Renormalization in Chemistry

We introduce the topic of renormalization in chemistry by considering calculation of ring currents in polycyclic conjugated hydrocarbons based on the conjugated circuit model. 

---

In good solvents, the mean force is of the repulsive type when the two polymer segments come to a close distance and the excluded volume is positive this tends to swell the polymer coil which deviates from the ideal chain behavior described previously by Eq. (1). Once the excluded volume effect is introduced into the model of a real polymer chain, an exact calculation becomes impossible and various schemes of simplification have been proposed. The excluded volume effect, first discussed by Kuhn [25], was calculated by Flory [24] and further refined by many different authors over the years [27]. The rigorous treatment, however, was only recently achieved, with the application of renormalization group theory. The renormalization group techniques have been developed to solve many-body problems in physics and chemistry. De Gennes was the first to point out that the same approach could be used to calculate the MW dependence of global properties... 

The Density Matrix Renormalization Group in Quantum Chemistry... 

Mitrushenkov, A.O., Fano, G., Linguerri, R., Palmieri, P. On the possibility to use non-orthogonal orbitals for density matrix renormalization group calculations in quantum chemistry. arXiv.cond-mat, 0306058vl, 2003. 

In the last section of this review, we elaborated on the relevance and consequences of these concepts for transition-metal cluster chemistry on the basis of new results. We discussed problems and pitfalls that may arise in present-day quantum chemical DFT calculations on open-shell clusters. Clearly, these obstacles point to the necessity of developing improved density functionals and also new ab initio electron correlation methods, like, for example, the density renormalization group algorithm (151). 

Fig. 28.4. The apparent renormalized law of mass action for a gene switch is shown in the outer panel. The probability of the gene being off versus average population of transcription factor is shown. The Shea-Ackers curve is the conventional macroscopic law of mass action. Single-molecule physical chemistry reigns ...

The renormalized diffusivity D1 accounts for the process of diffusion from cell to cell as a result of the nontrivial interaction of advection and molecular diffusion [6], The renormalized reaction time xeff is the time it takes for a single cell to be filled by inert material, and it depends on the interaction of advection and production. F indicates the functional form of the renormalized chemistry. Therefore, the limiting speed of the front in the moving medium is given by veff JDE /Teff [13,14]. The problem is now reduced to derive the expressions for the renormalized parameters by means of physical considerations. 

It seems that the e3q)lidtly correlated functions, in spite of serious problems at the integral level, can be generalized in future towards the collective motions of electrons, perhaps on the basis of the renormalization theory of Kenneth Wilson (introduced into chemistry for the first time by Martin Head-Gordon). ... 

K. H. Marti, M. Reiher. The Density Matrix Renormalization Group Algorithm in Quantum Chemistry. Z. Phys. Chem., 224... 

The necessity for summing over the negative-energy states raises the question of whether we should include QED renormalization effects. The answer is, in general, yes a rigorous treatment would involve virtual pairs and renormalization with counter-terms to remove the divergences in the perturbation sums, which is beyond the scope of relativistic quantum chemistry at present. For electric perturbations, the effect of renormalization is small, because the contribution is already It is therefore... 

Cammi, R., 8c Tomasi, J. (1995). Remarks on the use of the apparent surface charges (ASC) methods in solvation problems Iterative versus matrix-inversion procedures and the renormalization of the apparent charges. Journal of Computational Chemistry, 16,1449-1458. 

---