Electronic parity rule

Paddon-Row MN, Shephard MJ (1997) Through-bond orbital coupling, the parity rule, and the design of superbridges which exhibit greatly enhanced electronic coupling a natural bond orbital analysis. J Am Chem Soc 119 5355-5365... 

M. N. Paddon-Row, M. J. Shephard, Through-Bond Orbital Coupling, the Parity Rule, and the Design of Superbridges Which Exhibit Greatly Enhanced Electronic Coupling - a Natural Bond Orbital Analysis , J. Am. Chem. Soc 1997,119, 5355-5365. 

Thus, the chemical interconversion for equal electronic parity channels has four separated aspects i) activation via molding of reactants ii) population of TS rovibrational quantum states iii) population of reactants molded into configurations covered by the TS, and iv) relaxation towards products in their ground states. All such changes are submitted to energy and angular momentum conservation rules. 

The electronic quantum state ofthe pair H,ls> H+>= in> remains invariant at all distances. The electron transfer will not take place in a direct manner because the electronic parity is equal for both channels. The interconversion process requires aTS with parity -1. Among the states available to a system decomposable in one electron and two protons (or proton deuterium, etc) there are the hydrogen molecule ion species. The first electronic excited state (leu) ofthe molecular ion H2+ provides an "intermediate" (Q-state) for the interconversion once angular momentum conservation rules are fulfilled. The state (lau) is found above the in> and out> states leading to resonance in the cross section. This state may either relax to the (lrg) state yielding the hydrogen molecule ion and emitting a photon as this state is 2.8eV below dissociation, or it may take the product channels. This is a FC-like process. The reaction (27) is a prototype of electron transfer (ET). Thus, for any ET reaction whose in> and out> asymptotic electronic states share the same parity, the actual interconversion would require the mediation of a TS. 

The nitrogen rule requires that the molecular mass is always even when the number of nitrogen atoms is even or zero. This results from the fact that nitrogen has a different mass parity and valence electrons parity mass 14 u, five peripheral electrons. Both of these parities are identical in the case of any other atom. It should be noted that this holds only if we consider the mass of the predominant isotope. Thus, the chemical mass of bromine is 80 u, an even number, but its predominant isotope is that of mass 79 u, an odd mass. In the same way, isotopically labelled compounds do not always obey this rule. 

An odd number of nitrogen atoms brings about an odd molecular mass in daltons such as is defined in mass spectrometry NH3 17, CH3NH2 31, and so on. Thus, in the case of an odd number of nitrogens, the earlier rule must be inverted for the ion, the mass parity is the same as the electron parity. 

The fragmentation of these radical cations without any rearrangement or without any cleavage of an even number of bonds such as occurs in rings necessarily leads to an even-electron, or closed shell, ion and to a neutral radical. The parity rules were discussed in Section 6.6. 

McLafferty rearrangement through a six-atom ring intermediate. Figure 6.11 shows another example and details the rules linking the mass and electron parities. 

McLafferty [9] proposed classifying the reactions of even-electron ions that obey the parity rule (an even ion yields an even ion + neutral fragment) as follows ... 

The reactions considered up to now were limited to those of the McLafferty classification with regard to the parity rule. The reactions of even-electron ions (EE) that do not obey the parity rule are much rarer and more difficult to predict. They are often observed in ions with extended n systems, but they often imply complex rearrangements, as is shown in the case of tropylium ... 

The ground level electronic configuration of trivalent europium is / . Transitions within the / shell are responsible for the crystal spectra. Transitions are forbidden in a free ion by the parity rule for electric dipole transitions. In a crystal or glass, forced electric transitions become allowed as a consequence of coupling of odd electronic wave functions due to the odd parity terms in the crystal field expansion. Considering the static field approximation in the theory developed by Judd (4) and Ofelt (5), the contribution of the odd parity part of the cr5rstal field is calculated by mixing states of different parity. 

Stone [35] showed that for deltahedral clusters the L" MOs are generally bonding. The L" MOs are, therefore, generally antibonding, since the parity inversion operation leads to a reversal of the bonding properties of L" and L . He used the methodology of Tensor Surface Harmonic theory to derive the n + 1 skeletal electron pair rule for... 

In Fig. 5 we show the geometry assumed by a typical octahedral inorganic complex, and in Figs. 6, 7, and 8 we depict the behavior of the nuclear motions, electronic energies, and charge amplitude functions of an exemplary such system, TiF . As Ti + has the electronic structure [A]3< -, its ground electronic state is by Fig. 7, and its first excited state is Eg. By the parity rule g -K g, we see that the emission Eg is electronically for-... 

In the lowest optieally excited state of the molecule, we have one eleetron (ti ) and one hole (/i ), each with spin 1/2 which couple through the Coulomb interaetion and can either form a singlet 5 state (5 = 0), or a triplet T state (S = 1). Since the electric dipole matrix element for optical transitions — ep A)/(me) does not depend on spin, there is a strong spin seleetion rule (AS = 0) for optical electric dipole transitions. This strong spin seleetion rule arises from the very weak spin-orbit interaction for carbon. Thus, to turn on electric dipole transitions, appropriate odd-parity vibrational modes must be admixed with the initial and (or) final electronic states, so that the w eak absorption below 2.5 eV involves optical transitions between appropriate vibronic levels. These vibronic levels are energetically favored by virtue... 

A mistake often made by those new to the subject is to say that The Laporte rule is irrelevant for tetrahedral complexes (say) because they lack a centre of symmetry and so the concept of parity is without meaning . This is incorrect because the light operates not upon the nuclear coordninates but upon the electron coordinates which, for pure d ox p wavefunctions, for example, have well-defined parity. The lack of a molecular inversion centre allows the mixing together of pure d and p ox f) orbitals the result is the mixed parity of the orbitals and consequent non-zero transition moments. Furthermore, had the original statement been correct, we would have expected intensities of tetrahedral d-d transitions to be fully allowed, which they are not. 

Ti + belongs to the d configuration, which is the simplest one. The free ion has fivefold orbital degeneracy ( D), which is spht into two levels E and T2) in octahedral symmetry, which is quite common for transition metal ions. The only possible optical transition with excitation is from T2 to E. This transition is a forbidden one, since it occurs between levels of the d-sheU. Therefore the parity does not changed. The parity selection rule may be relaxed by the coupling of the electronic transition with vibrations of suitable symmetry. 

Electron configuration of Bp" is (6s) (6p) yielding a Pip ground state and a crystal field split Pap excited state (Hamstra et al. 1994). Because the emission is a 6p inter-configurational transition Pap- Pip. which is confirmed by the yellow excitation band presence, it is formally parity forbidden. Since the uneven crystal-field terms mix with the (65) (75) Si/2 and the Pap and Pip states, the parity selection rule becomes partly lifted. The excitation transition -Pl/2- S 1/2 is the allowed one and it demands photons with higher energy. 

Photoluminescence of ZnS Mn occurs when the phosphor absorbs photon energy corresponding to the band gap of ZnS and relaxes to release the excess energy of the exciton (a pair of an s-p electron and a hole). Based on the selection rule of Laporte, the symmetrical field of 6-coordinated Mn(ll) does not allow the d-d transition since it is not associated with the change in the parity. The 4-coordinated Mn(lI), in contrast, allows a partial d-p hybridization, enabling the d-d transition. 

---