# Manual:Linear Response

# Calculate Polarizabolities and Hyperpolarizabilites with Octopus

With version 2.0rc1 the calculation of static polarizability () and the first hyperpolarizability () is supported. There are two ways to do this:

## Finite differences

This is calculated doing a numerical derivative of the total energy with respect to an applied electric field, it only gives the polarizability.

To use this run with *RunMode = pol*, this will do several ground state calculations. The resulting tensor will be in the *linear/polarizability* file.

## Linear Response

To use this you first need a gs calculation for the system with very well converged wave functions, the following cnvergency parameters are recommended:

EigenSolverFinalTolerance = 1e-10 ConvAbsDens = 0 ConvRelDens = 0 ConvAbsEv = 1e-10 ConvRelEv = 0

After that you can calculate the hyperpolarizabity using *RunMode = pol_lr*. Results will be in the *linear/* directory in files *polarizability_lr* and *beta_lr*.