Predicting ESR Peaks in Titanium ( III ) , Vanadium ( IV ) and Copper ( II ) Complexes of Halo Ligands by NMR , ESR and NQR Techniques : A DFT Study

15 halo (I≥1/2) complexes of Ti (III), V (IV) and Cu (II) each possessing one unpaired electron were studied using DFT implemented in ADF.2010.02. A ten , NQCC and η parameters of metal ions and ligands were obtained from ESR/EPR program while their s and δ parameters were given by NMR/EPR program after optimization of complexes. Ligands having same values of these 5 parameters were spatially equivalent and, thus, would undergo same hyperfine interaction. Experimental determination of ESR lines in Cu (II) complexes became erroneous because the presence of both the large Jahn-Teller effect and the high value of its spin-orbit coupling constant (λ Cu (II) = -830 cm-1) affect the A ten parameter adversely. Cryoscopic conditions, generally required, in ESR experiments of Ti (III) and V (IV) complexes were difficult to obtain and cumbersome to maintain.


INTRODUCTION
We applied ADF 2010.02[1-10] to fifteen Ti (III), V (IV) and Cu (II) complexes with halo ligands.Each one of these three metal ions possessed only one unpaired electron.Cryoscopic conditions needed during ESR transitions of Ti (III) experimentally determined the A ten parameters.All these difficulties were overcome by the ADF software.
DFT enabled us to deeply understand the relation between magnetic parameters and electronic and geometrical structures of molecules.As ESR was related to the electronic structure and geometry of systems, DFT provided an alternative to the traditional Hartree -Fock (HF) and post-HF approaches to the calculation of ESR parameters.This had brought DFT on the forefront in calculating ESR parameters during the last decade.
The software gave one ESR [Hyperfine Coupling Constant (A ten )], two NQR [Nuclear Quadrupole Coupling Constant(Q) , Asymmetric Coefficient (h)] and two NMR parameters [Shielding Constant (σ),Chemical Shift (δ)] of metal ions and Coordinating Atoms (CA).With the help of the 5 parameters: A ten , NQCC,η, σ, δ ,we could predict the number of ESR peaks in halo complexes of these three univalent metal ions.
A very brief back ground of the development of DFT as applied to NMR of complexes of transition metal ions was given as follows: While the discussion on NMR of transition metal complexes encircled around ligand field theory 25 , in the late 70s, some review articles were collected 26 on small molecules.De Brouchere (1978) published a 100 page review containing 289 references 27 .But till then no calculations on nuclear shielding and spin-spin coupling parameters were carried out.HF approach given by Nakatsuzi 28 did present a paper on the calculation of the above named parameters of the complexes.But it was found lacking in high oxidation states of d 10 systems 29 .In 80s, NMR shielding codes based on HFS or X α α α α α method were developed which was latter known as DFT [29][30][31] .In 1993, Kohn-Sham DFT 32,33 employed IGLO method 32,33 to calculate nuclear shielding.LORG approach 34 as improved upon by GIAO DFT [35][36][37] and CSGT methods 37 was employed.The spin-spin coupling constants (j) of the metal complexes were first of all calculated by Malkin et al [38].In 1996, Dickson and Zieglar 39 calculated FC term [40] by finite-perturbation approach.Later on, SD term 41,42 was also included in spin-spin coupling values. The

Basis for prediction of the number of ESR peaks
As already stated, a total of 5 parameters of ESR (A ten ), NQR (NQCC,η) and NMR (σ, δ) of the metal ion and the coordinating atoms of ligands as obtained from the software were needed.The metal ion should have only one specific value for each one of these parameters, but these parameters might differ in values for coordinating atoms (CA) of the ligands.If the coordinating atoms had the same or nearly the same values of these five parameters, it would indicate that all the ligands were spatially equivalent.They might, further, undergo hyperfine interaction with the metal ion.Both the hyperfine interaction and relative magnitude of the parameters for metal and CA will form the basis to determine the number of ESR peaks.

Prediction of Hyperfine Interaction between Metals and Ligands in Ti (III) and V (IV) Complexes
After knowing the values of nuclear quantum number and g factor of the nucleus of metal (I M , g M ) and of the coordinating atoms (CA) of ligands (I CA , g CA ) from the literature, we would calculate the nuclear magnetic moments in terms of b n both for the metal (m M ) and the coordinating atoms (m CA ) of ligands as follows: Then [m M /m CA ] ratio called m n ratio was calculated to draw the following inferences: (a) If this ratio was comparable and isotopes with non zero I possessed appreciable % natural abundance, the unpaired electron would be delocalized both on the metal ion and the ligands.So the hyperfine interaction between metal and ligands should be possible.The peaks should arise both from the metal ion and the ligands.(b) Small or large ratios implied that m CA of ligands and the metal (m M ) differ largely.No hyperfine interaction between metal ion and ligands should be possible.The electron would be localized only on metal ion irrespective of the values of I and % abundance of metal ions and CA.
The peaks should arise only from the metal ion.

Prediction of Hyperfine Interaction between Metals and Ligands in Cu (II) Complexes
The presence of a large Jahn-Teller effect, generally, allowed the hyperfine interaction and the peaks should arise both from the Cu (II) and the coordinating atoms of the ligands irrespective of their [m Cu /m CA ] ratios.

Rules for calculating ESR Peaks in the metal ion Complexes
If I M and I CA were the nuclear spins of metal (M) and the CA respectively.Then: (A) Number of ESR peaks given by a metal ion would be 2I M +1 ..

.(b) (B)
Peaks arising from ligands could be predicted from their stereochemical arrangement if the hyperfine interaction was possible as follows: (i) When all the n ligands were spatially equivalent, then each ESR line of metal ion would split up into lines: If n 1 ligands were spatially of one type; n 2 of the other type and so on, then total number of lines into which one line of the metal ion split would be : If all the ligands were spatially nonequivalent, one line of metal ion would split into: In case, the A ten of the metal ion was higher than that of CA, then first the lines obtained from metal ion should be calculated.Each one of this line could, further, split into a number of lines given by coordinating atoms if hyperfine interaction among the metal ion and the ligands was possible.Conversely, if coordinating atoms possessed higher A ten value/s, then first the lines given by the ligands were calculated.Each line of ligands would, then, split by the metal ion.(d) There could happen an overlapping of ESR lines due to different reasons.So, experimentally observed number of lines might be less than theoretically predicted lines.Further, if the predicted number of lines were very large with small A ten values of species, the lines would merge to give a continuum.

Obtaining ESR and NQR parameters
After optimization of complexes, the software was run by Single Point, LDA, Default, Spin Orbit, Unrestricted, Collinear commands using DZ or TPZ Basis sets with Nosym symmetry in its "ESR/ EPR Program" to obtain ESR (A ten ) and NQR (NQCC,) parameters for the Cu(II) and the coordinating atoms ( 14 N, 35 Cl, 89 Br, 127 I) of the ligands [43-46].

Obtaining NMR Parameters
σ and δ values of Cu (II) and 14 N, 35 Cl, 89 Br, 127 I of ligands were obtained from "NMR/EPR Program" by the above commands except for replacing Spin Orbit by None [35, 9-10].

Table:
1A gave expanded forms of acronyms.Tables: 1B contained I M, I CA, g M , g CA , m M and m CA (in terms of b n ) and ratios (m n ) of m M and m CA to predict the possibility of hyperfine interaction between the metal ion and ligands.Tables:1C gave values of A ten , NQCC, η, σ, δ parameters of CA of ligands, number of spatially different ligands along with A ten ,σ, δ values of the metal ions along with the number of theoretically expected ESR peaks.; each A ten of Ti (III) was higher than those of the ligands. [iii] The unpaired electron was localized only on Ti (III) because the small m Ti / m CA ratio would not allow any hyperfine interaction.Their ESR spectra would show only a large sextet from Ti (III) [2.5/2+1].
[ii] A ten of Ti (III) was higher than all the chloro ligands.
[iii] Ti (III) and ligands had comparable m Ti / m Cl ratio to allow unpaired electron to be delocalized.So the hyperfine interaction was possible among them.
Its ESR spectrum would give a large sextet from Ti (III) [ of Ti (III) was higher than those of the ligands.[iii]The unpaired electron was delocalized both on Ti (III) and the ligands due to their comparable m Ti/ m C l ratio.
Its spectrum would give a sextet from Ti (III) [2.5/2+1].Each line of this sextet would, further, split into 100 lines (d ) from two types of spatially different Cl [2.3.3/2+1] 2 due to hyperfine interaction.In fact, a continuum should be observed.

Prediction of number of ESR peaks in V (IV) Complexes
Table : 1B predicted of Hyperfine Interaction between V (IV) and the halo ligands.Table : 1C contained A ten , ó , ä values of the parameters of V(IV) and the A ten , NQCC, h , ó , ä parameters of halo ligands for [VX4] ( X= F, Cl, Br, I) along with the predicted number of ESR peaks Their ESR discussion was divided into two parts:
[ii] A ten of V (IV) was more than those of the ligands.
[iii] With comparable m V / m CA ratios, the unpaired electron would be delocalized both on the V (IV) and the ligands.
[ii]A ten of V (IV) was more than those of the ligands.
[iii] The unpaired electron was localized only on V (IV) and not on ligands as their m V / m Cl ratio was large.
Ti(III) and the A ten , NQCC, η , σ , δ parameters of halo ligands for [TiX4] 1-( X= F, Cl, Br, I) along with the predicted number of ESR peaks.Their ESR discussion was divided into two parts:Prediction of ESR peaks in [Ti X 4 ] 1-(X =F, Br, I)They showed the following common Table 1(c): Prediction of Number of ESR peaks in Metal Ion 901.0 Two types ; each A large sextet (b)

3 -
2.5/2+1].Its each line would, further, split up into a tridecane from 4 equivalent Cl [2.4.3/2+1] due to hyperfine interaction.Prediction of ESR peaks in six-coordinate complexes [Ti X 6 ] 3-(X =F, Cl, Br) Again, two cases would arise: Prediction of ESR peaks in [Ti X 6 ] 3-(X=F, Br) They showed the following common features: [i]Six halo ligands possessed nearly the same values of their A ten , NQCC, that they were spatially equivalent.[ii]A ten of Ti (III) was higher than those of the ligands.[iii]With small m Ti / m CA ratios, the unpaired electron was localized only on Ti (III).Their spectra would give only a large sextet from Ti (III) [2.5/2+1] with no hyperfine interaction.Prediction of ESR peaks in [TiCl6 ] It showed the following features: [i] It gave two sets of values of A ten, NQCC, h, ó, ä parameters to indicate two types of chloro ligands; each type containing three ligands.[ii] A ten Their ESR spectra would first give a large octet from V (IV) [2.1.7/2+1].Each line of this octet would, further, split up into a quintet or 13 lines or 21 lines from four equivalent F [(2.4.1/2+1)] or Br [(2.4.3/2+1)] or I [2.4.5/2+1)] respectively due to hyperfine interaction.

Table 1 : Acronyms and their expanded forms
1B predicted of Hyperfine Interaction between Ti (III) and the halo ligands.Table: 1C contained A ten , σ ,δ values of the parameters of