Hydrogen bond quantum mechanical description

II. Quantum Mechanical Descriptions of Hydrogen-Bonded Systems... 

II. QUANTUM MECHANICAL DESCRIPTION OF HYDROGEN-BONDED SYSTEMS... 

Consider a quantum mechanical description of the hydrogen molecular ion in its simplest version. Let us use the molecular orbital theory with the atomic basis set composed of only two Slater Type Orbitals (STOs) Isa and Is , centered on the nuclei a and b. The mean value of the Hamiltonian computed with the bonding (+) and antibonding (—) orbital (see p. 439 and Appendix D available at booksite.elsevier.com/978-0-444-59436-5) reads as... 

The modern theory of chemical bonding begins with the article The Atom and the Molecule published by the American chemist G. N. Lewis in 1916 [1], In this article, which is still well worth reading, Lewis for the first time associates a single chemical bond with one pair of electrons held in common by the two atoms "After a brief review of Lewis model we turn to a quantum-mechanical description of the simplest of all molecules, viz. the hydrogen molecule ion H J. Since this molecule contains only one electron, the Schrodinger equation can be solved exactly once the distance between the nuclei has been fixed. We shall not write down these solutions since they require the use of a rather exotic coordinate system. Instead we shall show how approximate wavefunctions can be written as linear combinations of atomic orbitals of the two atoms. Finally we shall discuss so-called molecular orbital calculations on the simplest two-electron atom, viz. the hydrogen molecule. 

MolSurf parameters [33] are descriptors derived from quantum mechanical calculations. These descriptors are computed at a surface of constant electron density, with which a very fine description of the properties of a molecule at the Van der Waals surface can be obtained. They describe various electrostatic properties such as hydrogen-bonding strengths and polarizability, as well as Lewis base and acid strengths. MolSurf parameters are computed using the following protocol. 

A second quantum mechanical bonding theory is molecular orbital theory. This theory is based on a wave description of electrons. The molecular orbital theory assumes that electrons are not associated with an individual atom but are associated with the entire molecule. Delocalized molecular electrons are not shared by two atoms as in the traditional covalent bond. For the hydrogen molecule, the molecular orbitals are formed by the addition of wave functions for each Is electron in each hydrogen atom. The addition leads to a bonding molecular... 

Tapia, O. Quantum mechanics and the theory of hydrogen bond and proton transfer. Beyond a Bom-Oppenheimer description of chemical interconversions, J.Mol.Str.Theochem, 433 (1998) 95-105. 

The generalization of the Heitler-London equation, Eq. (3.31), to three hydrogen atoms was also considered in the early days of quantum mechanics (around 1930). This description contains the essence of the energetics associated with bond breaking and bond making. 

Each electron occupies a Is orbital on its home hydrogen, electron 1 on Ha and electron 2 on Hb. This distinction, however, is lost when the nuclear centers are brought within bonding distance of each other. At this close proximity, quantum mechanics requires that electrons be indistinguishable from one another. The simplest fimction in the valence bond description that accounts for this behavior is a linear combination of two possibilities (4). 

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