Documented AOs module

src/AOs/ASSUMPTIONS.rst

@@ -0,0 +1,8 @@
+* The atomic orbitals are normalized:
+
+  .. math::
+
+   \int \left(\chi_i({\bf r}) \right)^2 dr = 1
+
+* The AO coefficients in the EZFIO files are not normalized
+* The AO coefficients and exponents are ordered in increasing order of exponents

src/AOs/README.rst

@@ -2,6 +2,37 @@
 AOs Module
 ==========
 
+This module describes the atomic orbitals basis set.
+
+An atomic orbital :math:`\chi` centered on nucleus A is represented as:
+
+.. math::
+
+   \chi_i({\bf r}) = (x-X_A)^a (y-Y_A)^b (z-Z_A)^c \sum_k c_{ki} e^{-\gamma_{ki} |{\bf r} - {\bf R}_A|^2}
+
+
+The AO coefficients are normalized as:
+
+.. math::
+
+  {\tilde c}_{ki} = \frac{c_{ki}}{ \int \left( (x-X_A)^a (y-Y_A)^b (z-Z_A)^c  e^{-\gamma_{ki} |{\bf r} - {\bf R}_A|^2} \right)^2} dr
+
+Assumptions
+===========
+
+.. Do not edit this section. It was auto-generated from the
+.. ASSUMPTIONS.rst file.
+
+* The atomic orbitals are normalized:
+
+  .. math::
+
+   \int \left(\chi_i({\bf r}) \right)^2 dr = 1
+
+* The AO coefficients in the EZFIO files are not normalized
+* The AO coefficients and exponents are ordered in increasing order of exponents
+
+
 Needed Modules
 ==============
 

src/AOs/aos.irp.f

@@ -20,16 +20,18 @@ END_PROVIDER
 &BEGIN_PROVIDER [ double precision, ao_expo, (ao_num_align,ao_prim_num_max) ]
 &BEGIN_PROVIDER [ double precision, ao_coef, (ao_num_align,ao_prim_num_max) ]
  implicit none
+
+ BEGIN_DOC
+! Coefficients, exponents and powers of x,y and z
+! ao_coef(i,j) = coefficient of the jth primitive on the ith ao
+ END_DOC
+ PROVIDE ezfio_filename
+
  double precision, allocatable :: buffer(:,:)
  allocate ( buffer(ao_num,ao_prim_num_max) )
  integer :: ibuffer(ao_num,3)
  integer :: i,j,k
  ibuffer = 0
- BEGIN_DOC
-! coefficient of the primitives on the AO basis
-! ao_coef(i,j) = coefficient of the jth primitive on the ith ao
- END_DOC
- PROVIDE ezfio_filename
  call ezfio_get_ao_basis_ao_power(ibuffer)
  ao_power = 0
  do j = 1, 3