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There is this method called nucleus-independent chemical shift (NICS) to calculate the magnetic shielding values at different spatial coordinates of a molecular system. It can be used to estimate the aromatic character of a system by evaluating the magnetic shieldings inside a potentially aromatic cyclic system. The calculated values correspond to the magnetic shielding tensor, the elements of which are given by:

$\sigma = \frac{\partial^{2} E}{\partial B_{i} \partial m_{j}}$

Furthermore there is the method of gauge-including magnetically induced currents (GIMIC) which can also be used to estimate the aromaticity of a system based on ring currents of a conjugated cyclic system. In this case the current density susceptibility tensor is evaluated.

Because the quantities studied by the aforementioned methods arise from the influence of external magnetic fields I am wondering how high the external magnetic field implied in these calculations actually is. Is there even an external magnetic field implied in these calculations or am I missing something here ? I know that chemical shifts are basically independent of the external magnetic field but only because of the use of an NMR standard, which eliminates this dependency. The answer seems simple but I am kind of caught in confusion by now.

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When calculating nuclear magnetic shieldings or gauge-including magnetically induced currents, one only needs to determine the response of the system to an external magnetic field, and the derivatives are evaluated in the absence of external fields. It is also possible to do calculations with explicit magnetic fields in some programs, which allows e.g. the determination of nuclear magnetic shieldings with the use of finite difference rules. In either case, it is important to use gauge including atomic orbitals (GIAOs), as this will strongly accelerate the convergence to the basis set limit.

The other use for explicit magnetic fields is to investigate the electronic structure in astrophysical environments, such as neutron star atmospheres, where the magnetic fields can have significant effects on the electronic structure unlike the case of terrestrial magnetic fields, which usually have negligible effects. A challenge for such calculations is the strong effect that magnetic fields have on the electronic structure: (i) the field couples to the electronic spin, changing the character of the ground state, and (ii) the field introduces a parabolic constrainment potential perpendicular to the field axis. This qualitative change results in significant errors in linear combination of atomic orbitals (LCAO) approaches, as we have described in S. Lehtola, M. Dimitrova, and D. Sundholm, Mol. Phys. 118, e1597989 (2020) arXiv:1812.06274

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