Pavol Baňacký

Theory of particle transfer dynamics in solvated molecular complexes: analytic solutions of the discrete time-dependent nonlinear Schrödinger equation. I. Conservative system

Abstract The time-dependent nonlinear equation of motion for probability density of the proton in solvated symmetric H-bond systems is derived. The exact analytic solutions as well as phase trajectories representations diclose quite a complicated dependence of the proton dynamics on the strength of the nonlinear coupling. Our theoretical treatment describes in a unified way the transition from “free” proton transfer to a “self-trapped” behaviour when an initial structure is stabilised. The study concerns a conservative system and the results are compared with the dynamics of a linearly coupled model.

ADIABATIC CORRECTION TO THE ENERGY OF MOLECULAR SYSTEMS : THE CPHF EQUIVALENT OF THE BORN-HANDY FORMULA

Abstract The Born–Handy formula, recently shown by Kutzelnigg to be a rigorous expression for the calculation of the adiabatic correction, has been, on the level of a ground state SCF wavefunction, reformulated and linked to the coefficients of the standard coupled perturbed Hartree–Fock (CPHF) method. The contribution of the electron correlation via second-order perturbation theory is also presented. The solution of the corresponding secular equation of the nuclear motion enables the calculation of the adiabatic correction over the particular normal modes. The method offers the possibility of extending high-precision calculations of the adiabatic correction to more complex systems. Test calculations have been performed for H 2 , HD and D 2 and the results are in satisfactory agreement with the exact figures.

Nonlinearity and irreversibility in the theory of the solvent effect of proton transfer dynamics. II. Dissipative system

Abstract The quantum-statistical theory of the dynamics of proton transfer in solvated H-bond complexes is formulated. The theory takes into account a H-bond complex interaction with an environmental fast electronic polarisation as well as the coupling to the environment slow degrees of freedom that are connected with vibrational-rotational motion. The equation of motion for a reduced density matrix is derived in the form of a nonlinear generalised master equation. For the dynamics of the proton transfer in a symmetric double-well potential, the kinetic equation for the reactant state probability density has also been derived and solved. Results for different environments and temperatures are presented.

On the mechanism of high-temperature superconductivity in hydrogen sulfide at 200 GPa: Transition into superconducting anti-adiabatic state in coupling to H-vibrations

We have shown that adiabatic electronic structure of superconducting phase of sulphur hydride at 200 GPa is unstable toward vibration motion of H-atoms. Theoretical study indicates that in coupling to H-vibrations, system undergoes transition from adiabatic into stabilised anti-adiabatic multi-gap superconducting state at temperature which can reach 203 K.

Theoretical aspects of the effects of coupled coherent-incoherent dynamics on the primary processes of photosynthesis

Abstract The general method of the coupled coherent-incoherent mechanism including the effect of quenching has been applied to the study of excitation energy transfer in the model of the photosynthetic unit. Due to the rotational symmetry of the model used, the compact analytic form of the physical observables, e.g. time-dependent fluorescence intensities at the reaction center and antenna molecules, the rate of fluorescence quenching and the quantum yield have been derived. Based on the obtained results, the general mechanism of coupled coherent-incoherent transfer is compared to the extreme regimes of the purely coherent and purely incoherent transport. It is shown that the calculated high value of the quantum yield at infinitely long time, ≈0.93, of the incoherent transfer mechanism is not the factor evidencing the superiority of the incoherence at the energy transfer of the photosynthetic process assuming that the geometry of the photosynthetic unit is of centro-symmetric. In contrast, on the relevant pico-second time scale, this value is only ≈0.45. It is the presence of the coherent hopping coupled to incoherence that makes the energy transfer so extremely effective. Contribution of coherence increases the quantum yield on the relevant time scale up to 0.98. The time constants of the fluorescence, i.e. the rate of fluorescence quenching calculated by the general method of the coupled coherent-incoherent mechanism are in very good agreement with experiment.

Quantum-statistical theory of proton-transfer reactions. Dynamics of proton motion in an asymmetric double-well potential interacting with a heat bath

Abstract Quantum-statistical theory of open systems, based on the projected form of the Liouville-von Neumann equation, is applied to the study of proton motion in an asymmetric double-well potential interacting with a heat bath. In Born-Markoff approximation a set of coupled equations of motion for matrix elements of the relevant density matrix is derived. It is demonstrated by the corresponding time-dependent analytic form of the product state population that the method can describe the dynamics correctly. An incoherent gain of the product state population is determiend by both, the dephasing and the decay of levels population. The rate constant, derived within the postulated theory, describes in a consistent manner the temperature dependence as well as the non-classical behaviour of the system in the limit of zero temperature.

EFFECTS OF A QUANTUM HEAT BATH ON THE DYNAMICS OF A NONLINEAR SUBSYSTEM : REDUCED DENSITY MATRIX APPROACH

Abstract The investigation of a reaction field induced nonlinear subsystem dynamics coupled to a quantum heat bath is presented. Projection technique along with time-convolutionless treatment of the total Liouville equation is applied and a new reduced nonlinear dissipative Liouville (RNDL) equation for the subsystem dynamics is derived. It is shown that the new RNDL equation, due to the reaction field nonlinearity, contains besides the coherent nonlinear and standard dissipative terms also an extra dissipative term which mediates the bath influence on the subsystem dynamics over the reaction field nonlinear coupling. The approach presented describes correctly quantum effects and the description is not restricted to limiting temperature regimes. The application of the method to the degenerate symmetric nonlinear dimer with Ohmic intersite coupling to the quantum heat bath has revealed that in the long-time limit the effect of the nonlinearity, with the tendency for localization in the intermediate time regime, is destroyed. The subsystem is driven to the thermodynamic equilibrium with a symmetric steady state.

Dynamics of proton transfer and enzymatic activity

The rate-determining elementary reaction step, i.e. proton transfer from the chymotrypsin active centre to the scissile substrate bond had been studied in the present work. On the basis of our theoretical results a hypothesis was formulated to explain chymotrypsin enzymatic efficiency. After ES complex formation excited vibrational states are populated in the enzyme molecule. In the rate-determining elementary reaction step, the proton transfer takes place from the first excited vibrational state of the N-H bond in the imidazole group of His57. This proton transfer is realised by quantum mechanical tunneling mechanism.

Antiadiabatic Theory of Superconducting State Transition: Phonons and Strong Electron Correlations—The Old Physics and New Aspects

Complex electronic ground state of molecular and solid state system is analyzed on the ab initio level beyond the adiabatic Born-Oppenheimer approximation (BOA). The attention is focused on the band structure fluctuation (BSF) at Fermi level, which is induced by electron-phonon coupling in superconductors, and which is absent in the non-superconducting analogues. The BSF in superconductors results in breakdown of the adiabatic BOA. At these circumstances, chemical potential is substantially reduced and system is stabilized (effect of nuclear dynamics) in the antiadiabatic state at broken symmetry with a gap(s) in one-particle spectrum. Distorted nuclear structure has fluxional character and geometric degeneracy of the antiadiabatic ground state enables formation of mobile bipolarons in real space. It has been shown that an effective attractive e-e interaction (Cooper-pair formation) is in fact correction to electron correlation energy at transition from adiabatic into antiadiabatic ground electronic state. In this respect, Cooper-pair formation is not the primary reason for transition into superconducting state, but it is a consequence of antiadiabatic state formation. It has been shown that thermodynamic properties of system in antiadiabatic state correspond to thermodynamics of superconducting state. Illustrative application of the theory for different types of superconductors is presented.

Reduced density matrix solution of the coupled coherent-incoherent exciton dynamics with the effects of quenching

Abstract An effective theoretical method for the study of excitation energy transfer dynamics in molecular aggregates, based on the formalism of the reduced density matrix, has been developed. The influence of a dissipative environment has been incorporated on the microscopic level, and the new established model is applicable also to nonperiodic systems and finite temperatures. An irreversible exciton removal out of the states of the reduced density matrix by the quencher molecules has been simulated via the introduction of sink parameters into the Hamiltonian, which simulates the finite lifetime of the excitation. The proposed method yields an equation for the site probability densities which comprises the basic information on the exciton dynamics. The procedure developed avoids the necessity of the calculation of memory functions. An illustration of the application of the method to a model of a hexamer aggregate with an additional quencher placed in the middle is presented.