A heuristic model of damped quantum rotation effects in nuclear magnetic resonance spectra

The damped quantum rotation (DQR) theory describes temperature effects in NMR spectra of hindered molecular rotators composed of identical atoms arranged in regular N-gons. In the standard approach, the relevant coherent dynamics are described quantum mechanically and the stochastic, thermally activated motions classically. The DQR theory is consistent. In place of random jumps over one, two, etc., maxima of the hindering potential, here one has damping processes of certain long-lived coherences between spin-space correlated eigenstates of the rotator. The damping-rate constants outnumber the classical jump-rate constants. The jump picture is recovered when the former cluster appropriately around only as many values as the number of the latter. The DQR theory was confirmed experimentally for hindered methyl groups in solids and even in liquids above 170 K. In this paper it is shown that for three-, four-, and sixfold rotators, the Liouville space equations of NMR line shapes, derived previously with the use of the quantum mechanical reduced density matrix approach, can be be given a heuristic justification. It is based on an equation of motion for the effective spin density matrix, where the relevant spin hamiltonian contains randomly fluctuating terms. The occurrence of the latter can be rationalized in terms of fluctuations of the tunneling splittings between the torsional sublevels of the rotator, including momentary liftings of the Kramers degeneracies. The question whether such degeneracy liftings are physical or virtual is discussed. The random terms in the effective hamiltonian can be Monte Carlo modeled as piecewise constant in time, which affords the stochastic equation of motion to be solved numerically in the Hilbert spin space. For sixfold rotators, this way of calculating the spectra can be useful in the instances where the Liouville space formalism of the original DQR theory is numerically unstable.     

Some features of coherent optical effects in large molecules

In this paper we present a theoretical study of coherent optical effects such as optical free induction decay (OFID) and photon echoes (PE) from an ensemble of collision-free large molecules. We have introduced a generalized effective hamiltonian to account for the temporal characteristics of the macroscopic polarization. Explicit results have been obtained for the OFID and PE under short-time on-resonance optical pulsed excitation elucidating the nature of phase destruction effects originating from intramolecular interstate and intrastate coupling and from inhomogeneous broadening effects.     

On the nature of intramolecular dephasing processes in polyatomic molecules

Intramolecular dephasing processes in polyatomic molecules are discussed with relation to coherent transient spectroscopy, radiationless transitions, multiphoton molecular processes, and overtone spectroscopy. A distinction is made between proper and improper dephasing processes (PDP, IDP) depending on whether they arise due to changes in populations or not. It is shown that the type of experiment and, consequently, the way we partition the hamiltonian are closely related to this distinction. We consider several experimental and theoretical approaches for studying intramolecular dynamics and discuss under what conditions it is necessary and useful to introduce explicitly dephasing interactions.     

Electronic effect on the rotational energy of a diatomic molecule

The rotational hamiltonian for a diatomic molecule has been rederived from the total classical hamiltonian. This procedure directly introduces the effect of electronic motion which is ordinarily neglected in zero-order approximation. Kronig's rotational hamiltonian is discussed and shown to be an approximation of our findings. Our general result is then specialized to ¹Σ states, and the theory tested by calculating the observed fractional discrepancy between the experimentally determined H³⁵Cl energy level constant Y₀₂ and its predicted value from Dunham's theory. When all corrections are summed, the results are in good agreement with experiment.     

Temperature dependence of ESR lineshapes of triplet excitons in molecular pairs

The ESR lineshape of triplet excitons moving between two differently oriented molecules of a pair is calculated. Our model hamiltonian contains the electronic interaction matrix element for the coherent exciton transport, the Zeeman energy of the triplet spin in an external magnetic field, the fine structure of the differently oriented molecules, the phonons in the crystal which are described as a heat bath, and the microscopic interaction between excitons and phonons. For the naphthalene pair the lineshapes are discussed with respect to the temperature and a parameter characterizing the strength of the interaction between excitons and photons.     

Calculation of the exciton green's function of a molecular crystal from a two-site dynamical coherent potential approximation

A new two-site dynamical coherent potential approximation for exciton-phonon interaction models corresponding to a homomorphic partition of the hamiltonian is described. The renormalization of both the site energy and the exciton bandwidth is accomplished in contrast to single-site CPA models.     

A new mean field SA-SA' critical point in a symmetry breaking field

We consider a S_A-S_A' critical point in the presence of a symmetry-breaking external magnetic (electric) field with a positive magnetic (dielectric) anisotropy or a dislocation layer. Via a renormalization group analysis of the model hamiltonian, we show that the upper critical dimensions below which mean-field theory breaks down is d_c = 2·5. Thus the S_A-S_A' transition in three dimensions becomes mean-field like in the presence of a symmetry-breaking field. We estimate the reduced temperature region where we can expect to see the mean field S_A-S_A' critical point in the presence of a magnetic field or a dislocation layer.     

The nature of energy delocalization in molecular crystals

The eigenfrequencies for the lowest triplet state of the naphthalene resonance pair hamiltonian are calculated and compared with optical and magnetic resonance data. The importance of both coherent and incoherent processes in understanding exciton spectra is emphasized.     

Dynamic nuclear polarization at high magnetic fields

Dynamic nuclear polarization (DNP) is a method that permits NMR signal intensities of solids and liquids to be enhanced significantly, and is therefore potentially an important tool in structural and mechanistic studies of biologically relevant molecules. During a DNP experiment, the large polarization of an exogeneous or endogeneous unpaired electron is transferred to the nuclei of interest (I) by microwave (microw) irradiation of the sample. The maximum theoretical enhancement achievable is given by the gyromagnetic ratios (gamma(e)gamma(l)), being approximately 660 for protons. In the early 1950s, the DNP phenomenon was demonstrated experimentally, and intensively investigated in the following four decades, primarily at low magnetic fields. This review focuses on recent developments in the field of DNP with a special emphasis on work done at high magnetic fields (> or =5 T), the regime where contemporary NMR experiments are performed. After a brief historical survey, we present a review of the classical continuous wave (cw) DNP mechanisms-the Overhauser effect, the solid effect, the cross effect, and thermal mixing. A special section is devoted to the theory of coherent polarization transfer mechanisms, since they are potentially more efficient at high fields than classical polarization schemes. The implementation of DNP at high magnetic fields has required the development and improvement of new and existing instrumentation. Therefore, we also review some recent developments in microw and probe technology, followed by an overview of DNP applications in biological solids and liquids. Finally, we outline some possible areas for future developments.     

An Improved Method of Determining the zeta-Potential and Surface Conductance

In the classical "slope-intercept" method of determining the zeta potential and the surface conductance, the relationship between DeltaP and E(s) is measured experimentally at a number of different channel sizes (e.g., the height of a slit channel, h). The parameter (epsilon(r)epsilon(0)DeltaP/μE(s)lambda(b)) is then plotted as a function of 1/h and linear regression is performed. The y-intercept of the regressed line is then related to the zeta-potential and its slope to the surface conductance. However, in this classical method, the electrical double layer effect or the electrokinetic effects on the liquid flow are not considered. Consequently, this technique is valid or accurate only when the following conditions are met: (1) relatively large channels are used; (2) the electrical double layer is sufficiently thin; and (3) the streaming potential is sufficiently small that the electroosmotic body force on the mobile ions in the double layer region can be ignored. In this paper a more general or improved slope-intercept method is developed to account for cases where the above three conditions are not met. Additionally a general least-squares analysis is described which accounts for uncertainty in the measured channel height as well as unequal variance in the streaming potential measurements. In this paper, both the classical and the improved slope-intercept techniques have been applied to streaming potential data measured with slit glass channels, ranging in height from 3 μm to 66 μm, for several aqueous electrolyte solutions. The comparison shows that the classical method will always overestimate both the zeta-potential and the surface conductance. Significant errors will occur when the classical method is applied to systems with small channel heights and low ionic concentrations. Furthermore, it is demonstrated that traditional regression techniques where the uncertainty is confined only to the dependent variable and each measurement is given equal weight may produce physically inconsistent results. Copyright 2000 Academic Press.     

Double perturbation theory and symmetry

A formulation of double perturbation theory is described which allows symmetry to be included in those cases where the zero-order hamiltonian does not contain the full symmetry of the problem. As an example we apply the theory to the Epstein-Johnson spin model.     

Modification of the static polarizability by a perfect metallic surface

We calculate the modifications of the static polarizability of a general system (atom or molecule) induced by a perfect metallic surface. The calculations use the Feynman propagator and take retardation effects into account. For any distance from the mirror the induced polarizability is composed of two terms: a classical one without retardation and a quantum one which is always retarded. Two limiting cases are then considered: the Casimir limit where the classical term dominates and the near-zone limit (London limit) where the quantum correction must be added to the classical term.     

Hybrid classical quantum force field for modeling very large molecules

A coherent computational scheme on a very large molecule in which the subsystem that undergoes the most important electronic changes is treated by a semiempirical quantum chemical method, though the rest of the molecule is described by a classical force field, has been proposed recently. The continuity between the two subsystems is obtained by a strictly localized bond orbital, which is assumed to have transferable properties determined on model molecules. The computation of the forces acting on the atoms is now operating, giving rise to a hybrid classical quantum force field (CQFF ) which allows full energy minimization and modeling chemical changes in large biomolecules. As an illustrative example, we study the short hydrogen bonds and the proton-exchange process in the histidine-aspartic acid system of the catalytic triad of human neutrophil elastase. The CQFF approach reproduces the crystallographic data quite well, in opposition to a classical force field. The method also offers the possibility of switching off the electrostatic interaction between the quantum and the classical subsystems, allowing us to analyze the various components of the perturbation exerted by the macromolecule in the reactive part. Molecular dynamics confirm a fast proton exchange between the three possible energy wells. The method appears to be quite powerful and applicable to other cases of chemical interest such as surface reactivity of nonmetallic solids. © 1996 John Wiley & Sons, Inc.     

An ab initio effective potential for two particles in the field of the core: a reduction of (N + 2)-electron problem to two-electron problem

We have used many-body Green function theory and the two-electron Bethe—Salpeter equation to derive an approximate two-electron position space hamiltonian eigenvalue equation for two electrons in the presence of a closed shell core. The resulting effective hamiltonian is nonlocal, energy independent, hermitian and nonadiabatic. It includes all the core—valence, valence—valence exchange effects, core screening effects and electron—electron correlation effects. If a closed form solution of the equation is difficult because of the need to construct the hamiltonian, a semi-empirical approach can be taken which expresses much of the hamiltonian in terms of known properties of the core. A semi-empirical analysis of this effective hamiltonian is shown to give well-known phenomenological effective hamiltonians and the connections to them. Thus this work can also be viewed as a theoretical justification and extension of the two-electron model potential or pseudopotential theories.     

Memory effects on energy transport in substitutionally disordered molecular crystals

In this paper we consider the manifestations of coherence effects in electronic energy transport (EET) between randomly distributed donors. We have extended previous theoretical schemes for EET in an impurity band to incorporate a finite memory time for the EET. The short-time behaviour of the mean square displacement of the excitation. [x²(t)], and the initial-site survival probability, P₀(t), exhibit two distinct transport regimes: (i) A coherent regime at ultrashort times, where [x²(t)] ∝ t², and (ii) a partially coherent regime, which is characterized by [x²(t)] ∝ t^10/μ, where μ is the order of the multipolar transition rate, which is intermediate between coherent and conventional diffusive behaviour. Coherence effects also result in the retardation of the short-time decay of P₀(t). The short-time partially coherent transport regime may be amenable to experimental interrogation by utilizing sub-ps and fs laser excitation. On the time scale exceeding the memory time, the conventional dispersive diffusive behaviour and the subsequent onset of classical diffusion for EET are recovered.     

Thermal effects and vibrational corrections to transition metal NMR chemical shifts

Both zero-point and classical thermal effects on the chemical shift of transition metals have been calculated at appropriate levels of density functional theory for a number of complexes of titanium, vanadium, manganese and iron. The zero-point effects were computed by applying a perturbational approach, whereas classical thermal effects were probed by Car-Parrinello molecular dynamics simulations. The systematic investigation shows that both procedures lead to a deshielding of the magnetic shielding constants evaluated at the GIAO-B3 LYP level, which in general also leads to a downfield shift in the relative chemical shifts, delta. The effect is small for the titanium and vanadium complexes, where it is typically on the order of a few dozen ppm, and is larger for the manganese and iron complexes, where it can amount to several hundred ppm. Zero-point corrections are usually smaller than the classical thermal effect. The pronounced downfield shift is due to the sensitivity of the shielding of the metal centre with regard to the metal-ligand bond length, which increase upon vibrational averaging. Both applied methods improve the accuracy of the chemical shifts in some cases, but not in general.     

A causal look into the quantum Talbot effect

A well-known phenomenon in both optics and quantum mechanics is the so-called Talbot effect. This near field interference effect arises when infinitely periodic diffracting structures or gratings are illuminated by highly coherent light or particle beams. Typical diffraction patterns known as quantum carpets are then observed. Here the authors provide an insightful picture of this nonlocal phenomenon as well as its classical limit in terms of Bohmian mechanics, also showing the causal reasons and conditions that explain its appearance. As an illustration, theoretical results obtained from diffraction of thermal He atoms by both N-slit arrays and weak corrugated surfaces are analyzed and discussed. Moreover, the authors also explain in terms of what they call the Talbot-Beeby effect how realistic interaction potentials induce shifts and distortions in the corresponding quantum carpets.     

The nature of molecular excited states produced by weak light sources

It is shown that upon excitation of a molecule by light from a thermal source, the incident field tends to act as a projection operator for a subspace spanned by eigenstates of the molecular hamiltonian. Furthermore, for chaotic light sources there is an effective upper limit, τ, for the time during which there is coherent excitation. If τ is much greater than the uncertainty minimum, as is normally the case, the reduced density operator for the excited states of the molecule becomes “filtered”, the extent of which determines the pattern of subsequent radiative and radiationless decay processes. The limitation of the “filtering” process to the interval τ provides a new distinction for large- and small-molecule behavior.