Atomic orbitals phasing

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

Figure 7.30 (a) In-phase and (b) out-of-phase Is atomic orbitals on the hydrogen atoms of linear... 

It has been pointed out that a different array of atomic orbitals might be conceived of in large conjugated rings. The array, called a Mobius twist, results in there being one point in the ring at which the atomic orbitals would show a phase discontinuity. ... 

Valence bond and molecular orbital theory both incorporate the wave description of an atom s electrons into this picture of H2, but in somewhat different ways. Both assume that electron waves behave like more familiar waves, such as sound and light waves. One important property of waves is called interference in physics. Constructive interference occurs when two waves combine so as to reinforce each other (in phase) destructive interference occurs when they oppose each other (out of phase) (Figure 2.2). Recall from Section 1.1 that electron waves in atoms are characterized by then- wave function, which is the same as an orbital. For an electron in the most stable state of a hydrogen atom, for example, this state is defined by the I5 wave function and is often called the I5 orbital. The valence bond model bases the connection between two atoms on the overlap between half-filled orbitals of the two atoms. The molecular orbital model assembles a set of molecular- orbitals by combining the atomic orbitals of all of the atoms in the molecule. 

Among the diatomic molecules of the second period elements are three familiar ones, N2,02, and F2. The molecules Li2, B2, and C2 are less common but have been observed and studied in the gas phase. In contrast, the molecules Be2 and Ne2 are either highly unstable or nonexistent. Let us see what molecular orbital theory predicts about the structure and stability of these molecules. We start by considering how the atomic orbitals containing the valence electrons (2s and 2p) are used to form molecular orbitals. 

Figure 2.14. The molecular orbitals of gas phase carbon monoxide, (a) Energy diagram indicating how the molecular orbitals arise from the combination of atomic orbitals of carbon (C) and oxygen (O). Conventional arrows are used to indicate the spin orientations of electrons in the occupied orbitals. Asterisks denote antibonding molecular orbitals, (b) Spatial distributions of key orbitals involved in the chemisorption of carbon monoxide. Barring indicates empty orbitals.5 (c) Electronic configurations of CO and NO in vacuum as compared to the density of states of a Pt(lll) cluster.11 Reprinted from ref. 11 with permission from Elsevier Science.

The structure of CaB contains bonding bands typical of the boron sublattice and capable of accommodating 20 electrons per CaB formula, and separated from antibonding bands by a relatively narrow gap (from 1.5 to 4.4 eV) . The B atoms of the B(, octahedron yield only 18 electrons thus a transfer of two electrons from the metal to the boron sublattice is necessary to stabilize the crystalline framework. The semiconducting properties of M B phases (M = Ca, Sr ", Ba, Eu, Yb ) and the metallic ones of M B or M B5 phases (Y, La, Ce, Pr, Nd ", Gd , Tb , Dy and Th ) are directly explained by this model . The validity of these models may be questionable because of the existence and stability of Na,Ba, Bft solid solutions and of KB, since they prove that the CaB -type structure is still stable when the electron contribution of the inserted atom is less than two . A detailed description of physical properties of hexaborides involves not only the bonding and antibonding B bands, but also bonds originating in the atomic orbitals of the inserted metal . ... 

We have learned the interactions of the same orbitals and chemical bonds between the same atoms. The orbital phase plays a crucial role in the energies and the spacial extensions of the bond orbitals. Here we learn interactions of different orbitals and amplitude of orbitals, using an example of polar bonds between different atoms. 

The bond orbitals of o, and relate to the other property of waves apart from the phase, that is, the amplitude. The bonding orbitals have large amplitudes on the low-lying atomic orbitals, i.e., on C of o, and on O of (Scheme 8). The antibonding orbitals have large amplitudes on the high-lying atomic orbitals. 

The energy, the phase, and the amphtude characterize sahent features of orbitals. This can be seen in atomic orbitals and bond orbitals (Sect. 1). 

The in-phase and out-of-phase relations mean the same and opposite signs of the atomic orbitals in (j) and nearest to the charge. 

Acetylenes XCCY with n conjugated substituents, X and Y, on both carbon atoms have planar or perpendicular conformations. The substituents can be electron-donating or -accepting. The planar conformers are linear conjugate D-TI-D, D-IT-A, or A-IT-A systems whereas the perpendicular conformers are composed of ri-D and IT-A not in conjugation with each other. The orbital phase is continuous only in the planar conformations of D-TI-A (Scheme 23, cf. Scheme 4). The acetylenes with X=D (OR, NR ) and Y=A (RCO, ROCO) prefer planar conformations. When both substituents are electron-donating or accepting, the phase is discontinuous. The acetylenes then prefer perpendicular conformations. The predicted conformational preference was confirmed by ab initio molecular orbital calculations [32]. Diacetylenic molecules show similar conformational preference, which is, however, reduced as expected [32]. 

Cyclic conjugation is continuous in l,2-dihydro-l,2-azaborine with one N-B bond (Scheme 34). The nitrogen atom with a lone pair is donor. The B atom with a vacant p orbital is acceptor. Whether the remaining C=C bonds are donors or accepters, the donors are disposed on one side of the cychc chain while the acceptors are on the other side. The orbital phase property or the number of electrons is important. The phase continuity or the six n electrons predicts that 1,2-dihydro-l-,2-azaborine could be aromatic. 

K Relaxation mechanism was also proposed [130-133], The % relaxation originates from cyclic delocalization of % electrons in the double bond through the hyperconjugation with a bonds on the saturated ring atoms under control of the orbital phase property [134, 135],... 

Keywords Facial selection. Orbital phase, Secondary orbital interaction. Orbital unsymmetrization. Ketones, Olefins, Diels-Alder dienophiles, Diels-Alder dienes, Michael acceptor. Amine nitrogen atom... 

Fig. 1 A schematic illustration of the in-phase and out-of-phase combinations of the atomic orbitals into the bonding and antibonding molecular orbitals, respectively. The dissociation limit of a H molecule corresponds to a pure diradical with degenerate singlet and triplet states...

Such an orbital phase picture in Fig. 14 is also applicable to rationalize the relative S-T gaps of hetero diradicals 19 and 20. hi comparison with their parent system, 1,3-dimethylenecyclobutadiene (DMCBD, 10), the introduction of oxygen atoms does destabilize the triplet state. The calculated energy gap between singlet and triplet states, AE deaeases in the order 10 (18.2 kcal moF ) > 19 (7.7 kcal moF ) > 20 (-20.7 kcal moF ) [64]. These results supported the orbital phase predictions. 

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