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Anthony Scemama 2021-01-13 17:59:48 +01:00
parent 52ed6eff8d
commit 50dc730ea5
4 changed files with 283 additions and 12 deletions
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34
.github/workflows/gh-pages.yml vendored Normal file
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name: github pages
on:
push:
branches:
- master
jobs:
deploy:
runs-on: ubuntu-latest
steps:
- uses: actions/checkout@v2
- name: install extra repository
run: sudo add-apt-repository ppa:kelleyk/emacs
- name: refresh apt
run: sudo apt-get update
- name: install dependencies
run: sudo apt-get install emacs26
- name: install htmlize
run: git clone https://github.com/hniksic/emacs-htmlize && cp emacs-htmlize/htmlize.el docs/
- name: make
run: cd docs ; ./create.sh ../QMC.org
- name: Deploy
uses: peaceiris/actions-gh-pages@v3
with:
github_token: ${{ secrets.GITHUB_TOKEN }}
publish_dir: ./docs

176
QMC.org
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@ -1253,7 +1253,7 @@ gfortran hydrogen.f90 qmc_stats.f90 vmc.f90 -o vmc
that the acceptance rate is around 0.5 for a good efficiency of
the simulation.
**** TODO Exercise
**** Exercise
#+begin_exercise
Modify the previous program to introduce the accept/reject step.
@ -1303,11 +1303,12 @@ tau = 1.0
X = [MonteCarlo(a,tau,nmax) for i in range(30)]
E, deltaE = ave_error([x[0] for x in X])
A, deltaA = ave_error([x[1] for x in X])
print(f"E = {E} +/- {deltaE} {A} +/- {deltaA}")
print(f"E = {E} +/- {deltaE}\nA = {A} +/- {deltaA}")
#+END_SRC
#+RESULTS:
: E = -0.49387078389332206 +/- 0.0033326460286729792 0.4983000000000001 +/- 0.006825097363627021
: E = -0.4949730317138491 +/- 0.00012478601801760644
: A = 0.7887163333333334 +/- 0.00026834549840347617
*Fortran*
#+BEGIN_SRC f90
@ -1399,17 +1400,168 @@ gfortran hydrogen.f90 qmc_stats.f90 vmc_metropolis.f90 -o vmc_metropolis
:header-args:python: :tangle dmc.py
:header-args:f90: :tangle dmc.f90
:END:
** Hydrogen atom
**** Exercise
We will now consider the H_2 molecule in a minimal basis composed of the
$1s$ orbitals of the hydrogen atoms:
#+begin_exercise
Modify the Metropolis VMC program to introduce the PDMC weight.
In the limit $\tau \rightarrow 0$, you should recover the exact
energy of H for any value of $a$.
#+end_exercise
*Python*
#+BEGIN_SRC python :results output
from hydrogen import *
from qmc_stats import *
$$
\Psi(\mathbf{r}_1, \mathbf{r}_2) =
\exp(-(\mathbf{r}_1 - \mathbf{R}_A)) +
$$
where $\mathbf{r}_1$ and $\mathbf{r}_2$ denote the electron
coordinates and $\mathbf{R}_A$ and $\mathbf{R}_B$ the coordinates of
the nuclei.
def MonteCarlo(a,tau,nmax,Eref):
E = 0.
N = 0.
accep_rate = 0.
sq_tau = np.sqrt(tau)
r_old = np.random.normal(loc=0., scale=1.0, size=(3))
d_old = drift(a,r_old)
d2_old = np.dot(d_old,d_old)
psi_old = psi(a,r_old)
w = 1.0
for istep in range(nmax):
chi = np.random.normal(loc=0., scale=1.0, size=(3))
el = e_loc(a,r_old)
w *= np.exp(-tau*(el - Eref))
N += w
E += w * el
r_new = r_old + tau * d_old + sq_tau * chi
d_new = drift(a,r_new)
d2_new = np.dot(d_new,d_new)
psi_new = psi(a,r_new)
# Metropolis
prod = np.dot((d_new + d_old), (r_new - r_old))
argexpo = 0.5 * (d2_new - d2_old)*tau + prod
q = psi_new / psi_old
q = np.exp(-argexpo) * q*q
# PDMC weight
if np.random.uniform() < q:
accep_rate += w
r_old = r_new
d_old = d_new
d2_old = d2_new
psi_old = psi_new
return E/N, accep_rate/N
a = 0.9
nmax = 10000
tau = .1
X = [MonteCarlo(a,tau,nmax,-0.5) for i in range(30)]
E, deltaE = ave_error([x[0] for x in X])
A, deltaA = ave_error([x[1] for x in X])
print(f"E = {E} +/- {deltaE}\nA = {A} +/- {deltaA}")
#+END_SRC
#+RESULTS:
: E = -0.49654807434947584 +/- 0.0006868522447409156
: A = 0.9876193891840709 +/- 0.00041857361650995804
*Fortran*
#+BEGIN_SRC f90
subroutine variational_montecarlo(a,tau,nmax,energy,accep_rate)
implicit none
double precision, intent(in) :: a, tau
integer*8 , intent(in) :: nmax
double precision, intent(out) :: energy, accep_rate
integer*8 :: istep
double precision :: norm, sq_tau, chi(3), d2_old, prod, u
double precision :: psi_old, psi_new, d2_new, argexpo, q
double precision :: r_old(3), r_new(3)
double precision :: d_old(3), d_new(3)
double precision, external :: e_loc, psi
sq_tau = dsqrt(tau)
! Initialization
energy = 0.d0
norm = 0.d0
accep_rate = 0.d0
call random_gauss(r_old,3)
call drift(a,r_old,d_old)
d2_old = d_old(1)*d_old(1) + d_old(2)*d_old(2) + d_old(3)*d_old(3)
psi_old = psi(a,r_old)
do istep = 1,nmax
call random_gauss(chi,3)
r_new(:) = r_old(:) + tau * d_old(:) + chi(:)*sq_tau
call drift(a,r_new,d_new)
d2_new = d_new(1)*d_new(1) + d_new(2)*d_new(2) + d_new(3)*d_new(3)
psi_new = psi(a,r_new)
! Metropolis
prod = (d_new(1) + d_old(1))*(r_new(1) - r_old(1)) + &
(d_new(2) + d_old(2))*(r_new(2) - r_old(2)) + &
(d_new(3) + d_old(3))*(r_new(3) - r_old(3))
argexpo = 0.5d0 * (d2_new - d2_old)*tau + prod
q = psi_new / psi_old
q = dexp(-argexpo) * q*q
call random_number(u)
if (u<q) then
accep_rate = accep_rate + 1.d0
r_old(:) = r_new(:)
d_old(:) = d_new(:)
d2_old = d2_new
psi_old = psi_new
end if
norm = norm + 1.d0
energy = energy + e_loc(a,r_old)
end do
energy = energy / norm
accep_rate = accep_rate / norm
end subroutine variational_montecarlo
program qmc
implicit none
double precision, parameter :: a = 0.9
double precision, parameter :: tau = 1.0
integer*8 , parameter :: nmax = 100000
integer , parameter :: nruns = 30
integer :: irun
double precision :: X(nruns), accep(nruns)
double precision :: ave, err
do irun=1,nruns
call variational_montecarlo(a,tau,nmax,X(irun),accep(irun))
enddo
call ave_error(X,nruns,ave,err)
print *, 'E = ', ave, '+/-', err
call ave_error(accep,nruns,ave,err)
print *, 'A = ', ave, '+/-', err
end program qmc
#+END_SRC
#+begin_src sh :results output :exports both
gfortran hydrogen.f90 qmc_stats.f90 vmc_metropolis.f90 -o vmc_metropolis
./vmc_metropolis
#+end_src
#+RESULTS:
: E = -0.49499990423528023 +/- 1.5958250761863871E-004
: A = 0.78861366666666655 +/- 3.5096729498002445E-004
** Dihydrogen
We will now consider the H_2 molecule in a minimal basis composed of the
$1s$ orbitals of the hydrogen atoms:
$$
\Psi(\mathbf{r}_1, \mathbf{r}_2) =
\exp(-(\mathbf{r}_1 - \mathbf{R}_A)) +
$$
where $\mathbf{r}_1$ and $\mathbf{r}_2$ denote the electron
coordinates and $\mathbf{R}_A$ and $\mathbf{R}_B$ the coordinates of
the nuclei.

71
docs/config.el Executable file
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;; Thanks to Tobias's answer on Emacs Stack Exchange:
;; https://emacs.stackexchange.com/questions/38437/org-mode-batch-export-missing-syntax-highlighting
(package-initialize)
(require 'htmlize)
(require 'font-lock)
(require 'subr-x) ;; for `when-let'
(unless (boundp 'maximal-integer)
(defconst maximal-integer (lsh -1 -1)
"Maximal integer value representable natively in emacs lisp."))
(defun face-spec-default (spec)
"Get list containing at most the default entry of face SPEC.
Return nil if SPEC has no default entry."
(let* ((first (car-safe spec))
(display (car-safe first)))
(when (eq display 'default)
(list (car-safe spec)))))
(defun face-spec-min-color (display-atts)
"Get min-color entry of DISPLAY-ATTS pair from face spec."
(let* ((display (car-safe display-atts)))
(or (car-safe (cdr (assoc 'min-colors display)))
maximal-integer)))
(defun face-spec-highest-color (spec)
"Search face SPEC for highest color.
That means the DISPLAY entry of SPEC
with class 'color and highest min-color value."
(let ((color-list (cl-remove-if-not
(lambda (display-atts)
(when-let ((display (car-safe display-atts))
(class (and (listp display)
(assoc 'class display)))
(background (assoc 'background display)))
(and (member 'light (cdr background))
(member 'color (cdr class)))))
spec)))
(cl-reduce (lambda (display-atts1 display-atts2)
(if (> (face-spec-min-color display-atts1)
(face-spec-min-color display-atts2))
display-atts1
display-atts2))
(cdr color-list)
:initial-value (car color-list))))
(defun face-spec-t (spec)
"Search face SPEC for fall back."
(cl-find-if (lambda (display-atts)
(eq (car-safe display-atts) t))
spec))
(defun my-face-attribute (face attribute &optional frame inherit)
"Get FACE ATTRIBUTE from `face-user-default-spec' and not from `face-attribute'."
(let* ((face-spec (face-user-default-spec face))
(display-attr (or (face-spec-highest-color face-spec)
(face-spec-t face-spec)))
(attr (cdr display-attr))
(val (or (plist-get attr attribute) (car-safe (cdr (assoc attribute attr))))))
;; (message "attribute: %S" attribute) ;; for debugging
(when (and (null (eq attribute :inherit))
(null val))
(let ((inherited-face (my-face-attribute face :inherit)))
(when (and inherited-face
(null (eq inherited-face 'unspecified)))
(setq val (my-face-attribute inherited-face attribute)))))
;; (message "face: %S attribute: %S display-attr: %S, val: %S" face attribute display-attr val) ;; for debugging
(or val 'unspecified)))
(advice-add 'face-attribute :override #'my-face-attribute)

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docs/create.sh Executable file
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#!/bin/bash
INPUT=$1
if [[ -f ../docs/htmlize.el ]]
then
emacs --batch --load ../docs/htmlize.el --load ../docs/config.el $INPUT -f org-html-export-to-html
else
emacs --batch --load ../docs/config.el $INPUT -f org-html-export-to-html
fi
mv ../QMC.html index.html