18.3 Electric Field Gradient

The electric field gradient (EFG) can be used to calculate the nuclear quadrupole interaction (NQI) tensor for analysis purposes [188]. The EFG, \(\overset{\text{\scriptsize$\leftrightarrow$}}{V}\), is evaluated in atomic units (a.u.) and the NQI tensor in MHz follows as \[\begin{equation} \overset{\text{\scriptsize$\leftrightarrow$}}{Q} (\text{MHz}) = \frac{234.9648}{2 I (2 I-1)} \cdot Q_c(\text{b}) \cdot \overset{\text{\scriptsize$\leftrightarrow$}}{V} (\text{a.u.}) \end{equation}\](18.1) where \(Q_c\) refers to the quadrupole constant and \(I\) refers to the nuclear spin. The relativistic picture-change correction and large basis sets are crucial for accurate results.

The EFG is calculated by setting $efg in the control file. Additionally, the picture-change correction and the usual X2C keywords should be set. The spin–orbit two-component formalism is supported with

$soghf. As the EFG only requires the SCF density matrix, a proper run of dscf or ridft is sufficient. To calculate the EFG of selected nuclei only, the $nucsel keywords can be set. The principal axis system is also printed.

The mpshift run with $epr or $efg evaluates the EFG and calculates the NQI for nuclei with a spin of more than one half. Here, the relativistic picture-change correction [38] is always included with X2C for consistency with the other EPR properties.