Linear molecules orbital interactions

The expressions for the rotational energy levels (i.e., also involving the end-over-end rotations, not considered in the previous works) of linear triatomic molecules in doublet and triplet II electronic states that take into account a spin orbit interaction and a vibronic coupling were derived in two milestone studies by Hougen [72,32]. In them, the isomorfic Hamiltonian was inboduced, which has later been widely used in treating linear molecules (see, e.g., [55]). 

In linear molecules only the component of orbital momentum normal to the figure axis is destroyed, that along the figure axis being retained. In non-linear molecules with strong interatomic interactions the concept of orbital angular momentum loses its significance. 

Having dealt with the transformation of all the MOs of the linear molecules to those of the bent variety, there is a very important extra effect which is incorporated into Figure 5.20 as the result of the interaction of the orbitals 6a, and 7a,. Because these orbitals have the same symmetry and are fairly close to each other in energy, they may and do interact so that the 6a, orbital is stabilized at the expense of the 7a, orbital. The atomic orbital contributions to the MOs are shown in Figure 5.21 for the 2n -6a. and 5a +-7a. transformations. 

Additionally, Figure 6.4 shows the variation in the energy of the occupied 5d orbitals when the P-Au-P angle varies from 180° (linear coordination) to 120°. Thus, while the dzi orbital stabilizes slightly, the dxz destabilizes as a consequence of the interaction of this orbital with the 3px and 3pz orbitals of phosphorus. The main consequence is that, below 168°, the former HOMO (dz2 in linear molecules) is replaced by the dxz orbital, which displays a higher energy and, consequently, a lower energy is needed to reach the excited state. 

Polyatomic molecules. The same term classifications hold for linear polyatomic molecules as for diatomic molecules. We now consider nonlinear polyatomics. With spin-orbit interaction neglected, the total electronic spin angular momentum operator 5 commutes with //el, and polyatomic-molecule terms are classified according to the multiplicity 25+1. For nonlinear molecules, the electronic orbital angular momentum operators do not commute with HeV The symmetry operators Or, Os,. .. (corresponding to the molecular symmetry operations R, 5,. ..) commute... 

In the more general case S 0 and the molecular angular momenta can be coupled in various ways. It is of primary importance to ascertain to what extent the interaction of the spin momentum S with the orbital momentum L is comparable to the rotation of the molecule, as well as to the interaction of each of the momenta L and S with the internuclear axis. An attempt to establish a hierarchy of interactions yields a number of possible, certainly idealized, coupling cases between angular momenta, first considered by Hund and known as Hund s coupling cases. Here we will discuss the three basic (out of five) cases of coupling of momenta in a linear molecule. 

Calculate and display the orbitals for the linear molecule BeH2. Describe how they illustrate the interaction of the outer group orbitals with the orbitals on the central atom. 

A carbon-carbon triple bond results from the interaction of two sp-hybridized carbon atoms (Section 1.10). Recall that the two sp hybrid orbitals of carbon lie at an angle of 180° to each other along an axis perpendicular to the axes of the two unhybridized 2py and 2p orbitals. When two sp-hybridized carbons approach each other, one sp-sp cr bond and two p-p TT bonds are formed. The two remaining sp orbitals form bonds to other atoms at an angle of 180° from the carbon-carbon bond. Thus, acetylene, C2H2, is a linear molecule with H-C=C bond angles of 180° (Figure 8.1). 

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