Linear response functions: *CCLR

In the *CCLR section the input that is specific for coupled cluster linear response properties is read in. This section includes presently

• frequency-dependent linear response properties $\alpha_{AB}(\omega) = - \langle\langle A; B \rangle\rangle_\omega$ where $A$ and $B$ can be any of the one-electron operators for which integrals are available in the **INTEGRALS input part.
• dispersion coefficients $D_{AB}(n)$ for $\alpha_{AB}(\omega)$ which for $n \ge 0$ are defined by the expansion
  
  $$\alpha_{AB}(\omega) = \sum_{n=0}^{\infty} \omega^n \, D_{AB}(n)$$
  
  
  In addition to the dispersion coefficients for $n \ge 0$ there are also coefficients available for $n = -1, \ldots, -4$, which are related to the Cauchy moments by $D_{AB}(n) = S_{AB}(-n-2)$.
  Note, that for real response functions only even moments $D_{AB}(2n) = S_{AB}(-2n-2)$ with $n \ge -2$ are available, while for imaginary response functions only odd moments $D_{AB}(2n+1) = S_{AB}(-2n-3)$ with $n \ge -2$ are available.

Coupled cluster linear response functions and dispersion coefficients are implemented for the models CCS, CC2 and CCSD. The theoretical background for the implementation is detailed in Ref.
citeChristiansen:CCLR,Christiansen:QEL,Haettig:CAUCHY. The properties calculated are in the approach now generally known as coupled cluster linear response--in the frequency-independent limit this coincides with the so-called orbital-unrelaxed energy derivatives (and thus the orbital-unrelaxed finite field result).

.ASYMSD

Use an asymmetric formulation of the linear response function which does not require the solution of response equations for the operators $A$, but solves two sets of response equations for the operators $B$.

.AVERAG

READ (LUCMD,'(A)') AVERAGE
READ (LUCMD,'(A)') SYMMETRY

Evaluate special tensor averages of linear response functions. Presently implemented are the isotropic average of the dipole polarizability $\bar{\alpha}$ and the dipole polarizability anisotropy $\alpha_{ani}$. Specify ALPHA_ISO for AVERAGE to obtain $\bar{\alpha}$ and ALPHA_ANI to obtain $\alpha_{ani}$ and $\bar{\alpha}$. The SYMMETRY input defines the selection rules that can be exploited to reduce the number of tensor elements that have to be evaluated. Available options are ATOM, SPHTOP (spherical top), LINEAR, XYDEGN ($x$- and $y$-axis equivalent, i.e. a $C_z^n$ symmetry axis with $n \ge 3$), and GENER (use point group symmetry from geometry input).

.DIPOLE

Evaluate all symmetry allowed elements of the dipole polarizability (max. 6 components).

.DISPCF

READ (LUCMD,*) NLRDSPE

Calculate the dispersion coefficients $D_{AB}(n)$ up to $n =$ NLRDSPE.

.FREQUE

READ (LUCMD,*) NBLRFR
READ (LUCMD,*) (BLRFR(I),I=1,NBLRFR)

Frequency input for $\langle\langle A;B \rangle\rangle_{\omega}$.

.OPERAT

READ (LUCMD,'(2A)') LABELA, LABELB
DO WHILE (LABELA(1:1).NE.'.' .AND. LABELA(1:1).NE.'*')
READ (LUCMD,'(2A)') LABELA, LABELB
END DO

Read pairs of operator labels.

.PRINT

READ (LUCMD,*) IPRSOP

Set print level for linear response output.