Boundary homogenization for a sphere with an absorbing cap of arbitrary size.

This paper focuses on trapping of diffusing particles by a sphere with an absorbing cap of arbitrary size on the otherwise reflecting surface. We approach the problem using boundary homogenization which is an approximate replacement of non-uniform boundary conditions on the surface of the sphere by an effective uniform boundary condition with appropriately chosen effective trapping rate. One of the main results of our analysis is an expression for the effective trapping rate as a function of the surface fraction occupied by the absorbing cap. As the cap surface fraction increases from zero to unity, the effective trapping rate increases from that for a small absorbing disk on the otherwise reflecting sphere to infinity which corresponds to a perfectly absorbing sphere. The obtained expression for the effective trapping rate is applied to find the rate constant describing trapping of diffusing particles by an absorbing cap on the surface of the sphere. Finally, we find the capacitance of a metal cap of arbitrary size on a dielectric sphere using the relation between the capacitance and the rate constant of the corresponding diffusion-limited reaction. The relative error of our approximate expressions for the rate constant and the capacitance is less than 5% over the entire range of the cap surface fraction from zero to unity.

Trapping of diffusing particles by clusters of absorbing disks on a reflecting wall with disk centers on sites of a square lattice.

A simple approximate formula is derived for the rate constant that describes steady-state flux of diffusing particles through a cluster of perfectly absorbing disks on the otherwise reflecting flat wall, assuming that the disk centers occupy neighboring sites of a square lattice. A distinctive feature of trapping by a disk cluster is that disks located at the cluster periphery shield the disks in the center of the cluster. This competition of the disks for diffusing particles makes it impossible to find an exact analytical solution for the rate constant in the general case. To derive the approximate formula, we use a recently suggested approach [A. M. Berezhkovskii, L. Dagdug, V. A. Lizunov, J. Zimmerberg, and S. M. Bezrukov, J. Chem. Phys. 136, 211102 (2012)], which is based on the replacement of the disk cluster by an effective uniform partially absorbing spot. The formula shows how the rate constant depends on the size and shape of the cluster. To check the accuracy of the formula, we compare its predictions with the values of the rate constant obtained from Brownian dynamics simulations. The comparison made for 18 clusters of various shapes and sizes shows good agreement between the theoretical predictions and numerical results.

Diffusion in the presence of cylindrical obstacles arranged in a square lattice analyzed with generalized Fick-Jacobs equation.

The generalized Fick-Jacobs equation is widely used to study diffusion of Brownian particles in three-dimensional tubes and quasi-two-dimensional channels of varying constraint geometry. We show how this equation can be applied to study the slowdown of unconstrained diffusion in the presence of obstacles. Specifically, we study diffusion of a point Brownian particle in the presence of identical cylindrical obstacles arranged in a square lattice. The focus is on the effective diffusion coefficient of the particle in the plane perpendicular to the cylinder axes, as a function of the cylinder radii. As radii vary from zero to one half of the lattice period, the effective diffusion coefficient decreases from its value in the obstacle free space to zero. Using different versions of the generalized Fick-Jacobs equation, we derive simple approximate formulas, which give the effective diffusion coefficient as a function of the cylinder radii, and compare their predictions with the values of the effective diffusion coefficient obtained from Brownian dynamics simulations. We find that both Reguera-Rubi and Kalinay-Percus versions of the generalized Fick-Jacobs equation lead to quite accurate predictions of the effective diffusion coefficient (with maximum relative errors below 4% and 7%, respectively) over the entire range of the cylinder radii from zero to one half of the lattice period.

Diffusion in periodic two-dimensional channels formed by overlapping circles: comparison of analytical and numerical results.

We study two-dimensional diffusion in a channel formed by periodic overlapping circles. Periodic variation of the channel width leads to the slowdown of diffusion along the channel axis. There are several approximate approaches, which allow one to analyze the slowdown. We use these approaches to derive five expressions for the effective diffusion coefficient of a point Brownian particle in the channel. To check the accuracy of the expressions we compare their predictions with the effective diffusion coefficient obtained from Brownian dynamics simulations.

Unbiased diffusion in tubes with corrugated walls.

This study is devoted to unbiased motion of a point Brownian particle in a tube with corrugated walls made of conical sections of a varying length. Effective one-dimensional description in terms of the generalized Fick-Jacobs equation is used to derive a formula which gives the effective diffusion coefficient of the particle as a function of the geometric parameters of the tube. Comparison with the results of Brownian dynamics simulations allows us to establish the domain of applicability of both the one-dimensional description and the formula for the effective diffusion coefficient.

Theoretical study of cytosine-Al, cytosine-Cu and cytosine-Ag (neutral, anionic and cationic).

The binding of cytosine to Al, Cu and Ag has been analyzed using the hybrid B3LYP density functional theory method. The three metals all have open shell electronic configuration, with only one unpaired valence electron. Thus it is possible to study the influence of electronic configuration on the stability of these systems. Neutral, cationic and anionic systems were analyzed, in order to assess the influence of atomic charge on bond formation. We argue that in the case of anions, nonconventional hydrogen bonds are formed. It is generally accepted that the hydrogen bond A-H...B is formed by the union of a proton donor group A-H and a proton acceptor B, which contains lone-pair electrons. In this study, we found that in the case of (Cu-cytosine)(-1) and (Ag-cytosine)(-1), N-H...Cu and N-H...Ag bonds are geometrically described as nonconventional hydrogen bonds. Their binding energies fall within the range of -20.0 to -55.4 kcal/mol (depending on the scheme of the reaction) and thus they are classified as examples of strong (>10 kcal/mol) hydrogen bonds.

Diffusion in linear porous media with periodic entropy barriers: A tube formed by contacting spheres.

The problem of transport in quasi-one-dimensional periodic structures has been studied recently by several groups [D. Reguera et al., Phys. Rev. Lett.96, 130603 (2006); P. S. Burada et al., Phys. Rev. E75, 051111 (2007); B. Q. Ai and L. G. Liu, ibid.74, 051114 (2006); B. Q. Ai et al., ibid.75, 061126 (2007); B. Q. Ai and L. G. Liu, J. Chem. Phys.126, 204706 (2007); 128, 024706 (2008); E. Yariv and K. D. Dorfman, Phys. Fluids19, 037101 (2007); N. Laachi et al., Europhys. Lett.80, 50009 (2007); A. M. Berezhkovskii et al., J. Chem. Phys.118, 7146 (2003); 119, 6991 (2003)]. Using the concept of "entropy barrier" [R. Zwanzig, J. Phys. Chem.96, 3926 (1992)] one can classify such structures based on the height of the entropy barrier. Structures with high barriers are formed by chambers, which are weakly connected with each other because they are connected by small apertures. To escape from such a chamber a diffusing particle has to climb a high entropy barrier to find an exit that takes a lot of time [I. V. Grigoriev et al., J. Chem. Phys.116, 9574 (2002)]. As a consequence, the particle intrachamber lifetime tau(esc) is much larger than its intrachamber equilibration time, tau(rel), tau(esc)>>tau(rel). When the aperture is not small enough, the intrachamber escape and relaxation times are of the same order and the hierarchy fails. This is the case of low entropy barriers. Transport in this case is analyzed in the works of Schmid and co-workers, Liu and co-workers, and Dorfman and co-workers, while the work of Berezhkovskii et al. is devoted to diffusion in the case of high entropy barriers.

Ca, Cd, Zn, and their ions interacting with Cytosine: a theoretical study.

Metal atoms play a major role in the chemical behavior of biological systems. In this work, known issues of the metal-base interactions, such as the stabilization of different tautomers of cytosine that could be incompatible with the DNA double helix, are researched using DFT methods. Ca-, Zn-, and Cd-cytosine in neutral and ionic forms were studied at the B3LYP/LANL2DZ level. Several neutral and ionic isomers were found within an interval of 10 kcal/mol of relative stability, with the most stable isomer in each group being a compound derived from the canonical isomer of cytosine, except for the dications where two iso-energetic isomers were found. Interatomic lengths from each metal atom to the nearest atoms in cytosine's ring were larger than 2 A, discouraging the possibility of a covalent interaction, as supported by additional evidence from molecular orbitals. The interaction between metal and cytosine, electrostatic in nature, is reinforced with the increase of the metal's nuclear charge. Additionally, the ionization energies of the metal-cytosine compounds exhibit a significant reduction (below 6 eV) compared with that of plain cytosine (8.7 eV), posing an interesting possibility with respect to the experimental determination of the photoelectron spectra of these compounds. Analyses of the energetics of the global reactions to form cationic species show that metal cations bind more strongly to neutral cytosine than to neutral metals. Metal dications form the most stable compounds with neutral cytosine, and the stabilities of these systems decrease as (Zn-cyt)2+ > (Cd-cyt)2+ > (Ca-cyt)2+. Aromaticities computed via the HOMA indexes also support the observation regarding the greater affinity of cytosine for metal cations.

Metal-Molecule Interactions To Produce Hydrogen: What Do They Have in Common?

The main purpose of this work is to study metal-molecule interactions that can lead to the production of molecular hydrogen. Two systems were chosen for this analysis: yttrium atom and clusters interacting with the simple electron donor ammonia (NH3) and copper atoms and ions with imidazole. For yttrium with ammonia as well as for copper with imidazole there is a charge-transfer process from the metal to the molecule that promotes the dissociation of the hydrogen atoms.

Deprotonated cytosine anions: a theoretical prediction of photoelectron spectra.

Predictions on the photoelectron spectra of deprotonated cytosine anions (cytosinate, Cye(-)) have been made with ab initio electron propagator methods. Two imino-oxo forms are most stable, but four other isomers have energies within 10 kcal/mol. The first vertical electron detachment energies (VEDEs) for the three most stable Cye(-) isomers are approximately 3.4 eV. Imino-oxy VEDEs are about 0.3 eV smaller. For each anion, the lowest VEDE corresponds to a pi Dyson orbital. The order of higher final states is changed when relaxation and correlation effects are considered. Considerable mixing between lone-pair and bonding lobes occurs in the sigma Dyson orbitals.