Quantum Mechanical Degrees Of Freedom Research Articles

Reaction path potential for complex systems derived from combined ab initio quantum mechanical and molecular mechanical calculations.

Combined ab initio quantum mechanical and molecular mechanical calculations have been widely used for modeling chemical reactions in complex systems such as enzymes, with most applications being based on the determination of a minimum energy path connecting the reactant through the transition state to the product in the enzyme environment. However, statistical mechanics sampling and reaction dynamics calculations with a combined ab initio quantum mechanical (QM) and molecular mechanical (MM) potential are still not feasible because of the computational costs associated mainly with the ab initio quantum mechanical calculations for the QM subsystem. To address this issue, a reaction path potential energy surface is developed here for statistical mechanics and dynamics simulation of chemical reactions in enzymes and other complex systems. The reaction path potential follows the ideas from the reaction path Hamiltonian of Miller, Handy and Adams for gas phase chemical reactions but is designed specifically for large systems that are described with combined ab initio quantum mechanical and molecular mechanical methods. The reaction path potential is an analytical energy expression of the combined quantum mechanical and molecular mechanical potential energy along the minimum energy path. An expansion around the minimum energy path is made in both the nuclear and the electronic degrees of freedom for the QM subsystem internal energy, while the energy of the subsystem described with MM remains unchanged from that in the combined quantum mechanical and molecular mechanical expression and the electrostatic interaction between the QM and MM subsystems is described as the interaction of the MM charges with the QM charges. The QM charges are polarizable in response to the changes in both the MM and the QM degrees of freedom through a new response kernel developed in the present work. The input data for constructing the reaction path potential are energies, vibrational frequencies, and electron density response properties of the QM subsystem along the minimum energy path, all of which can be obtained from the combined quantum mechanical and molecular mechanical calculations. Once constructed, it costs much less for its evaluation. Thus, the reaction path potential provides a potential energy surface for rigorous statistical mechanics and reaction dynamics calculations of complex systems. As an example, the method is applied to the statistical mechanical calculations for the potential of mean force of the chemical reaction in triosephosphate isomerase.

Reversible work transition state theory: application to dissociative adsorption of hydrogen

A practical method for finding free energy barriers for transitions in high-dimensional classical and quantum systems is presented and used to calculate the dissociative sticking probability of H2 on a metal surface within the transition state theory. The reversible work involved in shifting the system confined to a hyperplane from the reactant region towards products is evaluated directly. Quantum mechanical degrees of freedom are included by using Feynman path integrals with the hyperplane constraint applied to the centroid of the cyclic paths. An optimal dividing surface for the rate estimated by the transition state theory is identified naturally in the course of the reversible work evaluation. The free energy barrier is determined relative to the reactant state directly so that an estimate of the transition rate can be obtained without requiring a solvable reference model for the transition state. The method has been applied to calculations of the sticking probability of a thermalized hydrogen gas on a Cu(110) surface. The two hydrogen atoms and eight surface Cu atoms were included quantum mechanically and over two hundred atoms in the Cu crystal where included classically. The activation energy for adsorption and desorption was determined and found to be significantly lowered by tunneling at low temperature. The calculated values agree quite well with experimental estimates for adsorption and desorption. Dynamical corrections to the classical transition state theory rate estimate were evaluated and found to be small.

FIELD THEORY APPROACH TO CRITICAL QUANTUM IMPURITY PROBLEMS AND APPLICATIONS TO THE MULTI-CHANNEL KONDO EFFECT

A new, general approach to finding exact solutions of Quantum Impurity Problems is reviewed, in which a local quantum mechanical degree of freedom is coupled to an extended variable, having gapless excitations. The principle ideas, using Conformal Field Theory techniques, are demonstrated in the example of the Multi-Channel Kondo effect, which exhibits unusual non-Fermi-liquid behavior at low temperatures and which appears to be relevant for Heavy Fermion Materials. In particular, static and dynamic Green's functions as well as transport and pairing properties are calculated exactly at low temperatures. Quantum Impurity Problems provide realizations of non-trivial, fully interacting Conformal Field Theories.