O NMR of Mono-Nuclear Carbonyls : A DFT Study

DFT implemented in ADF 2012.01 was applied to11 mono-nuclear carbonyls after their optimization to ascertain the stereo chemical and magnetic equivalence of CO groups and calculation of Effective Spin Hamiltonian(H Spin) values of the metals and the carbon atoms after obtaining NMR parameters like Chemical Shifts (d M n+, d13C, d17O),total NMR shielding tensors (s Mn+, s13C, s17O) consisting of 2 diamagnetic and 4 paramagnetic terms along with k and j parameters of constituents. This NMR study corroborated well the hitherto, already, reported IR/ Raman results to lend credence to the p acid character of carbonyls.


INTRODUCTION
DFT was, earlier, applied by Schreckenbach et al., [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] to study 13 C and 17 O NMR spectra of some mononuclear transition metal carbonyls.But the present work would include the study of a number of NMR parameters such as Chemical Shifts of metal, the carbon and the oxygen species (d M, d 13 C, d 17 O), their Total NMR Shielding Tensors (s M, s 13 C , s 17 O ) along with two While the discussion on NMR of transition metal complexes 16,17 encircled around ligand field theory 18 , in the late 70s, a number of review articles were collected 19 on small molecules.Debrochere (1978) published a 100 page review containing 289 references[ 20 .But till then, no calculations on nuclear shielding and spin-spin coupling parameters were carried out.H F approach given by Nakatsuzi 21 presented a paper on the calculation of the above named parameters of the complexes was found lacking in high oxidation states d 10 systems 22 .In 80s, the NMR shielding codes based on HFS or X d method were developed.It was afterward called DFT [23][24][25] .In 1993, Kohn-Sham DFT 26,27 employed IGLO [26][27] method to calculate nuclear shielding.Also, LORG approach 27 which was improved upon by GIAO DFT 28 and CSGT methods 29 was employed.Spin-spin coupling constant of complexes was first of all calculated by Malkin et al., 30 .Dicken and Zieglar 31 calculated FC term 32 in1996.Later, SD term 33,34 was included in spin-spin coupling values.

Need of the study
Three points necessitated this study as: ´No computational studies were reported on the magnetic equivalence of COs.Only their spatial displacements/ stereo chemical equivalences were studied.´An important NMR parameter-Effective Spin Hamiltonian (H Spin ) [17] which determines the energy of an NMR transition had, never, been calculated by DFT.´DFT had, hardly, been applied to NMR in ascertaining the pi-acid character of metal carbonyls though IR/ Raman techniques had abundantly been exploited.
After optimization of the carbonyl compound, different commands were filled into the software to obtain NMR and IR/Raman parameters as follows: NMR Parameters 36, 37 The software was run by filling in certain commands like Single Point, LDA, Default, None, Collinear, Nosym using DZ or TPZ Basis sets.The Unrestricted command was left blank.Then "NMR Program" was run in three steps.

IR and Raman Parameters
After Optimization, the software is run with Frequencies and Raman full to obtain values of frequencies of all the (3n-6) Fundamental vibration bands.

RESULTS
Table : 1 contained Acronyms and their expanded forms.Tables: 2-3 gave the optimization 38,39 and thermal parameters of the carbonyls respectively.

DISCUSSION
The discussion was divided into eight headings as follows: As stated, the software gave a number of parameters which were further related a number of other parameters as follow: Sum of 6 contributions was equal to their s M, s 13  The relation between (s) and (δ) of carbon was given as: Table 3:  ) Trans.

Total
Trans.
Total       [C] In D 3h stereochemistry, each one of the three 13 :4.The more the value of s 13 C, the lower was the Chemical shift (d 13 C) and higher was the Coordination Shift (Dd 13 C) for any stereochemistry.A positive D d 13  [D] As shielding constant (s) of a nucleus was directly related to its electron density, any change in its σ value would serve as an indicator of change in electron density on it.So, if CO were to act as a back acceptor, d 13 C of metal carbonyls should become more than s 13 C of CO (g).Some of the increased electron density on carbon was transmitted to oxygen to cause an increase in electron density on oxygen.So s 17 O would also increase.The NMR results corroborate with results obtained from their IR/Raman parameters in confirming their p -acid character as follows: pligand CO would donate electron density to the metal via a dative s bond (OC® M) .Simultaneously, there would be a s back donation from the filled d orbitals of metal (OC ¬ M) to energetically favorable and geometrically suitable vacant p* molecular orbitals of CO.The effect being synergic should cause a decrease in carbon oxygen double character and, thus, a decrease in )decreased, ν CO (cm 1-) would increase [41][42][43][44][45][46][47][48] to decrease the capacity to back accept electron cloud by CO.

Parameters[ p pm] [V(CO)
[E] Another important element of NMR symmetry was called the "magnetic equivalence" of nuclei .Enantiotopic or homotopic nuclei though possessed the same chemical shift (d), but might not necessarily be magnetically equivalent.Two magnetically equivalent nuclei would have the same values of s, d, k and j with other nuclei of the molecule in addition to having same values among themselves .Coupling between symmetry equivalent and magnetically nonequivalent nuclei would affect the appearance of NMR spectrum while coupling between both the symmetry and magnetically equivalent nuclei had no effect NMR spectra.
[F] With same d 13 C, d 13 C, k and j values, the four COs were both spatially and magnetically equivalent in T d .Again, the six CO groups in [V (CO) 6 ] 1-were both spatially and magnetically equivalent with the same s 13 C, d 13 C, k and j values.But the six COs in the remaining (O h ) mono-nuclear carbonyls were only spatially equivalent with same s 13 C, d 13 C values as they possessed different k and j values.They were of three types.Each type having two CO groups possessed both spatial and magnetic equivalence.The three types of CO pairs had the same set of four parameters respectively between themselves and with remaining four CO groups though the set of four COs show different values from the previous set of two COs.
The five COs (D 3h ) were neither spatially nor magnetically equivalent as they did not have the same set of four parameters.They consisted of two sets.The first set with two COs (a) and the second with three COs (e) showed both the spatial and magnetic equivalence among themselves as either type possessed same set of values of four parameters among its own members and also with members of other type of CO groups though the two sets have different values of these parameters.
(i) Spin-spin coupling (j) was fieldindependent and mutual (j AB = j BA ).It was affected by the nature of solvent ; metal"ligand bond distances and was transmitted through bonding electrons with its magnitude falling off rapidly with the increase in number of intervening bonds.Its sign was decided as: "it was positive if energy of A was lower when B had opposite spin as A (ab or ba), and negative if energy of A was lower when B had same spin as A (aa or bb )".
(ii) The parameter (j) was related to another important NMR called Effective Spin Hamiltonian (H Spin ).It was a mathematical expression that would determine the energy of an NMR transition.It term "effective" meant that its solutions reproduced nuclear magnetic energy levels in a molecular system without reference to electrons.In a fictitious absence of surrounding electrons, the shielding constants and indirect spin-spin coupling constants would vanish leaving the NMR spectrum to be determined by Nuclear Zeeman Term and direct dipolar coupling.(H Spin ) values of the metal ions and the bonded carbon atoms were related to their j [p pm] values as given below [6]  (17) .
H Spin = 6.023 j A B .I A. I B. MHz mol -1 ... [6]   Spin Hamiltonian [H Spin ] values of the metal and the bonded carbon atoms of the eleven carbonyls are calculated by applying [5] (Table : 10).
[G]Individual values of 6 diamagnetic and paramagnetic quantities in s M , d 13 C and d 17 O and their sums were given in Tables: 5-8 respectively.
[H] Table: 9 showed spatial displacements of 4, 5 or 6 CO groups around the metal.

CONCLUSIONS
The originality and relevance of present work and how it moved the body of scientific knowledge forward would lie in the fact that it reaffirmed the relative spatial displacements of CO groups; classified them according to their spatial and magnetic equivalence; lent credence to σacid character of carbonyls by corroborating with their IR/Raman studies and hence justified the need of taking up this study.
C, , s 17 O[p pm] respectively.s M =Sum of 2 diamagnetic and 4 paramagnetic contributions of M | s 13 C =Sum of 2 diamagnetic and 4 paramagnetic contributions of 13 C| [1] s 17 O =Sum of 2 diamagnetic and 4 paramagnetic contributions of 17 O|

*
Calculate values by relations: 2, 3, 4 and 5 types;3(e) and 2(a) 2 types ;3(e) and 2(a) Two 2 types ;3(e) and 2are both spatially and magnetically equivalent C and 17 O had the same values of s 13 C, d 13 C, s 17 O and d 17 O along with their six contributing terms respectively; meaning thereby that the three COs were stereo chemically equivalents.Each one of the remaining two COs also possessed same values of s 13 C, d 13 C, d 17 O and d 17 O along with their contributing terms respectively.But these values were quite different from those of the other three CO s.Thus these two COs were different from the other three COs spatially*.The values of 8 parameters : s M, d M, s 13 C, d 13 C, Dd 13 C, s 17 O, d 17 O and Dd 17 O [ pp m] for the11 mononuclear carbonyls were given in Table

Table 1 : Acronyms and their expanded forms
Table: 4 contained eight NMR parameters: three shielding constants(sM, s 13 C, s 17 O ),three Chemical Shifts (d M , d 13 C, d 17 O) and two Coordination Shifts(D d 13 C , D d 17 O ) .Six contributions consisting of two diamagnetic and four paramagnetic terms of three parameters (d M , d 13 C, d 17 O) were given in Tables:5-7[{a},{b}.{c},{d},{e}.{f}].Total values of two diamagnetic and four paramagnetic contributions in ó M, ó 13 C and ó 17 O were given in Table: 8. Table:9 represented Spatial and Magnetic Equivalence of CO groups.Table: 10 contained k and j parameters given by software

Table 10 : k, j and H spin values of Nuclei in Mononuclear Carbonyls Carbonyl Perturbing Responding k [10 19 kg j (p pm) H spin Nuclei Nuclei m -2 s -2 A -2 ] (10 17 MHzmol -1 )
C is reported in O h geometry which confirms the back-acceptor nature 0f CO.

6 ] 1- [Mn (CO) 6 ] 1+ [Re(CO) 6 ] 1+
CO in carbonyls with respect to CO(g) having n CO = 2143 cm 1-was expected if C O was to act as a back pi-acceptor.A comparison of s 13 C, d 13 C, D d 13 C and ν CO (cm -1 ) values of the 6 and 5 coordinate(axial) carbonyls in the above table lead to the conclusion that as the Chemical Shift (d13 C