Complete dynamics of a two-level quantum system in interaction with a radiation field

Using the general theory of systems of linear differential equations with periodic coefficients, we derive a complete set of solutions of the equations of motion of a two-level quantum system in interaction with a classical radiation field. The structure of the solutions is investigated and a method of obtaining approximate solutions is discussed. These solutions are compared quantitatively with those in the rotating-wave approximation in dependence of field amplitude, detuning from resonance, time of interaction between two-level system and field, and initial state of the two-level system. In an appendix it is shown that the semiclassical dynamics of a harmonically driven two-level system may be derived from an associated fully quantum-mechanical motion by an asymptotic limit.     

Extended spin-boson model for nonadiabatic hydrogen tunneling in the condensed phase

A nonadiabatic rate expression for hydrogen tunneling reactions in the condensed phase is derived for a model system described by a modified spin-boson Hamiltonian with a tunneling matrix element exponentially dependent on the hydrogen donor-acceptor distance. In this model, the two-level system representing the localized hydrogen vibrational states is linearly coupled to the donor-acceptor vibrational mode and the harmonic bath. The Hamiltonian also includes bilinear coupling between the donor-acceptor mode and the bath oscillators. This coupling provides a mechanism for energy exchange between the two-level system and the bath through the donor-acceptor mode, thereby facilitating convergence of the time integral of the probability flux correlation function for the case of weak coupling between the two-level system and the bath. The dependence of the rate constant on the model parameters and the temperature is analyzed in various regimes. Anomalous behavior of the rate constant is observed in the weak solvation regime for model systems that lack an effective mechanism for energy exchange between the two-level system and the bath. This theoretical formulation is applicable to a wide range of chemical and biological processes, including neutral hydrogen transfer reactions with small solvent reorganization energies.     

Ab initio calculations for the Zn 2s and 2p core level binding energies in Zn oxo compounds and ZnO

The Zn 2s and 2p core level binding energies of ZnO and a few Zn oxo compounds containing Zn in its oxidation state +2 were calculated by means of wave function based quantum chemical ab initio methods. The computations were performed at two levels of approximation. First, Hartree-Fock calculations were carried out for the ground state of the neutral systems yielding the "initial state" effects, i.e. the shifts of the core level binding energies due to the changes in the chemical environment of the Zn atom under consideration (Koopmans' theorem level, KT). In the second step, Hartree-Fock calculations were performed for the core ionized states in order to account for the relaxation effects after ionization, i.e. for the "final state" effects (DeltaSCF level). Scalar relativistic corrections and spin-orbit coupling were included in a "spin-orbit-coupling configuration interaction" (SOC-CI) treatment both at the KT and DeltaSCF levels. In all Zn oxo compounds (Zn(4)O(formate)(6), Zn(4)O(acetate)(6) and several ZnO cubanes) small negative initial state shifts between -1.0 and 0.0 eV (relative to the free Zn atom) were found which are caused by the negative charges at the surrounding O atoms. The relaxation effects vary between -1.0 and -0.5 eV, such that the calculated total shifts are moderately negative (-1.5 to -0.5 eV). Embedded ZnO clusters of increasing size, ranging from Zn(13)O(4) to Zn(69)O(38), were used as models for bulk ZnO, the Zn 2s and 2p core level shifts calculated for these clusters being extrapolated to infinite cluster size. The calculations show that bulk ZnO has a rather large negative initial state shift of -2.1 +/- 0.1 eV, due to the Madelung potential at the Zn atom, and a comparatively small relaxation contribution of -1.0 +/- 0.1 eV. This yields a total shift of -3.1 +/- 0.2 eV (both for 2s and 2p, relative to atomic Zn), which is in very good agreement with experiment, -2.9 +/- 0.2 eV. The surprising experimental observation that the Zn 2s and 2p XPS peak positions are nearly identical in Zn metal and ZnO is explained by the fact that the sum of initial and final state effects is accidentally the same for the two systems though the individual contributions differ quite significantly: the initial and final state shifts amount to +2.4 and -5.1 eV for Zn metal vs.-2.1 and -1.0 eV for ZnO.     

Dissipative geometric phase and decoherence in parity-violating chiral molecules

Within a generalized Langevin framework for open quantum systems, the cyclic evolution of a two-level system is analyzed in terms of the geometric phase extended to dissipative systems for Ohmic friction. This proposal is applied to the dynamics of chiral molecules where the tunneling and parity violating effects are competing. The effect of different system-bath coupling functions in the dissipated energy is shown to be crucial to understand the behavior of the geometric phase as well as the decoherence displayed by the corresponding interference patterns.     

Spin selective multiple quantum NMR for spectral simplification, determination of relative signs, and magnitudes of scalar couplings by spin state selection

In the present work we demonstrate a novel method for spectral simplification and determination of the relative signs of the scalar couplings using a spin selective multiple quantum NMR experiment. A spin selective excitation of double quantum coherence of A and M spins in a weakly coupled three spin system of the type AMX, results in a doublet in the double quantum dimension whose separation corresponds to the sum of couplings of the active spins to the passive spin X. One component of the doublet has the passive spin X in mid R:alpha state while the other component has the passive spin X in mid R:beta state. The spin selective conversion of double quantum coherence to single quantum coherence does not disturb the spin states of the passive spin thereby providing the spin state selection. There will be two domains of single quantum transitions in single quantum dimension at the chemical shift positions of A and M spins. The mid R:alpha domain of A spin is a doublet because of mid R:alpha and mid R:beta states of M spin only, while that of mid R:beta domain is another doublet in a different cross section of the spectra. The scalar coupling J(AM) can be extracted from any of the mid R:alpha and mid R:beta domain transitions while the relative displacements of the two doublets between the two domains at the two chemical shifts provides the magnitude and sign of the scalar coupling J(AX) relative to the coupling J(MX). Similar result is obtained for zero quantum studies on AMX spin system. The proposed technique is discussed theoretically using product operator approach. The new spin state selective double quantum J-resolved sequence has also been developed. The methodology is confirmed experimentally on a homonuclear weakly coupled three spin system and applied to two different heteronuclear five spin systems.     

Interaction between photons, “trapped electron” and vibronic excitation

The role of “trapped electron,” photon, and vibronic state coupling has been worked out in relation to an aspect of cancer, namely, to the activity of an anticancer drug. The main emphasis for such study comes from the fact that in cancerous systems the participation of usual electronic states of the molecule may not be sufficient. Because of disorder in the cancer tumour, additional states, viz. trapped electron states, could be formed in the manner of localised states in solids. The drug activity of mitomycin C obtained in this way agrees with the experimental values. An additional feature of the study is that it shows that it will be effective mainly in the initial phases of cancer.     

Correlations in single molecule photon statistics: renewal indicator

Multiple time scales are the intrinsic nature of complex systems and can be revealed through single molecule photon statistical analysis. The standard Poisson indicator defined by the time-averaged initial condition measures photon bunching and antibunching but cannot be directly related to multiple time scales. A new indicator defined by the event-averaged initial condition is proposed to detect the deviation from the renewal behavior and to directly probe the effects of conformational fluctuations. Detailed calculations of modulated two-level systems are carried out using the transfer matrix method to demonstrate the difference between the two indicators. The relationship between ensemble-averaged survival probabilities and photon statistics is also explored in the context of single molecule measurements.     

On the importance of the classically forbidden region in calculations of the relaxation rate for high-frequency vibrations: a model calculation

The quantum mechanical relaxation rate for a high-frequency vibrational mode is evaluated for a one-dimensional model system having two diatomic molecules involved in a collinear collision. The thermally averaged rate is obtained as an integral over energies for the relative translation of the two molecules. These calculations show that energies several times K(B)T make the largest contributions to the rate. Several orders of magnitude of cancellation due to phase interference is found in the evaluation of the coupling matrix elements between the initial and final states, and this is one of the main factors leading to the very small value for the relaxation rate. The region near the classical turning point in the relative translational motion of the colliding molecules dominates the calculation of the contribution to the rate at each energy. Calculations using low-order expansions of the translational potential energy and the interstate coupling about this turning point provide good approximations to the exact quantum mechanical rate. This suggests a possible method for performing calculations of the rate by means of realistic simulations of liquid systems.     

Nonexponential relaxation of the metastable state of the spin-crossover system [Fe(L)2](ClO4)2.H2O [L = 2,6-Bis(pyrazol-1-ylmethyl)pyridine

The relaxation of the metastable state of the spin-crossover compound [Fe(L)(2)](ClO(4))(2).H(2)O, with L = 2,6-bis(pyrazol-1-ylmethyl)pyridine, populated by the LIESST (light induced excited spin state trapping) effect, has been investigated by magnetic measurements. The time dependence of the relaxation curve at several temperatures, starting from different initial states, is in the shape of stretched exponentials, and the thermal variation of the photostationary state under constant photoexcitation is progressive and reversible. These features are satisfactorily modeled by considering noninteracting two-level systems with a distribution of activation energies. A suggested origin for the distribution is the conformational flexibility of the nonplanar heterocyclic ligands. The effect of the intensity distribution during the LIESST process is also accounted for in a simple way.     

Effects of Configurational Fluctuation on Electronic Coupling for Charge Transfer Dynamics

We advance a theory for the effects of bridge configurational fluctuations on the electronic coupling for electron transfer reactions in donor-bridge-acceptor systems. The theory of radiationless transitions was applied for activationless electron transfer, where the nuclear Franck–Condon constraints are minimized, with the initial vibronic state interacting directly with the final vibronic manifold, without the need for thermal activation. Invoking the assumption of energy-independent coupling, the time-dependent initial state population probability was analyzed in terms of a cumulant expansion. Two limiting situations were distinguished, i.e. the fast configurational fluctuation limit, where the electron transfer rate is given in terms of the configurational average of me squared electronic coupling, and the slow configurational fluctuation limit, where the dynamics is determined by a configurational averaging over a static distribution of electron transfer probability densities. The correlation times for configurational fluctuations of the electronic coupling will be obtained from the analysis of molecular dynamics, in conjunction with quantum mechanical calculations of the electronic coupling, to establish the appropriate limit for electron transfer dynamics.     

On the calculation of vibronic coupling matrix elements

The non-diagonal matrix elements in the adiabatic Born-Oppenheimer approximation are considered. The effect of the Q-dependence of the electronic energy denominator is calculated explicitly for an arbitrary initial and final state. It is shown that the inclusion of this effect does not change the relative values of the coupling matrix elements for different initial vibronic states.     

A theoretical investigation of charge transfer in several substituted acridinium ions

We present calculations for various properties of the ground and excited states of several arylamine-substituted acridinium ion systems that have been studied experimentally. Using ab initio and semiempirical quantum mechanical methods together with the generalized Mulliken-Hush (GMH) model, we examine the excitation energies, dipole moment shifts, and electronic coupling elements for the vertical charge shift (CSh) processes in these systems. We also examine solvent effects on these properties using a dielectric continuum reaction field model. The results are in generally good agreement with available experimental results and indicate that there is strong electronic coupling in these systems over a wide range of torsional angles. Nevetheless, the initial and final cationic states remain reasonably well-localized over this range, and thus TICT state formation is unlikely in these systems. Finally, a version of the GMH model based on Koopmans' Theorem is developed and found to yield coupling elements generally within a factor of 2 of the many-electron GMH for a sample acridinium system, but with overestimated adiabatic and diabatic dipole moment differences.     

Non-linear optical behavior in atomic fluorescence flame spectrometry

The non-linear dependence of the atomic fluorescence radiance upon the irradiance of the excitation source is discussed. Theoretical equations based on the assumption of steady state conditions are derived for a two-level atomic system and for a continuum source of excitation both on a relative as well as on an absolute basis. The theoretical results show that the approach of saturation sets a limit to the fluorescence radiance. The experimental results obtained with the use of a pulsed, tunable dye laser by nebulizing different elements in analytical flames are shown to be in satisfactory agreement with these theoretical results. The theory also predicts that, for a two-level system, the proportional dependence of the fluorescence signal upon the quantum efficiency observed at low irradiances is removed under saturation conditions.     

Spin-orbit vibronic coupling in 3Pi states of linear triatomic molecules

The Renner-Teller vibronic-coupling problem of a 3Pi electronic state of a linear molecule is analyzed with the inclusion of the spin-orbit coupling of the 3Pi electronic state, employing the microscopic (Breit-Pauli) spin-orbit coupling operator for the two unpaired electrons. The 6x6 Hamiltonian matrix in a diabatic spin-electronic basis is obtained by an expansion of the molecular Hamiltonian in powers of the bending amplitude. The symmetry properties of the Hamiltonian with respect to the time-reversal operator and the relativistic vibronic angular momentum operator are analyzed. It is shown that there exists a linear vibronic-coupling term of spin-orbit origin, which has not been considered so far in the Renner-Teller theory of 3Pi electronic states. While two of the six adiabatic electronic wave functions do not exhibit a geometric phase, the other four carry nontrivial topological phases which depend on the radius of the integration contour. The spectroscopic effects of the linear spin-orbit vibronic-coupling mechanism have been analyzed by numerical calculations of the vibronic spectrum for selected model examples.     

Toward a robust and general molecular simulation method for computing solid-liquid coexistence

A rigorous and generally applicable method for computing solid-liquid coexistence is presented. The method overcomes some of the technical difficulties associated with other solid-liquid simulation procedures and can be implemented within either a molecular dynamics or Monte Carlo framework. The method consists of three steps: First, relative Gibbs free energy curves are created for the solid and liquid phases using histogram reweighting. Next, the free energy difference between the solid and liquid phases is evaluated at a single state point by integrating along a pseudosupercritical transformation path that connects the two phases. Using this result, the solid and liquid free energy curves are referenced to a common point, allowing a single coexistence point to be determined. Finally, Gibbs-Duhem integration is used to determine the full coexistence curve. To evaluate its utility, this method is applied to the Lennard-Jones and NaCl systems. Results for solid-liquid coexistence agree with previous calculations for these systems. In addition, it is shown that the NaCl model does not correctly describe solid-liquid coexistence at high pressures. An analysis of the accuracy of the method indicates that the results are most sensitive to the transformation free energy calculation.     

Temperature dependence of relative modulus in filled polymer systems

The temperature dependence of relative modulus observed in filled thermoset, thermoplastic, and polyelectrolyte salt matrices is explained on the basis of induced stresses produced by the differences in the thermal expansion coefficients of the constituent materials. The analysis is based on the assumption that the modulus of the matrix in a filled polymer is less than that of the unfilled polymer. The temperature dependence of relative modulus is expressed as a function of the difference in thermal expansion coefficients, the volume fraction, the relative modulus in the unstressed state, and mechanical properties of the phases. Agreement is good between the analysis and experimental results for three systems: epoxy and glass, polyethylene and wollastonite, and a polyelectrolyte salt with mica and asbestos.     

New Trends in the Development of Methods for Catalyst Preparation for the Processes of Organochlorine Synthesis

The formation of heterogeneous mercury-, zinc-, and copper-containing catalytic systems obtained by supporting salt components (SCs) without a solvent is studied. It is shown that due to strong interaction between SC and support, the size of salt clusters on the surface and their relative contribution decrease. That is, the concentration of excess salt phases decreases. The dispersity increases up to molecular distribution. When surface-linked two-dimensional disordered structures are formed, the state of salt phases in the compositions of catalytic systems changes. The surface mobility of salt clusters during the contact with the reaction medium is found. Compared to the systems obtained by impregnation with aqueous solutions, the proposed systems are 2–3 times more thermally stable, their surface is enriched in defect structures that are active in catalysis, and the processes of organochlorine synthesis become more efficient.     

The Role of Spin-Orbit Coupling and Symmetry in Oxadi-pi-methane Rearrangements and Some Related Photochemical Reactions

The spin-orbit coupling components in the effective one-electron Hamiltonian operator, with the inclusion of symmetry, have been used to formulate mechanisms of spin inversion in triplet reactions for the radiationless decay of triplet complexes to singlet ground state products. This has been applied to investigate the photochemical behavior of oxadi-pi-methane rearrangement in beta,gamma-unsaturated carbonyl cyclic and acyclic systems. It is found that the 1,2-acyl-migrated endo isomer is the most favorable product due to its larger spin-orbit coupling expression as well as better initial overlaps (owing to the less atomic motion). Other related photorearrangements of some molecular systems, such as azadi-pi-methane rearrangement, 4-aryl-substituted cyclopentenones, spirocyclic beta,gamma,delta,epsilon-unsaturated ketones, and heavy atom effect, have also been investigated.     

Adsorption-state-dependent subpicosecond photoinduced desorption dynamics

Femtosecond laser excitation has been used to initiate desorption of molecular oxygen from the (111) surface of Pd and to study the adsorption-state dependence of the substrate-adsorbate coupling. The relative populations of the two chemical states, peroxo (O2(2-)) and superoxo (O2-), were varied by changing the total coverage. Two-pulse correlation measurements exhibit a dominant 400 fs response and a slower 10 ps decay that are relatively independent of the initial O2 coverage. In contrast, the photodesorption yield and the nonlinearity of the fluence dependence show a systematic coverage dependence. The coverage-independent subpicosecond response indicates that the photoinduced desorption from the two states is driven primarily by the same electron-mediated mechanism, while the coverage dependence of the yield indicates that the desorption efficiency from the superoxo state is greater than that from the peroxo state. These results are discussed in the context of the electron-phonon two-temperature model with an empirical adsorbate-electron frictional coupling that depends on both the electronic temperature and the activation energy for desorption. With a coupling strength that decreases as the activation energy decreases, the trends with varying coverage, absorbed fluence, and time delay can all be reproduced. The model is consistent with a transition from a resonantly enhanced (diabatic) regime to an adiabatic regime as the system relaxes, accounting for the biexponential correlation behavior.     

Computer simulation of quantum dynamics in a classical spin environment

In this paper, a formalism for studying the dynamics of quantum systems coupled to classical spin environments is reviewed. The theory is based on generalized antisymmetric brackets and naturally predicts open-path off-diagonal geometric phases in the evolution of the density matrix. It is shown that such geometric phases must also be considered in the quantum–classical Liouville equation for a classical bath with canonical phase space coordinates; this occurs whenever the adiabatics basis is complex (as in the case of a magnetic field coupled to the quantum subsystem). When the quantum subsystem is weakly coupled to the spin environment, non-adiabatic transitions can be neglected and one can construct an effective non-Markovian computer simulation scheme for open quantum system dynamics in classical spin environments. In order to tackle this case, integration algorithms based on the symmetric Trotter factorization of the classical-like spin propagator are derived. Such algorithms are applied to a model comprising a quantum two-level system coupled to a single classical spin in an external magnetic field. Starting from an excited state, the population difference and the coherences of this two-state model are simulated in time while the dynamics of the classical spin is monitored in detail. It is the author’s opinion that the numerical evidence provided in this paper is a first step toward developing the simulation of quantum dynamics in classical spin environments into an effective tool. In turn, the ability to simulate such a dynamics can have a positive impact on various fields, among which, for example, nanoscience.