Orbital, atomic phase

In some n molecular orbitals the phase at a given carbon atom may be zero and hence the p orbital in such a case is left unmarked. 

Johnson and Rice used an LCAO continuum orbital constructed of atomic phase-shifted coulomb functions. Such an orbital displays all of the aforementioned properties, and has only one obvious deficiency— because of large interatomic overlap, the wavefunction does not vanish at each of the nuclei of the molecule. Use of the LCAO representation of the wavefunction is equivalent to picturing the molecule as composed of individual atoms which act as independent scattering centers. However, all the overall molecular symmetry properties are accounted for, and interference effects are explicitly treated. Correlation effects appear through an assigned effective nuclear charge and corresponding quantum defects of the atomic functions. 

Just as an electromagnetic wave, or the wave on a vibrating string, or even an ocean wave possesses different phases (for example, the troughs and peaks of an ocean wave) so too do the atom s wave functions—the orbitals. After each node in an orbital, the phase of the wave function changes. In the... 

The third group of states, at about 0.8 eV, is formed by an antibonding configuration of s-type atomic orbitals. The antibonding combination of orbitals is phased so that the amplitudes subtract in the spatial region between the two atoms making up the unit cell. 

Fig. 5 One-dimensional model for coherent jt-bonding between metal atoms. M = Hf, and their O-atom neighbors utilizing Hf 5d-orbitals and O 2p it orbitals. Alternating phase establishes a coherence length equal to a sequence of 7 Hf atoms for enabling a cooperative J-T effect Hf(Zr)02 phase...

Figure 13.23 Ring current in the Mobius transition state of the electrocyclic reaction of octa-l,3,5,7-tetraene to cycloocta-1,3,5-triene. For details see Figure 13.21. Note that the basis orbitals (atomic orbitals that are involved in the reaction) can be written with arbitrary phase. The number of antibonding overlaps (sign inversion) will...

The 17-bonding molecular orbital has all the p orbitals in phase, whereas the 17-antibonding orbital has all the p orbitals out of phase. Each of the nonbonding orbitals has a node at the nitrogen atom. 

There are two mechanisms by which a phase change on the ground-state surface can take place. One, the orbital overlap mechanism, was extensively discussed by both MO [55] and VB [47] formulations, and involves the creation of a negative overlap between two adjacent atomic orbitals during the reaction (or an odd number of negative overlaps). This case was temied a phase dislocation by other workers [43,45,46]. A reaction in which this happens is... 

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

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

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