Valence-Bond Theory of the Hydrogen Molecule

 

1/3 The first successful explanation of chemical bonding using quantum mechanics was provided by the simple computation of Heitler and London on the hydrogen molecule in 1927, only one year after the Schrödinger equation was proposed. This gave the first rational explanation of the chemical concept of the covalent electron-pair bond, proposed by G. N. Lewis in 1916 and Irving Langmuir in 1919. The hydrogen molecule has a binding energy of (not including the zero-point vibrational energy). This represents the minimum of the Born–Oppenheimer potential curve for at an internuclear separation of (0.7414Å). This is shown as a thick black curve representing the ground electronic state. As , the molecule dissociates into two hydrogen atoms in their ground states, with antiparallel spins. Also shown, in red, is the antibonding potential curve for two hydrogen atoms with parallel spins. The Hamiltonian for the molecule, within the Born–Oppenheimer approximation, consists of the kinetic energies of the two electrons added to six Coulombic potential-energy contributions. In atomic units (): , where [more] Contributed by: S. M. Blinder SNAPSHOTS DETAILS Snapshot 1: primitive Heitler–London function Snapshot 2: optimized Wang function: Snapshot 3: optimized Weinbaum function: , References [1] S. M. Blinder, Introduction to Quantum Mechanics, Amsterdam: Elsevier, 2004 pp. 139–141. [2] L. Pauling and E. B. Wilson, Introduction to Quantum Mechanics, New York: McGraw–Hill, 1935 pp. 340–353. Mainly for historical perspective, we also cite the original papers: [3] W. Heitler and F. London, "Wechselwirkung Neutraler Atome und Homöopolare Bindung Nach der Quantenmechanik," Zeitschrift für Physik, 44, 1927 pp. 455–472. [4] Y. Sugiura, "Über die Eigenschaften des Wasserstoffmoleküls im Grundzustande," Zeitschrift für Physik, 45, 1927 pp. 484–492. [5] S. C. Wang, "The Problem of the Normal Hydrogen Molecule in the New Quantum Mechanics," Physical Review, 31(4), 1928 pp. 579–586. [6] S. Weinbaum, "The Normal State of the Hydrogen Molecule," Journal of Chemical Physics, 1(8), 1933 pp. 593–597. [7] H. M. James and A. S. Coolidge, "The Ground State of the Hydrogen Molecule," Journal of Chemical Physics, 1(12), 1933 pp. 825-835. RELATED LINKS Valence Bond Theory (ScienceWorld) PERMANENT CITATION  S. M. Blinder "Valence-Bond Theory of the Hydrogen Molecule"  http://demonstrations.wolfram.com/ValenceBondTheoryOfTheHydrogenMolecule/  Wolfram Demonstrations Project  Published: March 5, 2012

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