Fully Automatized Optimization of Ring-Opening Reactions in Lactone Derivatives via Two-Step Machine Learning.

Cyclization and cycloreversion of organic compounds are fundamental kinetic processes in the design of functional molecules, molecular machines, nanoscale sensors, and switches in the field of molecular and nanoelectronics. We present a fully automatic computational platform for the design of a class of five- and six-membered ring lactones by optimizing the ring-opening reaction rate. Starting from a minimal initial parent set, our algorithm generates iteratively cascades of pools of candidate lactone derivatives where optimization and down-selection are performed without human supervision. We employ the density functional theory combined with the transition state theory to elucidate the exact mechanism leading to the lactone ring-opening reaction. On the basis of the analysis of the reaction pathway and the frontier molecular orbitals, we identify a simple descriptor that can easily correlate with the reaction rate. Consequently, we can omit computationally expensive transition state calculations and deduce the reaction rate from simple ground-state and ionic calculations. To accelerate the platform, we use a data set of the order of 800 molecules to train machine learning models for the prediction of targeted chemical properties, reducing the computational time by a 90% factor. We developed an evolutionary algorithm capable of generating data sets 3 orders of magnitude larger than the initial parent set. Thus, we can explore a large domain of chemical space using minimal computational effort. Our entire platform is modular, and our current implementation for lactone can be further generalized to more complex systems via substitution of the quantum chemical and fingerprinting modules.

Stability Analysis of the Explicit Difference Scheme for Richards Equation.

A stable explicit difference scheme, which is based on forward Euler format, is proposed for the Richards equation. To avoid the degeneracy of the Richards equation, we add a perturbation to the functional coefficient of the parabolic term. In addition, we introduce an extra term in the difference scheme which is used to relax the time step restriction for improving the stability condition. With the augmented terms, we prove the stability using the induction method. Numerical experiments show the validity and the accuracy of the scheme, along with its efficiency.

Laser heating of dielectric particles for medical and biological applications.

We consider the general problem of laser pulse heating of a spherical dielectric particle embedded in a liquid. The discussed range of the problem parameters is typical for medical and biological applications. We focus on the case, when the heat diffusivity in the particle is of the same order of magnitude as that in the fluid. We perform quantitative analysis of the heat transfer equation based on interplay of four characteristic scales of the problem, namely the particle radius, the characteristic depth of light absorption in the material of the particle and the two heat diffusion lengths: in the particle and in the embedding liquid. A new quantitative characteristic of the laser action, that is the cooling time, describing the temporal scale of the cooling down of the particle after the laser pulse is over, is introduced and discussed. Simple analytical formulas for the temperature rise in the center of the particle and at its surface as well as for the cooling time are obtained. We show that at the appropriate choice of the problem parameters the cooling time may be by many orders of magnitude larger the laser pulse duration. It makes possible to minimize the undesirable damage of healthy tissues owing to the finite size of the laser beam and scattering of the laser radiation, simultaneously keeping the total hyperthermia period large enough to kill the pathogenic cells. An example of application of the developed approach to optimization of the therapeutic effect at the laser heating of particles for cancer therapy is presented.