# 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.