Natural atomic orbitals definition

From this wave function, one sees how even in the early beginning of molecular quantum mechanics, atomic orbitals were used to construct molecular wave functions. This explains why one of the first AIM definitions relied on atomic orbitals. Nowadays, molecular ab initio calculations are usually carried out using basis sets consisting of basis functions that mimic atomic orbitals. Expanding the electron density in the set of natural orbitals and introducing the basis function expansion leads to [15]... 

Wavefunctions of electrons in atoms are called atomic orbitals. The name was chosen to suggest something less definite than an orbit of an electron around a nucleus and to take into account the wave nature of the electron. The mathematical expressions for atomic orbitals—which are obtained as solutions of the Schrodinger equation—are more complicated than the sine functions for the particle in a box, but their essential features are quite simple. Moreover, we must never lose sight of their interpretation, that the square of a wavefunction tells us the probability density of an electron at each point. To visualize this probability density, we can think of a cloud centered on the nucleus. The density of the cloud at each point represents the probability of finding an electron there. Denser regions of the cloud therefore represent locations where the electron is more likely to be found. 

Mulliken s interest in the electronic levels in molecules in the 1920s was stimulated by suggestions that their molecular spectra bore similarities to atomic spectra and definite relationships could be discerned for isosteric molecules. He found that the spectroscopic analogy between isosteric molecules could be extended to atoms with the same number of electrons, and this relatirmship was to lead subsequently to the united atom approach. He and Birge classified the electronic states in diatomic molecules using the same Russell-Saunders classification used previously for atomic states. Himd s theoretical analysis [ 149,162-166] of the nature of electronic states in molecules therefore proved to be timely for Mulliken and led him to publish [167-171] a summary of the theory and provide extra experimental evidence supporting it. In the molecular orbital theory Hund showed how the concept of atomic orbitals and the mathematical procedures developed to define them could... 

One of the more successful devices to reconcile chemical behavior with quantum theory was the proposed definition of atomic orbitals to regulate the distribution of electrons on both atoms and molecules. A minor irritant in this application is the complex nature of the relevant wave functions that underlie the definition of atomic orbitals. As these complex functions invariably occur in orthogonal pairs, real functions can be constructed by suitable linear combinations of these pairs. 

All elements, by definition, have a unique proton number, but some also have a unique number of neutrons (at least, in naturally occurring forms) and therefore a unique atomic weight - examples are gold (Au Z = 79, N = 118, giving A =197), bismuth (Bi Z = 83, N = 126, A = 209), and at the lighter end of the scale, fluorine (F Z = 9, N = 10, A = 19) and sodium (Na Z = 11, N= 12, A = 23). Such behavior is, however, rare in the periodic table, where the vast majority of natural stable elements can exist with two or more different neutron numbers in their nucleus. These are termed isotopes. Isotopes of the same element have the same number of protons in their nucleus (and hence orbital electrons, and hence chemical properties), but... 

Theoretically, the radius of an ion extends from the nucleus to the outermost orbital occupied by electrons. The very nature of the angular wave function of an electron, which approaches zero asymptotically with increasing distance from the nucleus, indicates that an atom or ion has no definite size. Electron density maps compiled in X-ray determinations of crystal structures rarely show zero contours along a metal-anion bond. 

Both definitions are natural since wq turns out to be the ratio of the microwave frequency w and the Kepler firequency H of the Rydberg electron, and Sq is the ratio of the microwave field strength and the field strength experienced by an electron in the noth Bohr orbit of the hydrogen atom. Motivated by the above discussion we have redrawn the results obtained by Bayfield and Koch (1974) and present them in Fig. 7.2 as an ionization signal (in arbitrary units) versus the scaled field strength defined in (7.1.3). For no in (7.1.3) we chose no = 66, the centroid of the band of Rydberg states present in the atomic beam. 

The idea of electrons existing in definite energy states was fine, but another way had to be devised to describe the location of the electron about the nucleus. The solution to this problem produced the modern model of the atom, often called the quantum mechanical model. In this new model of the hydrogen atom, electrons do not travel in circular orbits but exist in orbitals with three-dimensional shapes that are inconsistent with circular paths. The modern model of the atom treats the electron not as a particle with a definite mass and velocity, but as a wave with the properties of waves. The mathematics of the quantum mechanical model are much more complex, but the results are a great improvement over the Bohr model and are in better agreement with what we know about nature. In the quantum mechanical model of the atom, the location of an electron about the nucleus is described in terms of probability, not paths, and these volumes where the probability of finding the electron is high are called orbitals. 

---