A Molecular Orbital Model of the Hydrogen Bond

To get an idea of the energy lowering involved in the formation of the hydrogen bond in some typical dimers, we use the model long-range formula  

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A Molecular Orbital Model of the Hydrogen Bond Electrostatic Interactions and the Hydrogen Bond... 

The author of [73] deduced a physical model of the hydrogen bond from ah initio molecular orbital wave functions. The characteristic of the model are as follows the dipole moment of the A-H bond /Ta-h ) the difference between the first ionization potential of the electron donor and the noble gas in its row of the Mendeleev Table A / the length R of the hydrogen bonding lone pair. A number of characteristic of the intermolecular strength can be described in terms of these quantities. 

Hydrogen normally exists as a diatomic molecule, H2, with a covalent bond connecting the two hydrogen atoms. Section 3.3 established that the orbitals of a molecule are different from those of an individual atom. Is it possible to use the hydrogen atom and its atomic orbitals to make predictions about the orbitals in a molecule In one model, the atomic orbitals of the atom are mixed and combining two such atoms may lead to a molecule. This idea of mixing atomic orbitals to form a molecular orbital is called the linear combination of atomic orbital (LCAO) model, and in some cases it helps predict the relative energy of these molecular orbitals. 

Figure 9.3 Shows the molecular orbitals for trans octatetraene ignoring, hydrogen-carbon bonds, and the filling of these orbitals with electrons. Both possible transitions that would result from a 1-electron model of the structure and the actual result including electron correlation effects are also shown, indicating that the lowest energy optical transitions are not from the HOMO to the LUMO states. Only a two-electron transition is allowed between these states for a photon-only process. Reprinted with permission from Bredas, Jean-Luc et al. Excited-state electronic structure of conjugated oligomers and polymers a quantum-chemical approach to optical phenomena . Accounts in Chemical Research 1999 32 267-276. [1] Copyright 1999 American Chemical Society.

Valence bond and molecular orbital theory both incorporate the wave description of an atom s electrons into this picture of H2 but m somewhat different ways Both assume that electron waves behave like more familiar waves such as sound and light waves One important property of waves is called interference m physics Constructive interference occurs when two waves combine so as to reinforce each other (m phase) destructive interference occurs when they oppose each other (out of phase) (Figure 2 2) Recall from Section 1 1 that electron waves m atoms are characterized by their wave function which is the same as an orbital For an electron m the most stable state of a hydrogen atom for example this state is defined by the Is wave function and is often called the Is orbital The valence bond model bases the connection between two atoms on the overlap between half filled orbifals of fhe fwo afoms The molecular orbital model assembles a sef of molecular orbifals by combining fhe afomic orbifals of all of fhe atoms m fhe molecule... 

Molecular Orbital Theory Model. Oxygen and hydrogen atoms in H2O are held together by a covalent bond. According to the quantum molecular orbital theory of covalent bonding between atoms, electrons in molecules occupy molecular orbitals that are described, using quantum mechanical language, by a linear combination of... 

Klemperer and co-workers. 31) In this model the hydrogen bond is viewed as an electron donor-acceptor complex in which a pair of electrons from the highest occupied molecular orbital of the Lewis base is donated to the lowest unoccupied molecular orbital of the Lewis acid. If the donor electron pair is assumed to have the appropriate hybridization, and the acceptor orbital to be axially symmetric, the above structures can be rationalized as giving maximal overlap between the HOMO and LUMO. 

The chemist is accustomed to think of the chemical bond from the valence-bond approach of Pauling (7)05), for this approach enables construction of simple models with which to develop a chemical intuition for a variety of complex materials. However, this approach is necessarily qualitative in character so that at best it can serve only as a useful device for the correlation and classification of materials. Therefore the theoretical context for the present discussion is the Hund (290)-Mulliken (4f>7) molecular-orbital approach. Nevertheless an important restriction to the application of this approach must be emphasized at the start viz. an apparently sharp breakdown of the collective-electron assumption for interatomic separations greater than some critical distance, R(. In order to illustrate the theoretical basis for this breakdown, several calculations will be considered, the first being those for the hydrogen molecule. 

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