Описание: Спецкурс читается на английском языке в весеннем семестре в объеме одной лекции (двух академических часов) в неделю. Он ориентирован на студентов 5-6 курса и аспирантов, специализирующихся в области физической химии, а также неорганической, органической и биологической химии. В рамках этого курса рассматривается иерархия подходов и концептуальная связь между квантово-механическими методами описания стационарных состояний и динамической эволюции молекулярных систем, в том числе результатов их реакционных столкновений, и базовыми теориями химической кинетики, изучавшимися слушателями ранее в общем курсе физической химии. Помимо этого, рассматриваются существующие в настоящее время квантово-химические подходы к анализу динамики конформационных и реакционных превращений молекулярных систем в различных внешних условиях и теоретически обосновываются варианты оценки классических индексов реакционной способности молекул на основании результатов стационарных квантовых расчетов.
Данный курс концептуально связывает и дополняет несколько базовых дисциплин, изучавшихся студентами химического факультета на 3-4 курсах (физическая химия, квантовая механика, квантовая химия и строение молекул), и нацелен на формирование у слушателей целостной картины теоретических основ химии.
Программа курса представлена ниже.
Wave functions of particles and molecular systems vs. waves of light. Time-dependent and stationary description of systems. Propagator and the time evolution of a molecular system. Computational approaches to modeling the quantum dynamics of a system.
Binary collisions. Scattering operator and S matrix. Probabilities of binary transformations depending on the internal quantum states of reagent and product particles and characteristics of their relative classical motion in space.
Reagent and product particle flows. Differential and total cross sections of binary reactive collisions. Velocity density probability functions. Canonical vs. grand canonical ensembles. State-to-state, microscopic, and macroscopic reaction rate constants.
Equilibrium approximation for the velocity density distribution functions of reagent particles: Maxwell distribution. Internal quantum state distribution of particles: canonical Gibbs ensemble. Validity of equilibrium approximation and the limits of applicability. State-to-state and macroscopic reaction rate constants under equilibrium conditions.
Adiabaticity of collisions. Transmission factor and Eyring kinetic equation. Structureless limit of the reactive collision model and Trautz–Lewis equation.
Adiabiatic vs. nonadiabatic description of a system. Stationary aspect: analysis of the nuclear problem; criterion expressed via Born–Fock relation; physical interpretation of the criterion. Dynamic aspect of the problem: Massey parameter and criterion and their generalizations for a multidimensional case in relation to the stationary criterion.
Nonempirical molecular dynamics at different levels of consistency between the evolution of electronic and nuclear subsystems: Born–Oppenheimer molecular dynamics; molecular dynamics with surface hopping; and Car–Parinello molecular dynamics. Approximations, limitations, and applicability of the methods.
Analytical approximations of potential energies. Force fields. Classical molecular dynamics. Nuclear states of molecules: independent harmonic oscillators or interacting vibrations and rotations. Relation between the redistribution of classical kinetic energy of nuclei and the solutions of nuclear quantum problems: complex vibrational states and resonance phenomena.
Molecules in electromagnetic fields and photochemical processes. Reaction paths in different electronic states. Basic assumptions for estimating transition probabilities. Induced and spontaneous transitions. Equilibrium conditions and tentative estimates of the lifetimes of molecules in excited states. Jabloński diagram and rate constants of diverse processes: vibrational relaxation and internal conversion; quenching; intersystem crossing, fluorescence and phosphorescence. Quantum yields of fluorescence and chemical transformation.
Reaction energetics. Beyond the one-determinant approximation: ideology of Møller-Plesset perturbation theory, configuration interaction, multiconfigurational self-consistent field, and coupled clusters approaches.
Reactions viewed as the electron density redistribution. Basic concepts of solving the electronic Schrödinger equation and interpretation of the solutions. Localized orbitals and frontier molecular orbital theory.
Reactants analyzed in terms of the electron density distribution. Electronegativity and chemical potential. Sanderson’s electronegativity equalization principle. Chemical hardness and global softness. Maximum hardness principle.
Density-functional based interpretation: reactivity indices. Pearson’s hard and soft acids and bases principle. Activation hardness concept. Electronic Fukui functions and the orientation effect in chemical reactions. Condensed Fukui functions and local softness; relative electro- and nucleophilicity.