Static and frequency dependent polarizabilities

Frequency-dependent polarizabilities is calculated from a set of linear response functions as described in Ref. [48]. In ABACUS the calculation of frequency-dependent linear response functions is requested through the keyword .ALPHA in the general input module to the property section. An input file requesting the calculation of the frequency dependent polarizability of a molecule may then be calculated using the following input:

**DALTON INPUT
.RUN PROPERTIES
**END OF DALTON INPUT
**WAVE FUNCTIONS
.HF
**PROPERTIES
.ALPHA
*ABALNR
.FREQUE
    2
0.0 0.09321471
**END OF DALTON INPUT

For a Second Order Polarization Propagator Approximation (SOPPA) [49,50,51,52] calculation of frequency-dependent polarizabilities the additional keyword .SOPPA has to be specified in the **PROPERTIES input module and an MP2 calculation has to be requested by the keyword .MP2 in the **WAVE FUNCTIONS input module. Similarly, for a SOPPA(CCSD) [53,52] calculation of frequency dependent polarizabilities the additional keyword .SOPPA(CCSD) has to be specified in the **PROPERTIES input module and an CCSD calculation has to be requested by the keyword .CC in the **WAVE FUNCTIONS input module with the option .SOPPA(CCSD) in the *CC INPUT section.

The *ABALNR input section controls the calculation of the frequency-dependent linear response function. We must here specify at which frequencies the polarizability is to be calculated. This is done with the keyword .FREQUE, and in this run the polarizability is to be evaluated at zero frequency (corresponding to the static polarizability) and at a frequency (in atomic units) corresponding to a incident laser beam of wavelength 488.8 nm.

There is also another way of calculating the static polarizability, and this is by using the keyword .POLARI in the **PROPERTIES input modules. Thus, if we only want to evaluate the static polarizability of a molecule, this may be achieved by the following input:

**DALTON INPUT
.RUN PROPERTIES
**WAVE FUNCTIONS
.HF 
**PROPERTIES
.POLARI
**END OF DALTON INPUT

Furthermore, the general RESPONSE program will also calculate the frequency-dependent polarizability as minus the linear response functions through the input

**DALTON INPUT
.RUN RESPONSE
**WAVE FUNCTIONS
.HF
**RESPONSE
*LINEAR
.DIPLEN
**END OF DALTON INPUT

For further details about input for the response program, we refer to Chapter 12.