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teaching:progappchim:matplotlib_gallery:potentiel_energy_surface [2015/05/08 11:01]
villersd
teaching:progappchim:matplotlib_gallery:potentiel_energy_surface [2016/12/14 11:57] (Version actuelle)
villersd [Références]
Ligne 32: Ligne 32:
 ==== Programme ==== ==== Programme ====
  
-==== Sorties graphiques ====+<sxh python; title : PES-contour-01.py>​ 
 +#​!/​usr/​bin/​env python 
 +# -*- coding: utf-8 -*- 
 +"""​ 
 +Tracés de lignes de niveau ou isolignes 
 +Application : Potentiel Energy Surface de la réaction 
 +H + H2 --> H2 + H
  
 +"""​
 +# ref : http://​bulldog2.redlands.edu/​facultyfolder/​deweerd/​tutorials/​Tutorial-ContourPlot.pdf
 +
 +import matplotlib.pyplot as plt  # directive d'​importation standard de Matplotlib
 +import numpy as np               # directive d'​importation standard de numpy
 +from mpl_toolkits.mplot3d import Axes3D ​ # Axes3D
 +
 +def Ebond(rAB):
 +    return D_e * (np.exp(-2.*beta*(rAB-r_e)) - 2.*np.exp(-beta*(rAB-r_e)))
 +def Eant(rAB):
 +    return 0.5 * D_e * (np.exp(-2.*beta*(rAB-r_e)) + 2.*np.exp(-beta*(rAB-r_e)))
 +def Q(rAB):
 +    return 0.5 * ((1.+k)*Ebond(rAB) + (1.-k)*Eant(rAB))
 +def a(rAB):
 +    return 0.5 * ((1.+k)*Ebond(rAB) - (1.-k)*Eant(rAB))
 +
 +beta=19.3E-3 # pm-1
 +r_e=74.1 # pm
 +D_e = .76 # E-18 J
 +k=0.18
 +rmin=10.
 +rmax=400.
 +num=100
 +x_1d = np.linspace(rmin,​rmax,​ num)
 +print x_1d.shape, x_1d.dtype, x_1d.ndim
 +y_1d = np.linspace(rmin,​rmax,​ num)
 +print y_1d.shape, y_1d.dtype, y_1d.ndim
 +X, Y = np.meshgrid(x_1d,​ y_1d)
 +print X.shape, X.dtype, X.ndim, Y.shape, Y.dtype, Y.ndim
 +E=(Q(X)+Q(Y)+Q(X+Y)-np.sqrt(2.*((a(X)-a(Y))**2.+(a(Y)-a(X+Y))**2.+(a(X+Y)-a(X))**2.)))/​(1.+k)
 +print np.min(E) ​ #valeur minimale de E
 +
 +fig = plt.figure(figsize=(12,​ 12), dpi=80)
 +ax = fig.add_subplot(111)
 +# cf. http://​stackoverflow.com/​questions/​7965743/​how-can-i-set-the-aspect-ratio-in-matplotlib
 +ax.set_aspect("​equal"​)
 +levels = np.linspace(-1.7,​ 1.0, 53)
 +CS1 = plt.contour(X,​ Y, E, levels, colors='​k'​)
 +plt.clabel(CS1,​ colors = '​k',​ fmt = '​%2.2f',​ fontsize=14)
 +CS2 = plt.contourf(X,​ Y, E, levels)
 +#​plt.colorbar(CS2) ​ # visualisation éventuelle de l'​échelle de couleur
 +
 +plt.title('​Isolignes'​)
 +plt.xlabel('​x (pm)')
 +plt.ylabel('​y (pm)')
 +
 +fig = plt.figure(2,​figsize=(15,​ 15))
 +ax = Axes3D(fig)
 +ax.plot_surface(X,​Y,​E,​ rstride=1,​cstride=1 ,​cmap=plt.cm.jet)
 +ax.set_xlabel('​X'​)
 +ax.set_ylabel('​Y'​)
 +ax.set_zlabel('​E'​)
 +plt.show()
 +</​sxh>​
 +
 +Avec les paramètres essayés, la valeur minimale de E est environ -1.603
 +==== Sorties graphiques ====
 === Lignes de contour === === Lignes de contour ===
 +
 +{{:​teaching:​progappchim:​matplotlib_gallery:​pes-contour-01.png|}}
 +
 +=== Surface 3D ===
 +
 +{{:​teaching:​progappchim:​matplotlib_gallery:​pes-3d-01.png?​300|}}
  
 ===== Références ===== ===== Références =====
Ligne 46: Ligne 115:
   * [[http://​scitation.aip.org/​content/​aip/​journal/​jcp/​23/​3/​10.1063/​1.1742043|On a New Method of Drawing the Potential Energy Surface]], Shin Sato, J. Chem. Phys. 23, 592 (1955)   * [[http://​scitation.aip.org/​content/​aip/​journal/​jcp/​23/​3/​10.1063/​1.1742043|On a New Method of Drawing the Potential Energy Surface]], Shin Sato, J. Chem. Phys. 23, 592 (1955)
   * [[http://​www.tc.chemie.uni-siegen.de/​jaquet/​Copy-of-introPEStexpowerlight.pdf|Introduction to potential energy surfaces and graphical interpretation]],​ Ralph Jaquet (2002)   * [[http://​www.tc.chemie.uni-siegen.de/​jaquet/​Copy-of-introPEStexpowerlight.pdf|Introduction to potential energy surfaces and graphical interpretation]],​ Ralph Jaquet (2002)
 +  * [[http://​onlinelibrary.wiley.com/​doi/​10.1002/​bbpc.192900025/​abstract|QUANTENMECHANISCHE DEUTUNG DES VORGANGS DER AKTIVIERUNG]] F. London Zeitschrift für Elektrochemie und angewandte physikalische Chemie. Volume 35, Issue 9, pages 552–555, September 1929
 +  * [[https://​www.youtube.com/​playlist?​list=PLkNVwyLvX_TFBLHCvApmvafqqQUHb6JwF|Computational Chemistry Universitu Minesota]], vidéos,...
 +  * W H Miller, Recent Advances in Quantum Mechanical Reactive Scattering Theory, Including Comparison of Recent Experiments with Rigorous Calculations of State-to-State Cross Sections for the H/​D+H2→H2/​HD+H Reactions, Annual Review of Physical Chemistry, Vol. 41: 245-281 (Volume publication date October 1990) DOI: 10.1146/​annurev.pc.41.100190.001333
 +  * Peterson, Kirk A., Woon, David E., Dunning, Thom H. , Benchmark calculations with correlated molecular wave functions. IV. The classical barrier height of the H+H2→H2+H reaction, ​ Journal of Chemical Physics. 5/15/1994, Vol. 100 Issue 10, p7410
 +
  
  
 +Voir aussi :
 +  * [[http://​chemistry.stackexchange.com/​questions/​47665/​ballistic-behavior-of-molecules-on-potential-energy-surfaces]]
 +  * [[http://​chemistry.stackexchange.com/​questions/​50253/​compute-minimum-energy-paths-from-arbitrary-positions-on-the-potential-energy-su]]
 +  * [[http://​pubs.acs.org/​doi/​full/​10.1021/​acs.jchemed.6b00572|Let Students Derive, by Themselves, Two-Dimensional Atomic and Molecular Quantum Chemistry from Scratch]], Yingbin Ge, J. Chem. Educ., 2016, 93 (12), pp 2033–2039 DOI: 10.1021/​acs.jchemed.6b00572
  
  
teaching/progappchim/matplotlib_gallery/potentiel_energy_surface.1431075703.txt.gz · Dernière modification: 2015/05/08 11:01 par villersd