Documentation

Basis/ContractedShellPair.ml

@@ -39,13 +39,13 @@ Format.printf "@[<2>shell_b :@ %a@]@;" Cs.pp s_b;
   let shell_pairs = 
     Array.mapi (fun i p_a ->
         let c_a = (Cs.coef s_a).(i) in
-        let make = make i p_a in
+        let make = make p_a in
         Array.mapi (fun j p_b ->
             let c_b = (Cs.coef s_b).(j) in
             let coef = c_a *. c_b in
             assert (coef <> 0.);
             let cutoff = cutoff /. abs_float coef in
-            coef, make j p_b cutoff) (Cs.prim s_b)) (Cs.prim s_a)
+            coef, make p_b cutoff) (Cs.prim s_b)) (Cs.prim s_a)
     |> Array.to_list
     |> Array.concat
     |> Array.to_list

Basis/PrimitiveShellPair.ml

@@ -15,8 +15,6 @@ type t = {
   totAngMom       : AngularMomentum.t; 
   shell_a         : PrimitiveShell.t;
   shell_b         : PrimitiveShell.t;
-  (*TODO*)
-  i : int; j : int;
 }
 
 exception Null_contribution
@@ -25,18 +23,20 @@ module Am = AngularMomentum
 module Co = Coordinate
 module Ps = PrimitiveShell
 
-(** Returns an integer characteristic of a primitive shell pair *)
+
 let hash a = 
   Hashtbl.hash a
 
+
 let equivalent a b =
-  a = b
-(*
-  Hashtbl.hash (a.expo, a.center_a, a.center_ab, a.coef, ContractedShell.totAngMom a.shell_a, ContractedShell.totAngMom a.shell_b) 
-*)
+  a.expo = b.expo &&
+  a.totAngMom = b.totAngMom &&
+  a.norm_coef = b.norm_coef &&
+  a.center = b.center &&
+  a.center_minus_a = b.center_minus_a &&
+  a.a_minus_b = b.a_minus_b
 
 
-(** Comparison function, used for sorting *)
 let cmp a b =
   hash a - hash b
 
@@ -63,20 +63,16 @@ let create_make_of p_a p_b =
     Am.( Ps.totAngMom p_a + Ps.totAngMom p_b )
   in
 
-  (* TODO *)
-  function i ->
   function p_a -> 
 
       let norm_coef_a =
         Ps.norm_coef p_a
       in
 
-      let alpha_a = (* p_a_expo_center *)
+      let alpha_a = 
         Co.( Ps.expo p_a |. Ps.center p_a )
       in
 
-      (*TODO *)
-      function j ->
       function p_b -> 
 
           let norm_coef =
@@ -113,7 +109,7 @@ let create_make_of p_a p_b =
                   in
 
                   Some {
-                    i ; j ; totAngMom ; 
+                    totAngMom ; 
                     expo ; expo_inv ; center ; center_minus_a ; a_minus_b ; 
                     a_minus_b_sq ; norm_coef ; norm_coef_scale ; shell_a = p_a;
                     shell_b = p_b }
@@ -126,7 +122,7 @@ let make p_a p_b =
   let f =
     create_make_of p_a p_b
   in
-  match f 0 p_a 0 p_b 0. with
+  match f p_a p_b 0. with
   | Some result -> result
   | None -> assert false
 

Basis/PrimitiveShellPair.mli

@@ -22,50 +22,27 @@ where
 \end{align*}
 %}
 
-Following Ref [1], we define three quantities associated with the shells on centers A and B:
-
-{%
-\begin{align*}
-\sigma_P & = \frac{1}{\alpha + \beta} \\
-\mathbf{P} & = \left( \alpha \mathbf{A} + \beta \mathbf{B} \right) \, \sigma_P \\
-U_P & = (\pi\,\sigma_P)^{3/2} \exp \left( \alpha \beta \sigma_P |\mathbf{A}-\mathbf{B}|^2 \right)
-\end{align*}
-%}
-
 
+{!a_minus_b}, {!a_minus_b_sq} and {!norm_coef_scale} depend only on the
+centering of the two shells, and {!totAngMom} only depends on the angular
+momenta of the two shells. Hence, these quantities need to be computed only
+once when a {!ContractedShellPair.t} is built. Hence, there is the
+{!create_make_of} function which creates a [make] function which is suitable
+for a {!ContractedShellPair.t}.
 
 References:
 
 [1] {{:http://dx.doi.org/10.1002/qua.560400604} P.M. Gill, B.G. Johnson, and J.A. Pople, International Journal of Quantum Chemistry 40, 745 (1991)}.
 *)
 
-type t = {
-  expo            : float;              (* alpha + beta *)
-  expo_inv        : float;              (* 1/(alpha + beta) *)
-  center          : Coordinate.t;       (* P = (alpha * A + beta B)/(alpha+beta) *)
-  center_minus_a  : Coordinate.t;       (* P - A *)
-  a_minus_b       : Coordinate.t;       (* A - B *)
-  a_minus_b_sq    : float;              (* |A-B|^2 *)
-  norm_coef_scale : float array lazy_t;
-  norm_coef       : float;              (* norm_coef_a * norm_coef_b * g, with
-                                           g = (pi/(alpha+beta))^(3/2) exp (-|A-B|^2 * alpha*beta/(alpha+beta)) *)
-  totAngMom       : AngularMomentum.t;
-  shell_a         : PrimitiveShell.t;
-  shell_b         : PrimitiveShell.t;
-  i : int; (*TODO remove *)
-  j : int; (*TODO remove *)
-}
-
+type t 
 
 
 val make : PrimitiveShell.t -> PrimitiveShell.t -> t
 (** Creates a primitive shell pair using two primitive shells. *)
 
 val create_make_of : PrimitiveShell.t -> PrimitiveShell.t ->
-  (int -> PrimitiveShell.t -> int -> PrimitiveShell.t -> float -> t option)
-  (* TODO
   (PrimitiveShell.t -> PrimitiveShell.t -> float -> t option)
-  *)
 (** Creates a make function [PrimitiveShell.t -> PrimitiveShell.t -> float -> t] in which
     all the quantities common to the shell and independent of the exponent
     are pre-computed.
@@ -75,30 +52,39 @@ val create_make_of : PrimitiveShell.t -> PrimitiveShell.t ->
 
 *)
 
-val equivalent : t -> t -> bool
-
-val hash : t -> int
-
-val cmp : t -> t -> int
-
-val monocentric : t -> bool
-
-val center : t -> Coordinate.t
-(** Coordinates of the center {%$\mathbf{P}$%}. *)
-
-val norm_coef_scale : t -> float array
-
-val expo : t -> float
-(** {% \\[ \alpha + \beta \\] %}*)
-
-val expo_inv : t -> float 
-(** {% \\[ \frac{1}{\alpha + \beta} \\] %}*)
-
 val totAngMom : t -> AngularMomentum.t
 (** Total angular momentum of the shell pair: sum of the angular momenta of
-    the shells.
+    the shells.  *)
+
+val center : t -> Coordinate.t
+(** Coordinates of the center {% $\mathbf{P}$ %}. *)
+
+val monocentric : t -> bool
+(** True if both shells of the pair have the same center. *)
+
+
+val shell_a : t -> PrimitiveShell.t
+(** Returns the first primitive shell that was used to build the shell pair. *)
+
+val shell_b : t -> PrimitiveShell.t
+(** Returns the second primitive shell that was used to build the shell pair. *)
+
+val norm_coef : t -> float
+(** Normalization coefficient of the shell pair. *)
+
+val norm_coef_scale : t -> float array
+(** Normalization factor, characteristic of the powers of x, y and z of
+    both shells of the pair. It is the outer product of the 2 
+    {!PrimitiveShell.norm_coef_scale} arrays of the shells consituting the
+    pair.
 *)
 
+val expo : t -> float
+(** Exponent of the Gaussian output of the Gaussian product : {% \\[ \alpha + \beta \\] %}*)
+
+val expo_inv : t -> float 
+(** Inverse of the exponent : {% \\[ \sigma_P = \frac{1}{\alpha + \beta} \\] %}*)
+
 val a_minus_b : t -> Coordinate.t
 (** {% $\mathbf{A}-\mathbf{B}$ %} *)
 
@@ -108,12 +94,13 @@ val a_minus_b_sq : t -> float
 val center_minus_a : t -> Coordinate.t
 (** {% $\mathbf{P}-\mathbf{A}$ %} *)
 
-val norm_coef : t -> float
-(** Normalization coefficient of the shell pair. *)
 
-val shell_a : t -> PrimitiveShell.t
-(** Returns the first primitive shell that was used to build the shell pair. *)
+val equivalent : t -> t -> bool
+(** True if two primitive shell pairs are equivalent. *)
 
-val shell_b : t -> PrimitiveShell.t
-(** Returns the second primitive shell that was used to build the shell pair. *)
+val hash : t -> int
+(** Returns an integer characteristic of the shell pair. *)
+
+val cmp : t -> t -> int
+(** Arbitray comparison function for sorting. *)