THE GRAND UNIFIED THEORY OF CLASSICAL PHYSICS

Volume 1 of 3

THE GRAND UNIFIED THEORY

OF CLASSICAL PHYSICS

BY

Dr. Randell L. Mills

December 10, 2018 Edition Volume 1 of 3

Copyright © 2018 by Dr. Randell L. Mills

All rights reserved. No part of this work covered by copyright hereon may be reproduced or used in any form, or by any means-graphic, electronic, or mechanical, including photocopying, recording, taping, or information storage and retrieval systems-without written permission of Dr. Randell L. Mills. Manufactured in the United States of America.

ISBN 978-0-9635171-5-9 Library of Congress Control Number 2015915593

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TABLE OF CONTENTS VOLUME 1 ATOMIC PHYSICS Preface ..................................................................................................................................................................................... xxv References ............................................................................................................................................................................... xxvi INTRODUCTION I.1 General Considerations ............................................................................................................................................... 1 I.2 CP Approach to the Solution of the Bound Electron .................................................................................................. 3 I.2.1 Spin and Orbital Parameters Arise from First Principles Only in the Case of CP............................................................................................................................................. 4 Box I.1 Misinterpretations of Observations as Weirdness of Quantum Mechanics is Revealed to be Due to Atomic-Scale Classical Physics ........................................................................ 5 References ................................................................................................................................................................... 8 I.2.2 Three Atomic Theories ................................................................................................................................... 9 I.2.3 Mathematical Relationship Between the Theories of Bohr and Schrödinger with Respect to Classical Atomic Theory ....................................................................................................... 11 I.2.4 Shortcomings of Quantum Theory and Reasons for a Complete Revision of Atomic Theory ............................................................................................................................ 15 I.3 Classical Atomic Theory ............................................................................................................................................. 16 I.3.1 One-Electron Atoms ....................................................................................................................................... 17 I.3.1.1 Nonradiation Condition ................................................................................................................ 17 I.3.1.2 Electron Source Current ................................................................................................................ 17 I.3.1.3 Moment of Inertia and Spin and Rotational Energies ................................................................... 20 I.4 Spin Function ............................................................................................................................................................. 21 I.4.1 Generation of the BECVF ............................................................................................................................... 22 I.4.2 Generation of the OCVF ................................................................................................................................. 22 I.4.3 Generation of 00 ( , ) Y ................................................................................................................................... 23 I.4.4 Force Balance Equation .................................................................................................................................. 25 I.4.5 Energy Calculations ........................................................................................................................................ 26 I.5 The Nature of the Photon is the Basis of Quantization and Existence of Excited and Hydrino States of Atomic Hydrogen ...................................................................................................... 26 I.5.1 Excited States .................................................................................................................................................. 27 I.5.2 Instability of Excited States ............................................................................................................................ 28 I.5.3 Hydrino States ................................................................................................................................................. 29 I.5.3.1 Extension of the Rydberg States to Lower Levels ........................................................................ 29 I.5.3.2 Photonic Equation ......................................................................................................................... 32 I.5.3.3 Stability of the “Ground” and Hydrino States .............................................................................. 32 I.5.3.4 Catalytic Lower-Energy Hydrogen Electronic Transitions .......................................................... 32 I.5.3.5 Catalyst Reaction Mechanism and Products ................................................................................. 33 I.5.3.6 Catalysts ........................................................................................................................................ 38 I.6 Outline of the Results of the Unified Theory Derived from First Principles .............................................................. 40 I.6.1 Foundations ..................................................................................................................................................... 40 I.6.2 Physical Concepts that Arise from CP Derivations on the Scale Range of 85 orders of Magnitude ............. 42 I.6.3 Summary of Foundations and Physical Phenomena Solved by Classical Physics ......................................... 44 References ................................................................................................................................................................... 50 1. The One-Electron Atom .............................................................................................................................................. 53 1.1 Electron Source Current .................................................................................................................................. 53 1.2 The Bound Electron “Atomic Orbital” ........................................................................................................... 57 1.2.1 Classical Physics of the de Broglie Relation ................................................................................ 61 1.3 Rotational Parameters of the Electron (Angular Momentum, Rotational Energy, Moment of Inertia) ........................................................................................................................... 62

1.3.1 Electron Mechanics and the Corresponding Classical Wave Equation for the Derivation of the Rotational Parameters of the Electron ................................... 63

1.4 The Atomic Orbital Equation of Motion for = 0 Based on the Current Vector Field (CVF) ...................... 66 1.4.1 Stern-Gerlach-Experiment Boundary Condition .......................................................................... 66 1.5 Generation of the Atomic Orbital-CVFS ........................................................................................................ 68 1.5.1 Generation of the BECVF ............................................................................................................. 69

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1.5.2 Generation of the OCVF ............................................................................................................... 73 1.5.3 Generation of 00 ( , )Y ................................................................................................................. 76 1.5.4 Uniformity of 00 ( , )Y ................................................................................................................. 81

1.6 Spin Angular Momentum of the Atomic Orbital Y00 , with = 0 ........................................................... 86

1.7 Resonant Precession of the Spin-1/2-Current-Density Function Gives Rise to the Bohr Magneton ............................................................................................................................. 88 1.8 Magnetic Parameters of the Electron (Bohr Magneton) ................................................................................. 92 1.8.1 The Magnetic Field of an Atomic Orbital from Spin ................................................................... 92 1.8.2 Derivation of the Magnetic Field .................................................................................................. 93 1.8.3 Derivation of the Energy ............................................................................................................... 94 Box 1.1 Boundary Conditions of the Electron in a Magnetic Field are Met .......................................................... 95 References ................................................................................................................................................................... 98 1.9 Electron g Factor ............................................................................................................................................. 99 1.9.1 Stored Magnetic Energy ............................................................................................................... 99 1.9.2 Stored Electric Energy .................................................................................................................. 100 1.9.3 Dissipated Energy ......................................................................................................................... 103 1.9.4 Total Energy of Spin-Flip Transition ............................................................................................ 104 1.10 Determination of Atomic Orbital Radii .......................................................................................................... 107 1.11 Energy Calculations ........................................................................................................................................ 110

1.12 Special Relativistic Effect on the Electron Radius and the Relativistic Ionization Energies ......................................................................................................................................... 113

References ................................................................................................................................................................... 123 2. Excited States of the One-Electron Atom (Quantization) ........................................................................................... 125 2.1 Equation of the Electric Field inside the Atomic Orbital ............................................................................... 125 2.2 Photon Absorption .......................................................................................................................................... 129 2.3 Instability of Excited States ............................................................................................................................ 130 2.4 Source Current of Excited States .................................................................................................................... 131 2.5 Selection Rules................................................................................................................................................ 133 2.6 Orbital and Spin Splitting ............................................................................................................................... 134 2.7 Stark Effect ..................................................................................................................................................... 136 2.8 State Lifetimes and Line Intensities ................................................................................................................ 139 Box 2.1 Condensed Formula for the Excited-State Lifetimes and Line Intensities .............................................. 149 2.9 Resonant Line Shape....................................................................................................................................... 151 2.10 Hydrogen Lamb Shift ..................................................................................................................................... 152 2.10.1 Energy Calculations ...................................................................................................................... 153 2.11 Muonic Hydrogen Lamb Shift ........................................................................................................................ 155 2.11.1 Energy Calculations ...................................................................................................................... 156 2.12 Hydrogen Spin-Orbit Coupling (Fine Structure) ............................................................................................ 157 2.12.1 Energy Calculations ...................................................................................................................... 159 2.13 Hydrogen Knight Shift .................................................................................................................................... 160 2.14 Spin-Nuclear Coupling (Hyperfine Structure) ................................................................................................ 160 2.14.1 Energy Calculations ...................................................................................................................... 162 2.15 Muonium Hyperfine Structure Interval .......................................................................................................... 163 2.15.1 Energy Calculations ...................................................................................................................... 164 References ................................................................................................................................................................... 166 3. Electron in Free Space ................................................................................................................................................ 169 3.1 Charge-Density Function ................................................................................................................................ 169 3.2 Electric Field of a Free Electron ..................................................................................................................... 172 3.3 Current-Density Function ............................................................................................................................... 174 3.4 Force Balance Based on the Radiation-Reaction Force .................................................................................. 177 3.5 Classical Physics of the de Broglie Relation .................................................................................................. 179 3.6 Stern-Gerlach Experiment .............................................................................................................................. 181 3.7 Free-Electron g Factor .................................................................................................................................... 188 3.7 Free-Electron Binding ..................................................................................................................................... 188 References ................................................................................................................................................................... 189 4. Equation of the Photon................................................................................................................................................ 191 4.1 Right and Left Hand Circular and Elliptically Polarized Photons .................................................................. 191 4.2 Fields Based on Invariance Under Gauss’ Integral Law ................................................................................ 194 4.3 Linear Polarized Photons ................................................................................................................................ 196

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4.4 Spherical Wave ............................................................................................................................................... 196 4.5 Photon Torpedoes ........................................................................................................................................... 197 4.6 Photoelectric Effect ......................................................................................................................................... 197 4.7 Compton Effect ............................................................................................................................................... 199 4.8 Transitions....................................................................................................................................................... 200 4.9 Free Electron Photon Absorption.................................................................................................................... 201 References ................................................................................................................................................................... 202 5. Hydrino Theory—BlackLight Process ....................................................................................................................... 203 5.1 BlackLight Process ......................................................................................................................................... 203 5.2 Energy Transfer Mechanism ........................................................................................................................... 207 5.3 Energy Hole Concept ...................................................................................................................................... 208 5.4 Catalysts .......................................................................................................................................................... 213 5.5 Energy Hole as a Multipole Expansion .......................................................................................................... 216 5.6 Disproportionation of Energy States ............................................................................................................... 217 5.7 Dipole-Dipole Coupling.................................................................................................................................. 222 5.8 Interstellar Disproportion Rate ....................................................................................................................... 224 5.9 Power Density of Gaseous Reactions ............................................................................................................ 225 5.10 Hydrino Catalyzed Fusion (HCF) ................................................................................................................... 227 5.11 Molecular BlackLight Process ........................................................................................................................ 228 5.11.1 Below “Ground” State Transitions of Hydrogen-Type Molecules and Molecular Ions ............... 228 5.11.2 Energy Holes ................................................................................................................................. 228 5.11.3 Catalytic Energy Holes for Hydrogen-Type Molecules ............................................................... 231 References ................................................................................................................................................................... 232 6. Stability of Atoms and Hydrinos ................................................................................................................................ 235 6.1 Stability of “Ground” and Hydrino States ...................................................................................................... 236 6.2 New “Ground” State ....................................................................................................................................... 236 6.3 Spin-Nuclear and Orbital-Nuclear Coupling of Hydrinos .............................................................................. 237 6.3.1 Energy Calculations ...................................................................................................................... 238 6.4 A Coefficient ................................................................................................................................................... 240 6.5 Intensity of Spin-Nuclear and Orbital-Nuclear Coupling Transitions of Hydrinos ........................................ 240 References ................................................................................................................................................................... 240 7. Two-Electron Atoms ................................................................................................................................................... 243 7.1 Determination of Atomic Orbital Radii .......................................................................................................... 243 7.2 Energy Calculations ........................................................................................................................................ 251 7.2.1 Conservation of Energy ................................................................................................................ 252 7.2.2 Ionization Energies ...................................................................................................................... 254 7.2.3 Dissipated Energy ......................................................................................................................... 254 7.3 Hydride Ion ..................................................................................................................................................... 257 7.3.1 Determination of the Atomic Orbital Radius, rn ......................................................................... 258 7.3.2 Ionization Energy .......................................................................................................................... 258 7.4 Hydrino Hydride Ion ....................................................................................................................................... 260 7.5 Hydrino Hydride Ion Nuclear Magnetic Resonance Shift .............................................................................. 261 7.6 Hydrino Hydride Ion Hyperfine Lines ............................................................................................................ 263 References ................................................................................................................................................................... 265 8. Classical Photon and Electron Scattering ................................................................................................................... 267 8.1 Classical Scattering of Electromagnetic Radiation ......................................................................................... 267 8.1.1 Delta Function ............................................................................................................................... 267 8.1.2 The Array Theorem ...................................................................................................................... 268 8.1.3 Applications of the Array Theorem ............................................................................................. 268 8.1.3.1 Two-Slit Interference (Wave-Particle Duality) .......................................................... 268 8.2 Classical Wave Theory of Electron Scattering ............................................................................................... 271 8.2.1 Classical Wave Theory Applied to Scattering from Atoms and Molecules ................................ 274 8.3 Electron Scattering Equation for the Helium Atom Based on the Atomic Orbital Model ............................. 276 8.3.1 Results ........................................................................................................................................... 278 8.4 Discussion ...................................................................................................................................................... 280 8.5 Physics of Classical Electron Diffraction Resolves the Wave-Particle Duality Mystery of Quantum Mechanics ....................................................................................................................................... 281 8.6 Equations of Classical Diffraction .................................................................................................................. 284 References ................................................................................................................................................................... 286 9. Excited States of Helium ............................................................................................................................................ 287

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9.1 Singlet Excited States with = 0 ( 12 11 1s s ns ) ....................................................................................... 289 9.2 Triplet Excited States with = 0 ( 12 11 1s s ns ) ........................................................................................ 291 9.3 Singlet Excited States with ≠ 0 ................................................................................................................... 293 9.4 Triplet Excited States with ≠ 0 .................................................................................................................... 296 9.5 All Excited He I States .................................................................................................................................... 299 9.6 Spin-Orbit Coupling of Excited States with ≠ 0 ......................................................................................... 303 References ................................................................................................................................................................... 304 10. Three- Through Twenty-Electron Atoms ................................................................................................................... 305 10.1 Three-Electron Atoms ..................................................................................................................................... 305 10.1.1 The Lithium Atom ........................................................................................................................ 305 10.1.2 The Radius of the Outer Electron of the Lithium Atom ............................................................... 309 10.1.3 The Ionization Energy of Lithium ................................................................................................ 309 10.1.4 Three Electron Atoms with a Nuclear Charge Z>3 ...................................................................... 310 10.1.5 The Radius of the Outer Electron of Three-Electron Atoms with a Nuclear Charge Z>3 ........... 312 10.1.6 The Ionization Energies of Three-Electron Atoms with a Nuclear Charge Z>3 .......................... 313 10.2 Four-Electron Atoms ...................................................................................................................................... 315 10.2.1 Radii of the Outer Electrons of Four-Electron Atoms .................................................................. 315 10.2.2 Energies of the Beryllium Atom ................................................................................................... 316 10.2.3 The Ionization Energies of Four-Electron Atoms with a Nuclear Charge Z>4 ............................ 317 10.3 2P-Orbital Electrons Based on an Energy Minimum ..................................................................................... 319 10.4 Five-Electron Atoms ....................................................................................................................................... 322 10.4.1 Radius and Ionization Energy of the Outer Electron of the Boron Atom ..................................... 322 10.4.2 The Ionization Energies of Five-Electron Atoms with a Nuclear Charge Z>5 ............................ 323 10.5 Six-Electron Atoms ......................................................................................................................................... 326 10.5.1 Radius and Ionization Energy of the Outer Electron of the Carbon Atom ................................... 326 10.5.2 The Ionization Energies of Six-Electron Atoms with a Nuclear Charge Z>6 .............................. 327 10.6 Seven-Electron Atoms .................................................................................................................................... 329 10.6.1 Radius and Ionization Energy of the Outer Electron of the Nitrogen Atom ................................ 329 10.6.2 The Ionization Energies of Seven-Electron Atoms with a Nuclear Charge Z>7 .......................... 330 10.7 Eight-Electron Atoms ..................................................................................................................................... 333 10.7.1 Radius and Ionization Energy of the Outer Electron of the Oxygen Atom .................................. 333 10.7.2 The Ionization Energies of Eight-Electron Atoms with a Nuclear Charge Z>8 ........................... 334 10.8 Nine-Electron Atoms ...................................................................................................................................... 337 10.8.1 Radius and Ionization Energy of the Outer Electron of the Fluorine Atom ................................. 337 10.8.2 The Ionization Energies of Nine-Electron Atoms with a Nuclear Charge Z>9 ............................ 338 10.9 Ten-Electron Atoms ........................................................................................................................................ 341 10.9.1 Radius and Ionization Energy of the Outer Electron of the Neon Atom ...................................... 341 10.9.2 The Ionization Energies of Ten-Electron Atoms with a Nuclear Charge Z>10 ........................... 342 10.10 General Equation for the Ionization Energies of Five Through Ten-Electron Atoms .................................... 344 10.11 Eleven-Electron Atoms ................................................................................................................................... 346 10.11.1 Radius and Ionization Energy of the Outer Electron of the Sodium Atom .................................. 346 10.11.2 The Ionization Energies of Eleven-Electron Atoms with a Nuclear Charge Z>11 ...................... 348 10.12 Twelve-Electron Atoms .................................................................................................................................. 350 10.12.1 Radius and Ionization Energy of the Outer Electron of the Magnesium Atom ............................ 350 10.12.2 The Ionization Energies of Twelve-Electron Atoms with a Nuclear Charge Z>12 ..................... 352 10.13 3P-Orbital Electrons Based on an Energy Minimum ..................................................................................... 354 10.14 Thirteen-Electron Atoms ................................................................................................................................ 357 10.14.1 Radius and Ionization Energy of the Outer Electron of the Aluminum Atom ............................. 357 10.14.2 The Ionization Energies of Thirteen-Electron Atoms with a Nuclear Charge Z>13 .................... 358 10.15 Fourteen-Electron Atoms ................................................................................................................................ 361 10.15.1 Radius and Ionization Energy of the Outer Electron of the Silicon Atom ................................... 361 10.15.2 The Ionization Energies of Fourteen-Electron Atoms with a Nuclear Charge Z>14 ................... 362 10.16 Fifteen-Electron Atoms ................................................................................................................................... 364 10.16.1 Radius and Ionization Energy of the Outer Electron of the Phosphorous Atom .......................... 364 10.16.2 The Ionization Energies of Fifteen-Electron Atoms with a Nuclear Charge Z>15 ...................... 366 10.17 Sixteen-Electron Atoms .................................................................................................................................. 368 10.17.1 Radius and Ionization Energy of the Outer Electron of the Sulfur Atom ..................................... 368 10.17.2 The Ionization Energies of Sixteen-Electron Atoms with a Nuclear Charge Z>16 ..................... 369 10.18 Seventeen-Electron Atoms .............................................................................................................................. 371 10.18.1 Radius and Ionization Energy of the Outer Electron of the Chlorine Atom ................................. 371

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10.18.2 The Ionization Energies of Seventeen-Electron Atoms with a Nuclear Charge Z>17 ................. 373 10.19 Eighteen-Electron Atoms ................................................................................................................................ 375 10.19.1 Radius and Ionization Energy of the Outer Electron of the Argon Atom .................................... 375 10.19.2 The Ionization Energies of Eighteen-Electron Atoms with a Nuclear Charge Z>18 ................... 377 10.20 General Equation for the Ionization Energies of Thirteen Through Eighteen-Electron Atoms .................... 379 10.21 Nineteen-Electron Atoms ................................................................................................................................ 382 10.21.1 Radius and Ionization Energy of the Outer Electron of the Potassium Atom .............................. 382 10.21.2 The Ionization Energies of Nineteen-Electron Atoms with a Nuclear Charge Z>19 ................... 383 10.22 Twenty-Electron Atoms .................................................................................................................................. 385 10.22.1 Radius and Ionization Energy of the Outer Electron of the Calcium Atom ................................ 385 10.22.2 The Ionization Energies of Twenty-Electron Atoms with a Nuclear Charge Z>20 ..................... 387 10.23 General Equation for the Ionization Energies of Atoms Having an Outer S-Shell ....................................... 389 10.24 The Electron Configuration of Atoms ............................................................................................................ 392 References ................................................................................................................................................................... 392

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TABLE OF CONTENTS VOLUME 2 MOLECULAR PHYSICS 11. The Nature of the Chemical Bond of Hydrogen-Type Molecules and Molecular Ions .............................................. 393 11.1 Hydrogen-Type Molecular Ions ...................................................................................................................... 393 11.1.1 Spheroidal Force Equations .......................................................................................................... 397 11.1.1.1 Electric Force ................................................................................................................. 397 11.1.1.2 Centrifugal Force ........................................................................................................... 402 11.1.1.3 Force Balance of Hydrogen-Type Molecular Ions ........................................................ 405 11.1.2 Energies of Hydrogen-Type Molecular Ions ................................................................................ 406 11.1.3 Vibration of Hydrogen-Type Molecular Ions ............................................................................... 407 11.1.4 The Doppler Energy Term of Hydrogen-Type Molecular Ions .................................................... 411 11.1.5 Total, Ionization, and Bond Energies of Hydrogen and Deuterium Molecular Ions .................... 413 11.2 Hydrogen-Type Molecules ............................................................................................................................. 414 11.2.1 Force Balance of Hydrogen-Type Molecules ............................................................................... 414 11.2.2 Energies of Hydrogen-Type Molecules ........................................................................................ 418 11.2.3 Vibration of Hydrogen-Type Molecules ....................................................................................... 419 11.2.4 The Doppler Energy Term of Hydrogen-Type Molecules ........................................................... 421 11.2.5 Total, Ionization, and Bond Energies of Hydrogen and Deuterium Molecules ............................ 422 11.3 The Hydrogen Molecular Ion .......................................................................................................................... 423 11.3.1 Force Balance of the Hydrogen Molecular Ion ............................................................................. 423 11.3.2 Energies of the Hydrogen Molecular Ion...................................................................................... 423 11.3.3 Vibration of the Hydrogen Molecular Ion .................................................................................... 424 11.4 The Hydrogen Molecule ................................................................................................................................. 425 11.4.1 Force Balance of the Hydrogen Molecule .................................................................................... 425 11.4.2 Energies of the Hydrogen Molecule ............................................................................................. 425 11.4.3 Vibration of the Hydrogen Molecule ............................................................................................ 426 11.5 The Dihydrino Molecular Ion ......................................................................................................................... 429 11.5.1 Force Balance of the Dihydrino Molecular Ion ............................................................................ 429 11.5.2 Energies of the Dihydrino Molecular Ion ..................................................................................... 429 11.5.3 Vibration of the Dihydrino Molecular Ion .................................................................................... 430 11.6 The Dihydrino Molecule ................................................................................................................................. 430 11.6.1 Force Balance of the Dihydrino Molecule .................................................................................... 430 11.6.2 Energies of the Dihydrino Molecule ............................................................................................. 430 11.6.3 Vibration of the Dihydrino Molecule ........................................................................................... 431 11.7 Geometry......................................................................................................................................................... 431 11.8 Dihydrino Ionization Energies ........................................................................................................................ 432 11.9 Sizes of Representative Atoms and Molecules ............................................................................................... 432 11.9.1 Atoms ............................................................................................................................................ 432 11.9.2 Molecules ...................................................................................................................................... 433 11.10 Nuclear Spin-Spin Transition of Hydrogen-Type Molecules ......................................................................... 434 11.11 Nuclear Magnetic Resonance Shift ................................................................................................................. 434 11.12 Quadrupole Moment ....................................................................................................................................... 435 References ................................................................................................................................................................... 440 12. Diatomic Molecular Energy States ............................................................................................................................. 443 12.1 Excited Electronic States of Ellipsoidal Molecular Orbitals .......................................................................... 443 12.2 Excited States of the Hydrogen Molecular Ion ............................................................................................... 443

12.2.1 Force Balance of the Excited States of the Hydrogen Molecular Ion .......................................... 443 12.2.2 Energies of the Excited States of the Hydrogen Molecular Ion .................................................... 444 12.2.3 Vibration of the Excited States of the Hydrogen Molecular Ion .................................................. 445

12.3 Magnetic Moment of an Ellipsoidal Molecular Orbital .................................................................................. 445 12.4 Magnetic Field of an Ellipsoidal Molecular Orbital ....................................................................................... 446 12.5 Excited States of the Hydrogen Molecule ...................................................................................................... 448 12.5.1 Force Balance of the Excited States of the Hydrogen Molecule .................................................. 448 12.5.1.1 Singlet Excited States .................................................................................................... 448 12.5.1.2 Triplet Excited States ..................................................................................................... 449 12.5.2 Energies of the Excited States of the Hydrogen Molecule ........................................................... 450

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12.6 Diatomic Molecular Rotation ......................................................................................................................... 453 12.6.1 Diatomic Molecular Rotation of Hydrogen-Type Molecules ....................................................... 453 12.6.2 Diatomic Molecular Rotation of Hydrogen-Type Molecular Ions ............................................... 454 12.7 Centrifugal Distortion ..................................................................................................................................... 454 References ................................................................................................................................................................... 458 13. General Diatomic and Polyatomic Molecular Ions and Molecules ............................................................................ 459 13.1 Triatomic Molecular Hydrogen-type Ion ( 3H

) .............................................................................................. 459 13.1.1 Force Balance of 3H

-Type Molecular Ions ................................................................................. 459 13.1.2 Energies of 3H

-Type Molecular Ions .......................................................................................... 461 13.1.3 Vibration of 3H

-Type Molecular Ions ......................................................................................... 461 13.1.4 The Doppler Energy Term of 3H

-Type Molecular Ions ............................................................. 462 13.1.5 Total and Bond Energies of 3 1/H p - and 3 1/D p -Type Molecular Ions ............................ 463 13.2 The 3H

Molecular Ion ................................................................................................................................... 464 13.2.1 Force Balance of the 3H

Molecular Ion ...................................................................................... 464 13.2.2 Energies of the 3H

Molecular Ion ............................................................................................... 464 13.3 Hydroxyl Radical (OH ) ................................................................................................................................. 465 13.3.1 Force Balance of OH ................................................................................................................... 466 13.3.2 Energies of OH ............................................................................................................................ 471 13.3.3 Vibration and Rotation of OH ..................................................................................................... 471 13.3.4 The Doppler Energy Terms of 16OH and 16OD .......................................................................... 474 13.3.5 Total and Bond Energies of 16OH and 16OD Radicals ................................................................ 475 13.4 Water Molecule ( 2H O ) .................................................................................................................................. 476 13.4.1 Force Balance of 2H O .................................................................................................................. 476 13.4.2 Energies of 2H O ........................................................................................................................... 481 13.4.3 Vibration of 2H O ......................................................................................................................... 481 13.4.4 The Doppler Energy Term of 2H O .............................................................................................. 482 13.4.5 Total and Bond Energies of 16H OH and 16D OD ....................................................................... 483 13.4.6 Bond Angle of 2H O ..................................................................................................................... 484 13.5 Hydrogen Nitride ( NH ) ................................................................................................................................. 485 13.5.1 Force Balance of NH ................................................................................................................... 486 13.5.2 Energies of NH ............................................................................................................................ 489 13.5.3 Vibration and Rotation of NH ..................................................................................................... 489 13.5.4 The Doppler Energy Terms of 14NH and 14ND .......................................................................... 491 13.5.5 Total and Bond Energies of 14NH and 14ND ............................................................................... 491 13.6 Dihydrogen Nitride ( 2NH ) ............................................................................................................................. 493 13.6.1 Force Balance of 2NH .................................................................................................................. 493 13.6.2 Energies of 2NH ........................................................................................................................... 495 13.6.3 Vibration of 2NH ......................................................................................................................... 495 13.6.4 The Doppler Energy Term of 2NH .............................................................................................. 496 13.6.5 Total and Bond Energies of 14 2NH and

142ND ............................................................................. 497

13.6.6 Bond Angle of 2NH ..................................................................................................................... 498 13.7 Ammonia ( 3NH ) ............................................................................................................................................. 499 13.7.1 Force Balance of 3NH .................................................................................................................. 499 13.7.2 Energies of 3NH ........................................................................................................................... 502 13.7.3 Vibration of 3NH .......................................................................................................................... 502 13.7.4 The Doppler Energy Term of 3NH .............................................................................................. 502 13.7.4 Total and Bond Energies of 14 3NH and

143ND ............................................................................. 503

13.7.5 Bond Angle of 3NH ..................................................................................................................... 504 13.8 Hydrogen Carbide (CH ) ................................................................................................................................ 505 13.8.1 Force Balance of CH ................................................................................................................... 505

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13.8.2 Energies of CH ............................................................................................................................ 509 13.8.3 Vibration and Rotation of CH ..................................................................................................... 509 13.8.4 The Doppler Energy Terms of 12CH and 12CD ........................................................................... 511 13.8.5 Total and Bond Energies of 12CH and 12CD ............................................................................... 511 13.9 Dihydrogen Carbide ( 2CH ) ............................................................................................................................ 513 13.9.1 Force Balance of 2CH .................................................................................................................. 513 13.9.2 Energies of 2CH ........................................................................................................................... 516 13.9.3 Vibration of 2CH .......................................................................................................................... 516 13.9.4 The Doppler Energy Terms of 12 2CH ........................................................................................... 516 13.9.5 Total and Bond Energies of 12 2CH ............................................................................................... 517 13.9.6 Bond Angle of 12 2CH ................................................................................................................... 518 13.10 Methyl Radical ( 3CH ) .................................................................................................................................... 519 13.10.1 Force Balance of 3CH .................................................................................................................. 519 13.10.2 Energies of 3CH ........................................................................................................................... 522 13.10.3 Vibration of 3CH .......................................................................................................................... 522 13.10.4 The Doppler Energy Terms of 12 3CH ........................................................................................... 522 13.10.5 Total and Bond Energies of 12 3CH ............................................................................................... 523 13.10.6 Bond Angle of 12 3CH ................................................................................................................... 524 13.11 Methane Molecule ( 4CH ) .............................................................................................................................. 524 13.11.1 Force Balance of 4CH .................................................................................................................. 524 13.11.2 Energies of 4CH ........................................................................................................................... 528 13.11.3 Vibration of 4CH .......................................................................................................................... 529 13.11.4 The Doppler Energy Terms of 12 4CH ........................................................................................... 529 13.11.5 Total and Bond Energies of 12 4CH ............................................................................................... 530 13.12 Nitrogen Molecule .......................................................................................................................................... 531

13.12.1 Force Balance of the 2 p Shell of the Nitrogen Atoms of the Nitrogen Molecule ....................... 531 13.12.2 Energies of the 2 p Shell of the Nitrogen Atoms of the Nitrogen Molecule ............................... 533

13.12.3 Force Balance of the MO of the Nitrogen Molecule ............................................................... 533 13.12.4 Sum of the Energies of the MO and the AOs of the Nitrogen Molecule ................................. 534 13.12.5 Vibration of 2N ............................................................................................................................ 535 13.12.6 The Doppler Energy Terms of the Nitrogen Molecule ................................................................. 535 13.12.7 Total and Bond Energies of the Nitrogen Molecule ..................................................................... 536 13.13 Oxygen Molecule ............................................................................................................................................ 536 13.13.1 Force Balance of the 2 p Shell of the Oxygen Atoms of the Oxygen Molecule .......................... 537 13.13.2 Energies of the 2 p Shell of the Oxygen Atoms of the Oxygen Molecule ................................... 538 13.13.3 Force Balance of the MO of the Oxygen Molecule ................................................................. 538 13.13.4 Sum of the Energies of the MO and the AOs of the Oxygen Molecule .................................. 540 13.13.5 Vibration of 2O ............................................................................................................................. 540 13.13.6 The Doppler Energy Terms of the Oxygen Molecule .................................................................. 540 13.13.7 Total and Bond Energies of the Oxygen Molecule ....................................................................... 541 13.14 Fluorine Molecule ........................................................................................................................................... 542 13.14.1 Force Balance of the 2 p Shell of the Fluorine Atoms of the Fluorine Molecule ........................ 542 13.14.2 Energies of the 2 p Shell of the Fluorine Atoms of the Fluorine Molecule ................................. 544 13.14.3 Force Balance of the MO of the Fluorine Molecule ................................................................ 544 13.14.4 Sum of the Energies of the MO and the AOs of the Fluorine Molecule ................................. 545 13.14.5 Vibration of 2F ............................................................................................................................. 546 13.14.6 The Doppler Energy Terms of the Fluorine Molecule .................................................................. 546 13.14.7 Total and Bond Energies of the Fluorine Molecule ...................................................................... 546 13.15 Chlorine Molecule .......................................................................................................................................... 547 13.15.1 Force Balance of 2Cl .................................................................................................................... 547 13.15.2 Energies of 2Cl ............................................................................................................................. 552

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13.15.3 Vibration and Rotation of 2Cl ...................................................................................................... 552 13.15.4 The Doppler Energy Terms of 2Cl ............................................................................................... 553 13.15.5 Total and Bond Energies of 2Cl ................................................................................................... 554 13.16 Carbon Nitride Radical ................................................................................................................................... 554 13.16.1 Force Balance of the 2 p Shell of the Carbon Atom of the Carbon Nitride Radical ................... 555 13.16.2 Force Balance of the 2 p Shell of the Nitrogen Atom of the Carbon Nitride Radical ................. 556 13.16.3 Energies of the 2 p Shells of the Carbon and Nitrogen Atoms of the Carbon Nitride Radical ... 557 13.16.4 Force Balance of the MO of the Carbon Nitride Radical ........................................................ 558 13.16.5 Sum of the Energies of the MO and the AOs of the Carbon Nitride Radical .......................... 559 13.16.6 Vibration of CN ........................................................................................................................... 560 13.16.7 The Doppler Energy Terms of the Carbon Nitride Radical .......................................................... 560 13.16.8 Total and Bond Energies of the Carbon Nitride Radical .............................................................. 561 13.17 Carbon Monoxide Molecule ........................................................................................................................... 562 13.17.1 Force Balance of the 2 p Shell of the Oxygen Atom of the Carbon Monoxide Molecule ............ 562 13.17.2 Energies of the 2s and 2 p Shells of the Carbon Atom and the 2 p Shell of the Oxygen Atom of the Carbon Monoxide Molecule ..................................................................................... 564 13.17.3 Force Balance of the MO of the Carbon Monoxide Molecule ................................................ 564 13.17.4 Sum of the Energies of the MO and the AOs of the Carbon Monoxide Molecule .................. 565 13.17.5 Vibration of CO ........................................................................................................................... 566 13.17.6 The Doppler Energy Terms of the Carbon Monoxide Molecule .................................................. 566 13.17.7 Total and Bond Energies of the Carbon Monoxide Molecule ...................................................... 567 13.18 Nitric Oxide Radical ....................................................................................................................................... 568 13.18.1 Force Balance of the 2 p Shell of the Nitrogen Atoms of the Nitric Oxide Radical ................... 568 13.18.2 Force Balance of the 2 p Shell of the Oxygen Atom of the Nitric Oxide Radical ....................... 570 13.18.3 Energies of the 2 p Shells of the Nitrogen Atom and Oxygen Atom of the Nitric Oxide Radical ................................................................................................................................ 571 13.18.4 Force Balance of the MO of the Nitric Oxide Radical ............................................................ 572 13.18.5 Sum of the Energies of the MO and the AOs of the Nitric Oxide Radical .............................. 573 13.18.6 Vibration of NO ........................................................................................................................... 574 13.18.7 The Doppler Energy Terms of the Nitric Oxide Radical .............................................................. 574 13.18.8 Total and Bond Energies of the Nitric Oxide Radical .................................................................. 575 References ................................................................................................................................................................... 578 14. More Polyatomic Molecules and Hydrocarbons ......................................................................................................... 581 14.1 Carbon Dioxide Molecule ............................................................................................................................... 581

14.1.1 Force Balance of the 2p Shell of the Oxygen Atom of the Carbon Dioxide Molecule ................ 582 14.1.2 Energies of the 2s and 2p Shells of the Carbon Atom and the 2p Shell of the Oxygen Atoms of the Carbon Dioxide Molecule ......................................................................... 583

14.1.3 Force Balance of the MO of the Carbon Dioxide Molecule .................................................... 583 14.1.4 Sum of the Energies of the MO and the AOs of the Carbon Dioxide Molecule ..................... 587

14.1.5 Vibration of 2CO .......................................................................................................................... 587 14.1.6 The Doppler Energy Terms of the Carbon Dioxide Molecule ..................................................... 588 14.1.7 Total and Bond Energies of the Carbon Dioxide Molecule .......................................................... 588 14.2 Nitrogen Dioxide Molecule ............................................................................................................................ 589

14.2.1 Force Balance of the 2p Shell of the Nitrogen Atom of Nitrogen Dioxide .................................. 590 14.2.2 Force Balance of the 2p Shell of Each Oxygen Atom of Nitrogen Dioxide ................................. 591 14.2.3 Energies of the 2p Shells of the Nitrogen Atom and Oxygen Atoms of Nitrogen Dioxide ......... 592

14.2.4 Force Balance of the MO of Nitrogen Dioxide ....................................................................... 593 14.2.5 Sum of the Energies of the MOs and the AOs of Nitrogen Dioxide ....................................... 595

14.2.6 Vibration of 2NO .......................................................................................................................... 596 14.2.7 The Doppler Energy Terms of Nitrogen Dioxide ......................................................................... 596 14.2.8 Total and Bond Energies of Nitrogen Dioxide ............................................................................. 597 14.2.9 Bond Angle of 2NO ...................................................................................................................... 598 14.3 Ethane Molecule ............................................................................................................................................. 599 14.3.1 Force Balance of the C C -Bond MO of Ethane ........................................................................ 599 14.3.2 Force Balance of the 3CH MOs of Ethane ................................................................................... 604 14.3.3 Bond Angle of the 3CH Groups ................................................................................................... 606

x

14.3.4 Energies of the 3CH Groups......................................................................................................... 609 14.3.5 Vibration of the 12 3CH Groups ..................................................................................................... 609 14.3.6 The Doppler Energy Terms of the 12 3CH Groups ........................................................................ 609 14.3.7 Total and Difference Energies f the 12 3CH Groups ...................................................................... 610 14.3.8 Sum of the Energies of the C C MO and the HOs of Ethane ............................................... 610 14.3.9 Vibration of Ethane ....................................................................................................................... 611 14.3.10 The Doppler Energy Terms of the C C -Bond MO of Ethane ................................................... 611 14.3.11 Total Energies of the C C -Bond MO of Ethane ........................................................................ 612 14.3.12 Bond Energy of the C C Bond of Ethane .................................................................................. 612 14.4 Ethylene Molecule .......................................................................................................................................... 612 14.4.1 Force Balance of the C C -Bond MO of Ethylene .................................................................... 613 14.4.2 Force Balance of the 2CH MOs of Ethylene ............................................................................... 617 14.4.3 Bond Angle of the 2CH Groups ................................................................................................... 619 14.4.4 Energies of the 2CH Groups ........................................................................................................ 621 14.4.5 Vibration of the 12 2CH Groups ..................................................................................................... 622 14.4.6 The Doppler Energy Terms of the 12 2CH Groups ........................................................................ 622 14.4.7 Total and Difference Energies of the 12 2CH Groups .................................................................... 622 14.4.8 Sum of the Energies of the C C MO and the HOs of Ethylene ............................................ 623 14.4.9 Vibration of Ethylene .................................................................................................................... 624 14.4.10 The Doppler Energy Terms of the C C -Bond MO of Ethylene ............................................... 624 14.4.11 Total Energies of the C C -Bond MO of Ethylene .................................................................... 625 14.4.12 Bond Energy of the C C -Bond of Ethylene.............................................................................. 625 14.5 Acetylene Molecule ........................................................................................................................................ 626 14.5.1 Force Balance of the C C -Bond MO of Acetylene .................................................................. 626 14.5.2 Force Balance of the CH MOs of Acetylene .............................................................................. 630 14.5.3 Energies of the CH Groups ......................................................................................................... 632 14.5.4 Vibration of the 12CH Groups ...................................................................................................... 632 14.5.5 The Doppler Energy Terms of the 12CH Groups ......................................................................... 632 14.5.6 Total and Difference Energies of the 12CH Groups ..................................................................... 633

14.5.7 Sum of the Energies of the C C MO and the HOs of Acetylene .......................................... 634 14.5.8 Vibration of Acetylene .................................................................................................................. 634

14.5.9 The Doppler Energy Terms of the C C -Bond MO of Acetylene ............................................. 635 14.5.10 Total Energies of the C C -Bond MO of Acetylene .................................................................. 635 14.5.11 Bond Energy of the C C Bond of Acetylene ............................................................................ 636 14.6 Benzene Molecule ........................................................................................................................................... 636 14.6.1 Force Balance of the C C -Bond MO of Benzene ..................................................................... 636 14.6.2 Force Balance of the CH MOs of Benzene ................................................................................. 640 14.6.3 Energies of the CH Groups ......................................................................................................... 643 14.6.4 Vibration of the 12CH Groups ...................................................................................................... 644 14.6.5 The Doppler Energy Terms of the 12CH Groups ......................................................................... 644 14.6.6 Total and Bond Energies of the 12CH Groups ............................................................................. 644

14.6.7 Sum of the Energies of the C C MO Element and the HOs of Benzene .............................. 645 14.6.8 Vibration of Benzene .................................................................................................................... 646

14.6.9 The Doppler Energy Terms of the C C -Bond MO Element of Benzene ................................. 646 14.6.10 Total Energies of the C C -Bond MO Element of Benzene ...................................................... 647 14.6.11 Total Bond Dissociation Energy of Benzene ................................................................................ 647 14.7 Continuous-Chain Alkanes ............................................................................................................................. 648

14.7.1 Force Balance of the C C -Bond MOs of Continuous-Chain Alkanes ...................................... 648 14.7.2 Force Balance of the 3CH MOs of Continuous-Chain Alkanes ................................................... 654 14.7.3 Bond Angle of the 3CH and 2CH Groups ................................................................................... 656 14.7.4 Energies of the 3CH Groups......................................................................................................... 658 14.7.5 Vibration of the 12 3CH Groups ..................................................................................................... 658 14.7.6 The Doppler Energy Terms of the 12 3CH Groups ........................................................................ 658 14.7.7 Total Bond Energies of the 12 3CH Groups ................................................................................... 659

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14.7.8 Force Balance of the 2CH MOs of Continuous-Chain Alkanes .................................................. 659 14.7.9 Energies of the 2CH Groups ........................................................................................................ 661 14.7.10 Vibration of the 12 2CH Groups ..................................................................................................... 662 14.7.11 The Doppler Energy Terms of the 12 2CH Groups ........................................................................ 662 14.7.12 Total Bond Energies of the 12 2CH Groups ................................................................................... 662

14.7.13 Sum of the Energies of the C C MOs and the HOs of Continuous-Chain Alkanes ............. 663 14.7.14 Vibration of Continuous-Chain Alkanes ...................................................................................... 664 14.7.15 The Doppler Energy Terms of the C C -Bond MOs of Continuous-Chain Alkanes ................. 664

14.7.16 Total Energies of the C C -Bond MOs of Continuous-Chain Alkanes ...................................... 664 14.7.17 Total Bond Energy of the C C Bonds of Continuous-Chain Alkanes ...................................... 665

14.7.18 Total Energy of Continuous-Chain Alkanes ................................................................................. 665 14.8 Propane ........................................................................................................................................................... 666 14.9 Butane ............................................................................................................................................................. 667 14.10 Pentane ............................................................................................................................................................ 668 14.11 Hexane ............................................................................................................................................................ 669 14.12 Heptane ........................................................................................................................................................... 670 14.13 Octane ............................................................................................................................................................. 671 14.14 Nonane ............................................................................................................................................................ 672 14.15 Decane ............................................................................................................................................................. 673 14.16 Undecane ......................................................................................................................................................... 674 14.17 Dodecane ......................................................................................................................................................... 675 14.18 Octadecane ...................................................................................................................................................... 676 References ................................................................................................................................................................... 678 15. Organic Molecular Functional Groups and Molecules ............................................................................................... 679

15.1 Derivation of the General Geometrical and Energy Equations of Organic Chemistry ................................... 679 15.2 MO Intercept Angles and Distances ............................................................................................................... 694 15.2.1 Bond Angles.................................................................................................................................. 694

15.2.2 Angles and Distances for an MO that Forms an Isosceles Triangle ............................................. 699 15.2.3 Dihedral Angle .............................................................................................................................. 699 15.2.4 General Dihedral Angle ................................................................................................................ 699 15.3 Solution of Geometrical and Energy Parameters of Major Functional Groups and Corresponding Organic Molecules .......................................................................................................................................... 701 15.3.1 Continuous-Chain Alkanes ........................................................................................................... 702 15.3.2 Branched Alkanes ......................................................................................................................... 707 15.3.3 Alkenes ......................................................................................................................................... 712 15.3.4 Alkynes ......................................................................................................................................... 718 15.3.5 Alkyl Fluorides ............................................................................................................................. 723 15.3.6 Alkyl Chlorides ............................................................................................................................. 728 15.3.7 Alkyl Bromides ............................................................................................................................. 734 15.3.8 Alkyl Iodides ................................................................................................................................. 739 15.3.9 Alkenyl Halides ............................................................................................................................ 745 15.3.10 Alcohols ........................................................................................................................................ 751 15.3.11 Ethers ............................................................................................................................................ 757 15.3.12 Primary Amines ............................................................................................................................ 763 15.3.13 Secondary Amines ........................................................................................................................ 768 15.3.14 Tertiary Amines ............................................................................................................................ 773 15.3.15 Aldehydes ..................................................................................................................................... 778 15.3.16 Ketones ......................................................................................................................................... 783 15.3.17 Carboxylic Acids .......................................................................................................................... 789 15.3.18 Carboxylic Acid Esters ................................................................................................................. 796 15.3.19 Amides .......................................................................................................................................... 804 15.3.20 Alkyl Amides ................................................................................................................................ 811 15.3.21 Urea ............................................................................................................................................... 818 15.3.22 Carboxylic Acid Halides ............................................................................................................... 822 15.3.23 Carboxylic Acid Anhydrides ........................................................................................................ 827 15.3.24 Nitriles........................................................................................................................................... 832 15.3.25 Thiols ............................................................................................................................................ 837 15.3.26 Sulfides ......................................................................................................................................... 844 15.3.27 Disulfides ...................................................................................................................................... 850

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15.3.28 Sulfoxides ..................................................................................................................................... 855 15.3.28.1 Dimethyl Sulfoxide Dihedral Angle ........................................................................... 860 15.3.29 Sulfones......................................................................................................................................... 861 15.3.30 Sulfites .......................................................................................................................................... 865 15.3.31 Sulfates .......................................................................................................................................... 871 15.3.32 Nitroalkanes .................................................................................................................................. 877 15.3.33 Alkyl Nitrites ................................................................................................................................ 882 15.3.34 Alkyl Nitrates ................................................................................................................................ 887 15.3.35 Cyclic and Conjugated Alkenes .................................................................................................... 892 15.3.36 Aromatic and Heterocyclic Compounds ....................................................................................... 898 15.3.37 Naphthalene .................................................................................................................................. 904 15.3.38 Toluene ......................................................................................................................................... 909 15.3.39 Halobenzenes ................................................................................................................................ 914 15.3.40 Phenol ........................................................................................................................................... 919 15.3.41 Aniline........................................................................................................................................... 923 15.3.42 Aryl Nitro Compounds ................................................................................................................. 928 15.3.43 Benzoic Acid Compounds ............................................................................................................ 932 15.3.44 Anisole .......................................................................................................................................... 938 15.3.45 Pyrrole ........................................................................................................................................... 942 15.3.46 Furan ............................................................................................................................................. 947 15.3.47 Thiophene ..................................................................................................................................... 951 15.3.48 Imidizole ....................................................................................................................................... 956 15.3.49 Pyridine ......................................................................................................................................... 961 15.3.50 Pyrimidine ..................................................................................................................................... 966 15.3.51 Pyrazine......................................................................................................................................... 970 15.3.52 Quinoline....................................................................................................................................... 974 15.3.53 Isoquinoline................................................................................................................................... 979 15.3.54 Indole ............................................................................................................................................ 984 15.3.56 Adenine ....................................................................................................................................