LCPQ/QCaml
10
1
Fork 0
mirror of https://gitlab.com/scemama/QCaml.git synced 2024-12-22 04:13:33 +01:00
Code Releases Activity

Localization

Browse Source
This commit is contained in:
Anthony Scemama 2021-01-30 19:07:59 +01:00
parent 8502befb65
commit 0b6fe42e55
10 changed files with 1056 additions and 41 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

10
docs/linear_algebra.html
View File

@ -3,7 +3,7 @@
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
<head>
<!-- 2021-01-27 Wed 23:44 -->
<!-- 2021-01-29 Fri 15:35 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<meta name="viewport" content="width=device-width, initial-scale=1" />
<title>Linear Algebra</title>
@ -250,18 +250,18 @@ org_html_manager.setup(); // activate after the parameters are set
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#org6e14c98">1. Summmary</a></li>
<li><a href="#org73480ff">1. Summmary</a></li>
</ul>
</div>
</div>
<div id="outline-container-org6e14c98" class="outline-2">
<h2 id="org6e14c98"><span class="section-number-2">1</span> Summmary</h2>
<div id="outline-container-org73480ff" class="outline-2">
<h2 id="org73480ff"><span class="section-number-2">1</span> Summmary</h2>
</div>
</div>
<div id="postamble" class="status">
<p class="author">Author: Anthony Scemama</p>
<p class="date">Created: 2021-01-27 Wed 23:44</p>
<p class="date">Created: 2021-01-29 Fri 15:35</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div>
</body>

194
docs/mo.html
View File

@ -3,7 +3,7 @@
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
<head>
<!-- 2021-01-27 Wed 23:44 -->
<!-- 2021-01-30 Sat 19:07 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<meta name="viewport" content="width=device-width, initial-scale=1" />
<title>Molecular orbitals</title>
@ -238,6 +238,28 @@ org_html_manager.setup(); // activate after the parameters are set
/*]]>*///-->
// @license-end
</script>
<script type="text/x-mathjax-config">
MathJax.Hub.Config({
displayAlign: "center",
displayIndent: "0em",
"HTML-CSS": { scale: 100,
linebreaks: { automatic: "false" },
webFont: "TeX"
},
SVG: {scale: 100,
linebreaks: { automatic: "false" },
font: "TeX"},
NativeMML: {scale: 100},
TeX: { equationNumbers: {autoNumber: "AMS"},
MultLineWidth: "85%",
TagSide: "right",
TagIndent: ".8em"
}
});
</script>
<script type="text/javascript"
src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.0/MathJax.js?config=TeX-AMS_HTML"></script>
</head>
<body>
<div id="org-div-home-and-up">
@ -250,36 +272,46 @@ org_html_manager.setup(); // activate after the parameters are set
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#orgdaf938b">1. Summmary</a></li>
<li><a href="#org9acb3b3">2. Frozen core</a>
<li><a href="#org5ae1447">1. Summmary</a></li>
<li><a href="#org5d6abfd">2. Frozen core</a>
<ul>
<li><a href="#org64a252c">2.1. Type</a></li>
<li><a href="#org987723c">2.2. Creation</a></li>
<li><a href="#orgc89d6d7">2.3. Access</a></li>
<li><a href="#org5c73928">2.4. Printers</a></li>
<li><a href="#org6013f02">2.1. Type</a></li>
<li><a href="#orgc66d8bd">2.2. Creation</a></li>
<li><a href="#org7a06aed">2.3. Access</a></li>
<li><a href="#org7d4d0a2">2.4. Printers</a></li>
</ul>
</li>
<li><a href="#org80b59a6">3. Orbital localization</a>
<ul>
<li><a href="#org3a774bd">3.1. Type</a></li>
<li><a href="#org3792219">3.2. Edmiston-Rudenberg</a></li>
<li><a href="#org2a12adf">3.3. Boys</a></li>
<li><a href="#org7f7571f">3.4. Access</a></li>
<li><a href="#orgd0fc6f0">3.5. Printers</a></li>
<li><a href="#org93f02d0">3.6. Tests</a></li>
</ul>
</li>
</ul>
</div>
</div>
<div id="outline-container-orgdaf938b" class="outline-2">
<h2 id="orgdaf938b"><span class="section-number-2">1</span> Summmary</h2>
<div id="outline-container-org5ae1447" class="outline-2">
<h2 id="org5ae1447"><span class="section-number-2">1</span> Summmary</h2>
</div>
<div id="outline-container-org9acb3b3" class="outline-2">
<h2 id="org9acb3b3"><span class="section-number-2">2</span> Frozen core</h2>
<div id="outline-container-org5d6abfd" class="outline-2">
<h2 id="org5d6abfd"><span class="section-number-2">2</span> Frozen core</h2>
<div class="outline-text-2" id="text-2">
<p>
Defines how the core electrons are frozen, for each atom.
</p>
</div>
<div id="outline-container-org64a252c" class="outline-3">
<h3 id="org64a252c"><span class="section-number-3">2.1</span> Type</h3>
<div id="outline-container-org6013f02" class="outline-3">
<h3 id="org6013f02"><span class="section-number-3">2.1</span> Type</h3>
<div class="outline-text-3" id="text-2-1">
<div class="org-src-container">
<pre class="src src-ocaml" id="org92bd127"><span class="org-tuareg-font-lock-governing">type</span> <span class="org-type">kind</span> <span class="org-tuareg-font-lock-operator">=</span>
<pre class="src src-ocaml" id="org7e482ab"><span class="org-tuareg-font-lock-governing">type</span> <span class="org-type">kind</span> <span class="org-tuareg-font-lock-operator">=</span>
<span class="org-tuareg-font-lock-operator">|</span> <span class="org-tuareg-font-lock-constructor">All_electron</span>
<span class="org-tuareg-font-lock-operator">|</span> <span class="org-tuareg-font-lock-constructor">Small</span>
<span class="org-tuareg-font-lock-operator">|</span> Large
@ -293,8 +325,8 @@ Defines how the core electrons are frozen, for each atom.
</div>
</div>
<div id="outline-container-org987723c" class="outline-3">
<h3 id="org987723c"><span class="section-number-3">2.2</span> Creation</h3>
<div id="outline-container-orgc66d8bd" class="outline-3">
<h3 id="orgc66d8bd"><span class="section-number-3">2.2</span> Creation</h3>
<div class="outline-text-3" id="text-2-2">
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">make</span> <span class="org-tuareg-font-lock-operator">:</span> kind <span class="org-tuareg-font-lock-operator">-&gt;</span> <span class="org-tuareg-font-lock-module">Particles.Nuclei.</span>t <span class="org-tuareg-font-lock-operator">-&gt;</span> t
@ -330,7 +362,7 @@ Defines how the core electrons are frozen, for each atom.
</tbody>
</table>
<pre class="example" id="org8539b48">
<pre class="example" id="orgd0bea50">
let f = Frozen_core.(make Small nuclei) ;;
val f : Frozen_core.t = [|0; 2; 2; 0|]
@ -340,8 +372,8 @@ val f : Frozen_core.t = [|0; 2; 2; 0|]
</div>
</div>
<div id="outline-container-orgc89d6d7" class="outline-3">
<h3 id="orgc89d6d7"><span class="section-number-3">2.3</span> Access</h3>
<div id="outline-container-org7a06aed" class="outline-3">
<h3 id="org7a06aed"><span class="section-number-3">2.3</span> Access</h3>
<div class="outline-text-3" id="text-2-3">
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">num_elec</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> int
@ -370,7 +402,7 @@ val f : Frozen_core.t = [|0; 2; 2; 0|]
</tbody>
</table>
<pre class="example" id="org5deb173">
<pre class="example" id="org8a415bd">
Frozen_core.num_elec f ;;
- : int = 4
@ -380,8 +412,8 @@ Frozen_core.num_mos f ;;
</div>
</div>
<div id="outline-container-org5c73928" class="outline-3">
<h3 id="org5c73928"><span class="section-number-3">2.4</span> Printers</h3>
<div id="outline-container-org7d4d0a2" class="outline-3">
<h3 id="org7d4d0a2"><span class="section-number-3">2.4</span> Printers</h3>
<div class="outline-text-3" id="text-2-4">
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">pp</span> <span class="org-tuareg-font-lock-operator">:</span> <span class="org-tuareg-font-lock-module">Format.</span>formatter <span class="org-tuareg-font-lock-operator">-&gt;</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> unit
@ -390,10 +422,126 @@ Frozen_core.num_mos f ;;
</div>
</div>
</div>
<div id="outline-container-org80b59a6" class="outline-2">
<h2 id="org80b59a6"><span class="section-number-2">3</span> Orbital localization</h2>
<div class="outline-text-2" id="text-3">
<p>
Molecular orbital localization function.
</p>
<p>
Boys:
</p>
<p>
Edmiston-Rudenberg:
</p>
</div>
<div id="outline-container-org3a774bd" class="outline-3">
<h3 id="org3a774bd"><span class="section-number-3">3.1</span> Type</h3>
<div class="outline-text-3" id="text-3-1">
<div class="org-src-container">
<pre class="src src-ocaml" id="org7ba3fe2"><span class="org-tuareg-font-lock-governing">open </span><span class="org-tuareg-font-lock-module">Linear_algebra</span>
<span class="org-tuareg-font-lock-governing">type</span> <span class="org-type">localization_kind</span> <span class="org-tuareg-font-lock-operator">=</span>
<span class="org-tuareg-font-lock-operator">|</span> <span class="org-tuareg-font-lock-constructor">Edmiston</span>
<span class="org-tuareg-font-lock-operator">|</span> <span class="org-tuareg-font-lock-constructor">Boys</span>
<span class="org-tuareg-font-lock-governing">type</span> <span class="org-type">mo</span> <span class="org-tuareg-font-lock-operator">=</span> <span class="org-tuareg-font-lock-module">Mo_dim.</span>t
<span class="org-tuareg-font-lock-governing">type</span> <span class="org-type">ao</span> <span class="org-tuareg-font-lock-operator">=</span> <span class="org-tuareg-font-lock-module">Ao.Ao_dim.</span>t
<span class="org-tuareg-font-lock-governing">type</span> <span class="org-type">loc</span>
</pre>
</div>
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">type</span> <span class="org-type">localization_data</span>
<span class="org-tuareg-font-lock-governing">type</span> <span class="org-type">t</span>
</pre>
</div>
</div>
</div>
<div id="outline-container-org3792219" class="outline-3">
<h3 id="org3792219"><span class="section-number-3">3.2</span> Edmiston-Rudenberg</h3>
</div>
<div id="outline-container-org2a12adf" class="outline-3">
<h3 id="org2a12adf"><span class="section-number-3">3.3</span> Boys</h3>
</div>
<div id="outline-container-org7f7571f" class="outline-3">
<h3 id="org7f7571f"><span class="section-number-3">3.4</span> Access</h3>
<div class="outline-text-3" id="text-3-4">
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">kind</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> localization_kind
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">simulation</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> <span class="org-tuareg-font-lock-module">Simulation.</span>t
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">selected_mos</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> int list
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">kappa</span> <span class="org-tuareg-font-lock-operator">:</span>
<span class="org-tuareg-font-lock-label">kind</span><span class="org-tuareg-font-lock-operator">:</span>localization_kind <span class="org-tuareg-font-lock-operator">-&gt;</span>
<span class="org-tuareg-font-lock-module">Basis.</span>t <span class="org-tuareg-font-lock-operator">-&gt;</span>
<span class="org-tuareg-font-lock-operator">(</span> ao<span class="org-tuareg-font-lock-operator">,</span>loc<span class="org-tuareg-font-lock-operator">)</span> <span class="org-tuareg-font-lock-module">Matrix.</span>t <span class="org-tuareg-font-lock-operator">-&gt;</span>
<span class="org-tuareg-font-lock-operator">(</span>loc<span class="org-tuareg-font-lock-operator">,</span>loc<span class="org-tuareg-font-lock-operator">)</span> <span class="org-tuareg-font-lock-module">Matrix.</span>t <span class="org-tuareg-font-lock-operator">*</span> float
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">make</span> <span class="org-tuareg-font-lock-operator">:</span>
<span class="org-tuareg-font-lock-label">kind</span><span class="org-tuareg-font-lock-operator">:</span>localization_kind <span class="org-tuareg-font-lock-operator">-&gt;</span>
<span class="org-tuareg-font-lock-label">?max_iter</span><span class="org-tuareg-font-lock-operator">:</span>int <span class="org-tuareg-font-lock-operator">-&gt;</span>
<span class="org-tuareg-font-lock-label">?convergence</span><span class="org-tuareg-font-lock-operator">:</span>float <span class="org-tuareg-font-lock-operator">-&gt;</span>
<span class="org-tuareg-font-lock-module">Basis.</span>t <span class="org-tuareg-font-lock-operator">-&gt;</span>
int list <span class="org-tuareg-font-lock-operator">-&gt;</span>
t
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">to_basis</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> <span class="org-tuareg-font-lock-module">Basis.</span>t
</pre>
</div>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-left" />
<col class="org-left" />
</colgroup>
<tbody>
<tr>
<td class="org-left"><code>kappa</code></td>
<td class="org-left">Returns the \(\kappa\) antisymmetric matrix used for the rotation matrix and the value of the localization function</td>
</tr>
<tr>
<td class="org-left"><code>make</code></td>
<td class="org-left">Performs the orbital localization</td>
</tr>
</tbody>
</table>
</div>
</div>
<div id="outline-container-orgd0fc6f0" class="outline-3">
<h3 id="orgd0fc6f0"><span class="section-number-3">3.5</span> Printers</h3>
<div class="outline-text-3" id="text-3-5">
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-comment-delimiter">(*</span>
<span class="org-comment"> val pp : Format.formatter -&gt; t -&gt; unit</span>
<span class="org-comment"> </span><span class="org-comment-delimiter">*)</span>
</pre>
</div>
</div>
</div>
<div id="outline-container-org93f02d0" class="outline-3">
<h3 id="org93f02d0"><span class="section-number-3">3.6</span> Tests</h3>
</div>
</div>
</div>
<div id="postamble" class="status">
<p class="author">Author: Anthony Scemama</p>
<p class="date">Created: 2021-01-27 Wed 23:44</p>
<p class="date">Created: 2021-01-30 Sat 19:07</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div>
</body>

10
docs/top.html
View File

@ -3,7 +3,7 @@
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
<head>
<!-- 2021-01-28 Thu 00:32 -->
<!-- 2021-01-30 Sat 19:07 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<meta name="viewport" content="width=device-width, initial-scale=1" />
<title>Top-level</title>
@ -250,18 +250,18 @@ org_html_manager.setup(); // activate after the parameters are set
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#org55c0065">1. Summmary</a></li>
<li><a href="#org6d8977c">1. Summmary</a></li>
</ul>
</div>
</div>
<div id="outline-container-org55c0065" class="outline-2">
<h2 id="org55c0065"><span class="section-number-2">1</span> Summmary</h2>
<div id="outline-container-org6d8977c" class="outline-2">
<h2 id="org6d8977c"><span class="section-number-2">1</span> Summmary</h2>
</div>
</div>
<div id="postamble" class="status">
<p class="author">Author: Anthony Scemama</p>
<p class="date">Created: 2021-01-28 Thu 00:32</p>
<p class="date">Created: 2021-01-30 Sat 19:07</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div>
</body>

12
linear_algebra/lib/matrix.ml
View File

@ -393,7 +393,7 @@ let qr a =
q, r
let exponential_iterative a =
let exponential a =
assert (dim1 a = dim2 a);
let rec loop result accu n =
let b = scale (1./.n) a in
@ -413,7 +413,7 @@ let exponential_iterative a =
loop id id 1.
let exponential a =
let exponential_antisymmetric a =
let n = dim1 a in
assert (n = dim2 a);
@ -433,8 +433,12 @@ let exponential a =
|> amax
|> abs_float
in
assert (test < Constants.epsilon);
result
(* If the exponential failed, fall back to the iterative exponential *)
if test < 10. *. Constants.epsilon then
result
else
exponential a
let to_file ~filename ?(sym=false) ?(cutoff=0.) t =

4
linear_algebra/lib/matrix.mli
View File

@ -306,8 +306,8 @@ val diagonalize_symm : ('a,'a) t -> ('a,'a) t * 'a Vector.t
val exponential : ('a,'a) t -> ('a,'a) t
(** Computes the exponential of a square matrix. *)
val exponential_iterative : ('a,'a) t -> ('a,'a) t
(** Computes the exponential of a square matrix with an iteratve algorithm. *)
val exponential_antisymmetric: ('a,'a) t -> ('a,'a) t
(** Computes the exponential of an antisymmetric square matrix. *)
val xt_o_x : o:('a,'a) t -> x:('a,'b) t -> ('b,'b) t
(** Computes {% $\mathbf{X^\dag\, O\, X}$ %} *)

4
mo/lib/hartree_fock.ml
View File

@ -7,7 +7,7 @@ type mo = Mo_dim.t
type hartree_fock_data =
{
iteration : int ;
iteration : int ;
coefficients : (ao, mo) Matrix.t option ;
eigenvalues : mo Vector.t option ;
error : float option ;
@ -77,7 +77,7 @@ let n_iterations t =
let last_iteration t =
Util.of_some @@ Lazy.force (t.data.(n_iterations t - 1))
Util.of_some @@ Lazy.force t.data.(n_iterations t - 1)
let eigenvectors t =
let data = last_iteration t in

331
mo/lib/localization.ml Normal file
View File

@ -0,0 +1,331 @@
(* [[file:~/QCaml/mo/localization.org::*Type][Type:3]] *)
open Linear_algebra
type localization_kind =
| Edmiston
| Boys
type mo = Mo_dim.t
type ao = Ao.Ao_dim.t
type loc
type localization_data =
{
coefficients : (ao, loc) Matrix.t ;
kappa : (loc, loc) Matrix.t ;
scaling : float ;
loc_value : float ;
iteration : int ;
}
type t =
{
kind : localization_kind ;
mo_basis : Basis.t ;
data : localization_data option lazy_t array ;
selected_mos : int list ;
}
open Common
(* Type:3 ends here *)
(* Edmiston-Rudenberg *)
(* [[file:~/QCaml/mo/localization.org::*Edmiston-Rudenberg][Edmiston-Rudenberg:1]] *)
let kappa_edmiston in_basis m_C =
let ao_basis =
Basis.simulation in_basis
|> Simulation.ao_basis
in
let ee_ints = Ao.Basis.ee_ints ao_basis in
let n_ao = Ao.Basis.size ao_basis in
let n_mo = Matrix.dim2 m_C in
(* Temp arrays for integral transformation *)
let m_pqr =
Bigarray.(Array3.create Float64 fortran_layout n_ao n_ao n_ao)
in
let m_qr_i = Matrix.create (n_ao*n_ao) n_mo in
let m_ri_j = Matrix.create (n_ao*n_mo) n_mo in
let m_ij_k = Matrix.create (n_mo*n_mo) n_mo in
let m_a12 = Bigarray.(Array2.create Float64 fortran_layout n_mo n_mo) in
let m_b12 = Bigarray.(Array2.create Float64 fortran_layout n_mo n_mo) in
Bigarray.Array2.fill m_b12 0.;
Bigarray.Array2.fill m_a12 0.;
let v_d =
Vector.init n_mo (fun _ -> 0.)
|> Vector.to_bigarray_inplace
in
Array.iter (fun s ->
Array.iter (fun r ->
Array.iter (fun q ->
Array.iter (fun p ->
m_pqr.{p,q,r} <- Four_idx_storage.get_phys ee_ints p q r s
) (Util.array_range 1 n_ao)
) (Util.array_range 1 n_ao)
) (Util.array_range 1 n_ao);
let m_p_qr =
Bigarray.reshape (Bigarray.genarray_of_array3 m_pqr) [| n_ao ; n_ao*n_ao |]
|> Bigarray.array2_of_genarray
|> Matrix.of_bigarray_inplace
in
(* (qr,i) = <i r|q s> = \sum_p <p r | q s> C_{pi} *)
Matrix.gemm_tn_inplace ~c:m_qr_i m_p_qr m_C;
let m_q_ri =
let x = Matrix.to_bigarray_inplace m_qr_i |> Bigarray.genarray_of_array2 in
Bigarray.reshape_2 x n_ao (n_ao*n_mo) |> Matrix.of_bigarray_inplace
in
(* (ri,j) = <i r | j s> = \sum_q <i r | q s> C_{qj} *)
Matrix.gemm_tn_inplace ~c:m_ri_j m_q_ri m_C;
let m_r_ij =
let x = Matrix.to_bigarray_inplace m_ri_j |> Bigarray.genarray_of_array2 in
Bigarray.reshape_2 x n_ao (n_mo*n_mo) |> Matrix.of_bigarray_inplace
in
(* (ij,k) = <i k | j s> = \sum_r <i r | j s> C_{rk} *)
Matrix.gemm_tn_inplace ~c:m_ij_k m_r_ij m_C;
let m_ijk =
let x = Matrix.to_bigarray_inplace m_ij_k |> Bigarray.genarray_of_array2 in
Bigarray.reshape x [| n_mo ; n_mo ; n_mo |]
|> Bigarray.array3_of_genarray
in
let m_Cx = Matrix.to_bigarray_inplace m_C in
Array.iter (fun j ->
Array.iter (fun i ->
m_b12.{i,j} <- m_b12.{i,j} +. m_Cx.{s,j} *. (m_ijk.{i,i,i} -. m_ijk.{j,i,j});
m_a12.{i,j} <- m_a12.{i,j} +. m_ijk.{i,i,j} *. m_Cx.{s,j} -.
0.25 *. ( (m_ijk.{i,i,i} -. m_ijk.{j,i,j}) *. m_Cx.{s,i} +.
(m_ijk.{j,j,j} -. m_ijk.{i,j,i}) *. m_Cx.{s,j})
) (Util.array_range 1 n_mo);
v_d.{j} <- v_d.{j} +. m_ijk.{j,j,j} *. m_Cx.{s,j}
) (Util.array_range 1 n_mo)
) (Util.array_range 1 n_ao);
let f i j =
if i=j then
0.
else
begin
let x = 1./. sqrt (m_b12.{i,j} *. m_b12.{i,j} +. m_a12.{i,j} *. m_a12.{i,j} ) in
if asin (m_b12.{i,j} /. x) > 0. then
0.25 *. acos( -. m_a12.{i,j} *. x)
else
-. 0.25 *. acos( -. m_a12.{i,j} *. x )
end
in
(
Matrix.init_cols n_mo n_mo ( fun i j -> if i<=j then f i j else -. (f j i) ),
Vector.sum (Vector.of_bigarray_inplace v_d)
)
(* Edmiston-Rudenberg:1 ends here *)
(* Boys *)
(* [[file:~/QCaml/mo/localization.org::*Boys][Boys:1]] *)
let kappa_boys in_basis =
let ao_basis =
Basis.simulation in_basis
|> Simulation.ao_basis
in
let multipole = Ao.Basis.multipole ao_basis in
fun m_C ->
let n_mo = Matrix.dim2 m_C in
let phi_x_phi = Matrix.xt_o_x ~x:m_C ~o:(multipole "x") in
let phi_y_phi = Matrix.xt_o_x ~x:m_C ~o:(multipole "y") in
let phi_z_phi = Matrix.xt_o_x ~x:m_C ~o:(multipole "z") in
let m_b12 =
let g x i j =
let x_ii = x%:(i,i) in
let x_jj = x%:(j,j) in
let x_ij = x%:(i,j) in
(x_ii -. x_jj) *. x_ij
in
Matrix.init_cols n_mo n_mo (fun i j ->
let x =
(g phi_x_phi i j) +. (g phi_y_phi i j) +. (g phi_z_phi i j)
in
if (abs_float x > 1.e-15) then x else 0.
)
in
let m_a12 =
let g x i j =
let x_ii = x%:(i,i) in
let x_jj = x%:(j,j) in
let x_ij = x%:(i,j) in
let y = x_ii -. x_jj in
(x_ij *. x_ij) -. 0.25 *. y *. y
in
Matrix.init_cols n_mo n_mo (fun i j ->
let x =
(g phi_x_phi i j) +. (g phi_y_phi i j) +. (g phi_z_phi i j)
in
if (abs_float x > 1.e-15) then x else 0.
)
in
let f i j =
let pi = Constants.pi in
if i=j then
0.
else
let x = atan2 (m_b12%:(i,j)) (m_a12%:(i,j)) in
if x >= 0. then
0.25 *. (pi -. x)
else
-. 0.25 *. ( pi +. x)
in
(
Matrix.init_cols n_mo n_mo ( fun i j -> if i>j then f i j else -. (f j i) ),
let r2 x y z = x*.x +. y*.y +. z*.z in
Vector.init n_mo ( fun i ->
r2 (phi_x_phi%:(i,i)) (phi_y_phi%:(i,i)) (phi_z_phi%:(i,i)))
|> Vector.sum
)
(* Boys:1 ends here *)
(* | ~kappa~ | Returns the $\kappa$ antisymmetric matrix used for the rotation matrix and the value of the localization function |
* | ~make~ | Performs the orbital localization | *)
(* [[file:~/QCaml/mo/localization.org::*Access][Access:2]] *)
let kind t = t.kind
let simulation t = Basis.simulation t.mo_basis
let selected_mos t = t.selected_mos
let kappa ~kind =
match kind with
| Edmiston -> kappa_edmiston
| Boys -> kappa_boys
let n_iterations t =
Array.fold_left (fun accu x ->
match Lazy.force x with
| Some _ -> accu + 1
| None -> accu
) 0 t.data
let last_iteration t =
Util.of_some @@ Lazy.force t.data.(n_iterations t - 1)
(*
let ao_basis t = Simulation.ao_basis (simulation t)
*)
let make ~kind ?(max_iter=500) ?(convergence=1.e-8) mo_basis selected_mos =
let kappa_loc = kappa ~kind mo_basis in
let mo_array = Matrix.to_col_vecs (Basis.mo_coef mo_basis) in
let mos_vec_list = List.map (fun i -> mo_array.(i-1)) selected_mos in
let x: (ao,loc) Matrix.t =
Matrix.of_col_vecs_list mos_vec_list
in
let next_coef kappa =
let r = Matrix.exponential_antisymmetric kappa in
let m_C = Matrix.gemm_nt x r in
m_C
in
let data_initial =
let iteration = 0
and kappa, loc_value = kappa_loc x
and scaling = 1.0
in
let coefficients = next_coef kappa in
{ coefficients ; kappa ; scaling ; loc_value ; iteration }
in
let iteration data =
let x = data.coefficients in
let iteration = data.iteration + 1
and kappa, loc_value = kappa_loc x
and scaling = data.scaling
in
let coefficients = next_coef kappa in
Printf.printf "%4d %20f\n" iteration loc_value ;
{ coefficients ; kappa ; scaling ; loc_value ; iteration }
in
let array_data =
let storage =
Array.make max_iter None
in
let rec loop = function
| 0 -> Some (iteration data_initial)
| n -> begin
match storage.(n) with
| Some result -> Some result
| None -> begin
let data = loop (n-1) in
match data with
| None -> None
| Some data -> begin
(* Check convergence *)
let converged =
abs_float data.loc_value < convergence
in
if converged then
None
else
begin
storage.(n-1) <- Some data ;
storage.(n) <- Some (iteration data);
storage.(n)
end
end
end
end
in
Array.init max_iter (fun i -> lazy (loop i))
in
{ kind ; mo_basis ; data = array_data ; selected_mos }
let to_basis t =
let mo_basis = t.mo_basis in
let simulation = Basis.simulation mo_basis in
let mo_occupation = Basis.mo_occupation mo_basis in
let data = last_iteration t in
let mo_coef_array = Matrix.to_col_vecs (Basis.mo_coef mo_basis) in
let new_mos =
Matrix.to_col_vecs data.coefficients
in
selected_mos t
|> List.iteri (fun i j -> mo_coef_array.(j) <- new_mos.(i)) ;
let mo_coef = Matrix.of_col_vecs mo_coef_array in
Basis.make ~simulation ~mo_type:(Localized "Boys") ~mo_occupation ~mo_coef ()
(* Access:2 ends here *)
(* [[file:~/QCaml/mo/localization.org::*Printers][Printers:2]] *)
(* Printers:2 ends here *)

54
mo/lib/localization.mli Normal file
View File

@ -0,0 +1,54 @@
(* Type
*
* #+NAME: types *)
(* [[file:~/QCaml/mo/localization.org::types][types]] *)
open Linear_algebra
type localization_kind =
| Edmiston
| Boys
type mo = Mo_dim.t
type ao = Ao.Ao_dim.t
type loc
(* types ends here *)
(* [[file:~/QCaml/mo/localization.org::*Type][Type:2]] *)
type localization_data
type t
(* Type:2 ends here *)
(* Access *)
(* [[file:~/QCaml/mo/localization.org::*Access][Access:1]] *)
val kind : t -> localization_kind
val simulation : t -> Simulation.t
val selected_mos : t -> int list
val kappa :
kind:localization_kind ->
Basis.t ->
( ao,loc) Matrix.t ->
(loc,loc) Matrix.t * float
val make :
kind:localization_kind ->
?max_iter:int ->
?convergence:float ->
Basis.t ->
int list ->
t
val to_basis : t -> Basis.t
(* Access:1 ends here *)
(* Printers *)
(* [[file:~/QCaml/mo/localization.org::*Printers][Printers:1]] *)
(*
val pp : Format.formatter -> t -> unit
*)
(* Printers:1 ends here *)

477
mo/localization.org Normal file
View File

@ -0,0 +1,477 @@
#+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
* Orbital localization
:PROPERTIES:
:header-args: :noweb yes :comments both
:END:
Molecular orbital localization function.
Boys:
Edmiston-Rudenberg:
** Type
#+NAME: types
#+begin_src ocaml :tangle (eval mli)
open Linear_algebra
type localization_kind =
| Edmiston
| Boys
type mo = Mo_dim.t
type ao = Ao.Ao_dim.t
type loc
#+end_src
#+begin_src ocaml :tangle (eval mli)
type localization_data
type t
#+end_src
#+begin_src ocaml :tangle (eval ml) :exports none
<<types>>
type localization_data =
{
coefficients : (ao, loc) Matrix.t ;
kappa : (loc, loc) Matrix.t ;
scaling : float ;
loc_value : float ;
iteration : int ;
}
type t =
{
kind : localization_kind ;
mo_basis : Basis.t ;
data : localization_data option lazy_t array ;
selected_mos : int list ;
}
open Common
#+end_src
** Edmiston-Rudenberg
#+begin_src ocaml :tangle (eval ml) :exports none
let kappa_edmiston in_basis m_C =
let ao_basis =
Basis.simulation in_basis
|> Simulation.ao_basis
in
let ee_ints = Ao.Basis.ee_ints ao_basis in
let n_ao = Ao.Basis.size ao_basis in
let n_mo = Matrix.dim2 m_C in
(* Temp arrays for integral transformation *)
let m_pqr =
Bigarray.(Array3.create Float64 fortran_layout n_ao n_ao n_ao)
in
let m_qr_i = Matrix.create (n_ao*n_ao) n_mo in
let m_ri_j = Matrix.create (n_ao*n_mo) n_mo in
let m_ij_k = Matrix.create (n_mo*n_mo) n_mo in
let m_a12 = Bigarray.(Array2.create Float64 fortran_layout n_mo n_mo) in
let m_b12 = Bigarray.(Array2.create Float64 fortran_layout n_mo n_mo) in
Bigarray.Array2.fill m_b12 0.;
Bigarray.Array2.fill m_a12 0.;
let v_d =
Vector.init n_mo (fun _ -> 0.)
|> Vector.to_bigarray_inplace
in
Array.iter (fun s ->
Array.iter (fun r ->
Array.iter (fun q ->
Array.iter (fun p ->
m_pqr.{p,q,r} <- Four_idx_storage.get_phys ee_ints p q r s
) (Util.array_range 1 n_ao)
) (Util.array_range 1 n_ao)
) (Util.array_range 1 n_ao);
let m_p_qr =
Bigarray.reshape (Bigarray.genarray_of_array3 m_pqr) [| n_ao ; n_ao*n_ao |]
|> Bigarray.array2_of_genarray
|> Matrix.of_bigarray_inplace
in
(* (qr,i) = <i r|q s> = \sum_p <p r | q s> C_{pi} *)
Matrix.gemm_tn_inplace ~c:m_qr_i m_p_qr m_C;
let m_q_ri =
let x = Matrix.to_bigarray_inplace m_qr_i |> Bigarray.genarray_of_array2 in
Bigarray.reshape_2 x n_ao (n_ao*n_mo) |> Matrix.of_bigarray_inplace
in
(* (ri,j) = <i r | j s> = \sum_q <i r | q s> C_{qj} *)
Matrix.gemm_tn_inplace ~c:m_ri_j m_q_ri m_C;
let m_r_ij =
let x = Matrix.to_bigarray_inplace m_ri_j |> Bigarray.genarray_of_array2 in
Bigarray.reshape_2 x n_ao (n_mo*n_mo) |> Matrix.of_bigarray_inplace
in
(* (ij,k) = <i k | j s> = \sum_r <i r | j s> C_{rk} *)
Matrix.gemm_tn_inplace ~c:m_ij_k m_r_ij m_C;
let m_ijk =
let x = Matrix.to_bigarray_inplace m_ij_k |> Bigarray.genarray_of_array2 in
Bigarray.reshape x [| n_mo ; n_mo ; n_mo |]
|> Bigarray.array3_of_genarray
in
let m_Cx = Matrix.to_bigarray_inplace m_C in
Array.iter (fun j ->
Array.iter (fun i ->
m_b12.{i,j} <- m_b12.{i,j} +. m_Cx.{s,j} *. (m_ijk.{i,i,i} -. m_ijk.{j,i,j});
m_a12.{i,j} <- m_a12.{i,j} +. m_ijk.{i,i,j} *. m_Cx.{s,j} -.
0.25 *. ( (m_ijk.{i,i,i} -. m_ijk.{j,i,j}) *. m_Cx.{s,i} +.
(m_ijk.{j,j,j} -. m_ijk.{i,j,i}) *. m_Cx.{s,j})
) (Util.array_range 1 n_mo);
v_d.{j} <- v_d.{j} +. m_ijk.{j,j,j} *. m_Cx.{s,j}
) (Util.array_range 1 n_mo)
) (Util.array_range 1 n_ao);
let f i j =
if i=j then
0.
else
begin
let x = 1./. sqrt (m_b12.{i,j} *. m_b12.{i,j} +. m_a12.{i,j} *. m_a12.{i,j} ) in
if asin (m_b12.{i,j} /. x) > 0. then
0.25 *. acos( -. m_a12.{i,j} *. x)
else
-. 0.25 *. acos( -. m_a12.{i,j} *. x )
end
in
(
Matrix.init_cols n_mo n_mo ( fun i j -> if i<=j then f i j else -. (f j i) ),
Vector.sum (Vector.of_bigarray_inplace v_d)
)
#+end_src
** Boys
#+begin_src ocaml :tangle (eval ml) :exports none
let kappa_boys in_basis =
let ao_basis =
Basis.simulation in_basis
|> Simulation.ao_basis
in
let multipole = Ao.Basis.multipole ao_basis in
fun m_C ->
let n_mo = Matrix.dim2 m_C in
let phi_x_phi = Matrix.xt_o_x ~x:m_C ~o:(multipole "x") in
let phi_y_phi = Matrix.xt_o_x ~x:m_C ~o:(multipole "y") in
let phi_z_phi = Matrix.xt_o_x ~x:m_C ~o:(multipole "z") in
let m_b12 =
let g x i j =
let x_ii = x%:(i,i) in
let x_jj = x%:(j,j) in
let x_ij = x%:(i,j) in
(x_ii -. x_jj) *. x_ij
in
Matrix.init_cols n_mo n_mo (fun i j ->
let x =
(g phi_x_phi i j) +. (g phi_y_phi i j) +. (g phi_z_phi i j)
in
if (abs_float x > 1.e-15) then x else 0.
)
in
let m_a12 =
let g x i j =
let x_ii = x%:(i,i) in
let x_jj = x%:(j,j) in
let x_ij = x%:(i,j) in
let y = x_ii -. x_jj in
(x_ij *. x_ij) -. 0.25 *. y *. y
in
Matrix.init_cols n_mo n_mo (fun i j ->
let x =
(g phi_x_phi i j) +. (g phi_y_phi i j) +. (g phi_z_phi i j)
in
if (abs_float x > 1.e-15) then x else 0.
)
in
let f i j =
let pi = Constants.pi in
if i=j then
0.
else
let x = atan2 (m_b12%:(i,j)) (m_a12%:(i,j)) in
if x >= 0. then
0.25 *. (pi -. x)
else
-. 0.25 *. ( pi +. x)
in
(
Matrix.init_cols n_mo n_mo ( fun i j -> if i>j then f i j else -. (f j i) ),
let r2 x y z = x*.x +. y*.y +. z*.z in
Vector.init n_mo ( fun i ->
r2 (phi_x_phi%:(i,i)) (phi_y_phi%:(i,i)) (phi_z_phi%:(i,i)))
|> Vector.sum
)
#+end_src
** Access
#+begin_src ocaml :tangle (eval mli)
val kind : t -> localization_kind
val simulation : t -> Simulation.t
val selected_mos : t -> int list
val kappa :
kind:localization_kind ->
Basis.t ->
( ao,loc) Matrix.t ->
(loc,loc) Matrix.t * float
val make :
kind:localization_kind ->
?max_iter:int ->
?convergence:float ->
Basis.t ->
int list ->
t
val to_basis : t -> Basis.t
#+end_src
| ~kappa~ | Returns the $\kappa$ antisymmetric matrix used for the rotation matrix and the value of the localization function |
| ~make~ | Performs the orbital localization |
#+begin_src ocaml :tangle (eval ml) :exports none
let kind t = t.kind
let simulation t = Basis.simulation t.mo_basis
let selected_mos t = t.selected_mos
let kappa ~kind =
match kind with
| Edmiston -> kappa_edmiston
| Boys -> kappa_boys
let n_iterations t =
Array.fold_left (fun accu x ->
match Lazy.force x with
| Some _ -> accu + 1
| None -> accu
) 0 t.data
let last_iteration t =
Util.of_some @@ Lazy.force t.data.(n_iterations t - 1)
(*
let ao_basis t = Simulation.ao_basis (simulation t)
*)
let make ~kind ?(max_iter=500) ?(convergence=1.e-8) mo_basis selected_mos =
let kappa_loc = kappa ~kind mo_basis in
let mo_array = Matrix.to_col_vecs (Basis.mo_coef mo_basis) in
let mos_vec_list = List.map (fun i -> mo_array.(i-1)) selected_mos in
let x: (ao,loc) Matrix.t =
Matrix.of_col_vecs_list mos_vec_list
in
let next_coef kappa =
let r = Matrix.exponential_antisymmetric kappa in
let m_C = Matrix.gemm_nt x r in
m_C
in
let data_initial =
let iteration = 0
and kappa, loc_value = kappa_loc x
and scaling = 1.0
in
let coefficients = next_coef kappa in
{ coefficients ; kappa ; scaling ; loc_value ; iteration }
in
let iteration data =
let x = data.coefficients in
let iteration = data.iteration + 1
and kappa, loc_value = kappa_loc x
and scaling = data.scaling
in
let coefficients = next_coef kappa in
Printf.printf "%4d %20f\n" iteration loc_value ;
{ coefficients ; kappa ; scaling ; loc_value ; iteration }
in
let array_data =
let storage =
Array.make max_iter None
in
let rec loop = function
| 0 -> Some (iteration data_initial)
| n -> begin
match storage.(n) with
| Some result -> Some result
| None -> begin
let data = loop (n-1) in
match data with
| None -> None
| Some data -> begin
(* Check convergence *)
let converged =
abs_float data.loc_value < convergence
in
if converged then
None
else
begin
storage.(n-1) <- Some data ;
storage.(n) <- Some (iteration data);
storage.(n)
end
end
end
end
in
Array.init max_iter (fun i -> lazy (loop i))
in
{ kind ; mo_basis ; data = array_data ; selected_mos }
let to_basis t =
let mo_basis = t.mo_basis in
let simulation = Basis.simulation mo_basis in
let mo_occupation = Basis.mo_occupation mo_basis in
let data = last_iteration t in
let mo_coef_array = Matrix.to_col_vecs (Basis.mo_coef mo_basis) in
let new_mos =
Matrix.to_col_vecs data.coefficients
in
selected_mos t
|> List.iteri (fun i j -> mo_coef_array.(j) <- new_mos.(i)) ;
let mo_coef = Matrix.of_col_vecs mo_coef_array in
Basis.make ~simulation ~mo_type:(Localized "Boys") ~mo_occupation ~mo_coef ()
#+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
#+end_src
** Tests
#+begin_src ocaml :tangle (eval test-ml) :exports none
let test_localization =
let nuclei =
Particles.Nuclei.of_xyz_string
" 10
Hydrogen chain, d=1.8 Angstrom
H -4.286335 0.000000 0.000000
H -3.333816 0.000000 0.000000
H -2.381297 0.000000 0.000000
H -1.428778 0.000000 0.000000
H -0.476259 0.000000 0.000000
H 0.476259 0.000000 0.000000
H 1.428778 0.000000 0.000000
H 2.381297 0.000000 0.000000
H 3.333816 0.000000 0.000000
H 4.286335 0.000000 0.000000
" in
let basis_file = "/home/scemama/qp2/data/basis/sto-6g" in
let ao_basis =
Ao.Basis.of_nuclei_and_basis_filename ~nuclei basis_file
in
let charge = 0 in
let multiplicity = 1 in
let simulation =
Simulation.make ~charge ~multiplicity ~nuclei ao_basis
in
let hf =
Mo.Hartree_fock.make ~guess:`Hcore simulation
in
let mo_basis =
Mo.Basis.of_hartree_fock hf
in
let localized_mo_basis =
Mo.Localization.make
~kind:Mo.Localization.Boys
mo_basis
[4;5;6;7;8]
|> Mo.Localization.to_basis
in
Format.printf "%a" (Mo.Basis.pp ~start:1 ~finish:10) localized_mo_basis
(*
open Common
open Alcotest
let wd = Qcaml.root ^ Filename.dir_sep ^ "test" in
let test_xyz molecule length repulsion charge core =
let xyz = Nuclei.of_xyz_file (wd^Filename.dir_sep^molecule^".xyz") in
check int "length" length (Array.length xyz);
check (float 1.e-4) "repulsion" repulsion (Nuclei.repulsion xyz);
check int "charge" charge (Charge.to_int @@ Nuclei.charge xyz);
check int "small_core" core (Nuclei.small_core xyz);
()
let tests = [
"caffeine", `Quick, (fun () -> test_xyz "caffeine" 24 917.0684 102 28);
"water", `Quick, (fun () -> test_xyz "water" 3 9.19497 10 2);
]
,*)
#+end_src

1
top/lib/install_printers.ml
View File

@ -15,6 +15,7 @@ let printers =
"Gaussian.Atomic_shell_pair.pp" ;
"Gaussian.Atomic_shell_pair_couple.pp" ;
"Mo.Frozen_core.pp" ;
"Mo.Localization.pp" ;
"Particles.Electrons.pp" ;
"Particles.Element.pp" ;
"Particles.Nuclei.pp" ;