Perspectives On Charge-circulation, Susceptibility, Induced-fields and NMR Chemical Shifts Section: CHEMICAL SCIENCES Oral Presentation O2 Wednesday, January 13, S.Aravamudhan ISC102 Mumbai University

NORTH EASTERN HILL UNIVERSITY S.ARAVAMUDHAN Department of Chemistry North Eastern Hill University Shillong Key words: Chemical Shift, Induced fields, Magnetic Susceptibility, Nuclear Magnetic Resonance January 13, S.Aravamudhan ISC102 Mumbai University

Induced fields at proton sites from magnetic dipole model; relating values to absolute NMR shifts and referenced chemical shifts. In presence of an external magnetic field, the possible extent of change in the electron charge-cloud circulations is indicated by the magnetic susceptibility. Changes in electron circulations result in changes in induced fields in the molecule and hence the NMR chemical shifts depend on the physical quantity susceptibility. In view of a more convenient method for calculating demagnetization factors, experimental determination of susceptibilities and chemical shifts together with the quantum chemical methods seem to provide a refreshing way to comprehend the electronic structure of molecules. Thus experimental measurements lead to improve calculations for comparable values; and theoretical trends lead to look for novel variations in structures to study experimentally. Wednesday, January 13, 20163S.Aravamudhan ISC102 Mumbai University

Calculating with the magnetic dipole model is a parallel independent way to relate experimentally measured quantity to the theoretically calculated values Absolute Shielding Values Experimentally measured values Calculations using Magnetic Point- Dipole model. Theoretical Values by QM calculations Magnetic Susceptibility data for molecules, functional groups, bonded regions & atoms Wednesday, January 13, 20164S.Aravamudhan ISC102 Mumbai University

As a consequence of trying to relate the experimentally ( HR PMR in Solid State) determined Shielding Tensor values to the values obtained from ab initio QM methods to infer about the molecular electronic structures, the magnetic dipole model could be successfully employed and further calculations of demagnetization factors by a more convenient summation method proved that the dipole model would be more versatile for several contexts than what could have been envisaged earlier. The feasibility of calculating intra molecular shielding was encouraging as reported in the ISMAR- CA’98 conference, and the possibilities and prerequisites have been elucidated in the report at the 101 st ISC Important finding from the recent report as above is that the magnetic dipole model based convenient summation procedure can be applicable at such small electron charge cloud region within a molecule as the C-H bond. This possibility revealed that the assumption of a uniform susceptibility tensor for the entire region (though for a region of only a bond distance of 1.2 A º ), which in turn would have an implication on the actual amount of charge on hydrogen for that bonding, and such details could enable a reflection on the use of Chemical shifts (experimental) in comparison to the Absolute shielding values. Implications here are for the way of referencing which is necessary, to set arbitrarily a ‘0’ value assignment to the reference line Wednesday, January 13, 20165S.Aravamudhan ISC102 Mumbai University

To apply the magnetic dipole model, it is required to fragment the molecule under consideration with the possibility of assigning a magnetic susceptibility tensor to each fragment. These values assigned to the fragments of the molecule, when appropriately summed, should result in the total molecular susceptibility value. Even when such a task is accomplished, theoretical justification for this possibility may not be conclusive enough. Calculating intra molecular shielding of protons could be a factor that reinforces and justifies the fragmentation procedure since calculating by the magnetic dipole model is more or less a classical approach ( and hence less ambiguous) than a QM methods which depend on the formalisms and algorithms.. As above the procedure can reinforce and justify the fragmenting, yet, in which way this would reveal the requirements for improving the QM formalisms remains to be ascertained. Wednesday, January 13, 20166S.Aravamudhan ISC102 Mumbai University

To apply the magnetic dipole model, it is required to fragment the molecule under consideration with the possibility of assigning a magnetic susceptibility tensor to each fragment. These values assigned to the fragments of the molecule, when appropriately summed, should result in the total molecular susceptibility value. W.H.Flygare (Chemical Reviews, 1974, Vol.74, Page 682, second column), for a series of non strained, non aromatic molecules made an empirical fit of the Molecular Susceptibility values to obtain set of bond suceptibility values. When all these set of molecules have the similar bond, empirical fit of the fragments (bond level fragmentation) for a consistent set of susceptibility tensor value for a specific bond type of possible. Thus including all types of bonds and making a fit resulted in a Suceptibility tensor value of that bond type. Thus using these bond type values and gathering all the tensors corresponding to making up a specific molecule, the total molecular susceptibility tensor could be obtained. Similarly, independently atom-wise break ups was possible, resulting in a consistent type. However, from the atom type values the effort to get bond type Tensor values was not successful, even though independently atom susceptibility and bond susceptibility can result in the same total molecular susceptibility value. Wednesday, January 13, 20167S.Aravamudhan ISC102 Mumbai University

From the above fragmentation find that for H12 contributions from C-H, C atom local diamagnetic (isotropic), and C atom local π (anisotropic), have been taken into account and only the C-H bond  (anisotropic susceptibility) contribution is subjected to the method of regional volume fragmenting (slide # 8) into small volume elements and subsequent summation. Thus assuming that this C-H sigma bond region to have homogeneous charge distribution may not be realistic. Wednesday, January 13, 20168S.Aravamudhan ISC102 Mumbai University

Calculated isotropic shielding/chemical shifts 24 susc tensors ppm ppm ppm One C-H bond susc isotropic isotropic -total Abs shift= Abs shift H ppm = approx 25.6 ppm δ=7.4ppm Abs shift= Abs shift H ppm = approx 22.7 ppm δ=10.3ppm Bare nucleus 0 33 ppm TMS reference Increasing “Shielding” effect 33 ppm 0 Increasing “Deshielding” effect ‘ δ’ 17.5 ppm 15.5 ppm χ. H 0 = -σ.H 0 χ. H 0 for field strength unity will numerically be the same but dimensions would be that of field “gauss” Wednesday, January 13, 20169S.Aravamudhan ISC102 Mumbai University

As per the report in this work, the results of calculating intra molecular proton shielding tensor/chemical shift in benzene molecule brings a point of view to consider further. Would it be a consistent procedure, if after calculating the induced field values at proton in benzene molecule, to refer to the absolute shielding values (theoretical) of the reference molecule for obtaining chemical shift values to compare with experimentally measured chemical shifts. This brings into attention the calculated details in this work which gives the following results: Taking the results of calculated contribution from 24 tensors (leaving out the C-H bond ‘  ’ susceptibility) the value obtainable for the chemical shift is  = ppm. Taking the contribution of all the 25 tensors (without leaving any contributions) the value is  = 7.44 ppm. Of the 2 values, it is gratifying to note that 7.44 ppm is well comparable with experimental values w.r.to TMS. Wednesday, January 13, S.Aravamudhan ISC102 Mumbai University

If one considers the charge distribution in bonded region for the C-H bond and the susceptibility tensor being assumed as homogeneous over this region, then the value of 15.5 ppm used for H atom requires further justification. Wednesday, January 13, S.Aravamudhan ISC102 Mumbai University

Absoulte Proton shielding ppm (exptl) Absolute Proton shielding ppm (exptl) Assigning one electron (-1.0 e)to the Hydrogen atom, the value for the charge means, under the bonding situation only e charge is on the hydrogen atom. Similarly for the proton charge from QM on the hydrogen atom being , it corresponds to the presence of – e charge on the hydrogen atom. Benzene proton is deshielded by 1.93 ppm from ethylene proton. (1)  d AA is the contribution to the secondary magnetic field at nucleus A due to the (local) diamagnetic Langevin-type currents on the atom A itself, which give the corresponding susceptibility term χ d A. In the theory of Chemical shifts, this term conventionally known as the factor 1 which can be related to the charge density data from the Quantum Chemical computation. When the experimental trends does not get an explanation from the factor 1 consistently, then the factor 2 as below would be called for to account for the deviations and sometimes the factor 2 may be predominant and significant in determining the chemical shift variations. (2)  p AA is the contribution due to the paramagnetic-type currents on atom A which give the susceptibility term  p AA. The paramagnetic circulations cannot be as easily localized as the diamagnetic circulations. The paramagnetic circulations characteristically when the charge distribution is not spherical as for diamagnetic case……. From the discussions found in standard text books on NMR Wednesday, January 13, S.Aravamudhan ISC102 Mumbai University

x y z C atom Valence Orbital 2s, 2p x, 2p y 2p z Configuration: 2s 2, 2p 2 The three in plane sp 2 Hybrids have in plane p character and hence a localized π contribution is accountable. Along the  bonding direction, the Hydrogen S orbital and an sp 2 hybrid of the carbon. Having taken into account the localized π contribution. the bonding region charge distribution would have axial symmetry around the bond The distribution along the bond direction is not homogeneous.. Hence assuming homogeneus C-H  susceptibility requires reconsideration. Wednesday, January 13, S.Aravamudhan ISC102 Mumbai University

The distribution along the bond direction is not homogeneous.. Hence assuming homogeneous C-H  susceptibility requires reconsideration. H C FIG 10 b. C atom Increasing distance along the bond Charge Density Black Continuous line: realistic profile Red Dotted line: the profile averaged to homogenous distribution of the same total charge in the bonded region. Wednesday, January 13, S.Aravamudhan ISC102 Mumbai University

The inferences and trends on the nature of charge density distribution and the requirement on the Susceptibity in the corresponding region are all based on Quantum Chemical Semi empirical calculations including only Valence Electrons. When the above induced field calculations at such short ranges of distances have to be made with greater attention to the Charge distribution profiles in that region (not assuming that the distribution is homogeneous for the reason that the region is of small volume), then more accurate calculations of the Ab initio type with much more improved basis set versions, and with algorithms such as the DFT. Wednesday, January 13, S.Aravamudhan ISC102 Mumbai University