suitable Ni+2 complexes has already been reported, yet a correlation of their ESR, NQR, Reflectance and Magnetic parameters with the help of a software is rarely found in the literature. With certain commands, the software gave five ESR and NQR parameters. They were together used to calculate two more ESR parameters [effective spin Hamiltonian (H^) and hyperfine coupling energy (?Ehf)]. The giso parameter was further correlated to two Reflectance parameters [spin orbit coupling constant (?complex), % covalent character]. The ESR and the Reflectance parameters were together used to calculate and correlate five magnetic parameters [magnetic moments namely total (?t), net (?net) and that containing contributions from spin and orbital (?soc or ?ADF), t2g electron delocalization and its constant (k)]. The software also gave dipole moments and symmetry symbols of complexes. We could also verify Laplace equation for the complexes. The following points necessitated the present study to be taken up with the help of software: i) There had hardly been any attempt made to theoretically calculate and correlate ESR, NQR, Reflectance and Magnetic parameters of complexes of transition metal ions. ii) With ESR transitions falling in low energy microwave region (X band: 9000-10000 MHz), the experiments required cumbersome cryoscopic† conditions. 14 ESR, NQR, Reflectance and Magnetic parameters were correlated in 20 Co2+ and Ni2+ complexes of coordination numbers 4 and 6 by using ADF (Amsterdam Density Functional) 2010.02 software by applying of D.F.T. (Density Functional Theory) (7-9). The 5 parameters given by the software (g, a, q, NQCC,?) were used to calculate 9 other parameters [H^, ?Ehf, ?complex, % covalent character, ?t , ?net, ?soc , t2g electron delocalization and its constant (k)]. 23 relations were selectively used to calculate these parameters of complexes like [CoX4] 2- (X = F, Cl, Br, I), [Co(OH2)4] 2+, [Co(NCO)4] 2- , [CoX6] 4- (X = F, Cl), [NiX4] 2- (X = Cl , Br, I, NCO), [NiX6] 4- (X = F, Cl, Br, I) [Ni(H2O)6] 2+ , [Ni(NH3)6] 2+, [Ni(CH3NH2)6] 2+ , [Ni(NH3)4(NCS)2]. These complexes possessed both regular (Td, Oh) as well as distorted stereochemistries (C1,C2, D?h,D4h, D6h ,D2d ).
(1) Calculation of ESR parameters (10-25)
(a) Effective Spin Hamiltonian (H^):
Four factors which contributed to H^ (MHz) were: g, a, Q and interaction of nuclear magnetic moment with external magnetic field (I). Three relations were used to calculate H^ having contributions from these four factors:
[1] Was used for systems with different values of g and a. [2] Was used for axially symmetric systems while [3] was used when g and/or a parameters had the same or nearly the same values. The first and the last terms in these relations were in ergs and the other two were in MHz (6.627 ? 10-21 erg = one MHz; ?e=1.3994 MHz/Gauss; ? n= ?e/1836. gn had a specific value for each metal).
Here, ?soc was the magnetic moment given by spin orbit coupling. The (?t) was total magnetic moment while ?tip ‡ and ?tip were Zeeman Second Order molar magnetic susceptibility and Zeeman Second Order magnetic moment respectively. ?t was the total molar magnetic susceptibility and (k) was t2g electron delocalization constant. Molar
magnetic susceptibilities (?Mol s.o) of Ni2+ and Co2+ with 2 and 3 unpaired electrons respectively were 3333.33 Χ10-6 and 6250.0?10-6 cgs/mol. ?metal ion and ? complex were the spin-orbit coupling constants of the free metal ion and of the same metal ion present in the complex respectively. Free ?Co 2+ and free ? Ni 2+ had values -172.0 and -316.0 cm-1 respectively. Total value of g called gt and similar term geff were calculated by [16
METHODOLOGY
After optimization of the complexes(42-43) by ADF 2010.02, the SW was run by applying Single Point, LDA* , Default, Spin Orbit, Unrestricted, None and Collinear commands by using DZ* or TPZ* Basis sets in all the Co2+ complexes and octahedral Ni2+ complexes. In Ni+2
tetrahedral complexes, LDA was replaced by GGABP*. All the complexes have Nysom* symmetry.
Complexes of Cobalt (II)
Co2+, with three unpaired electrons and a quartet ground state, should show both the Zero Field Splitting (D) and Jahn-Teller effect. But in the four coordinate complexes like [CoX4]2± (X= H2O, F, Cl, Br, I, CNS), an almost tetrahedral symmetry was enforced. Also, the two high spin six coordinate complexes [CoX6] 4- (X= Cl, F) possessed an axial and nearly an axial symmetry respectively. Moreover, this software did not take an account of Zero Field Splitting. So, both these effects were neglected. Only a few relevant papers on Reflectance and Magnetic (44-57) and ESR studies (58-62) of Co2+ complexes were reported. Theoretically calculated parameters obtained from the results of the software agreed well with their experimental values (53-54) .
RESULTS
Each OUTPUT file of a complex gave values of two ESR (g11, g22, g33 and g iso, product of g n and a11,a22,a33,Aten)and three NQR(?, q11,q22,q33,NQCC) parameters along with its optimization parameters [geometry, dipole moment, bonding energy and total energy(Xc)].
Xc was made up from LDA and GGA components; each being further made up of Exchange and Correlation parts]. The bonding energy was computed as an energy difference between molecule and fragments. When the fragments were single atoms, they were usually computed as Spherically Symmetric and SpinRestricted. This, usually, did not represent the true atomic ground state (42-43) . Tables: 1. 1 and1.1 A give the optimization parameters of cobalt metal and all the Co2+ complexes. Tables: 1.2 -1.3 give values of all the five ESR and NQR parameters, verification of Laplace equation and (?) for four and six coordinate Co2+ complexes respectively. Table: 1 .2 A and 1.3A give g iso , A ten and Q values along with contributions from their respective factors. They also give contribution from the fourth factor called interaction of nuclear magnetic moment with external magnetic field factor (I) into H^ along with ?Eh f (≈ 0.5 A ten) values for both the four and six coordinate Co2+ complexes respectively. Tables: 1.4, 1.4 A and 1.5 contain magnetic parameters of four and six coordinate Co2+ complexes as calculated by applying the results from ESR and Reflectance techniques.
DISCUSSION
The necessity, the originality, the relevance, the objective of present work and how it moved the body of scientific knowledge forward had already been explained in our previous communication. We could successfully calculate/correlate 14 parameters of the four techniques in 36 Ti2+,3+ , V +2,3+,4+ and Cr3+ complexes(63) . The discussion was divided into two parts: [l] Calculation of ESR and NQR parameters (a) Effective Spin Hamiltonian (H^) (i) The four complexes [CoX4] 2- (X=F, Cl, Br, I) were of Td symmetry while both [Co (OH2)4] 2+ and [Co(NCO)4] 2- complexes possessed C1 symmetry. But in both these types of complexes, the software gave nearly the same values of g. Also, none of them would obey the conditions of axial symmetry. So, for all these six complexes, the H^ was calculated by [3]. (ii) [CoF6] 4- and [CoCl6] 4- with point groups D?h and D6h respectively had axial symmetry with (a) Two of the three g called g ? had the same values and third of higher value was called g?? (b) Two a parameters called a? were of the same value and third of higher value was named a11. (c) Two of the three q parameters were of the same value (d) ?=0. Relation [2] was used to calculate H^.[S_x=S_y=S_z=3/2; I_x=I_y=I_z=3.5 and g n= 1.3220000]. Individual contributions from four factors in the total value of H^ for the eight Co 2+ complexes are given in small brackets of horizontal row shown at the bottom (?) in Tables: 1.2A and 1.3A. (b) Relation [7] was used for the verification of Laplace Equation (Table: 1.2-1.3) while parameters such as ? and ? E hf (Tables: 1.2 A1. 3A) were calculated by [5, 4] respectively.
[2] Calculation of Reflectance and Magnetic parameters from ESR parameters
(a) ADF and t parameters: The discussion was divided into two parts:
(i) Four Coordinate Complexes: Table:
1.4 gave values of magnetic moments due to spin orbit coupling (?ADF) as calculated from giso values by applying [8].This moment arose from an intermixing of ground 4A2 term of Co2+ with its immediately higher in energy 4T2 term which made 4A2 to acquire some T character. Contribution of magnetic moment from Second Order Zeeman Effect (?t.i.p) was calculated by [9 and10]. The former gave ?t.i p. while the latter gave ?t i p. Finally, the sum of ?ADF and ?tip resulted in ?t which was calculated by [11].
(ii) Six Coordinate Complexes: Table:1.5 contained ?t values of two high spin six coordinate Co2+ complexes as calculated by a different relation [11c] because the ground term in octahedral Co+2 complexes was 4T1g while its tetrahedral complexes had 4A2 ground state. (b) Calculations of t 2g electron delocalization, its constant (k), ?complex, % covalent character, ?net and gt
(i) Four Coordinate Complexes: [Table: 1.4A] First we calculated total molar magnetic susceptibility (?t) by applying [12].Then (k) was calculated by [13].The term 8 N ? 2/10Dq, called the Second Order molar magnetic susceptibility, i.e. ?t.i.p had already been calculated by [9] (Table: 1.4). Knowing (k), we could calculate ?complex by [14]. It gave the weight by which ?Co 2+ (-172.0 cm-1 ) was reduced to give ?complex on the formation of Co2+ complexes. This decrease was due to delocalization of electron cloud which had brought about covalence in metal-ligand bonds (64). The % covalent character was calculated by [15].The gt values of complexes were calculated by [16] .They were found in agreement with geff . The geff values, in turn, were calculated from 10Dq values of complexes given by reflectance spectra by [17]. Similarly, t2g electron delocalization was calculated either indirectly from gt values [18] or from geff [18a] . The values obtained from both these methods would almost agree. Lastly, ?net was calculated by [11a]. It was noticed that (k) did not agree well with Nephelauxetic Ratio (?35) in tetrahedral Co2+ complexes. On the contrary, the ?complex as calculated by [14] as well as its value obtained from reflectance spectral method agreed well with each other (53-54). This difference in (k) and (?35) values was due to the fact that in tetrahedral Co2+ complexes, the lowest energy band (?1) , being so low in energy would not fall in u v.- vis. region (?300-1000 nm). In such cases, (?35) was calculated from the ratio of ?2 and ?3 bands. Both these bands had vibration character i.e. were quite broad and errors occurred in locating the exact positions of their ?max values.
(ii) Six Coordinate Complexes:
With negligible t2g electron delocalization, parameters like gt , ?complex , (k) and the % covalent character could not be calculated.
Table: 1.1. Energies (kJmole-1 ) of Co Sum of orbital energies = -78854.221 Total energy = - 134234.270 Kinetic energy = 136350.812 Nuclear attraction energy = - 346177.790 Electron repulsion energy = 57226.702 Exchange energy = - 5539.960 For Co nucleus I =3.5 and gn = 1.322000
Complexes of Nickel (II)
[A] Octahedral Complexes of Nickel (II)
Ni 2+ is a non-Kramer ion. With S=1, it had m j =0, ?1, ----- j ?1 states. Their degeneracy was completely removed even by the crystal field. So they gave only the singlet levels. There were only a few cases where ESR spectra of Ni2+ octahedral complexes could be observed at room temperature(4-6) because its ground state m j =0 was separated from the first excited state (m j =1) by an energy more than the energy of microwave region. No doubt, the detailed studies were reported on Reflectance and Magnetic data of Ni2+ complexes (66-83), yet a further study was needed to know as to how the results thus obtained could be correlated with their ESR parameters.
RESULTS
Tables: 2.1 and 2.1A give optimization parameters of nickel metal and the Ni+2 complexes. Table: 2.2 gives values of the five ESR and NQR parameters, verification of Laplace equation and another parameter (?) for the six coordinate Ni2+ complexes. Table: 2 .2 A gives g iso, Aten and Q values and contributions from their respective factors. It also gives contribution from the fourth factor called interaction of nuclear magnetic moment with external magnetic field factor (I) into H^ as well as ?Ehf (≈0.5 Aten) values.Tables:2.3-2.3A contain magnetic parameters of the six coordinate Ni2+ complexes as calculated by applying the results from ESR and reflectance techniques.
DISCUSSION
The discussion was divided into two parts: [l] Calculation of ESR and NQR parameters (a) Effective Spin Hamiltonian: All the eight Ni+2 complexes had nearly the same values of g parameters. Also, none of them obeyed all the conditions of axial symmetry. So relation [3] was applied to calculate H^ values for all. [Put S_x=S_y=S_z=1; I_x=I_y=I_z=1.5 and g n = - 0.5000133]. The individual contributions from four factors in the total value of H^ were given in small brackets of horizontal row shown at the bottom (?) of each complex [Table: 2.2A]. (b) Relation [7] was used for the verification of Laplace Equation (Table: 2.2) and parameters such as ? and ? Ehf (Tables: 2.2- 2. 2A) were calculated by [5, 4] respectively.
[2] Calculation of Reflectance and Magnetic parameters from ESR parameters
(a)Calculation of ?ADF and ?t: Table: 2.3 gave values of magnetic moments due to spin-orbit coupling (?soc or ?ADF) as calculated from giso by [8].These values were generally more than their respective ?so. values. This was due to intermixing of ground 3A2g term of Ni2+ with its immediately higher in energy 3T2g term of same multiplicity. This made its 3A2g term to acquire some T character. The contribution from Second Order Zeeman Effect (?tip) was calculated by [9and10]. The former gave ?t.i.p. and latter gave ?t i.p. Sum of ?ADF and ?tip was equal to the total magnetic moment (?t) [11]. As expected, the net magnetic moments (?net) of these complexes were somewhat more than their respective (?so) values. (b)Calculation of t2g electron delocalization constant (k), ?complex and % covalent character (Table: 2.3A): Total molar magnetic susceptibility (?t) and its constant (k) were calculated by [12, 13] respectively. The term 8 N ? 2/10 Dq representing the Second Order molar magnetic susceptibility (?t. i. p) had already been calculated [Table: 2.3]. ?complex was calculated by [14]. It gave the weight by which ? Ni 2+ [-316.0 cm-1 ] was reduced in Ni2+ complexes. This reduction was due to the delocalization of electron cloud which had brought about covalence (64) in metal-ligand bonds by intermixing of electron clouds of Ni2+ t2g orbitals with ligand orbitals as both the metal ion and ligand orbitals were of suitable symmetry and comparable energies. The % covalent character was calculated by [15]. The calculated (k) values agreed well with Nephelauxetic Ratios (?35) of Ni2+ complexes wherever reported in literature or were theoretically calculated from three reflectance spectral bands of the complexes (66, 83) . (c)Calculation of total value of g called gt , t2g electron delocalization and ?net (Table: 2.3 A): Total value of g called gt was calculated by [16] while the total magnetic moment (?t) was calculated by [11] .Theoretical gt values were well in agreement with geff values as calculated by [17] from 10Dq values obtained from reflectance data. Same was the case of t2g electron delocalization values. Whether they were calculated from gt by [18] or were calculated from g eff by [18a], their values were found to be in agreement. The ? net was calculated by [11a].
Tables: 2.1.Energies (kJ mole-1 ) of Ni
Sum of orbital energies = -85650.855 Total energy = -146522.795 Kinetic energy = 148997.799 Nuclear attraction energy = -352449.098 Electron repulsion energy = 62843.648 Exchange energy = -8809.705 For Ni nucleus I =1.5 and g n = -0.500133
[B] Tetrahedral Complexes of Ni (II)
The presence of an extensive spin–orbit coupling in 3T1 ground state of Ni2+ made spin relaxation times very small. So it became quite difficult to observe ESR spectra of four coordinate Ni2+ complexes (83-89). Of course, like octahedral Ni2+complexes, numerous papers were reported on Reflectance spectral and Magnetic properties of Ni2+ tetrahedral complexes.
RESULTS
Table: 2.4 gives values of all the five ESR and NQR parameters, verification of Laplace equation and the parameter (?) for four coordinate Ni2+ complexes. Table: 2 .4 A gives giso , Aten and Q values along with contributions from their respective factors .It also gives contribution from the fourth factor called interaction of nuclear magnetic moment with external magnetic field factor (I) into H^ as well as ?Eh f (≈ 0.5 Aten) values for the four coordinate Ni2+ complexes. Tables: 2.5 and 2.5A contain magnetic parameters of four coordinate Ni2+ complexes as calculated by applying the ESR and Reflectance spectral results.
DISCUSSION
[l] Calculation of ESR and NQR parameters
(a) Effective Spin Hamiltonian H^ The complexes like [NiX4] -2 (X= Cl, Br, I) belonged of Td point group while the complex (X=NCO) had a D2d symmetry. All these complexes had different values of parameters like g and a. So Relation [1] was applied to calculate their H^ (Table: 2.4 A). (b) Relation [7] was used for the verification of Laplace Equation (Table: 2.4) and parameters such as ? and ? E hf (Tables: 2.4- 2. 4A) were calculated by [5, 4] respectively. [
2] Calculation of Reflectance and Magnetic parameters from ESR parameters
(a) Calculation of ? ADF and ?t (Table: 2.5): ?ADF was calculated from giso by [8] while ?t was calculated by [11a] while the relation [11] was used to calculate the same parameter in Ni2+ octahedral complexes. It was due to the reason that Ni2+ had 3T1 ground state in its tetrahedral complexes while it had 3A2g state in the octahedral complexes.Net magnetic moments (?net) of these tetrahedral complexes, as expected, were found to be some what more than the six coordinate complexes because of spin–orbit coupling. [2(b)] Calculation of t2g electron delocalization, its delocalization constant (k), ?complex and % covalent character (Table:2.5 A):Total value of g called gt was calculated from the total magnetic moment by [16] .The average of the difference between gt and giso with a negative sign gave t2g electron delocalization parameter [18a]. It was, then, related to another parameter called t2g electron delocalization constant (k) by [13a]. Again, the relations [18a] and [13a] used here were different from those of [18] and [13] relations as the two latter relations were used to calculate the same parameters respectively in octahedral Ni2+complexes.This, again, was because of the difference in ground states of Ni2+ in its octahedral and tetrahedral geometries. The values of (k) as calculated by [13a] and the experimentally determined Nephelauxetic Ratios (?35) of tetrahedral Ni2+ complexes (54a, 84) were given in Table ; 2.5 A** for a comparison. Lastly, the constant (k) was related to the covalent character in these complexes by [15].This covalence was brought about by intermixing of electron clouds of Ni2+ “e” orbitals with the ligand orbitals.
**If we look into the Table: 2.5 A, we find that the theoretical (k) values differ slightly from the experimental (?35) values. It is, again, due to the fact that like Co2+ tetrahedral complexes, the lowest energy band (?1) in the tetrahedral Ni2+ complexes is also low lying in energy. So it does not fall in u v. - vis. region. The (?35) parameter in such cases is calculated from the ratio of ?2 and ?3 bands. As both these bands have vibration character ,i.e. are quite broad and errors occur, invariably, in locating the exact positions of their ?max values.
CONCLUSIONS
With certain commands, the ADF software gave five ESR and NQR parameters. These parameters were used to calculate nine other ESR, NQR, Reflectance and Magnetic parameters by the selective use of 23 relations. So these14 parameters of the four techniques were correlated in the 20 Co+2 and Ni+2 complexes without the help of any diagnostic instruments. Theoretically calculated values of these parameters were found to be fairly in agreement with their experimental values reported in the literature. The authors had already proved this fact in 36 Ti2+,3+ , V 2+,3+,4+ and Cr3+ complexes in the previous communication and hope to prove the same in forty five more complexes of 2nd and 3rd transition series metal ions in the forthcoming communication.
ACKNOWLEDGEMENTS
Authors acknowledge the immense help received from the scholars whose articles are cited and included in references of this manuscript. The authors are also grateful to authors/ editors/ publishers of all those articles, journals and books from where the literature for this article has been reviewed and discussed. They are indebted to Mr. S.R. Heer , Chief Engineer (Retd.), North Zone, Doordarshan, New Delhi (India), for his invaluable cooperation in the installation and smooth working of the ADF software.
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