(** Gaussian basis

  Data structure for Gaussian Atomic Orbitals:

  \[
  \chi_i(\mathbf{r}) = P_i(\mathbf{r}) \sum_k c_k \exp\left( -\alpha_k (\mathbf{r-R_A})^2 \r$
  \]

  where the polynomial $P_i$ and the Gaussian part are both centered on
  nucleus $A$.

*)

open Common
open Particles
open Linear_algebra
open Gaussian_integrals
open Operators

type t

(** Access *)

val basis : t -> Gaussian.Basis.t
(**  One-electron basis set *)

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

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

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

val eN_ints : t -> Electron_nucleus.t
(** Electron-nucleus potential integrals *)

val f12_ints : t -> F12.t
(** Electron-electron potential integrals *)

val f12_over_r12_ints : t -> Screened_eri.t
(**lectron-electron potential integrals *)

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

val multipole : t -> Multipole.t
(** Multipole matrices *)

val ortho : t -> Orthonormalization.t
(** Orthonormalization matrix of the overlap *)

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

val size : t -> int
(** Number of atomic orbitals *)


(** Computation *)

val values : t -> Coordinate.t -> Gaussian.Basis.t Vector.t
(** Returns the values of all the AOs evaluated at a given point *)


(** Creation *)

val make : basis:Gaussian.Basis.t ->
           ?operators:Operator.t list ->
           ?cartesian:bool ->
           Nuclei.t -> t

(** Creates the data structure for atomic orbitals from a Gaussian basis and the
   molecular geometry ~Nuclei.t~.

   Defaults:
   - ~operators~ : ~[]~
   - ~cartesian~ : ~false~

   Example:
   #+begin_example
let b = Ao.Basis_gaussian.make ~basis nuclei ;;
val b : Ao.Basis_gaussian.t = Gaussian Basis, spherical, 15 AOs
   #+end_example
*)


(** Printers *)

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