Nuclear-electron attraction, electronic structure

A molecule is composed of positively charged nuclei surrounded by electrons. The stability of a molecule is due to a balance among the mutual repulsions of nuclear pairs, attractions of nuclear-electron pairs, and repulsions of electron pairs as modified by the interactions of their spins. Both the nuclei and the electrons are in constant motion relative to the center of mass of the molecule. However, the nuclear masses are much greater than the electronic mass and, as a result, the nuclei move much more slowly than the electrons. Thus, the basic molecular structure is a stable framework of nuclei undergoing rotational and vibrational motions surrounded by a cloud of electrons described by the electronic probability density. 

Later methods, especially that of Gordy (1955), and later Allred and Rochow (1958) make use of screening constants of the electron structure for the nuclear charge of each atom. This determines the attraction between the nucleus of the atom and an electron outside the normal electron complement, and is the effective nuclear charge. The empirical equation for the values of electronegativity obtained in this manner by Allred and Rochow is... 

On the right in Fig. 32 is an electron-domain representation of Lin-nett s model of an Octet-Rule satisfying atom in field-free space. For domains of (i) fixed size and distribution of charge, (ii) fixed distances from the nucleus, and (iii) fixed tetrahedral disposition with respect to other domains of the same spin-set, three of the four contributions to the total energies of the two structures in Fig. 32 are identical, namely the energies arising from (i) electronic motion, (ii) nuclear-electron attractions, and (iii) electron-electron repulsions between electrons of the same... 

Theoreticians thought that stable heavier elements might be in prospect. The stability of a nucleus (based on a model of nuclear stability analogous to that of the Rutherford-Bohr model of electronic structure) is determined by the inter-nucleon forces (nucleons are protons and neutrons), an attractive force between all nucleons and a Coulombic repulsion force between protons, the latter becoming proportionately more important as the number of protons increases. Extra stability is associated with filled shells of nucleons, magic numbers for neutrons they are 2,8,20,28,50,82,126,184, and 196 and for protons they are 2, 8, 20, 28, 50, 82, 114, and 164. 

Under normal conditions, a chemical reaction involves the electrons occupying the outermost shells, or valence shells, of the atoms involved. Hence the chemical properties of an atom arise from its tendency to lose electrons from, or to attract electrons to, its valence shell. This tendency will depend upon the electronic structure of the atom and the nuclear charge experienced by the valence shell electrons. Thus, in order to explain the chemistry of a transition element, it is first necessary to consider its atomic structure and how this influences the binding of its valence shell electrons. 

The nuclear theory of atomic structure, put forward by Rutherford, regarded the electrons as moving in orbits round the nucleus. The dynamical theory of this system was developed by Bohr, who found it necessary to supplement classical mechanics by the quantum mechanics of Planck. According to classical theory, a system consisting of an electron moving in a circular orbit round a nucleus, to which it is attracted according to Coulomb s law, would lose energy, with the result that the electron would approach and finally collide with the nucleus. Thus on the basis of classical theory, the Rutherford atom would only be stable for about io seconds, after which time the electron would have fallen into the nucleus. 

The fact that the calculation of Ee as well as of its derivatives with respect to nuclear coordinates with accurate electronic-structure methods is non-trivial and often time-consuming, makes the use of simpler, parameterized methods attractive, in particular when studying larger systems of low symmetry and/or studying (very) many structures (which easily is the case when attempting to optimize the structure). With these, the total energy is given as some analytical or numerical function of the nuclear coordinates and atom types, i.e.,... 

Theoretical methods that combine ab initio MD on the fly with the Wigner distribution approach, which is based on classical treatment of nuclei and on quantum chemical treatment of electronic structure, represent an important theoretical tool for the analysis and control of ultrashort processes in complex systems. Moreover, the possibility to include, in principle, quantum effects for nuclear motion by introducing appropriate corrections makes this approach attractive for further developments. However, for this purpose, new proposals for improving the efficient inclusion of quantum effects for the motion of nuclei and fast but accurate calculations of MD on the fly in the electronic excited states are mandatory. Both aspects represent attractive and important theoretical research areas for the future. 

As illustrated in Fig. 1, compressing molecules loosens the electronic structure. When the neighboring electron clouds crowd in, the consequent repulsions markedly attenuate the otherwise major role of attraction of valence electrons to the nuclear framework of the molecule. Thereby, compression experiments can markedly alter a wide range of chemical interactions and dial up behavior not acceptable to uncrowded molecules. From a... 

Note the structural similarity between equation (Al.6.72) and equation (Al.6.41). with and being replaced by and H, the BO Hamiltonians governing the quantum mechanical evolution in electronic states a and b, respectively. These Hamiltonians consist of a nuclear kinetic energy part and a potential energy part which derives from nuclear-electron attraction and nuclear-nuclear repulsion, which differs in the two electronic states. 

As an example for an open-shell system, we carried out calculations for Th2. Th clusters have been attracting increasing attention due to potential nuclear energy applications. The calculated structural, electronic structure and energetic properties are summarized in Table 2. We have identified three low-lying electronic states without spin-orbit interactions, the sa dn da db sa g, sa dn da sa X, and sa dn sa 11+ states. 

The first term of the hamiltonian describes the kinetic energy of the electron. The second term describes the attractive interaction between the electron and the nuclei where ri and Rg refer to the positions of electron i and atom a. The number of electrons is defined as n and the number of nuclei as N. The third term describes electron-electron repulsion. The final term refers to the nuclear-nuclear repulsive interactions. Since the nuclear charges are decoupled from the electronic wavefunction, this summation can be computed in a straight forward manner and does not change upon the solution to the electronic structure. 

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