Intramolecular perturbation

In Chapters 4 and 5 we made use of the theory of radiationless transitions developed by Robinson and Frosch.(7) In this theory the transition is considered to be due to a time-dependent intramolecular perturbation on non-stationary Bom-Oppenheimer states. Henry and Kasha(8) and Jortner and co-workers(9-12) have pointed out that the Bom-Oppenheimer (BO) approximation is only valid if the energy difference between the BO states is large relative to the vibronic matrix element connecting these states. When there are near-degenerate or degenerate zeroth-order vibronic states belonging to different configurations the BO approximation fails. 

The transition is postulated to occur as the result of a stationary intramolecular perturbation which mixes the initial and final states of... 

As neither H nor P is specified, this amounts to a mere change in notation We only need to replace or. by E° and /). by P.. The intramolecular perturbation of qt by itself, Ptt, may be neglected, because we will only study bimolecular reactions and will invariably use the (nonperturbed) frontier orbitals of the starting materials. This point is discussed on p. 51. 

From the limited data available, we may assume that the two S-S distances are normally equal for isolated molecules of symmetrically substituted 1,6,6aS rv-trithi apentalenes, but these S-S bonds involving d orbitals seem very sensitive to extramolecular influences in the crystal lattice111 and to intramolecular perturbations, such as unsymmetrical substitution. Unequal spacing of the sulfur atoms may perhaps also result from steric interactions between symmetrically placed substituents.114... 

Reaction type Reaction scheme Intramolecular perturbation by substituents Extramolecular perturbation by medium... 

The solution (dichloromethane) spectra of polymers X, XI, and IX can be seen in Fig. 1. Surprisingly, the absorption spectrum of the l.c. p-methoxycinnamate polymer, IX, showed a 10 nm red shift relative to the two non-l.c.-cinnamate polymers, X and XI. We suggest that, in the thermodynamically most stable conformation the p-methoxycinnamate moiety was intramolecularly perturbed by the phenyl ester group. The ester, phenyl p-methoxycinnamate also shows this perturbation, but the alkyl and cycloalkyl esters do not. CPK (Corey-Pauling-Koltun) molecular models sow that the phenyl ester group could assume an orientation that was almost coplanar with the cinnamate moiety which could easily give rise to a 10 nm red shift (see Fig. 2). 

The presence of the p-methoxycinnamate moiety allowed the films of these polymers to be probed spectrophotometrically. The surprising difference in the solution vs film spectra of the l.c. polymers was accounted for by the unexpected intramolecular perturbation of the p-methoxycinnamate moiety by the phenyl ester group. The unexpected spectral changes during UV irradiation of the l.c. polymer films could be attributed to conformational changes, isomerization, and cyclobutane formation. 

Radford (1961, 1962) and Radford and Broida (1962) presented a complete theory of the Zeeman effect for diatomic molecules that included perturbation effects. This led to a series of detailed investigations of the CN B2E+ (v — 0) A2II (v = 10) perturbation in which many of the techniques of modern high-resolution molecular spectroscopy and analysis were first demonstrated anticrossing spectroscopy (Radford and Broida, 1962, 1963), microwave optical double resonance (Evenson, et at, 1964), excited-state hyperfine structure with perturbations (Radford, 1964), effect of perturbations on radiative lifetimes and on inter-electronic-state collisional energy transfer (Radford and Broida, 1963). A similarly complete treatment of the effect of a magnetic field on the CO a,3E+ A1 perturbation complex is reported by Sykora and Vidal (1998). The AS = 0 selection rule for the Zeeman Hamiltonian leads to important differences between the CN B2E+ A2II and CO a/3E+ A1 perturbation plus Zeeman examples, primarily in the absence in the latter case of interference effects between the Zeeman and intramolecular perturbation terms. 

Either electronegativity or geometry perturbation leads to orbital mixings among the orbitals of a single molecule under consideration and hence may be termed intramolecular perturbation. Lor such perturbation, the and terms of equation 3.3 are given by... 

Consider for the case of intramolecular perturbation that some of the unperturbed levels i///,. are degenerate so that = ej = -. Most common situations of... 

Two conjugated systems can differ in any of three respects. The atoms involved may be different the topology of overlap may be different and the total number of conjugated atoms may be different. We can then express any overall difference as a sum of individual perturbations of three kinds. First, monocentric perturbations, in which a given atom is altered or replaced by some other atom second, intramolecular perturbations, in which we alter the connectivity of the conjugated system and third, intermolecular perturbations, in which two smaller conjugated systems unite tjo form a larger system. 

The magnetic Hamiltonians describe the interaction of electrons with the intramolecular perturbation, that is, the intrinsic magnetic dipoles m/, via the vector potential XXi A , and with an external, spatially uniform and time-independent magnetic field B = V x A ,... 

It is expedient to employ the Rayleigh-Schrbdinger perturbation theory, or equivalent theoretical tools (e.g., equation-of-motion and propagator methods) to evaluate explicit expressions for the properties appearing in equations (4) and (5). In the presence of time-independent, spatially uniform external perturbations (e.g static homogeneous fields) or intramolecular perturbations (nuclear magnetic dipole or electric quadrupoles), described via first- and second-order interaction Hamiltonians and the expressions for the contributions to the energy up to fourth order can be written as... 

Halpern, A.M. and Weiss, K. (1968) Intramolecular perturbation effects in diamine-iodine charge-transfer complexes. J. Am. Chem. Soc., 90, 6297—6302. 

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