1. Department of Chemistry North Eastern Hill University
Classical dipole model and the Abinitio QM method for Calculation of Magnetic Shielding in Molecules
S . ARAVAMUDHAN
Department of Chemistry
North Eastern Hill University
SHILLONG MEGHALAYA
INDIA
CHEMICAL SCIENCES
Indian Science Congress – 2017
ISC SV University - TIRUPATI
4/6/2019 2:25:58 AM
S.Aravamudhan ISC104 SVU

2. Classical dipole model and the Abinitio QM method for
Calculation of Magnetic Shielding in Molecules ISC104 – Year2017
INTRODUCTION TO THE CONTEXT OF THESE RESULTS Link:-
Calculating Intra-molecular Proton Shielding Tensors
Using Magnetic Dipole model; Possible Procedures and Prerequisites ISC101- Year
Perspectives On Charge Circulation, Susceptibility,
Induced Fields and NMR Chemical Shifts ISC102 – Year 2015
Molecular Susceptibility Tensor And The Susceptibility
Tensor For Molecular Fragments ISC103 – Year 2016
4/6/2019 2:25:58 AM
S.Aravamudhan ISC104 SVU

3. These results have relevance to this context:
Nuclear shielding is essentially the induced field changes due to the changes in electron-charge circulation, caused by the application of an external magnetic field.
By the classical dipole model equations or by QM formalisms, by calculation, what one can obtain is the extent of such changes in the induced fields.
It is also possible to obtain the classical dipole model equations as a special case of the equations for shielding obtained by the general QM formalisms.
Therefore the values obtained for shielding at a particular point due to electronic charge cloud in a molecule must be the same from either of the two equations and hence it should be so established by comparing the two methods.
Results to be presented at this ISC104
These results have relevance to this context:
“Hence it has now become prevalent to obtain Nucleus Independent Chemical Shifts (NICS)” Mostly isotropic chemical shifts obtained in liquids.
4/6/2019 2:25:58 AM
S.Aravamudhan ISC104 SVU

4. Figure-2: The benzene ring and the various points in the neighborhood; a small circle represents a hydrogen atom or a proton and at these points the shielding values can be calculated. Numerical results pertaining to this situation displayed in Figure-1b.
4/6/2019 2:25:58 AM
S.Aravamudhan ISC104 SVU

5. To get to compare Dipole Model and QM ab initio Calculation results:----
Figure-3. The benzene molecule and the molecule of methane in the neighborhood. (1). Methane is placed along the symmetry axis above the plane. (2) Methane is placed in the molecular plane at a distance from the center of the molecule along an axis in the plane.
Before Calculating the Shielding of this combined system, Energy of the combined system as a function of distance of separation is to be ascertained (by QM Calculations) for reasons to follow:
Beyond a distance of 4 Aº separation between the molecules the total energy (by QM calculations) of the combined molecular system does not change
4/6/2019 2:25:58 AM
S.Aravamudhan ISC104 SVU

6. Corresponding to the energy calculation of the Methane-Benzene Combined system, the Chemical shifts for the combined system also can be obtained.
Methane protons appear to have varying chemical shifts for distances less than 6.4 Aº while benzene protons are all appearing as a single line with intensity 6.
The interactions between the two molecules at distances in the range of Aº is mainly in terms of secondary fields and no significant energy consequences !!
4/6/2019 2:25:58 AM
S.Aravamudhan ISC104 SVU

7. When the distances of separations are large only the long range secondary magnetic fields are present mutually. This depends on magnitude of Susceptibility values. Classical dipole equations would indicate entirely the changes in chemical shifts
At much smaller distance ranges, since total energy is different from the simply added total, what contributes to energy differences is a question to be answered.
Results published:-
QM Chemical Shift Calculations to Infer on the Long-Range Aromatic Ring Current-Induced Field Contributions DOI: / /
Journal of Materials Science and Engineering A 5 (5-6) (2015)
4/6/2019 2:25:58 AM
S.Aravamudhan ISC104 SVU

8. Import from the published result:-
At ranges of smaller distance of separation:
The classical dipole equations can be valid if susceptibility values are the same.
Since the total energy differs, (since no changes in geometry would have occurred – since no G.O. is effected) could be by long range electrostatic interactions play a role in altering electron cloud distributions within each molecule, without causing any charge movements/transfers from one molecule to the other (typical weak interactions – intermolecular forces).
The individual molecules have different energies; but when one of the molecule is simply deleted, the molecule has the same energy as the original molecule.\
This could result in changes in molecular susceptibilities of each molecule due to the presence of the other molecule; to apply classical equations this altered susceptibility at these proximities should be ascertained. This change is not amenable for experimental measurements and must be deduced only from theoretical calculations of the type reported herein. Such molecular combinations may not be formed since there seems no adduct formations or complexes which would call for geometry changes and not merely induced secondary magnetic fields.
Further…….. (next slide)
4/6/2019 2:25:58 AM
S.Aravamudhan ISC104 SVU

9. There seems a possibility (how
There seems a possibility (how?) for obtaining the C-C and C-H sigma bond susceptibility values from the calculated Chemical shift values. Such molecular fragment susceptibilities are necessary to adapt classical dipole model for intra molecular calculations of Shielding. As pointed out in the references 1-a,b, and c there has been ambiguities in obtaining such susceptibility values of molecular fragments.
The long standing inconsistency of bond susceptibities and atom susceptibilities may also get resolved if this method extends provide such consistent sets, and an explanation could later may be enabled as to why the strangely partial inconsistency among the two sets arose but independently either one of the two sets could result in experimental susceptibility data to the same confidence level.
4/6/2019 2:25:58 AM
S.Aravamudhan ISC104 SVU

10. The two molecules can be rotated independently with their molecular centers being at the same relative distance
Typically corresponding to the bond susceptibities each bond could have a dipole moment at the center of the bond., and/or center of the molecule j
Rotation of Molecule I
θij
Rotation would vary the relative disposition of the bonds (distance and angle with magnetic field) where as the total molecular susceptibility tensor would remain the same and the break ups as well. If there is change in electron charge clouds within the molecules, the total susceptibilities would not be the same. Thus by calculating the spectra by QM MO method and also using a set of break up values, an optimization of the break ups may be possible at long and short ranges of distances along with values from classical equation. This optimization can be carried out at the various distances of separations. This is a kind of fitting which was carried with theoretical calculations, which was earlier carried out on an empirical basis with several molecules of similar structures.
Rij i
Rotation of Molecule II
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S.Aravamudhan ISC104 SVU

11. 4/6/2019 2:25:58 AM
S.Aravamudhan ISC104 SVU