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Schrodinger equation hydrogen bonds

This review has attempted to illustrate the relevance and the widespread utility of the CM model. Indeed, the author believes it is difficult to specify any area of structural or mechanistic chemistry where the CM approach is not applicable. The reason is not hard to find the CM model has its roots in the Schrodinger equation and as such its relevance to chemistry cannot be easily overstated. Even the fundamental chemical concept of a covalent bond derives from the CM approach. The covalent bond (e.g. in H2) owes its energy to the configuration mix HfiH <— H H. A wave-function for the hydrogen molecule based on just one spin-paired form does not lead to a stable bond. Both spin forms are necessary. Addition of ionic configurations improves the bond further and in the case of heteroatomic bonds generates polar covalent bonds. [Pg.190]

Unfortunately, the Schrodinger equation can be solved exactly only for one-electron systems such as the hydrogen atom. If it could be solved exactly for molecules containing two or more electrons,3 we would have a precise picture of the shape of the orbitals available to each electron (especially for the important ground state) and the energy for each orbital. Since exact solutions are not available, drastic approximations must be made. There are two chief general methods of approximation the molecular-orbital method and the valence-bond method. [Pg.3]

For the hydrogen molecule ion it is possible to solve the Schrodinger equation and calculate the energy of formation of the molecule. The solution is only approximate, however, and the value for the energy cannot be regarded as exact, but the solution does permit a picture of the forces involved in a chemical bond to be obtained. As pointed out above, when the distance between the nuclei is great, the system may be considered as an atom a and a separate nucleus b. The Schrodinger equation then has the form... [Pg.47]

This chapter begins with a description of the quantum picture of the chemical bond for the simplest possible molecule, Hj, which contains only one electron. The Schrodinger equation for Hj can be solved exactly, and we use its solutions to illustrate the general features of molecular orbitals (MOs), the one-electron wave functions that describe the electronic structure of molecules. Recall that we used the atomic orbitals (AOs) of the hydrogen atom to suggest approximate AOs for complex atoms. Similarly, we let the MOs for Hj guide us to develop approximations for the MOs of more complex molecules. [Pg.212]

The simplest example is that of the shallow P donor in Si. Four of its five valence electrons participate in the covalent bonding to its four Si nearest neighbours at the substitutional site. The energy of the fifth electron which, at 0 K, is in an energy level just below the minimum of the CB, is approximated by fi t /2MP plus the screened Coulomb attraction to the ion, e /er, where e is the dielectric constant or the frequency-dependent dielectric function. The Schrodinger equation for this electron reduces to that of the hydrogen atom, but m replaces the electronic mass and s screens the Coulomb attraetion. [Pg.2887]

The molecular Schrodinger equation can be solved exactly for the case of H, for the hydrogen ion. It is a case of the true covalent bond. Here we have two nuclei repulsing each other, and both exerting a Coulomb attraction on the single electron. [Pg.44]


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