#+TITLE: Integrals

#+PROPERTY

In this example, we write a program that reads the geometry of a
molecule in =xyz= format and a Gaussian atomic basis set in GAMESS
format. The output is a set of files containing the one- and two-
electron integrals.

* Header 

#+BEGIN_SRC ocaml :comments link :exports code :tangle ex_integrals.ml  
module Command_line = Qcaml.Common.Command_line
module Util = Qcaml.Common.Util
open Qcaml.Linear_algebra

let () =
#+END_SRC

* Command-line arguments

  We use the =Command_line= module to define the following possible
  arguments:
  - =-b --basis= : The name of the file containing the basis set
  - =-x --xyz=   : The name of the file containing the atomic coordinates
  - =-u --range-separation= : The value of $\mu$, the range-separation
    parameter in range-separated DFT. If this option is not present,
    no output file will be generated for the range-separated integrals.

** Definition

   #+BEGIN_SRC ocaml :comments link :exports code :tangle ex_integrals.ml  
let open Command_line in
begin
  set_header_doc (Sys.argv.(0));
  set_description_doc "Computes the one- and two-electron integrals on the Gaussian atomic basis set.";
  set_specs
    [ { short='b' ; long="basis" ; opt=Mandatory;
	arg=With_arg "<string>";
	doc="Name of the file containing the basis set"; } ;

      { short='x' ; long="xyz" ; opt=Mandatory;
	arg=With_arg "<string>";
	doc="Name of the file containing the nuclear coordinates in xyz format"; } ;

      { short='u' ; long="range-separation" ; opt=Optional;
	arg=With_arg "<float>";
	doc="Range-separation parameter."; } ;
    ]
end;
   #+END_SRC

** Interpretation

   #+BEGIN_SRC ocaml :comments link :exports code :tangle ex_integrals.ml  
let basis_file  = Util.of_some @@ Command_line.get "basis" in
let nuclei_file = Util.of_some @@ Command_line.get "xyz" in

let range_separation =
  match Command_line.get "range-separation" with
  | None -> None
  | Some mu -> Some (float_of_string mu)
in

let operators =
  match range_separation with
  | None -> []
  | Some mu -> [ Qcaml.Operators.Operator.of_range_separation mu ]
in
   #+END_SRC

* Computation
  We first read the =xyz= file to create a molecule:
  #+BEGIN_SRC ocaml :comments link :exports code :tangle ex_integrals.ml  
let nuclei =
  Qcaml.Particles.Nuclei.of_xyz_file nuclei_file
in
  #+END_SRC

  Then we create an Gaussian AO basis using the atomic coordinates,
  and we optionally introduce the range-separation parameter via the
  =operators=:
  #+BEGIN_SRC ocaml :comments link :exports code :tangle ex_integrals.ml  
let ao_basis =
  Qcaml.Ao.Basis.of_nuclei_and_basis_filename ~kind:`Gaussian
    ~operators ~cartesian:true ~nuclei basis_file
in
  #+END_SRC

  We compute the required one-electron integrals:
  #+BEGIN_SRC ocaml :comments link :exports code :tangle ex_integrals.ml  
let overlap   = Qcaml.Ao.Basis.overlap   ao_basis in
let eN_ints   = Qcaml.Ao.Basis.eN_ints   ao_basis in
let kin_ints  = Qcaml.Ao.Basis.kin_ints  ao_basis in
let multipole = Qcaml.Ao.Basis.multipole ao_basis in
let x_mat     = multipole "x" in
let y_mat     = multipole "y" in
let z_mat     = multipole "z" in
  #+END_SRC

  and the two-electron integrals (1/r and long range):
  #+BEGIN_SRC ocaml :comments link :exports code :tangle ex_integrals.ml  
let ee_ints   = Qcaml.Ao.Basis.ee_ints   ao_basis in
let lr_ints   = 
  match range_separation with
  | Some _mu -> Some (Qcaml.Ao.Basis.ee_lr_ints ao_basis)
  | None -> None
in
  #+END_SRC

* Output

  We write the one-electron integrals:
  #+BEGIN_SRC ocaml :comments link :exports code :tangle ex_integrals.ml  
Matrix.to_file ~filename:"overlap.dat" ~sym:true overlap;
Matrix.to_file ~filename:"eN.dat" ~sym:true eN_ints;
Matrix.to_file ~filename:"kinetic.dat" ~sym:true kin_ints;
Matrix.to_file ~filename:"x.dat" ~sym:true x_mat;
Matrix.to_file ~filename:"y.dat" ~sym:true y_mat;
Matrix.to_file ~filename:"z.dat" ~sym:true z_mat;
  #+END_SRC

  and the the two-electron integrals:
  #+BEGIN_SRC ocaml :comments link :exports code :tangle ex_integrals.ml  
Four_idx_storage.to_file ~filename:"eri.dat" ee_ints;
match lr_ints with
| Some integrals -> Four_idx_storage.to_file ~filename:"eri_lr.dat" integrals;
| None -> ()
  #+END_SRC