From 934d3de77a4439be966d97c847fcb2a2c37fc073 Mon Sep 17 00:00:00 2001 From: Anthony Scemama Date: Wed, 6 Jan 2021 09:03:26 +0100 Subject: [PATCH] Atomic shell in org --- docs/gaussian.html | 251 +++++++++++++++++++++++++++++++++- docs/top.html | 6 +- gaussian/atomic_shell.org | 217 +++++++++++++++++++++++++++++ gaussian/lib/atomic_shell.ml | 98 +++++++------ gaussian/lib/atomic_shell.mli | 58 +++----- top/lib/install_printers.ml | 1 + 6 files changed, 547 insertions(+), 84 deletions(-) create mode 100644 gaussian/atomic_shell.org diff --git a/docs/gaussian.html b/docs/gaussian.html index 99de80f..ffdef66 100644 --- a/docs/gaussian.html +++ b/docs/gaussian.html @@ -3,7 +3,7 @@ "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> - + Gaussian @@ -221,18 +221,263 @@ /*]]>*///--> // @license-end + +

Gaussian

+
+

Table of Contents

+
+ +
+
-
"Gaussian basis sets"
+
"Gaussian basis sets"
+ + +
+

1 Atomic shell

+
+

+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)
    • +
+
+ + +
+

1.1 Type

+
+
+
type t
+
+open Common
+
+
+
+
+ +
+

1.2 Access

+
+
+
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}. *)
+
+
+
+ + + + +++ ++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
indexIndex in the basis set, represented as an array of contracted shells.
centerCoordinate of the center \(\mathbf{A} = (X_A,Y_A,Z_A)\).
ang_momTotal angular momentum : \(l = n_x + n_y + n_z\).
sizeNumber of contracted functions, \(n\) in the definition.
contracted_shells:Array of contracted gaussians
exponentsArray of exponents \(\alpha_{ij}\). The first index is the index of the contracted function, and the second index is the index of the primitive.
coefficientsArray 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.
normalizationsNormalization 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_scalesScaling factors \(f(n_x,n_y,n_z)\), given in the same order as Angular_momentum.zkey_array ang_mom.
size_of_shellNumber of contracted functions in the shell: length of norm_coef_scale.
+ +
+
+
+
+
+ +
+

1.3 Creation

+
+
+
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. *)
+
+
+ + + + +++ ++ + + + + + + + + + + + +
makeCreates a contracted shell from a list of coefficients and primitives.
with_indexReturns a copy of the contracted shell with a modified index.
+ +
+
+
+
+
+ +
+

1.4 Printers

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

Author: Anthony Scemama

-

Created: 2021-01-04 Mon 23:32

+

Created: 2021-01-06 Wed 09:02

Validate

diff --git a/docs/top.html b/docs/top.html index 51adb28..e5cfafe 100644 --- a/docs/top.html +++ b/docs/top.html @@ -3,7 +3,7 @@ "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> - + Top-level @@ -226,13 +226,13 @@

Top-level

-
"Installs pretty printers for top-level."
+
"Installs pretty printers for top-level."

Author: Anthony Scemama

-

Created: 2021-01-04 Mon 23:51

+

Created: 2021-01-06 Wed 09:03

Validate

diff --git a/gaussian/atomic_shell.org b/gaussian/atomic_shell.org new file mode 100644 index 0000000..f127bc0 --- /dev/null +++ b/gaussian/atomic_shell.org @@ -0,0 +1,217 @@ +#+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 "@["; + 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 + diff --git a/gaussian/lib/atomic_shell.ml b/gaussian/lib/atomic_shell.ml index 1d2f37a..78b672a 100644 --- a/gaussian/lib/atomic_shell.ml +++ b/gaussian/lib/atomic_shell.ml @@ -1,3 +1,4 @@ +(* [[file:~/QCaml/gaussian/atomic_shell.org::*Type][Type:2]] *) open Common type t = { @@ -14,8 +15,59 @@ type t = { module Am = Angular_momentum module Co = Coordinate module Cs = Contracted_shell +(* Type:2 ends here *) + +(* | ~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 *) + + +(* [[file:~/QCaml/gaussian/atomic_shell.org::*Access][Access:2]] *) +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 +(* Access:2 ends here *) + + + +(* | ~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 *) + + +(* [[file:~/QCaml/gaussian/atomic_shell.org::*Creation][Creation:2]] *) let make ?(index=0) contr = assert (Array.length contr > 0); @@ -50,47 +102,11 @@ let make ?(index=0) contr = let with_index a i = { a with index = i } +(* Creation:2 ends here *) - -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 - - -(** {2 Printers} *) - -open Format - -(* -let pp_debug ppf x = - fprintf ppf "@[<2>{@ "; - fprintf ppf "@[<2>expo =@ %a ;@]@ " pp_float_2darray_size x.expo; - fprintf ppf "@[<2>coef =@ %a ;@]@ " pp_float_2darray_size x.coef; - fprintf ppf "@[<2>center =@ %a ;@]@ " Co.pp_angstrom x.center; - fprintf ppf "@[<2>ang_mom =@ %a ;@]@ " Am.pp_string x.ang_mom; - fprintf ppf "@[<2>norm_coef =@ %a ;@]@ " pp_float_2darray_size x.norm_coef; - fprintf ppf "@[<2>norm_coef_scale =@ %a ;@]@ " pp_float_array_size x.norm_coef_scale; - fprintf ppf "@[<2>index =@ %d ;@]@ " x.index; - fprintf ppf "}@,@]" -*) - +(* [[file:~/QCaml/gaussian/atomic_shell.org::*Printers][Printers:2]] *) 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 "@["; @@ -98,6 +114,4 @@ let pp ppf s = e_arr c_arr; fprintf ppf "@;@]") s.expo s.coef; fprintf ppf "@]" - - - +(* Printers:2 ends here *) diff --git a/gaussian/lib/atomic_shell.mli b/gaussian/lib/atomic_shell.mli index 9b1860b..9774592 100644 --- a/gaussian/lib/atomic_shell.mli +++ b/gaussian/lib/atomic_shell.mli @@ -1,43 +1,16 @@ -(** 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 center. +(* Type *) - 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 t +(* [[file:~/QCaml/gaussian/atomic_shell.org::*Type][Type:1]] *) +type t open Common - -val make : ?index:int -> Contracted_shell.t array -> t -(** Creates a contracted shell from a list of coefficients and primitives. *) +(* Type:1 ends here *) -val with_index : t -> int -> t -(** Returns a copy of the contracted shell with a modified index. *) +(* Access *) + +(* [[file:~/QCaml/gaussian/atomic_shell.org::*Access][Access:1]] *) val index : t -> int (** Index in the basis set, represented as an array of contracted shells. *) @@ -74,9 +47,22 @@ val norm_scales : t -> float array val size_of_shell : t -> int (** Number of contracted functions in the shell: length of {!norm_coef_scale}. *) +(* Access:1 ends here *) + +(* Creation *) -(** {2 Printers} *) +(* [[file:~/QCaml/gaussian/atomic_shell.org::*Creation][Creation:1]] *) +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. *) +(* Creation:1 ends here *) + +(* Printers *) + + +(* [[file:~/QCaml/gaussian/atomic_shell.org::*Printers][Printers:1]] *) val pp : Format.formatter -> t -> unit - +(* Printers:1 ends here *) diff --git a/top/lib/install_printers.ml b/top/lib/install_printers.ml index e6b7720..e0c48c5 100644 --- a/top/lib/install_printers.ml +++ b/top/lib/install_printers.ml @@ -11,6 +11,7 @@ let printers = "Common.Range.pp" ; "Common.Spin.pp" ; "Common.Zkey.pp" ; + "Gaussian.Atomic_shell.pp" ; "Mo.Frozen_core.pp" ; "Particles.Electrons.pp" ; "Particles.Element.pp" ;