Linear response

A well-known example of a linear response function is the polarizability. A typical input for SCF static and dynamic polarizability tensors $\alpha_{ij}(-\omega;\omega)\equiv-\langle\!\langle x_i;x_j\rangle\!\rangle_\omega$ for a few selected frequencies (in atomic units) will be:

**DALTON INPUT
.RUN RESPONSE
**WAVE FUNCTIONS
.HF
**RESPONSE
*LINEAR
.DIPLEN
.FREQUENCIES
 3
 0.0 0.5 1.0
**END OF DALTON INPUT

The .DIPLEN keyword has the effect of defining the $A$ and $B$ operators as all components of the electric dipole operator.

A Second Order Polarization Propagator Approximation (SOPPA)[49,50,51] calculation of linear response functions can be invoked if the additonal keyword .SOPPA is specified in the **RESPONSE input module and an MP2 calculation is requested by the keyword .MP2 in the **WAVE FUNCTIONS input module. A typical input for SOPPA dynamic polarizability tensors will be:

**DALTON INPUT
.RUN RESPONSE
**WAVE FUNCTIONS
.HF
.MP2
**RESPONSE
.SOPPA
.NOITRA
*LINEAR
.DIPLEN
.FREQUENCIES
 3
 0.0 0.5 1.0
**END OF DALTON INPUT

The .NOITRA keyword has the effect that the transformation of the two electron integrals necessary for a MP2 and SOPPA calculation is only perfomed once in the **WAVE FUNCTIONS module.

A Second Order Polarization Propagator Approximation with Coupled Cluster Singles and Doubles Amplitudes - SOPPA(CCSD)[53] calculation of linear response functions can be invoked if the additonal keyword .SOPPA(CCSD) is specified in the **RESPONSE input module and an CCSD calculation is requested by the keyword .CC in the **WAVE FUNCTIONS input module. A typical input for SOPPA(CCSD) dynamic polarizability tensors will be:

**DALTON INPUT
.RUN RESPONSE
**WAVE FUNCTIONS
.HF
.CC
*CC INPUT
.SOPPA(CCSD)
**RESPONSE
.SOPPA(CCSD)
*LINEAR
.DIPLEN
.FREQUENCIES
 3
 0.0 0.5 1.0
**END OF DALTON INPUT

The linear response function contains a wealth of information about the spectrum of a given Hamiltonian. It has poles at the excitation energies, relative to the reference state (not necessarily the ground state) and the corresponding residues are transition moments between the reference and excited states. To calculate the excitation energies and dipole transition moments for the three lowest excited states in the fourth symmetry, a small modification of the input above will suffice;

**RESPONSE
*LINEAR
.SINGLE RESIDUE
.DIPLEN
.ROOTS
 0 0 0 3