(** Atomic shell pair couple *)

(** An atomic shell pair couple is the cartesian product between two sets of
  * functions, one set over electron one and one set over electron two. Both
  * sets are atomic shell pairs.
  *)

(** These are usually called /shell quartets/ in the literature, but we
  * prefer to use /pair/ for two functions with the same electron, and
  * /couple/ for two functions acting on different electrons, since they will
  * be coupled by a two-electron operator.
  *)


(** Type *)

type t

open Common


(** Access *)

val ang_mom                       : t -> Angular_momentum.t
(** Total angular momentum of the shell pair couple: sum of the angular
  * momenta of all the shells.
  *)

val atomic_shell_a                : t -> Atomic_shell.t
(** Returns the first atomic shell of the first shell pair. *)

val atomic_shell_b                : t -> Atomic_shell.t
(** Returns the second atomic shell of the first shell pair. *)

val atomic_shell_c                : t -> Atomic_shell.t
(** Returns the first atomic shell of the second shell pair. *)

val atomic_shell_d                : t -> Atomic_shell.t
(** Returns the second atomic shell of the second shell pair. *)

val atomic_shell_pair_p           : t -> Atomic_shell_pair.t
(** Returns the first atomic shell pair that was used to build the shell
  * pair.
  *)

val atomic_shell_pair_q           : t -> Atomic_shell_pair.t
(** Returns the second atomic shell pair that was used to build the shell
  * pair.
  *)

val contracted_shell_pair_couples : t -> Contracted_shell_pair_couple.t list
(** Returns the list of significant contracted shell pair couples. *)

val monocentric                   : t -> bool
(** True if all four atomic shells have the same center. *)

val norm_scales                   : t -> float array
(** Scaling factors of normalization coefficients inside the shell. The
  * ordering is the same as ~zkey_array~.
  *)

val zkey_array                    : t -> Zkey.t array
(** Returns the array of ~Zkey.t~ relative to the four shells of the shell
  * pair couple.
  *)


(** Creation *)

val make : ?cutoff:float -> Atomic_shell_pair.t -> Atomic_shell_pair.t -> t option
(** Creates an atomic shell pair couple using two atomic shell pairs.
  * Default cutoff is $\epsilon$.
  *)


(** Printers *)

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