# Chemical shieldings, magnetizability, and rotational g-tensor

Bibliography:
$[1]$ S. Loibl, F.R. Manby, M. Schütz, Density fitted, local Hartree-Fock treatment of NMR chemical shifts using London atomic orbitals, Mol. Phys. 108, 477 (2010).
$[2]$ S. Loibl and M. Schütz, NMR shielding tensors for density fitted local second-order Møller-Plesset perturbation theory using gauge including atomic orbitals, J. Chem. Phys. 137, 084107 (2012).
$[3]$ S. Loibl and M. Schütz, Magnetizability and rotational g tensors for density fitted local second-order Møller-Plesset perturbation theory using gauge-including atomic orbitals, J. Chem. Phys. 141, 024108 (2014).

All publications resulting from use of this program must acknowledge the above.

The command nmrshld invokes the calculation of NMR chemical shielding tensors at the level of (local) density-fitted HF (GIAO-DF-HF) or local density-fitted MP2 (GIAO-DF-LMP2). Note: Chemical shieldings at the level of MP2 are only implemented for DF-LMP2.
For the calculation of the chemical shieldling tensor a preceding DF-HF, respectively, DF-LMP2 calculation is required. Symmetry has to be set to nosym. For the GIAO-DF-HF code one can use canonical orbitals from the DF-HF run or localized orbitals (recommended).
Example:

***,Chemical shielding tensors for water molecule
symmetry,nosym
GEOMETRY={    !geometry input
h1;o,h1,r1;h2,o,r2,h1,theta}
r1=0.9583 ang
r2=0.9583 ang
theta=104.2
basis={       !specify basis
default,cc-pVDZ
set,mp2fit
default,vdz/mp2fit
set,jkfit
default,vdz/jkfit
}
df-hf,df_basis=jkfit
df-lmp2,df_basis=mp2fit
nmrshld;comp      !invoke calculations of shieldings, print the components

The shielding calculation returns the chemical shielding tensors $\sigma$ and a summary of the chemical shifts (i.e. the arithmetic mean of the diagonal elements) for each nucleus in the order they were specified in the geometry input. The directive comp additionally prints the diamagnetic and paramagnetic contributions (for further information see R. Ditchfield, Mol. Phys. 27(4), 789 (1974)) for all shielding tensors.
Additionally, the calculation of magnetizabilities and rotational $g$ tensors has been implemented: the command magprop invokes the calculation of magnetizabilities and chemical shielding tensors. The directive comp can be specified. The command magnetiz invokes a pure magnetizability calculation. Note that a pure magnetizability calculation takes nearly as long as a chemical shielding calculation and hence does not provide any advantage in comparison to magprop. See also the input examples gly1_mag.inp and h2o_mag.inp.
If one is interested in the calculation of rotational $g$ tensors the molecule has to be aligned in the principal axis system with the command orient,mass. Otherwise, the results are meaningless.