Nuclear charges

The Sclnodinger equation for a one-electron atom with nuclear charge Z is... 

These hold quite well for light atoms but become less dependable with greater nuclear charge. The tenu mtercombination bands is used for spectra where the spin quantum number S changes for example, singlet-triplet transitions. They are very weak in light atoms but quite easily observed in heavy ones. 

The electron distribution, p(r), has been computed by quantum mechanics for all neutral atoms and many ions and the values off(Q), as well as coefficients for a useful empirical approximation, are tabulated in the International Tables for Crystallography vol C [2]. In general,is a maximum equal to the nuclear charge, Z, lor Q = 0 and decreases monotonically with increasing Q. 

The electrostatic interaction between a structureless projectile ion P of charge ZpC and an atom A with nuclear charge Z e is... 

We assume that the nuclei are so slow moving relative to electrons that we may regard them as fixed masses. This amounts to separation of the Schroedinger equation into two parts, one for nuclei and one for electrons. We then drop the nuclear kinetic energy operator, but we retain the intemuclear repulsion terms, which we know from the nuclear charges and the intemuclear distances. We retain all terms that involve electrons, including the potential energy terms due to attractive forces between nuclei and electrons and those due to repulsive forces... 

We shall also investigate the OPTIONS prompt that was set to 0 in Computer Project 8-3. At the prompt OPTIONS , one has the choices 0, 1,2, or 3. Note the II format. Taking the choices in reverse order, 3 permits one to input a value for nuclear charge. This option will not be used here. 

The subscripts i and j denote two nuclei one in the QM region and one in the MM region. The atomic charges for the MM atoms are obtained by any of the techniques commonly used in MM calculations. The atomic charges for the QM atoms can be obtained by a population analysis scheme. Alternatively, there might be a sum of interactions with the QM nuclear charges plus the interaction with the electron density, which is an integral over the electron density. 

The point r is the position of a positive probe charge. is the nuclear charge on atom Alocated at position R. The function p(r ) is the electronic density. In the above equation, the first term represents the contribution of the nuclei to the electrostatic potential and the second term is the electronic contribution. Substituting the electron density expression ... 

Electronegativity x is the relative attraction of an atom for the valence electrons in a covalent bond. It is proportional to the effective nuclear charge and inversely proportional to the covalent radius ... 

The functions are the associated Legendre polynomials of which a few are given in Table 1.1. They are independent of Z, the nuclear charge number, and therefore are the same for all one-electron atoms. 

As in atoms, the selection rule breaks down as the nuclear charge increases. For example, triplet-singlet transitions are strictly forbidden in FI2 but in CO the a U — transition is observed weakly. 

---