mirror of
https://gitlab.com/scemama/QCaml.git
synced 2024-07-17 00:20:23 +02:00
218 lines
7.9 KiB
Org Mode
218 lines
7.9 KiB
Org Mode
|
#+begin_src elisp tangle: no :results none :exports none
|
||
|
(setq pwd (file-name-directory buffer-file-name))
|
||
|
(setq name (file-name-nondirectory (substring buffer-file-name 0 -4)))
|
||
|
(setq lib (concat pwd "lib/"))
|
||
|
(setq testdir (concat pwd "test/"))
|
||
|
(setq mli (concat lib name ".mli"))
|
||
|
(setq ml (concat lib name ".ml"))
|
||
|
(setq test-ml (concat testdir name ".ml"))
|
||
|
(org-babel-tangle)
|
||
|
#+end_src
|
||
|
|
||
|
* Atomic shell
|
||
|
:PROPERTIES:
|
||
|
:header-args: :noweb yes :comments both
|
||
|
:END:
|
||
|
|
||
|
Set of contracted Gaussians differing only by the powers of $x$, $y$ and $z$, with a
|
||
|
constant ~Angular_momentum.t~, all centered on the same point.
|
||
|
|
||
|
In other words, it is the set of all contracted shells sharing the same center.
|
||
|
|
||
|
\begin{align*}
|
||
|
\chi_{n_x,n_y,n_z}(r) & = f(n_x,n_y,n_z) \sum_{j=1}^{n} \sum_{i=1}^{m} \mathcal{N}_{ij}\, d_{ij}\, g_{ij\,n_x,n_y,n_z}(r) \\
|
||
|
& = (x-X_A)^{n_x} (y-Y_A)^{n_y} (z-Z_A)^{n_z} f(n_x,n_y,n_z) \sum_{j=1}^{n} \sum_{i=1}^{m} \mathcal{N}_{ij}\, d_{ij}\, \exp \left( -\alpha_{ij} |r-R_A|^2 \right)
|
||
|
\end{align*}
|
||
|
|
||
|
where:
|
||
|
|
||
|
- $g_{ij\,n_x,n_y,n_z}(r)$ is the $i$-th ~PrimitiveShell.t~ of the $j$-th ~Contracted_shell.t~
|
||
|
- $n_x + n_y + n_z = l$, the total angular momentum
|
||
|
- $\alpha_{ij}$ are the exponents (tabulated) of the $j$-th ~Contracted_shell.t~
|
||
|
- $d_{ij}$ are the contraction coefficients of the $j$-th ~Contracted_shell.t~
|
||
|
- $\mathcal{N}_{ij}$ is the normalization coefficient of the $i$-th primitive shell
|
||
|
(~PrimitiveShell.norm_coef~) of the $j$-th ~Contracted_shell.t~
|
||
|
- $f(n_x,n_y,n_z)$ is a scaling factor adjusting the normalization coefficient for the
|
||
|
particular powers of $x,y,z$ (~PrimitiveShell.norm_coef_scale~)
|
||
|
|
||
|
|
||
|
** Type
|
||
|
|
||
|
#+begin_src ocaml :tangle (eval mli)
|
||
|
type t
|
||
|
|
||
|
open Common
|
||
|
#+end_src
|
||
|
|
||
|
#+begin_src ocaml :tangle (eval ml) :exports none
|
||
|
open Common
|
||
|
|
||
|
type t = {
|
||
|
expo : float array array;
|
||
|
coef : float array array;
|
||
|
norm_coef : float array array;
|
||
|
norm_coef_scale : float array;
|
||
|
contr : Contracted_shell.t array;
|
||
|
index : int;
|
||
|
center : Coordinate.t;
|
||
|
ang_mom : Angular_momentum.t;
|
||
|
}
|
||
|
|
||
|
module Am = Angular_momentum
|
||
|
module Co = Coordinate
|
||
|
module Cs = Contracted_shell
|
||
|
#+end_src
|
||
|
|
||
|
** Access
|
||
|
|
||
|
#+begin_src ocaml :tangle (eval mli)
|
||
|
val index : t -> int
|
||
|
(** Index in the basis set, represented as an array of contracted shells. *)
|
||
|
|
||
|
val center : t -> Coordinate.t
|
||
|
(** Coordinate of the center {% $\mathbf{A} = (X_A,Y_A,Z_A)$ %}. *)
|
||
|
|
||
|
val ang_mom : t -> Angular_momentum.t
|
||
|
(** Total angular momentum : {% $l = n_x + n_y + n_z$ %}. *)
|
||
|
|
||
|
val size : t -> int
|
||
|
(** Number of contracted functions, {% $n$ %} in the definition. *)
|
||
|
|
||
|
val contracted_shells: t -> Contracted_shell.t array
|
||
|
(** Array of contracted gaussians *)
|
||
|
|
||
|
val exponents : t -> float array array
|
||
|
(** Array of exponents {% $\alpha_{ij}$ %}. The first index is the index of
|
||
|
the contracted function, and the second index is the index of the primitive.
|
||
|
*)
|
||
|
|
||
|
val coefficients : t -> float array array
|
||
|
(** Array of contraction coefficients {% $d_{ij}$ %}. The first index is the index of
|
||
|
the contracted function, and the second index is the index of the primitive.
|
||
|
*)
|
||
|
|
||
|
val normalizations : t -> float array array
|
||
|
(** Normalization coefficients {% $\mathcal{N}_{ij}$ %}. The first index is the index of
|
||
|
the contracted function, and the second index is the index of the primitive.
|
||
|
*)
|
||
|
|
||
|
val norm_scales : t -> float array
|
||
|
(** Scaling factors {% $f(n_x,n_y,n_z)$ %}, given in the same order as
|
||
|
[Angular_momentum.zkey_array ang_mom]. *)
|
||
|
|
||
|
val size_of_shell : t -> int
|
||
|
(** Number of contracted functions in the shell: length of {!norm_coef_scale}. *)
|
||
|
|
||
|
#+end_src
|
||
|
|
||
|
| ~index~ | Index in the basis set, represented as an array of contracted shells. |
|
||
|
| ~center~ | Coordinate of the center $\mathbf{A} = (X_A,Y_A,Z_A)$. |
|
||
|
| ~ang_mom~ | Total angular momentum : $l = n_x + n_y + n_z$. |
|
||
|
| ~size~ | Number of contracted functions, $n$ in the definition. |
|
||
|
| ~contracted_shells:~ | Array of contracted gaussians |
|
||
|
| ~exponents~ | Array of exponents $\alpha_{ij}$. The first index is the index of the contracted function, and the second index is the index of the primitive. |
|
||
|
| ~coefficients~ | Array of contraction coefficients $d_{ij}$. The first index is the index of the contracted function, and the second index is the index of the primitive. |
|
||
|
| ~normalizations~ | Normalization coefficients $\mathcal{N}_{ij}$. The first index is the index of the contracted function, and the second index is the index of the primitive. |
|
||
|
| ~norm_scales~ | Scaling factors $f(n_x,n_y,n_z)$, given in the same order as ~Angular_momentum.zkey_array ang_mom~. |
|
||
|
| ~size_of_shell~ | Number of contracted functions in the shell: length of ~norm_coef_scale~. |
|
||
|
|
||
|
#+begin_example
|
||
|
|
||
|
#+end_example
|
||
|
|
||
|
#+begin_src ocaml :tangle (eval ml) :exports none
|
||
|
let exponents x = x.expo
|
||
|
|
||
|
let coefficients x = x.coef
|
||
|
|
||
|
let center x = x.center
|
||
|
|
||
|
let ang_mom x = x.ang_mom
|
||
|
|
||
|
let size x = Array.length x.contr
|
||
|
|
||
|
let normalizations x = x.norm_coef
|
||
|
|
||
|
let norm_scales x = x.norm_coef_scale
|
||
|
|
||
|
let index x = x.index
|
||
|
|
||
|
let size_of_shell x = Array.length x.norm_coef_scale
|
||
|
|
||
|
let contracted_shells x = x.contr
|
||
|
#+end_src
|
||
|
|
||
|
** Creation
|
||
|
|
||
|
#+begin_src ocaml :tangle (eval mli)
|
||
|
val make : ?index:int -> Contracted_shell.t array -> t
|
||
|
(** Creates a contracted shell from a list of coefficients and primitives. *)
|
||
|
|
||
|
val with_index : t -> int -> t
|
||
|
(** Returns a copy of the contracted shell with a modified index. *)
|
||
|
#+end_src
|
||
|
|
||
|
| ~make~ | Creates a contracted shell from a list of coefficients and primitives. |
|
||
|
| ~with_index~ | Returns a copy of the contracted shell with a modified index. |
|
||
|
|
||
|
#+begin_example
|
||
|
|
||
|
#+end_example
|
||
|
|
||
|
#+begin_src ocaml :tangle (eval ml) :exports none
|
||
|
let make ?(index=0) contr =
|
||
|
assert (Array.length contr > 0);
|
||
|
|
||
|
let coef = Array.map Cs.coefficients contr
|
||
|
and expo = Array.map Cs.exponents contr
|
||
|
in
|
||
|
|
||
|
let center = Cs.center contr.(0) in
|
||
|
let rec unique_center = function
|
||
|
| 0 -> true
|
||
|
| i -> if Cs.center contr.(i) = center then (unique_center [@tailcall]) (i-1) else false
|
||
|
in
|
||
|
if not (unique_center (Array.length contr - 1)) then
|
||
|
invalid_arg "ContractedAtomicShell.make Coordinate.t differ";
|
||
|
|
||
|
let ang_mom = Cs.ang_mom contr.(0) in
|
||
|
let rec unique_angmom = function
|
||
|
| 0 -> true
|
||
|
| i -> if Cs.ang_mom contr.(i) = ang_mom then (unique_angmom [@tailcall]) (i-1) else false
|
||
|
in
|
||
|
if not (unique_angmom (Array.length contr - 1)) then
|
||
|
invalid_arg "Contracted_shell.make: Angular_momentum.t differ";
|
||
|
|
||
|
let norm_coef =
|
||
|
Array.map Cs.normalizations contr
|
||
|
in
|
||
|
let norm_coef_scale = Cs.norm_scales contr.(0)
|
||
|
in
|
||
|
{ index ; expo ; coef ; center ; ang_mom ; norm_coef ;
|
||
|
norm_coef_scale ; contr }
|
||
|
|
||
|
|
||
|
let with_index a i =
|
||
|
{ a with index = i }
|
||
|
#+end_src
|
||
|
|
||
|
|
||
|
** Printers
|
||
|
|
||
|
#+begin_src ocaml :tangle (eval mli)
|
||
|
val pp : Format.formatter -> t -> unit
|
||
|
#+end_src
|
||
|
|
||
|
#+begin_src ocaml :tangle (eval ml) :exports none
|
||
|
let pp ppf s =
|
||
|
let open Format in
|
||
|
fprintf ppf "@[%3d-%-3d@]" (s.index+1) (s.index+ (size_of_shell s)*(size s));
|
||
|
fprintf ppf "@[%a@ %a@] @[" Am.pp_string s.ang_mom Co.pp s.center;
|
||
|
Array.iter2 (fun e_arr c_arr -> fprintf ppf "@[<v>";
|
||
|
Array.iter2 (fun e c -> fprintf ppf "@[%16.8e %16.8e@]@;" e c)
|
||
|
e_arr c_arr;
|
||
|
fprintf ppf "@;@]") s.expo s.coef;
|
||
|
fprintf ppf "@]"
|
||
|
#+end_src
|
||
|
|