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Chemical reactions involving diffusion of reactants and subsequent chemical fixation steps are generally termed "diffusion-influenced" (DI). Virtually all biochemical processes in living media can be counted among them, together with those occurring in an ever-growing number of emerging nano-technologies. The role of the environment's geometry (obstacles, compartmentalization) and distributed reactivity (competitive reactants, traps) is key in modulating the rate constants of DI reactions, and is therefore a prime design parameter. Yet, it is a formidable challenge to build a comprehensive theory able to describe the environment's "reactive geometry". Here we show that such a theory can be built by unfolding this many-body problem through addition theorems for special functions. Our method is powerful and general and allows one to study a given DI reaction occurring in arbitrary "reactive landscapes", made of multiple spherical boundaries of given size and reactivity. Importantly, ready-to-use analytical formulas can be derived easily in most cases. Diffusion-influenced reactions (DIR) are ubiquitous in many contexts in physics, chemistry and biology [1,2] and keep on sparking intense theoretical and computational activity in many fields [3][4][5][6][7][8][9][10][11]. Modern examples of emerging nanotechnologies that rely on controlled alterations of diffusion and reaction pathways in DIRs include different sorts of chemical and biochemical catalysis involving complex nano-reactors [12,13], nanopore-based sequencing engines [14] and morphology control and surface functionalization of inorganic-based delivery vehicles for controlled intracellular drug release [15,16].However, while the mathematical foundations for the description of such problems have been laid nearly a century ago [17], many present-day problems of the utmost importance at both the fundamental and applied level are still challenging. Notably, arduous difficulties arise in the quantification of the important role played by the environment's geometry (obstacles, compartmentalization) [18] and distributed reactivity (patterns of competitive reaction targets or traps) in coupling transport and reaction pathways in many natural and artificial (bio)chemical reactions [1,19,20].A formidable challenge in modeling environmentrelated effects on chemical reactions is represented by the intrinsic many-body nature of the problem. This is brought about essentially by two basic features, common to virtually all realistic situations, namely (i) finite density of reactants and other inert species (in biology also referred to as macromolecular crowding [21,22]) and (ii) confining geometry of natural or artificial reaction domains in 3D space. In general, the presence of multiple reactive and non-reactive particles/boundaries cannot be neglected in the study of (bio)chemical reactions occurring in real milieux, where the geometrical compactness of the environment may have profound effects, such as first-passage times that are non-trivially influenced by the starti...

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We apply the generalized method of separation of variables (GMSV) to solve boundary value problems for the Laplace operator in three-dimensional domains with disconnected spherical boundaries (i.e., an arbitrary configuration of non-overlapping partially reactive spherical sinks or obstacles). We consider both exterior and interior problems and all most common boundary conditions: Dirichlet, Neumann, Robin, and conjugate one. Using the translational addition theorems for solid harmonics to switch between the local spherical coordinates, we obtain a semi-analytical expression of the Green function as a linear combination of partial solutions whose coefficients are fixed by boundary conditions. Although the numerical computation of the coefficients involves series truncation and matrix inversion, the use of the solid harmonics as basis functions naturally adapted to the intrinsic symmetries of the problem makes the GMSV particularly efficient, especially for exterior problems. The obtained Green function is the key ingredient to solve boundary value problems and to determine various characteristics of stationary diffusion such as reaction rate, escape probability, harmonic measure, residence time, and mean first passage time, to name but a few. The relevant aspects of the numerical implementation and potential applications in chemical physics, heat transfer, electrostatics, and hydrodynamics are discussed.

The effect of an external electric field on fluorescence quenching due to electron transfer from a photoexcited electron donor to an acceptor has been analyzed theoretically. The model predicts that at weak fields the variation ΔI(c,F)/I(c,0) in the steady-state monomer fluorescence intensity induced by an external electric field is proportional to the square of the field strength F and to the concentration of acceptors c. Similar relations have been reported for the fluorescence intensity of ethylcarbazole doped in poly-methyl-methacrylate films in the presence of dimethyl terephtathalate and an external electric field with a strength up to 0.01 V/Å. The effect of the free energy change of the electron transfer reaction on the c and F dependencies of ΔI(c,F)/I(c,0) has been discussed within the framework of the present model.

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Articles you may be interested inNonadiabatic dynamics of electron transfer in solution: Explicit and implicit solvent treatments that include multiple relaxation time scales J. Chem. Phys. 140, 034113 (2014); 10.1063/1.4855295Effect of an external electric field on the diffusion-influenced geminate reversible reaction of a neutral particle and a charged particle in three dimensions. III. Ground-state ABCD reactionWe theoretically investigate the effect of an external electric field on the free energy change of electron transfer reaction in polar solvents. The external electric field produces polarization both on the solutes and in the solvent. Since the polarization produced on the solute differs from that in the solvent, apparent surface charge is created on the surface of the solutes. The polarization charge on the surface of the solutes interacts with the charge associated with the electron transfer. The free energy change of the reaction including such effect is calculated rigorously. A simple formula is derived and compared to the exact result in the case of spherical solutes in the dielectric continuum media. Only slight deviations are observed for any values of the solvent polarity and of the ratio between the radii of the donor and the acceptor molecules. In addition, we also applied the same method to evaluate the reorganization energy rigorously: The Marcus expression for the reorganization energy is an approximate one. The accuracy of the Marcus expression is assessed by comparing it with the exact result.

We consider the steady-state competition between perfectly absorbing sinks distributed uniformly in a spherical region. An equation for the coarse-grained concentration of diffusing particles inside the region is derived following the renormalization group approach. The total flux of diffusing particles, their coarse-grained concentration, and the characteristic penetration length are found. We then compare our results with so-called mean field approximation, and show that the latter approach cannot correctly describe the coarse-grained concentration in the system under consideration.