Documentation in Basis/PrimitiveShell.mli

Basis/PrimitiveShell.ml

@@ -41,17 +41,18 @@ let make totAngMom center expo =
   let norm_coef_func =
     compute_norm_coef expo totAngMom
   in
-  let norm_coef =
+  let norm =
-    norm_coef_func [| Am.to_int totAngMom ; 0 ; 0 |]  
+    1. /. norm_coef_func [| Am.to_int totAngMom ; 0 ; 0 |] 
   in
   let powers =
     Am.zkey_array (Am.Singlet totAngMom) 
   in
   let norm_coef_scale = lazy (
     Array.map (fun a ->
-      (norm_coef_func (Zkey.to_int_array a)) /. norm_coef
+      (norm_coef_func (Zkey.to_int_array a)) *. norm
     ) powers )
   in
+  let norm_coef = 1. /. norm in
   { expo ; norm_coef ; norm_coef_scale ; center ; totAngMom }
 
 
@@ -75,6 +76,8 @@ let center x = x.center
 
 let totAngMom x = x.totAngMom
 
+let norm x = 1. /. x.norm_coef
+
 let norm_coef x = x.norm_coef
 
 let norm_coef_scale x = Lazy.force x.norm_coef_scale

Basis/PrimitiveShell.mli

@@ -1,11 +1,17 @@
-(** Set of Gaussians with a given {!AngularMomentum.t}
+(** Set of Gaussians differing only by the powers of x, y and z, with a
+    constant {!AngularMomentum.t}.
 
 {% \\[
-g(r) = (x-X_A)^{n_x} (y-Y_A)^{n_y} (z-Z_A)^{n_z} \exp \left( -\alpha |r-R_A|^2 \right)
+g_{n_x,n_y,n_z}(\mathbf{r}) = (x-X_A)^{n_x} (y-Y_A)^{n_y} (z-Z_A)^{n_z}
+    \exp \left( -\alpha |\mathbf{r}-\mathbf{A}|^2 \right)
    \\] %}
 
 where:
 
+- {% $\mathbf{r} = (x,y,z)$ %} is the electron coordinate
+
+- {% $\mathbf{A} = (X_A,Y_A,Z_A)$ %} is the coordinate of center A
+
 - {% $n_x + n_y + n_z = l$ %}, the total angular momentum
 
 - {% $\alpha$ %} is the exponent
@@ -22,31 +28,34 @@ val make : AngularMomentum.t -> Coordinate.t -> float -> t
     center and the exponent. *)
 
 val expo : t -> float 
-(** Returns the exponent {% $\alpha$ %}. *)
+(** Exponent {% $\alpha$ %}. *)
 
 val center : t -> Coordinate.t
-(** Coordinate of the center {% $\mathbf{A} = (X_A,Y_A,Z_A)$ %}. *)
+(** Coordinate {% $\mathbf{A}$ %}.of the center. *)
 
 val totAngMom : t -> AngularMomentum.t
 (** Total angular momentum : {% $l = n_x + n_y + n_z$ %}. *)
 
-val norm_coef : t -> float 
+val norm : t -> float 
-(** Normalization coefficient of the shell:
+(** Norm of the shell, defined as
+    {% \\[ || g_{l,0,0}(\mathbf{r}) || = 
+      \sqrt{ \iiint \left[ (x-X_A)^{l}
+      \exp (-\alpha |\mathbf{r}-\mathbf{A}|^2) \right]^2 \, dx\, dy\, dz}
+    \\] %}
+*)
 
-    {% \\[
+val norm_coef : t -> float 
-    \mathcal{N} = \sqrt{\iiint \left[ (x-X_A)^{l}
+(** Normalization coefficient by which the shell has to be multiplied
-                  \exp (-\alpha |r-R_A|^2) \right]^2 \, dx\, dy\, dz}
+    to be normalized :
-      \\] %}
+    {% \\[ \mathcal{N} = \frac{1}{|| g_{l,0,0}(\mathbf{r}) ||} \\] %}.
 *)
 
 val norm_coef_scale : t -> float array
-(** Scaling factors adjusting the normalization coefficient for the.
+(** Scaling factors {% $f(n_x,n_y,n_z)$ %} adjusting the normalization coefficient
-  particular powers of {% $x,y,z$ %}.  They are given in the same order as
+    for the powers of {% $x,y,z$ %}. The normalization coefficients of the
-  [AngularMomentum.zkey_array totAngMom]: 
+    functions of the shell are given by {% $\mathcal{N}\times f$ %}.  They are
-
+    given in the same order as [AngularMomentum.zkey_array totAngMom]: 
-  {% \\[
+    {% \\[ f(n_x,n_y,n_z) = \frac{|| g_{l,0,0}(\mathbf{r}) ||}{|| g_{n_x,n_y,n_z}(\mathbf{r}) ||} \\] %}
-  f = \frac{1}{\mathcal{N}} \sqrt{\iiint [g(r)]^2 \, d^3r}
-    \\] %}
 *)
 
 val size_of_shell : t -> int