Rydberg orbital

The Seetion Simple Molecular Orbital Theory deals with atomie and moleeular orbitals in a qualitative manner, ineluding their symmetries, shapes, sizes, and energies. It introduees bonding, non-bonding, and antibonding orbitals, deloealized, hybrid, and Rydberg orbitals, and introduees Hiiekel-level models for the ealeulation of moleeular orbitals as linear eombinations of atomie orbitals (a more extensive treatment of  [c.2]

Rydberg orbitals (i.e., very diffuse orbitals having prineipal quantum numbers higher than the atoms valenee orbitals) ean arise in moleeules just as they do in atoms. They do not usually give rise to bonding and antibonding orbitals beeause the valenee-orbital interaetions bring the atomie eenters so elose together that the Rydberg orbitals of eaeh atom subsume both atoms. Therefore as the atoms are brought together, the atomie Rydberg orbitals usually pass through the intemuelear distanee region where they experienee (weak) bonding-antibonding interaetions all the way to mueh shorter distanees at whieh they have essentially reaehed their united-atom limits. As a result, moleeular Rydberg orbitals are moleeule-eentered and display little, if any, bonding or antibonding eharaeter. They are usually labeled with prineipal quantum numbers beginning one higher than the highest n value of the eonstituent atomie valenee orbitals, although they are sometimes labeled by the n quantum number to whieh they eorrelate in the united-atom limit.  [c.158]

An example of the interaetion of 3 s Rydberg orbitals of a moleeule whose 2s and 2p orbitals are the valenee orbitals and of the evolution of these orbitals into united-atom orbitals is given below.  [c.158]

Overlap of the Rydberg Orbitals Begins  [c.160]

The In-Phase ( 3s + 3s) Combination of Rydberg Orbitals Correlates to an s-type Orbital of the United Atom  [c.160]

The Out-of-Phase Combination of Rydberg Orbitals ( 3s - 3s ) Correlates to a p-type United-Atom Orbital  [c.160]

Rather than using the molecular orbitals directly, NBO uses the natural orbitals. Natural orbitals are the eigenfunctions of the first-order reduced density matrix. These are then localized and orthogonalized. The localization procedure allows orbitals to be defined as those centered on atoms and those encompassing pairs of atoms. These can be integrated to obtain charges on the atoms. Analysis of the basis function weights and nodal properties allows these transformed orbitals to be classified as bonding, antibonding, core, and Rydberg orbitals. Further decomposition into three-body orbitals will yield a characterization of three center bonds. There is also a procedure that searches for the 7t bonding patterns typical of a resonant system. This is not a rigorous assignment as there may be some electron occupancy of antibonding orbitals, which a simple Lewis model would predict to be unoccupied.  [c.101]

Diffuse functions are those functions with small Gaussian exponents, thus describing the wave function far from the nucleus. It is common to add additional diffuse functions to a basis. The most frequent reason for doing this is to describe orbitals with a large spatial extent, such as the HOMO of an anion or Rydberg orbitals. Adding diffuse functions can also result in a greater tendency to develop basis set superposition error (BSSE), as described later in this chapter.  [c.231]

In the ground configuration of H2O there are two electrons in the 3aj orbital strongly favouring a bent molecule. The only excited states known for H2O are those in which an electron has been promoted from Ihj to a so-called Rydberg orbital. Such an orbital is large compared with the size of the molecule and resembles an atomic orbital. Because it is so large it resembles the Ihj orbital in that it does not influence the geometry. So H2O, in such Rydberg states, has an angle similar to that in the ground state.  [c.265]

When aos are eombined to form mos, eore, bonding, nonbonding, antibonding, and Rydberg moleeular orbitals ean result. The mos (j) are usually expressed in terms of the eonstituent atomie orbitals Xa iii the linear-eombination-of-atomie-orbital-moleeular-orbital (LCAO-MO) manner  [c.153]

It is essential to keep in mind that all atoms possess excited orbitals that may become involved in bond formation if one or more electrons occupies these orbitals. Whenever aos with principal quantum number one or more unit higher than that of the conventional aos becomes involved in bond formation, Rydberg mos are formed.  [c.158]

In summary, an atom or molecule has many orbitals (core, bonding, non-bonding, Rydberg, and antibonding) available to it occupancy of these orbitals in a particular manner gives rise to a configuration. If some orbitals are partially occupied in this configuration.  [c.239]

When dealing with anions or Rydberg states, one must augment the above basis sets by adding so-ealled diffuse basis orbitals. The eonventional valenee and polarization funetions deseribed above do not provide enough radial flexibility to adequately deseribe either of these eases. Energy-optimized diffuse funetions appropriate to anions of most lighter main group elements have been tabulated in the literature (an exeellent souree of Gaussian basis set information is provided in Handbook of Gaussian Basis Sets, R.  [c.473]

The scheme assigns charges very differently, placing most of the negative charge on one carbon atom. Its more detailed analysis also includes the number of core electrons, valence electrons, and Rydberg electrons, located in diffuse orbitals. It also partitions the charge on each atom among the atomic orbitals.  [c.196]

The NAOs will normally resemble the pure atomic orbitals (as calculated for an isolated atom), and may be divided into a natural minimal basis (corresponding to the occupied atomic orbitals for the isolated atom), and a remaining set of natural Rydberg orbitals based on the magnitude of the occupation numbers. The minimal set of NAOs will normally be strongly occupied (i.e. having oceupation numbers significantly different from zero), while the Rydberg NAOs usually will be weakly oceupied (i.e. having occupation numbers close zero). There are as many NAOs as the size of the atomic basis set, and the number of Rydberg NAOs thus inereases as the basis  [c.230]

Most electronic transitions of interest fall into the visible and near-ultraviolet regions of the spectmm. This range of photon energies commonly corresponds to electrons being moved among valence orbitals. These orbitals are important to an understandmg of bonding and stmcture, so are of particular interest in physical chemistry and chemical physics. For this reason, most of this chapter will concentrate on visible and near-UV spectroscopy, roughly the region between 200 and 700 mn, but there are no definite boundaries to the wavelengths of interest. Some of the valence orbitals will be so close in energy as to give spectra in the near-infrared region. Conversely, some valence transitions will be at high enough energy to lie in the vacuum ultraviolet, below about 200 mn, where air absorbs strongly and instmmentation must be evacuated to allow light to pass. In this region are also transitions of electrons to states of higher principal quantum number, known as Rydberg states. At still higher energies, in the x-ray region, are transitions of iimer-shell electrons, and their spectroscopy has become an extremely usefiil tool, especially for studying solids and their surfaces. However, these other regions will not be covered in detail here.  [c.1119]

The excited states of a Rydberg series have an electron in an orbital of higher principal quantum number, n, in which it spends most of its time far from the molecular framework. The idea is that the electron then feels mainly a Coulomb field due to the positive ion remaining behind at the centre, so its behaviour is much like that of the electron in the hydrogen atom. The constant 8 is called the quantum defect and is a measure of the extent to which the electron interacts with the molecular framework. It has less influence on the energy levels as n gets larger, i.e. as the electron gets farther from the central ion. The size of 8 will also depend on the angrilar momentum of the electron. States of lower angrilar momentum have more probability of penetrating the charge cloud of the central ion and so may have larger values of 8. Actual energy levels of Rydberg atoms and molecules can be subject to theoretical calculations [27]. Sometimes the higher states have orbitals so large that other molecules may fall within their volume, causing interesting effects [28].  [c.1145]

Diffuse functions. When dealing with anions or Rydberg states, one must fiirdier augment the basis set by adding so-called diflfiise basis orbitals. The valence and polarization fiinctions described above do not provide enough radial flexibility to adequately describe either of these cases. Once again, the PNNL web site data base [45] offers a good source for obtaining diflhise fiinctions appropriate to a variety of atoms.  [c.2172]

See pages that mention the term Rydberg orbital : [c.158]    [c.160]    [c.82]    [c.473]   
Modern spectroscopy (2004) -- [ c.265 ]