２原子分子の分子軌道ができる様子をアニメーションで見てみよう

import numpy as np
import matplotlib.pyplot as plt
import matplotlib.animation as animation
from matplotlib.animation import PillowWriter
from IPython.display import Image

x = np.linspace(-2, 2, 100)
y = np.linspace(-2.5, 2.5, 100)
X, Y = np.meshgrid(x, y)

def atomic_orbital(x, y, center_x, center_y, zeta=1.0):
    r = np.sqrt((x - center_x)**2 + (y - center_y)**2)
    N = (2 * zeta)**1.5 / np.sqrt(np.pi)
    return N * np.exp(-zeta * r)

def bonding_mo(x, y, d, zeta=1.0):
    return atomic_orbital(x, y, -d / 2, 0, zeta) + atomic_orbital(x, y, d / 2, 0, zeta)

def antibonding_mo(x, y, d, zeta=1.0):
    return atomic_orbital(x, y, -d / 2, 0, zeta) - atomic_orbital(x, y, d / 2, 0, zeta)

fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(10, 6))
fig.subplots_adjust(left=0.06, right=0.99, top=0.95, bottom=0.1)

def plot_mo(frame):
    ax1.clear()
    ax2.clear()
    
    if frame < 100:
        ax1.set_title(f"Bonding")
        d = 4 - frame * 0.03
        contour_plot  = bonding_mo(X, Y, d)
        cross_section = bonding_mo(x, 0, d)
    else:
        ax1.set_title(f"Antibonding")
        d = 4 - (frame - 100) * 0.03
        contour_plot  = antibonding_mo(X, Y, d)
        cross_section = antibonding_mo(x, 0, d)

    ax1.contourf(X, Y, contour_plot, levels=100, cmap="coolwarm")
    ax1.axhline(0, color='grey', linestyle='--', linewidth=1)
    ax1.axvline(0, color='grey', linestyle='--', linewidth=1)
    ax1.set_xlim(-2, 2)
    ax1.set_ylim(-2.5, 2.5)
    ax1.set_xlabel("x")
    ax1.set_ylabel("y")

    ax2.set_title(f"Distance: {d:.2f}")
    ax2.plot(x, cross_section, lw=2)
    ax2.axhline(0, color='grey', linestyle='--', linewidth=1)
    ax2.axvline(0, color='grey', linestyle='--', linewidth=1)
    ax2.set_xlim(-2, 2)
    ax2.set_ylim(-2.5, 2.5)
    ax2.set_xlabel("x")
    ax2.set_ylabel("Amplitude")

ani = animation.FuncAnimation(fig, plot_mo, frames=200, interval=50, repeat=True)

gif = "mo.gif"
writer = PillowWriter(fps=20)
ani.save(gif, writer=writer)

Image(gif)