3D-Orbitals.py

%matplotlib inline
import matplotlib.pyplot as plt
from matplotlib import cm, colors
from mpl_toolkits.mplot3d import Axes3D
import numpy as np
import scipy.integrate as integrate
from IPython.display import set_matplotlib_formats
set_matplotlib_formats('retina')
import ipywidgets as widgets
import ipyvolume as ipv
import scipy.special as spe


def psi_R(r,n=15,l=8):

    coeff = np.sqrt((2.0/n)**3 * spe.factorial(n-l-1) /(2.0*n*spe.factorial(n+l)))
    
    laguerre = spe.assoc_laguerre(2.0*r/n,n-l-1,2*l+1)
    
    return coeff * np.exp(-r/n) * (2.0*r/n)**l * laguerre



r = np.linspace(0,100,1000)

R = psi_R(r,n=15,l=8)

plt.plot(r, R**2, lw=3)

plt.xlabel('$r [a_0]$',fontsize=20)

plt.ylabel('$R_{nl}(r)$', fontsize=20)

plt.grid('True')




nmax=70

@widgets.interact(n = np.arange(1,nmax,1), l = np.arange(0,nmax-1,1))

def plot_radial(n=15,l=8):
    
    r =    np.linspace(0,250,10000)
    
    psi2 = psi_R(r,n,l)**2 * (r**2)
    
    plt.plot(r, psi2, lw=2, color='red')
    

    
    
    plt.xlabel('$r [a_0]$')

    plt.ylabel('$R_{nl}(r)$')
    
    rmax = n**2*(1+0.5*(1-l*(l+1)/n**2))
    
    plt.xlim([0, 2*rmax])


def psi_ang(phi,theta,l=8,m=0):
    
    sphHarm = spe.sph_harm(m,l,phi,theta)
    
    return sphHarm.real

phi, theta = np.linspace(0, np.pi, 100), np.linspace(0, 2*np.pi, 100)

phi, theta = np.meshgrid(phi, theta)

Ylm = psi_ang(theta,phi,l=2,m=0)



x = np.sin(phi) * np.cos(theta) * abs(Ylm)
y = np.sin(phi) * np.sin(theta) * abs(Ylm)
z = np.cos(phi) * abs(Ylm)


fig = plt.figure(figsize=(10,10))
ax = fig.add_subplot(111, projection='3d')



fcolors = (Ylm - Ylm.min())/(Ylm.max() - Ylm.min())



ax.plot_surface(x, y, z, facecolors=cm.seismic(fcolors), alpha=0.3)




cset = ax.contour(x, y, z,20, zdir='z',offset = -1, cmap='summer')
cset = ax.contour(x, y, z,20, zdir='y',offset =  1, cmap='winter' )
cset = ax.contour(x, y, z,20, zdir='x',offset = -1, cmap='autumn')


ax.set_xlim(-1, 1)
ax.set_ylim(-1, 1)
ax.set_zlim(-1, 1)