Topological effects

Muller M, Wittmer J P and Cates M E 1996 Topological effects in ring polymers a computer simulation study Phys. Rev. E 53 5063... 

As mentioned in the introduction, the simplest way of approximately accounting for the geomehic or topological effects of a conical intersection incorporates a phase factor in the nuclear wave function. In this section, we shall consider some specific situations where this approach is used and furthermore give the vector potential that can be derived from the phase factor. 

It is known that multivalued adiabatic electronic manifolds create topological effects [23,25,45]. Since the newly introduced D matrix contains the information relevant for this manifold (the number of functions that flip sign and their identification) we shall define it as the Topological Matrix. Accordingly, K will be defined as the Topological Number. Since D is dependent on the contour F the same applies to K thus K = f(F),... 

The general formula and the individual cases as presented in Eq. (97) indicate that indeed the number of conical intersections in a given snb-space and the number of possible sign flips within this sub-sub-Hilbert space are interrelated, similar to a spin J with respect to its magnetic components Mj. In other words, each decoupled sub-space is now characterized by a spin quantum number J that connects between the number of conical intersections in this system and the topological effects which characterize it. 

Patoux C, Coudret C, Launay J-P, Joachim C, Gourdon A (1997) Topological effects on intramolecular electron transfer via quantum interference. Inorg Chem 36(22) 5037-5049... 

Annelation of additional aromatic units to the basic cis-1,2-diphenylethylene system exerts strong effects on its inherent reactivity. In the usual MO description these effects can be traced to the effect of the structure of the new skeleton on the highest occupied and lowest unoccupied orbitals at the atoms forming the new bond and therefore can be properly considered as topological effects. As such effects are quite numerous we shall limit ourseivs to only a few examples. Thus o-terphenyl 103) does not give any DHP under usual conditions ... 

These methods model the log P by adding the specific contributions of elementary building blocks of a molecule, that is, the chemical monoatomic or multiatomic fragments. The geometrical and topological effects that operate in such a case mean that several correction factors have to be added to the additivity scheme. 

ClogP This method developed by Leo and Hansch presents some similarities with the method of Rekker, since the log P of a molecule is calculated by adding lipophUicity values attributed to multiatomic fragments and numerous corrections factors which take into account not only geometrical and topological effects but also electronic and steric effects (Equation 5.3) [39-41]. 

Guldi DM, Giacalone E, de la Torre G et al (2005) Topological effects of a rigid chiral spacer on the electronic interactions in donor-acceptor ensembles. Chem Eur J 11 7199-7210... 

C. Topological Effect Associated with Voltage Measurement... 

The existence of topological effects affecting the validity of Stokes ... 

The same is true for low-dimensional systems, d — 1 and 2. The point is not only that for such systems the better statistics could be achieved accompanied with reasonable computational time spent for it. Another circumstance is that we can expect here that the superposition approximation gives greater errors. For example, for one-dimensional contact recombination the so-called bus effect is known [17] given particles A and B can react only after particles separating them disappear during reaction. This topological effect is not foreseen by the superposition approximation but can affect considerably the reaction rate. 

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