Predicting ESR Peaks in the 4 d and 5 d Transition Metal Ion Complexes by NMR , ESR and NQR Parameters : A DFT Study

Computational chemistry was used to predict the number of ESR peaks in the 2nd and 3rd transition metal ion complexes by applying DFT implemented in ADF 2012.01.Only a limited experimental ESR research had been carried out in this field because high values of spin orbit coupling constants of these metal ions which provide an important energy transfer mechanism would adversely affect the values of ESR and NMR parameters (especially Aten) of their complexes. Therefore, theoretical predictions were useful. ESR (Aten) and NQR (NQCC,h) parameters of transition metal ions and the coordinating atoms of ligands were obtained from the ESR/EPR program while their shielding constants (s) and chemical shifts (d) were obtained from the NMR/EPR program after optimization of the complexes. Ligands whose coordinating atoms (CA) possessed the same values of the five parameters (Aten, NQCC, d,h, s) were expected to be spatially equivalent and would undergo the same hyperfine interaction with the central metal ion. 34 complexes of 10 metal ions consisting of five congeners: Zr (III), Hf (III) ; Nb (IV) ,Ta(IV) ; Tc (II), Re (II); Ru (III) ,Os(III) ;Rh (IV), Ir (IV) were selected to predict the number of ESR peaks.

As DFT had, hardly, been applied to determine number of ESR peaks in these metal  4+ belonging to 10 metal ions of the 2 nd and 3 rd transition series.All these six coordinate complexes containing either weak halo or comparatively stronger (ammine and thiocyanato -N) ligands belonged to five congeners of the 2 nd and 3 rd transition series.They, invariably, possessed one unpaired electron because their large Crystal Field Stabilization Energies (CFSE) would cause pairing of electrons even with the week ligands.

Need of the Study
There were two main reasons which tempted us to take up the present study: (i) Only a limited research work had been done in the experimental determination of number of ESR peaks in 4d and 5d metal ion complexes because their authentic 10 Dq values were difficult to determine experimentally due to their high values of spin orbit coupling constants (l M n+ ) which, in turn, would adversely affect ESR parameters (especially A ten ).(ii) ESR transitions energies falling in microwave region, generally, needed cryogenic conditions which were difficult to obtain and cumbersome to maintain.

RESULTS
Results for 34 complexes of 10 metal ions were tabulated in Tables: 1-2.
Table : 1 contained values of I M, I C A, g M and g CA as well as µ M and µ CA (in terms of b n ) and ratios of m M and m CA to predict the possibility of hyperfine interaction between metal ions and ligands.

DISCUSSION
It was taken up under the following headings:

basis for prediction of number of ESR peaks
Five parameters (A ten, NQCC, h, s, d) of metal ions and coordinating atoms (CA) of ligands were obtained from the software by giving it certain commands.A metal ion possessed only one value of each one of these 5 parameters while the values of the parameters might differ in case of the coordinating atoms (CA) of ligands.When, the ligands possessed the same or nearly the same values of these 5 parameters, it indicated that all the ligands were spatially equivalent.The relative magnitudes of the values of the parameters of metal ion and CA would also be taken into account while predicting ESR peaks of the complexes.

Relation to Calculate of nuclear magnetic moment ((µ M ) in terms of b n
After knowing the values of nuclear spin quantum numbers and g factors of metals (I M , g M ) and of coordinating atoms (CA) of ligands (I CA , g CA ) from the literature, we could calculate nuclear magnetic moments of both the metal (µ M ) and coordinating atoms (µ CA ) of ligands in terms of b n by the following relation: ...(a*)

Knowing whether hyperfine interaction was possible or not
From [µ M /µ CA ] ratio called µ n ratio, we could draw the following conclusions: (a) A comparable µ n ratio for isotopes with I >0 having appreciable % natural abundance would mean that the unpaired electron was delocalized both on the metal and the ligands.So the hyperfine interaction between the metal ion and the ligands was most probable.The peaks would arise both from the ligands and the metal ion.(b) Very small or very large ratios implied that µ n of ligands and metal differ largely.In such a case, no hyperfine interaction between the metal and the ligands was possible.
Electron would remain localized on the metal irrespective of the values of I and the % abundance.The peaks would arise only from the metal ion.*Analogous to an electronic spin: m e =g e [s (s+1)] (V) There might occur overlapping of ESR lines from different factors.So experimentally observed number of lines might be less than the theoretically predicted lines.Also, when the predicted number of lines was large and A ten value/s of species undergoing hyperfine interaction was/were very small, the lines would merge to give a continuum.
The ESR peaks of the following 34 complexes were theoretically predicted.The metal wise discussion was subdivided into ten headings (5.2-5.11).

Prediction of number of ESR peaks in Zr (III) Complexes
ESR spectra of [ZrX 6 ] 3-(X=F, Cl, Br) were discussed in two parts: (a) [ZrX 6 ] 3-(X=F, br) They showed the following features: (1)  The six F or Br possessed same values of A ten , NQCC, h, s, d respectively so that all the ligands were spatially equivalent.(2) A ten value of Zr (III) was more than F but lesser than Br.(3)  With small µ n ratios, the unpaired electron was localized only on Zr(III).Their ESR spectra gave only a large sextet (b) from Z r (III) [2*5/2+1].

(b) [ZrCl 6 ] 3-
It showed the following features: (1) As the six Cl had the same A ten , NQCC, h, s, d values respectively, they should be spatially equivalent.
(2) Unpaired electron was delocalized both on Zr (III) and Cl as their µ n ratio was comparable 3 .A ten value of Zr (III) was more than those of the six Cl.

Prediction of number of ESR peaks in Hf (III) Complexes
Complexes like [HfX 6 ] 3-(X=F, Cl, Br) and [Hf (NH 3 ) 6 ] 3+ were studied as follows: (a) [HfX 6 ] 3-(X=F, br) They showed the following common features: (1) The six F or Br were spatially equivalent as they showed the same A ten , NQCC, h, s, d values respectively.
(2) As their µ n ratios were small, the unpaired electron would remain localized only on Hf (III) with no hyperfine interaction.
(3) A ten value of Hf (III) was more than those of the F and the Br.

Prediction of number of ESR peaks in Nb (IV) Complexes
The study included 5 complexes such as: (2) With comparable µ n ratio, the unpaired electron was delocalized both on Nb (IV) and the F.
(3) A ten of Nb (IV) was more than those of the F ligands.
Its spectrum gave a large decane (b)  ESR spectra would give only a large decane (b) from Nb (IV) [2*9/2+1] with no hyperfine interaction between Nb (IV) and Cl or NH 3 as their µ n ratios were large.

It showed the following features:
(1) There were three sets of A ten , NQCC, h, s, d values respectively for the iodo ligands; each set having two values.So there were three types of stereo chemically different ligands respectively.
(2) Unpaired electron was delocalized both on Nb (IV) and ligands as µ n ratio of Nb and I was comparable respectively.
(3) A ten value of Nb (IV) was more than those of the iodo ligands respectively.
A ten value of Nb (IV) was more than N of ligands.
Its spectrum should give only a large decane (b) from Nb (IV) [2*9/2+1] with no hyperfine interaction between Nb (IV) and the six isothiocyanato ligands.

Prediction of number of ESR peaks in Ta (IV) Complexes
Two complexes such as [Ta X 6 ] 2-(X= Cl, Br) were studied (a) [Ta Cl 6 ] 2- It showed the following features: (1) Six chloro ligands were equivalent as they possessed the same A ten , NQCC, h, s, d values respectively.
(2) As their µ n ratio was small, the unpaired electron remained localized only on Ta (IV) with no hyperfine interaction.
(3) A ten of Ta (IV) was more than those of six equivalent chloro ligands.So its ESR spectrum would give a large octet (b) from Ta (IV) [2*7/2+1] only.

(b) [Tabr 6 ] 2-
It showed the following features: (1) Six bromo ligands were equivalent with same A ten , NQCC, h, s, d values respectively.(2)  With comparable m n ratio, the unpaired electron was delocalized both on ligands and Ta (IV). (3) A ten of Ta (IV) was more than the bromo ligands.
Thus its spectrum would give a large octet (b) from Ta (IV) [2*7/2+1] whose each line split into 19 lines (c) by the hyperfine interaction between Ta(IV) and six equivalents Br

It showed the following features: (1)
With same A ten , NQCC,h, ó, ä values respectively, the six bromo ligands were equivalent.(2)  With comparable µ n ratio, unpaired electron was delocalized both on Tc (II) and Br ligands. (3) A ten of Tc (II) was more than the Br ligands.
-332.2 3202.0 -3202.0 A large decane (b) 6.43, 0.   With the same A ten , NQCC, h, s, d values respectively, six NH 3 ligands were equivalent. (2) As their µ n ratio was large, the unpaired electron was localized on Tc (II) only. (3) A ten value of Tc (II) was less than those of N of NH 3 ligands.
Its ESR spectrum would give only a large decane (b) from Tc (II) [2*9/2+1] with no hyperfine splitting between Tc (II) and NH 3 ligands as their m n ratio was large.
(a) [Re Cl 6 ] 4-and [Re (NH 3 ) 6 ] 2+ Both showed the following features: (1)  With the same A ten , NQCC, h, s, d values respectively, the six Cl and the NH 3 ligands were equivalent. (2) Unpaired electron was localized only on Re (II) as there was no hyperfine interaction between Re (II) and ligands due to large µ n ratios respectively.With the same A ten , NQCC, h, s, d values respectively, the six bromo ligands were equivalent. (2) Unpaired electron was delocalized both on Re (II) and stereo chemically equivalent bromo ligands as their µ n ratio was comparable. (3) A ten of Re (II) was more than those of bromo ligands.

features: (1)
With the same A ten , NQCC, h, s, d values respectively, the ligands like F, Cl, Br, NH 3 were equivalent. (2) The unpaired electron was present only on Rh (IV). (3) A ten of Rh (IV) was more than the F, Cl or Br or N of NH 3 .
Their ESR spectra should give only a large doublet (b) from Rh (IV) [2*1/2+1] with no hyperfine interaction between Rh (IV) and any one of the four different types of ligands due to small µ n ratios between Rh (IV) and the ligands respectively.

Prediction of number of ESR peaks in Ir (IV) Complexes
It included four complexes: [IrX 6 ] 2-(X= F, Cl, Br) and [Ir (NH 3 ) 6 ] 4+ which showed the following features: (1)  With the same A ten , NQCC, h, s, d values respectively, the ligands like F, Cl, Br, NH 3 were equivalent. (2) The unpaired electron was present only on Ir (IV) (3) A ten of Ir (IV) was more than the F, Cl or Br or N of NH 3 .
Their ESR spectra would give only a large quartet (b) from Ir (IV) [2*3/2+1] because no hyperfine interaction between Ir (IV) and any one of four different types of ligands due to small µ n ratios between Ir(IV) and ligands respectively.

CONCLUSION
Simply by knowing I and g n of metals and coordinating atoms (CA) of the ligands from the literature; calculating their nuclear magnetic moments and thus their relative µ n ratios, we could predict the number or ESR lines in a vast number of complexes of 10 metal ions of 2 nd and 3 rd transition series which, hitherto, seemed tenacious experimentally..In addition, there lies a future use of this study in predicting the number of ESR peaks in complexes containing a very large variety of spatially different NMR and ESR active both quadrupolar and nonquadrupolar coordinating nuclei because the software allows us to select or ignore the interacting nuclei at our choice.This clearly makes the DFT a very powerful diagnostic tool at the hands of the theoretical Chemists to deduce the future applications of transition metal complexes.

Table 2 :
Prediction of Number of ESR peaks in continuum is expected.

Table : 2
contained A ten , s, d values of metal ions and A ten , NQCC, h, s, d and CA of ligands, number of spatially different ligands along with the theoretically predicted number of ESR peaks in these complexes.

Table 1 : Prediction of Hyperfine Interaction between Metals and Ligands
ratio of Nb and N of NCS 1-was small.