APOLAR — Compute nonlinear optical properties using analytic gradient.

APOLAR=`n.n`

APOLAR computes the nonlinear optical properties (dipole, polarizability, 1st and 2nd
hyperpolarizability) of a molecule. See Chapter 12, *Polarizability Methods*
for a description of this method and an example. The value n.n is the finite field strength
and should only be adjusted by experienced users. The default value for n.n is 0.001 au
(0.05142 V/cm) and 0.01 au < n.n < 5 × 10^{-4} au.

APOLAR, KPOLAR, and BRUTEKPOLAR all compute polarizability and hyperpolarizability. Both KPOLAR and BRUTEKPOLAR use the finite difference method of Henry Kurtz to compute these properties. APOLAR instead relies on the analytical gradient of the energy with respect to the an electric field and so is more reliable and less sensitive to the finite field strength. The only difference between KPOLAR and BRUTEKPOLAR is that KPOLAR reports its results in the inertial frame while BRUTEKPOLAR reports its results in the genuine Cartesian frame. APOLAR gives its results in both the inertial frame and the genuine Cartesian frame (at no extra cost). APOLAR is faster than KPOLAR and BRUTEKPOLAR because it relies on analytic gradients.

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