(** Data structure for Atomic Orbitals.  *)

type t
type ao = Ao_dim.t

open Common
open Particles
open Operators
open Linear_algebra

(** Conversions *)

val of_nuclei_and_basis_filename :
  ?kind:[> `Gaussian ] ->
  ?operators:Operator.t list ->
  ?cartesian:bool ->
  nuclei:Nuclei.t ->
  string -> t
(** Creates the data structure for the atomic orbitals basis from a
    molecule ~Nuclei.t~ and the name of the basis-set file.

   Defaults:
   - ~kind~ : ~`Gaussian~
   - ~operators~ : ~[]~
   - ~cartesian~ : ~false~

   Example:
   #+begin_example
let b = Ao.Basis.of_nuclei_and_basis_filename ~nuclei filename;;
val b : Ao.Basis.t = Gaussian Basis, spherical, 15 AOs
   #+end_example

*)


val of_nuclei_and_basis_string :
  ?kind:[> `Gaussian ] ->
  ?operators:Operator.t list ->
  ?cartesian:bool ->
  nuclei:Nuclei.t ->
  string -> t
(** Creates the data structure for the atomic orbitals basis from a
    molecule ~Nuclei.t~ and a basis-set string.

   Defaults:
   - ~kind~ : ~`Gaussian~
   - ~operators~ : ~[]~
   - ~cartesian~ : ~false~

   Example:
   #+begin_example
let b = Ao.Basis.of_nuclei_and_basis_string ~nuclei "
HYDROGEN
S  1
  1        0.0395061728     1.00000000

"
;;
val b : Ao.Basis.t = Gaussian Basis, spherical, 1 AOs
   #+end_example

*)


(** Access *)

val size : t -> int
(** Number of atomic orbitals in the AO basis set *)

val ao_basis : t -> Basis_poly.t
(** One-electron basis set *)

val overlap : t -> (ao,ao) Matrix.t
(** Overlap matrix *)

val multipole : t -> string -> (ao,ao) Matrix.t
(** Multipole matrices *)

val ortho : t -> (ao,'a) Matrix.t
(** Orthonormalization matrix of the overlap *)

val eN_ints : t -> (ao,ao) Matrix.t
(** Electron-nucleus potential integrals *)

val kin_ints : t -> (ao,ao) Matrix.t
(** Kinetic energy integrals *)

val ee_ints : t -> ao Four_idx_storage.t
(** Electron-electron potential integrals *)

val ee_lr_ints : t -> ao Four_idx_storage.t
(** Electron-electron long-range potential integrals *)

val f12_ints : t -> ao Four_idx_storage.t
(** Electron-electron potential integrals *)

val f12_over_r12_ints : t -> ao Four_idx_storage.t
(** ectron-electron potential integrals *)

val cartesian : t -> bool
(** If true, use cartesian Gaussians (6d, 10f, ...) *)

val values : t -> Coordinate.t -> ao Vector.t
(** Values of the AOs evaluated at a given point *)


(** TREXIO *)

(*
val of_trexio : Trexio.trexio_file -> t
(** Reads the basis set from a TREXIO file *)

val to_trexio : Trexio.trexio_file -> t -> unit
(** Writes the basis set to a TREXIO file *)
*)


(* Printers *)

val pp : Format.formatter -> t -> unit