QCaml/common/angular_momentum.org

• Angular Momentum
  • Type
  • Conversions
    • of_char
    • to_string
    • to_char
    • to_int
    • of_int
  • Shell functions
    • n_functions
    • zkey_array
  • Arithmetic
  • Printers
  • Tests

Angular Momentum

Azimuthal quantum number, repsesented as \( s,p,d,\dots \) .

Type

type t =
| S | P | D | F | G | H | I | J | K | L | M | N | O
| Int of int

exception Angular_momentum_error of string

type kind =
 Singlet of t
| Doublet of (t * t)
| Triplet of (t * t * t)
| Quartet of (t * t * t * t)

An exception is raised when the Angular_momentum.t element can't be created.

The kind is used to build shells, shell doublets, triplets or quartets, use in the two-electron operators.

Conversions

of_char

Returns an Angular_momentum.t when a shell is given as a character (case insensitive):

Angular_momentum.of_char 'p' -> Angular_momentum.P

val of_char : char -> t

to_string

Converts the angular momentum into a string:

Angular_momentum.(to_string D) -> "D"

val to_string : t -> string

to_char

Converts the angular momentum into a char:

Angular_momentum.(to_char D) -> 'D'

val to_char : t -> char

to_int

Returns the $l_{max}$ value of the shell:

Angular_momentum.(to_char D) -> 2

val to_int : t -> int

of_int

Returns a shell given an $l$ value.

Angular_momentum.of_int 3 -> Angular_momentum.F

val of_int : int -> t

Shell functions

n_functions

Returns the number of cartesian functions in a shell.

Angular_momentum.n_functions D -> 6

val n_functions : t -> int

zkey_array

Array of Zkey.t, where each element is a a key associated with the the powers of $x,y,z$.

Angular_momentum.( zkey_array Doublet (P,S) ) ->
[| {Zkey.left = 0; right = 1125899906842624} ;
   {Zkey.left = 0; right = 1099511627776}    ;
   {Zkey.left = 0; right = 1073741824}       |]
=

let s,x,y,z =
  Powers.( of_int_tuple (0,0,0),
           of_int_tuple (1,0,0),
           of_int_tuple (0,1,0),
           of_int_tuple (0,0,1) )
in
Array.map (fun (a,b) -> {!Zkey.of_powers_six} a b)
  [| (x,s) ; (y,s) ; (z,s) |]

val zkey_array : kind -> Zkey.t array

Arithmetic

val ( + ) : t -> t -> t
val ( - ) : t -> t -> t

Printers

Printers can print as a string (pp_string) or as an integer (pp_int).

val pp_string : Format.formatter -> t -> unit
val pp_int : Format.formatter -> t -> unit

TODO Tests