Procedures

This subroutine receives a rotation matrix and determines the rotation angle.

This subroutine receives an improper rotation matrix and determines the rotation angle.

This function returns the angle, in degrees, between two vectors.

Apply residual symmetries if present

Calculate polarization in terms of geometric Berry phase

This function compares two 3x3 matrix ($A$ and $B$) and returns .TRUE. if they coincide.

It gives $C = A \cdot (B \cdot A^T)$.

Find degeneracy in a sorted energy array

@var ib(1) lowest valence, ib(2) upper conduction @var ib_lim(1) top valence, ib_lim(2) bottom conduction

Calculate overlaps between wave-function <\psi_k | \psi_{k+q} > for q = 1,2

This is the equation according to the notes. However it looks like here DIP_O = O^\dag In case the above equation is the correct one & +(DIP_D(1)conjg(DIP_O(iv,in_d))-DIP_O(ic,in_d)conjg(DIP_D(2)))/2._SP/q0_shift_norm

This subroutine receives as input a set of $\text{nrot}$ 3x3 matrices $\text{smat}$, which are assumed to be the operations of the point group given by $\texttt{code_group}$. The matrices $\text{smat}$ are in cartesian coordinates.
This routine divides the group in classes and finds:

DEBUG

Calculate real and imaginary part of the electron-phonon self-energy

This subroutine interpolate energies at k+q for the double-grid q-points

Calculate exciton-dipole

Calculate phonon-assisted absorption and emission (see PRL 122, 187401 )

EXCPH_gkkp_driver - Exciton-Phonon Coupling Matrix Element Calculation

EXCPH_gkkp_eval - Core Exciton-Phonon Matrix Element Computation

EXCPH_lifetime - Non-Radiative Exciton Lifetime from Phonon Scattering

EXCPH_optics - Phonon-Assisted Optical Properties Calculation

EXCPH_X_phass - Phonon-Assisted Optical Susceptibility

Calculate PL(w) satellites including ph-assisted transitions

!!DEV_OMPGPU ???

!!!!! & reduction(max:ln_1,ln_2,ln_3)

Given a group of $\text{nrot}$ rotation matrices $\text{smat}$ (in cartesian coordinates) this routine finds the name of the point group. It assumes but does not check that:

Remove Symmetries *

Return phonon energy in the double-grid

This function receives a code of the group and provides the name of the group. The order is the following:

Complex dim

Write info about k-points

Read and write scattering indexes

Calculate ionic contribution to the polariation

This is a logical function that returns .TRUE. if $\text{ax}$ is the versor of the axis x ($\text{iflag}=1$) or y ($\text{iflag}=2$) or z ($\text{iflag}=3$).

This subroutine receives the indeces of a $C_2$ axis $\text{iax}$, with the convention of the routine $\texttt{which_c2}$, and of the perpendicular of two mirrors, $\text{ibx}$ and $\text{icx}$ with the same convention. It returns .TRUE. in $\text{isok}$ if the combination corresponds to a known possibility for $C_2v$. Usually $\text{isok}$ .FALSE. means that the two mirrors are not in the correct order.

This function receives a code of the group and provides .TRUE. or .FALSE. if the group, respectively, HAS or HAS NOT complex irreducible representations. The order is the following:

This routine receives as input the indices of three $C_2$ axes, with the same codes as in $\texttt{which_c2}$, and gives as output the array $\text{ind2(3)}$ of intergers, that gives the positions of $\text{iax, ibx, icx}$ in the list $C_2$, $C_2'$, $C_2''$. The $\text{ind2}(1)$ says which is the position of $\text{iax}$, etc.
For instance $\text{ind2} = (3, 2, 1)$ says that $\text{iax}$ is $C_2''$, $\text{ibx}$ is $C_2'$ and $\text{icx}$ is $C_2$. If on output $\text{ind2}= (0,0,0)$ means that $\text{iax, ibx}$, and $\text{icx}$ do not belong to a possible $D_2$.

This function returns .TRUE. if $a(3)$ and $b(3)$ are parallel vectors

X1 | X2 | | |

Vn+1> = H |Vn>

f< = fc(1-fv)

This function receives a code of the point group and provides the code of the point group that defines the Laue class (that is the point group obtained by multipling by inversion).
The order is the following:

This subroutine receives a mirror symmetry and determine the normal to the mirror plane. The sign of the normal is undefined.