562 lines
22 KiB
Python
562 lines
22 KiB
Python
#!/usr/bin/env python3
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"""
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periodic_table_comparison.py
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Generates a comprehensive comparison of Coulomb force vs Spin-tether force
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across the periodic table using Bohr radius scaling.
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Note to a reader: With this script we detected that s must be == 1 for
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the formula to work.
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Author: Andre Heinecke & AI Collaborators
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Date: June 2025
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"""
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import numpy as np
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import matplotlib.pyplot as plt
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from matplotlib.gridspec import GridSpec
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import pandas as pd
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# Physical constants (CODATA 2018 values)
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HBAR = 1.054571817e-34 # J·s (reduced Planck constant)
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ME = 9.1093837015e-31 # kg (electron mass)
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E = 1.602176634e-19 # C (elementary charge)
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K = 8.9875517923e9 # N·m²/C² (Coulomb constant)
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A0 = 5.29177210903e-11 # m (Bohr radius)
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C = 299792458 # m/s (speed of light)
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ALPHA = 1/137.035999084 # Fine structure constant
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# Element data with effective nuclear charges
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# Format: (Symbol, Name, Z, Z_eff_1s, n_valence, l_valence)
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# Z_eff values are calculated using Slater's rules and empirical data
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ELEMENTS = [
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# Period 1-2
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("H", "Hydrogen", 1, 1.00, 1, 0),
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("He", "Helium", 2, 1.69, 1, 0),
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("Li", "Lithium", 3, 2.69, 2, 0),
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("Be", "Beryllium", 4, 3.68, 2, 0),
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("B", "Boron", 5, 4.68, 2, 1),
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("C", "Carbon", 6, 5.67, 2, 1),
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("N", "Nitrogen", 7, 6.66, 2, 1),
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("O", "Oxygen", 8, 7.66, 2, 1),
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("F", "Fluorine", 9, 8.65, 2, 1),
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("Ne", "Neon", 10, 9.64, 2, 1),
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# Period 3
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("Na", "Sodium", 11, 10.63, 3, 0),
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("Mg", "Magnesium", 12, 11.61, 3, 0),
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("Al", "Aluminum", 13, 12.59, 3, 1),
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("Si", "Silicon", 14, 13.57, 3, 1),
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("P", "Phosphorus", 15, 14.56, 3, 1),
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("S", "Sulfur", 16, 15.54, 3, 1),
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("Cl", "Chlorine", 17, 16.52, 3, 1),
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("Ar", "Argon", 18, 17.51, 3, 1),
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# Period 4 - Transition metals
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("K", "Potassium", 19, 18.49, 4, 0),
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("Ca", "Calcium", 20, 19.47, 4, 0),
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("Sc", "Scandium", 21, 20.45, 3, 2),
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("Ti", "Titanium", 22, 21.44, 3, 2),
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("V", "Vanadium", 23, 22.42, 3, 2),
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("Cr", "Chromium", 24, 23.41, 3, 2),
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("Mn", "Manganese", 25, 24.40, 3, 2),
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("Fe", "Iron", 26, 25.38, 3, 2),
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("Co", "Cobalt", 27, 26.37, 3, 2),
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("Ni", "Nickel", 28, 27.35, 3, 2),
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("Cu", "Copper", 29, 28.34, 3, 2),
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("Zn", "Zinc", 30, 29.32, 3, 2),
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("Ga", "Gallium", 31, 30.31, 4, 1),
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("Ge", "Germanium", 32, 31.29, 4, 1),
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("As", "Arsenic", 33, 32.28, 4, 1),
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("Se", "Selenium", 34, 33.26, 4, 1),
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("Br", "Bromine", 35, 34.25, 4, 1),
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("Kr", "Krypton", 36, 35.23, 4, 1),
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# Period 5
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("Rb", "Rubidium", 37, 36.21, 5, 0),
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("Sr", "Strontium", 38, 37.20, 5, 0),
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("Y", "Yttrium", 39, 38.18, 4, 2),
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("Zr", "Zirconium", 40, 39.17, 4, 2),
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("Nb", "Niobium", 41, 40.15, 4, 2),
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("Mo", "Molybdenum", 42, 41.14, 4, 2),
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("Tc", "Technetium", 43, 42.12, 4, 2),
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("Ru", "Ruthenium", 44, 43.11, 4, 2),
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("Rh", "Rhodium", 45, 44.09, 4, 2),
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("Pd", "Palladium", 46, 45.08, 4, 2),
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("Ag", "Silver", 47, 46.06, 4, 2),
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("Cd", "Cadmium", 48, 47.04, 4, 2),
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("In", "Indium", 49, 48.03, 5, 1),
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("Sn", "Tin", 50, 49.01, 5, 1),
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("Sb", "Antimony", 51, 50.00, 5, 1),
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("Te", "Tellurium", 52, 50.98, 5, 1),
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("I", "Iodine", 53, 51.97, 5, 1),
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("Xe", "Xenon", 54, 52.95, 5, 1),
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# Period 6 - Including lanthanides (simplified)
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("Cs", "Cesium", 55, 53.94, 6, 0),
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("Ba", "Barium", 56, 54.92, 6, 0),
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("La", "Lanthanum", 57, 55.91, 5, 2),
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("Ce", "Cerium", 58, 56.89, 4, 3), # f-electron
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("Pr", "Praseodymium", 59, 57.88, 4, 3),
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("Nd", "Neodymium", 60, 58.86, 4, 3),
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("Pm", "Promethium", 61, 59.85, 4, 3),
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("Sm", "Samarium", 62, 60.83, 4, 3),
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("Eu", "Europium", 63, 61.82, 4, 3),
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("Gd", "Gadolinium", 64, 62.80, 4, 3),
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("Tb", "Terbium", 65, 63.78, 4, 3),
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("Dy", "Dysprosium", 66, 64.77, 4, 3),
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("Ho", "Holmium", 67, 65.75, 4, 3),
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("Er", "Erbium", 68, 66.74, 4, 3),
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("Tm", "Thulium", 69, 67.72, 4, 3),
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("Yb", "Ytterbium", 70, 68.71, 4, 3),
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("Lu", "Lutetium", 71, 69.69, 5, 2),
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("Hf", "Hafnium", 72, 70.68, 5, 2),
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("Ta", "Tantalum", 73, 71.66, 5, 2),
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("W", "Tungsten", 74, 72.65, 5, 2),
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("Re", "Rhenium", 75, 73.63, 5, 2),
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("Os", "Osmium", 76, 74.62, 5, 2),
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("Ir", "Iridium", 77, 75.60, 5, 2),
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("Pt", "Platinum", 78, 76.58, 5, 2),
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("Au", "Gold", 79, 77.57, 6, 0), # 6s electron
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("Hg", "Mercury", 80, 78.55, 6, 0),
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("Tl", "Thallium", 81, 79.54, 6, 1),
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("Pb", "Lead", 82, 80.52, 6, 1),
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("Bi", "Bismuth", 83, 81.51, 6, 1),
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("Po", "Polonium", 84, 82.49, 6, 1),
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("At", "Astatine", 85, 83.48, 6, 1),
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("Rn", "Radon", 86, 84.46, 6, 1),
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# Period 7 - Including some actinides
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("Fr", "Francium", 87, 85.45, 7, 0),
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("Ra", "Radium", 88, 86.43, 7, 0),
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("Ac", "Actinium", 89, 87.42, 6, 2),
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("Th", "Thorium", 90, 88.40, 6, 2),
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("Pa", "Protactinium", 91, 89.39, 5, 3), # f-electron
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("U", "Uranium", 92, 90.37, 5, 3),
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("Np", "Neptunium", 93, 91.36, 5, 3),
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("Pu", "Plutonium", 94, 92.34, 5, 3),
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("Am", "Americium", 95, 93.32, 5, 3),
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("Cm", "Curium", 96, 94.31, 5, 3),
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("Bk", "Berkelium", 97, 95.29, 5, 3),
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("Cf", "Californium", 98, 96.28, 5, 3),
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("Es", "Einsteinium", 99, 97.26, 5, 3),
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("Fm", "Fermium", 100, 98.25, 5, 3),
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]
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def calculate_effective_z(Z, shell):
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"""Calculate effective nuclear charge using Slater's rules (simplified)"""
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if shell == 1:
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if Z == 1:
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return 1.0
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else:
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return Z - 0.31 # Approximate screening for 1s
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elif shell == 2:
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# Simplified for 2s/2p
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return Z - 2.0 - 0.85 * (min(Z-2, 8) - 1)
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elif shell == 3:
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# Very simplified for 3s/3p/3d
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return Z - 10.0 - 0.85 * (min(Z-10, 8) - 1)
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else:
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# Rough approximation for higher shells
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return Z * 0.3
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def get_actual_z_eff(Z, n, l):
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"""Get more accurate Z_eff for specific orbitals in heavy atoms"""
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# For s-orbitals in heavy atoms, use empirical corrections
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if Z > 70 and l == 0: # Heavy s-orbitals
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# 6s orbitals experience strong relativistic contraction
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if n == 6:
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return 0.15 * Z # Approximately 15% of Z for 6s
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elif n == 7:
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return 0.12 * Z # Even more screening for 7s
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elif Z > 50 and l == 2: # Heavy d-orbitals
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return 0.35 * Z # d-orbitals are less penetrating
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elif l == 3: # f-orbitals
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return 0.25 * Z # f-orbitals experience heavy screening
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# Default to simple calculation
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return calculate_effective_z(Z, n)
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def calculate_radius(Z_eff, n, l=0):
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"""Calculate mean orbital radius"""
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# Base radius using quantum numbers
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r = n * A0 / Z_eff
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# Orbital shape corrections
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if l == 1: # p-orbital
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r *= 1.0 # Already accounted for in mean radius
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elif l == 2: # d-orbital
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r *= 0.35 # d-orbitals are more compact
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elif l == 3: # f-orbital
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r *= 0.25 # f-orbitals are even more compact
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return r
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def relativistic_factor(Z, n=1):
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"""Calculate relativistic correction factor for heavy elements"""
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# More sophisticated relativistic correction
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v_over_c = Z * ALPHA / n
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# For very heavy elements, use better approximation
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if Z > 70:
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# Account for multiple effects in heavy atoms
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# Including spin-orbit coupling and Darwin term
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gamma_base = np.sqrt(1 + v_over_c**2)
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# Additional correction for s-orbitals (they penetrate nucleus)
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if n <= 2: # 1s or 2s
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gamma = gamma_base * (1 + 0.1 * (Z/100)**2)
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else:
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gamma = gamma_base
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else:
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# Standard relativistic correction for lighter elements
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gamma = np.sqrt(1 + v_over_c**2)
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return gamma
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def spin_tether_force(r, s=1, m=ME, gamma=1):
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"""Calculate spin-tether force"""
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return HBAR**2 * s**2 / (gamma * m * r**3)
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def coulomb_force(r, Z_eff, gamma=1):
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"""Calculate Coulomb force with screening"""
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return K * Z_eff * E**2 / (gamma * r**2)
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def analyze_element(symbol, name, Z, Z_eff_1s, n, l):
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"""Analyze forces for a single element"""
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# For consistency, we use 1s orbital for all elements
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# This allows direct comparison across the periodic table
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Z_eff = Z_eff_1s
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# Special handling for very heavy elements
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if Z > 70:
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# For gold and heavier, use actual valence orbital
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if symbol == "Au": # Gold special case
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# Gold's 6s electron with proper Z_eff
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Z_eff = 11.8 # Well-known value for Au 6s
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n = 6
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l = 0
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elif Z > 86: # Very heavy elements
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# Use more realistic Z_eff for outer electrons
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Z_eff = get_actual_z_eff(Z, n, l)
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# Calculate radius
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r = calculate_radius(Z_eff, n if Z > 70 else 1, l if Z > 70 else 0)
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# Relativistic correction
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gamma = 1
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if Z > 20:
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gamma = relativistic_factor(Z, n if Z > 70 else 1)
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# For f-electrons, use higher angular momentum
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s = 1
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if l == 2: # d-orbital
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s = 2
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elif l == 3: # f-orbital
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s = 3
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# Calculate forces
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F_spin = spin_tether_force(r, s=s, gamma=gamma)
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F_coulomb = coulomb_force(r, Z_eff, gamma=gamma)
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# Agreement percentage
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agreement = (min(F_spin, F_coulomb) / max(F_spin, F_coulomb)) * 100
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return {
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'Symbol': symbol,
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'Name': name,
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'Z': Z,
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'Z_eff': Z_eff,
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'n': n if Z > 70 else 1,
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'l': l if Z > 70 else 0,
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'Radius (m)': r,
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'Gamma': gamma,
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'F_spin (N)': F_spin,
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'F_coulomb (N)': F_coulomb,
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'Agreement (%)': agreement,
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'Ratio': F_spin / F_coulomb
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}
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def main():
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"""Generate comprehensive analysis and plots"""
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print("Analyzing Coulomb vs Spin-Tether Forces Across the Periodic Table")
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print("Extended to 100 elements with relativistic corrections")
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print("=" * 70)
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# Analyze all elements
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results = []
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for element_data in ELEMENTS:
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result = analyze_element(*element_data)
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results.append(result)
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# Print detailed results for key elements
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if result['Symbol'] in ['H', 'He', 'C', 'Fe', 'Au', 'U']:
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print(f"\n{result['Name']} ({result['Symbol']}):")
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print(f" Z = {result['Z']}, Z_eff = {result['Z_eff']:.2f}")
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print(f" n = {result['n']}, l = {result['l']}")
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print(f" Radius = {result['Radius (m)']:.3e} m")
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if result['Gamma'] > 1.001:
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print(f" Relativistic γ = {result['Gamma']:.4f}")
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print(f" F_spin = {result['F_spin (N)']:.3e} N")
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print(f" F_coulomb = {result['F_coulomb (N)']:.3e} N")
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print(f" Agreement = {result['Agreement (%)']:.1f}%")
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# Create DataFrame
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df = pd.DataFrame(results)
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# Save detailed results
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df.to_csv('periodic_force_comparison_extended.csv', index=False)
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print(f"\nDetailed results saved to: periodic_force_comparison_extended.csv")
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# Create comprehensive plot with subplots
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fig = plt.figure(figsize=(20, 16))
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gs = GridSpec(4, 2, figure=fig, height_ratios=[2, 1, 1, 1])
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# Main comparison plot
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ax1 = fig.add_subplot(gs[0, :])
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atomic_numbers = df['Z'].values
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# Color by period
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colors = []
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for z in atomic_numbers:
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if z <= 2: colors.append('red')
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elif z <= 10: colors.append('orange')
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elif z <= 18: colors.append('yellow')
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elif z <= 36: colors.append('green')
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elif z <= 54: colors.append('blue')
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elif z <= 86: colors.append('purple')
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else: colors.append('black')
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ax1.scatter(atomic_numbers, df['F_coulomb (N)'].values,
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label='Coulomb Force', color=colors, s=60, alpha=0.7, edgecolors='black')
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ax1.scatter(atomic_numbers, df['F_spin (N)'].values,
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label='Spin-Tether Force', color=colors, s=60, alpha=0.7, marker='^', edgecolors='black')
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ax1.set_yscale('log')
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ax1.set_xlabel('Atomic Number (Z)', fontsize=14)
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ax1.set_ylabel('Force (N)', fontsize=14)
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ax1.set_title('Coulomb vs Spin-Tether Forces Across the Extended Periodic Table\n' +
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'Including Relativistic Effects for Heavy Elements', fontsize=16)
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ax1.legend(fontsize=12)
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ax1.grid(True, alpha=0.3)
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# Add element labels for notable elements
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for _, row in df.iterrows():
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if row['Symbol'] in ['H', 'He', 'C', 'O', 'Si', 'Fe', 'Cu', 'Ag', 'Au', 'U', 'Pu']:
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ax1.annotate(row['Symbol'],
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(row['Z'], row['F_coulomb (N)']),
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xytext=(5, 5), textcoords='offset points', fontsize=10, fontweight='bold')
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# Agreement percentage subplot
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ax2 = fig.add_subplot(gs[1, 0])
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bars = ax2.bar(atomic_numbers, df['Agreement (%)'].values, color='green', alpha=0.7)
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# Highlight elements with <99% agreement
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low_agreement = df[df['Agreement (%)'] < 99]
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if len(low_agreement) > 0:
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ax2.bar(low_agreement['Z'].values, low_agreement['Agreement (%)'].values,
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color='red', alpha=0.7)
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ax2.set_xlabel('Atomic Number (Z)', fontsize=12)
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ax2.set_ylabel('Agreement (%)', fontsize=12)
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ax2.set_title('Force Agreement Percentage', fontsize=14)
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ax2.set_ylim(90, 101)
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ax2.grid(True, alpha=0.3)
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# Force ratio subplot
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ax3 = fig.add_subplot(gs[1, 1])
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ax3.plot(atomic_numbers, df['Ratio'].values, 'o-', color='purple', alpha=0.7, markersize=3)
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ax3.axhline(y=1.0, color='black', linestyle='--', alpha=0.5)
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ax3.set_xlabel('Atomic Number (Z)', fontsize=12)
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ax3.set_ylabel('F_spin / F_coulomb', fontsize=12)
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ax3.set_title('Force Ratio', fontsize=14)
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ax3.set_ylim(0.90, 1.10)
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ax3.grid(True, alpha=0.3)
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# Relativistic effects subplot
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ax4 = fig.add_subplot(gs[2, :])
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gamma_values = df['Gamma'].values
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ax4.plot(atomic_numbers, gamma_values, 'b-', linewidth=2)
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ax4.set_xlabel('Atomic Number (Z)', fontsize=12)
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ax4.set_ylabel('Relativistic Factor γ', fontsize=12)
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ax4.set_title('Relativistic Corrections Across the Periodic Table', fontsize=14)
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ax4.grid(True, alpha=0.3)
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# Add annotations for significant relativistic effects
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for _, row in df.iterrows():
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if row['Gamma'] > 1.1 and row['Symbol'] in ['Au', 'Hg', 'Pb', 'U']:
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ax4.annotate(f"{row['Symbol']}\nγ={row['Gamma']:.3f}",
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(row['Z'], row['Gamma']),
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xytext=(5, 5), textcoords='offset points', fontsize=9)
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# Agreement distribution histogram
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ax5 = fig.add_subplot(gs[3, 0])
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ax5.hist(df['Agreement (%)'].values, bins=20, color='blue', alpha=0.7, edgecolor='black')
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ax5.set_xlabel('Agreement (%)', fontsize=12)
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ax5.set_ylabel('Number of Elements', fontsize=12)
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ax5.set_title('Distribution of Agreement Percentages', fontsize=14)
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ax5.axvline(x=99, color='red', linestyle='--', label='99% threshold')
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ax5.legend()
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# Special elements showcase
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ax6 = fig.add_subplot(gs[3, 1])
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special_elements = df[df['Symbol'].isin(['H', 'C', 'Fe', 'Au', 'U'])]
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x_pos = np.arange(len(special_elements))
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ax6.bar(x_pos - 0.2, special_elements['F_spin (N)'].values, 0.4,
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label='F_spin', alpha=0.8)
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ax6.bar(x_pos + 0.2, special_elements['F_coulomb (N)'].values, 0.4,
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label='F_coulomb', alpha=0.8)
|
||
|
||
ax6.set_yscale('log')
|
||
ax6.set_xticks(x_pos)
|
||
ax6.set_xticklabels(special_elements['Symbol'].values)
|
||
ax6.set_ylabel('Force (N)', fontsize=12)
|
||
ax6.set_title('Key Elements Comparison', fontsize=14)
|
||
ax6.legend()
|
||
|
||
plt.tight_layout()
|
||
plt.savefig('periodic_force_comparison_extended.png', dpi=300, bbox_inches='tight')
|
||
plt.savefig('periodic_force_comparison_extended.pdf', bbox_inches='tight')
|
||
print(f"\nPlots saved to: periodic_force_comparison_extended.png and .pdf")
|
||
|
||
# Statistical summary
|
||
print(f"\n" + "="*70)
|
||
print("STATISTICAL SUMMARY:")
|
||
print(f"Total elements analyzed: {len(df)}")
|
||
print(f"Mean agreement: {df['Agreement (%)'].mean():.2f}%")
|
||
print(f"Median agreement: {df['Agreement (%)'].median():.2f}%")
|
||
print(f"Std deviation: {df['Agreement (%)'].std():.2f}%")
|
||
print(f"Min agreement: {df['Agreement (%)'].min():.2f}% ({df.loc[df['Agreement (%)'].idxmin(), 'Name']})")
|
||
print(f"Max agreement: {df['Agreement (%)'].max():.2f}% ({df.loc[df['Agreement (%)'].idxmax(), 'Name']})")
|
||
|
||
# Elements with >99% agreement
|
||
high_agreement = df[df['Agreement (%)'] > 99]
|
||
print(f"\nElements with >99% agreement: {len(high_agreement)}/{len(df)} ({100*len(high_agreement)/len(df):.1f}%)")
|
||
|
||
# Elements with highest relativistic effects
|
||
print(f"\nElements with strongest relativistic effects (γ > 1.1):")
|
||
relativistic = df[df['Gamma'] > 1.1].sort_values('Gamma', ascending=False)
|
||
for _, row in relativistic.head(10).iterrows():
|
||
print(f" {row['Symbol']:3} ({row['Name']:15}) γ = {row['Gamma']:.4f}")
|
||
|
||
# Save LaTeX table for paper (top 20 elements)
|
||
latex_elements = df[df['Symbol'].isin(['H', 'He', 'Li', 'Be', 'B', 'C', 'N', 'O', 'F', 'Ne',
|
||
'Na', 'Al', 'Si', 'Cl', 'Fe', 'Cu', 'Ag', 'Au', 'Hg', 'U'])]
|
||
|
||
latex_table = latex_elements[['Symbol', 'Name', 'Z', 'F_spin (N)', 'F_coulomb (N)', 'Agreement (%)']].to_latex(
|
||
index=False,
|
||
float_format=lambda x: f'{x:.3e}' if x < 0.01 or x > 1000 else f'{x:.2f}',
|
||
caption="Comparison of Spin-Tether and Coulomb Forces for Selected Elements",
|
||
label="tab:periodic_comparison_extended"
|
||
)
|
||
|
||
with open('periodic_force_table_extended.tex', 'w') as f:
|
||
f.write(latex_table)
|
||
print(f"\nLaTeX table saved to: periodic_force_table_extended.tex")
|
||
|
||
# Create a special plot for transition metals
|
||
fig2, ax = plt.subplots(figsize=(12, 8))
|
||
transition_metals = df[(df['Z'] >= 21) & (df['Z'] <= 30)] # Sc to Zn
|
||
|
||
ax.plot(transition_metals['Z'].values, transition_metals['Agreement (%)'].values,
|
||
'o-', linewidth=2, markersize=8, label='3d Transition Metals')
|
||
|
||
# Add 4d transition metals
|
||
transition_4d = df[(df['Z'] >= 39) & (df['Z'] <= 48)] # Y to Cd
|
||
ax.plot(transition_4d['Z'].values, transition_4d['Agreement (%)'].values,
|
||
's-', linewidth=2, markersize=8, label='4d Transition Metals')
|
||
|
||
# Add 5d transition metals
|
||
transition_5d = df[(df['Z'] >= 72) & (df['Z'] <= 80)] # Hf to Hg
|
||
ax.plot(transition_5d['Z'].values, transition_5d['Agreement (%)'].values,
|
||
'^-', linewidth=2, markersize=8, label='5d Transition Metals')
|
||
|
||
ax.set_xlabel('Atomic Number (Z)', fontsize=14)
|
||
ax.set_ylabel('Agreement (%)', fontsize=14)
|
||
ax.set_title('Agreement for Transition Metal Series\nShowing d-orbital Effects', fontsize=16)
|
||
ax.legend(fontsize=12)
|
||
ax.grid(True, alpha=0.3)
|
||
ax.set_ylim(95, 101)
|
||
|
||
# Annotate specific elements
|
||
for series, marker in [(transition_metals, 'o'), (transition_4d, 's'), (transition_5d, '^')]:
|
||
for _, row in series.iterrows():
|
||
if row['Symbol'] in ['Fe', 'Ru', 'Os', 'Au']:
|
||
ax.annotate(row['Symbol'],
|
||
(row['Z'], row['Agreement (%)']),
|
||
xytext=(5, 5), textcoords='offset points', fontsize=10)
|
||
|
||
plt.tight_layout()
|
||
plt.savefig('transition_metals_comparison.png', dpi=300, bbox_inches='tight')
|
||
print(f"\nTransition metals plot saved to: transition_metals_comparison.png")
|
||
|
||
# Create a special plot for lanthanides and actinides
|
||
fig3, (ax_lan, ax_act) = plt.subplots(2, 1, figsize=(14, 10))
|
||
|
||
# Lanthanides (Ce to Lu, Z=58-71)
|
||
lanthanides = df[(df['Z'] >= 58) & (df['Z'] <= 71)]
|
||
ax_lan.plot(lanthanides['Z'].values, lanthanides['Agreement (%)'].values,
|
||
'o-', linewidth=2, markersize=8, color='purple', label='Lanthanides (4f)')
|
||
ax_lan.set_ylabel('Agreement (%)', fontsize=12)
|
||
ax_lan.set_title('Agreement for Lanthanides (4f elements)\nShowing f-orbital Effects', fontsize=14)
|
||
ax_lan.grid(True, alpha=0.3)
|
||
ax_lan.set_ylim(95, 101)
|
||
|
||
# Annotate each lanthanide
|
||
for _, row in lanthanides.iterrows():
|
||
ax_lan.annotate(row['Symbol'],
|
||
(row['Z'], row['Agreement (%)']),
|
||
xytext=(0, 5), textcoords='offset points',
|
||
fontsize=9, ha='center')
|
||
|
||
# Actinides (Th to Fm, Z=90-100)
|
||
actinides = df[(df['Z'] >= 90) & (df['Z'] <= 100)]
|
||
ax_act.plot(actinides['Z'].values, actinides['Agreement (%)'].values,
|
||
's-', linewidth=2, markersize=8, color='darkred', label='Actinides (5f)')
|
||
ax_act.set_xlabel('Atomic Number (Z)', fontsize=12)
|
||
ax_act.set_ylabel('Agreement (%)', fontsize=12)
|
||
ax_act.set_title('Agreement for Actinides (5f elements)', fontsize=14)
|
||
ax_act.grid(True, alpha=0.3)
|
||
ax_act.set_ylim(95, 101)
|
||
|
||
# Annotate each actinide
|
||
for _, row in actinides.iterrows():
|
||
ax_act.annotate(row['Symbol'],
|
||
(row['Z'], row['Agreement (%)']),
|
||
xytext=(0, 5), textcoords='offset points',
|
||
fontsize=9, ha='center')
|
||
|
||
plt.tight_layout()
|
||
plt.savefig('f_elements_comparison.png', dpi=300, bbox_inches='tight')
|
||
print(f"\nf-elements plot saved to: f_elements_comparison.png")
|
||
|
||
# Print specific results for Gold to verify relativistic effects
|
||
print(f"\n" + "="*70)
|
||
print("DETAILED GOLD (Au) ANALYSIS:")
|
||
gold = df[df['Symbol'] == 'Au'].iloc[0]
|
||
print(f"Atomic number: Z = {gold['Z']}")
|
||
print(f"Effective nuclear charge: Z_eff = {gold['Z_eff']:.2f}")
|
||
print(f"Quantum numbers: n = {gold['n']}, l = {gold['l']}")
|
||
print(f"Orbital radius: r = {gold['Radius (m)']:.3e} m")
|
||
print(f"Relativistic factor: γ = {gold['Gamma']:.4f}")
|
||
print(f"Spin-tether force: F_spin = {gold['F_spin (N)']:.3e} N")
|
||
print(f"Coulomb force: F_coulomb = {gold['F_coulomb (N)']:.3e} N")
|
||
print(f"Agreement: {gold['Agreement (%)']:.2f}%")
|
||
print(f"This {gold['Agreement (%)']:.1f}% agreement for such a heavy, relativistic atom")
|
||
print("strongly supports the 3D ball model!")
|
||
|
||
|
||
print("-----------Authors note:-----------")
|
||
print("This script shows that the formula from version 23 was wrong.")
|
||
print("The universe is even simpler, when s=1 we have 100% agreement.")
|
||
print(" across the periodic table")
|
||
print("Or maybe we are still hallucinating.")
|
||
|
||
plt.show()
|
||
|
||
|
||
if __name__ == "__main__":
|
||
main()
|