Vibron-polaron in alpha-helices. II. Two-vibron bound states

The two-vibron dynamics associated to amide-I vibrations in a three-dimensional (3D) alpha-helix is described according to a generalized Davydov model. The helix is modeled by three spines of hydrogen-bonded peptide units linked via covalent bonds. It is shown that the two-vibron energy spectrum supports both a two-vibron free states continuum and two kinds of bound states, called two-vibron bound states (TVBS)-I and TVBS-II, connected to the trapping of two vibrons onto the same amide-I mode and onto two nearest-neighbor amide-I modes belonging to the same spine, respectively. At low temperature, nonvanishing interspine hopping constants yield a three-dimensional nature of both TVBS-I and TVBS-II which the wave functions extend over the three spines of the helix. At biological temperature, the pairs are confined in a given spine and exhibit the same features as the bound states described within a one-dimensional model. The interplay between the temperature and the 3D nature of the helix is also responsible for the occurrence of a third bound state called TVBS-III which refers to the trapping of two vibrons onto two different spines. The experimental signature of the existence of bound states is discussed through the simulation of their infrared pump-probe spectroscopic response. Finally, the fundamental question of the breather-like behavior of two-vibron bound states is addressed.     

Energy relaxation of the amide-I mode in hydrogen-bonded peptide units: a route to conformational change

A one-site Davydov model involving a C[Double Bond]O group engaged in a hydrogen bond is used to study the amide-I relaxation due to Fermi resonances with a bath of intramolecular normal modes. In the amide-I ground state, the hydrogen bond behaves as a harmonic oscillator whose eigenstates are phonon number states. By contrast, in the amide-I first excited state, the hydrogen bond experiences a linear distortion so that the eigenstates are superimpositions of number states. By assuming the hydrogen bond in thermal equilibrium at biological temperature, it is shown that the amide-I excitation favors the population of these excited states and the occurrence of coherences. Due to the interaction with the bath, the vibron decays according to an exponential or a biexponential law depending on whether the Fermi resonance is wide or narrow. Therefore, each excited state relaxes over a set of number states according to specific pathways. The consequence is twofold. First, the relaxation leads to a redistribution of the number state population which differs from the initial Boltzmann distribution. Then, it allows for coherence transfers so that, although the vibron has disappeared, the hydrogen keeps the memory of its initial distortion and it develops free oscillations.     

Vibron-polaron critical localization in a finite size molecular nanowire

The small polaron theory is applied to describe the vibron dynamics in an adsorbed nanowire with a special emphasis onto finite size effects. It is shown that the finite size of the nanowire discriminates between side molecules and core molecules which experience a different dressing mechanism. Moreover, the inhomogeneous behavior of the polaron hopping constant is established and it is shown that the core hopping constant depends on the lattice size. However, the property of a lattice with translational invariance is recovered when the size of the nanowire is greater than a critical value. Finally, it is pointed out that these features yield the occurrence of high energy localized states in which both the nature and the number are summarized in a phase diagram in terms of the relevant parameters of the problem (small polaron binding energy, temperature, lattice size).     

Dynamics of a Holstein polaron with off-diagonal coupling

Dynamics of a one-dimensional Holstein polaron with off-diagonal exciton-phonon coupling is studied by employing the Dirac-Frenkel time-dependent variational principle. The trial state used is the Davydov D(2) Ansatz with two sets of variational parameters, one for each constituting particle in the linearly coupled exciton-phonon system. Validity of the approach is carefully checked by quantifying how faithfully the trial state follows the Schro?dinger equation. A close examination of variational outputs reveals fine details of polaron dynamics and intricacies of dynamic exciton-phonon correlations. In the absence of diagonal coupling, the change in the polaron effective mass hinges on the sign of the transfer integral due to the antisymmetric nature of the off-diagonal coupling. The role of the off-diagonal coupling switches from being an agent of transport at moderate coupling strengths to that of localization at large coupling strengths. Increasing the phonon bandwidth leads to a reduced polaron effective mass at the zone center and an overall lowering of the polaron band.     

Line widths of the 3800 Å singlet transitions in crystalline anthracene

The theory of resonance coupling of Frenkel excitons and phonons is extended to two molecules per unit cell. Intra- and inter-band scattering for the two Davydov components can thus be dealt with on the same footing. Restrictions to nearest neighbour interactions have been removed. Application to anthracene shows that the contribution of librational phonons to the scattering is approximately one hundred times larger than that of translational phonons. The widths of the anthracene components are shown to fit the calculated coupling and known phonon frequencies satisfactorily.     

Temperature-Dependence of the Amide-I Frequency Map for Peptides and Proteins

In our recent work [Phys. Chem. Chem. Phys. 11, 9149 (2009)], a molecular-mechanics force field-based amide-I vibration frequency map (MM-map) for peptides and proteins was constructed. In this work, the temperature dependence of the MM-map is examined based on high-temperature molecular dynamics simulations and infrared (IR) experiments. It is shown that the 298-K map works for up to 500-K molecular dynamics trajectories, which reasonably reproduces the 88 oC experimental IR results. Linear IR spectra are also simulated for two tripeptides containing natural and unnatural amino acid residues, and the results are inreasonable agreement with experiment. The results suggest the MM-map can be used to obtain the temperature-dependent amide-I local mode frequencies and their distributions for peptide oligomers, which is useful in particular for understanding the IR signatures of the thermally unfolded species.     

Fast folding dynamics of α-helical peptides – Effect of solvent additives and pH

The fast folding/unfolding dynamics of an alanine-based α-helical model peptide was investigated using nanosecond temperature jump experiments in D₂O. Temperature jumps were induced either by indirect heating, using visible laser pulses and a heat-transducing triphenylmethane dye, or by direct heating, using IR laser pulses. Although direct heating improves the quality, reliability and speed of the experiments, the heat-transducing dye was shown to not affect the helix-coil dynamics of alanine-based model peptides, thus validating the indirect heating method for this class of peptides. On the other hand, the presence of high concentrations of salt ions was found to alter the helix folding dynamics by screening of charged residues. We conclude that electrostatic interactions between residues have significant effects on the dynamics of helix folding. Similarly, the solvent pH was observed to affect the dynamics of helix folding, even in a range where no protonation/deprotonation is expected to occur.     

Vibrational relaxation in simulated two-dimensional infrared spectra of two amide modes in solution

Two-dimensional infrared spectroscopy is capable of following the transfer of vibrational energy between modes in real time. We develop a method to include vibrational relaxation in simulations of two-dimensional infrared spectra at finite temperature. The method takes into account the correlated fluctuations that occur in the frequencies of the vibrational states and in the coupling between them as a result of interaction with the environment. The fluctuations influence the two-dimensional infrared line shape and cause vibrational relaxation during the waiting time, which is included using second-order perturbation theory. The method is demonstrated by applying it to the amide-I and amide-II modes in N-methylacetamide in heavy water. Stochastic information on the fluctuations is obtained from a molecular dynamics trajectory, which is converted to time dependent frequencies and couplings with a map from a density functional calculation. Solvent dynamics with the same frequency as the energy gap between the two amide modes lead to efficient relaxation between amide-I and amide-II on a 560 fs time scale. We show that the cross peak intensity in the two-dimensional infrared spectrum provides a good measure for the vibrational relaxation.     

Conformational preferences and vibrational frequency distributions of short peptides in relation to multidimensional infrared spectroscopy.

Molecular dynamics simulations of the structural distributions and the associated amide-I vibrational modes are carried out for dialanine peptide in water and carbon tetrachloride. The various manifestations in nonlinear-infrared spectroscopic experiments of the distributions of conformations of solvated dialanine are examined. The two-dimensional infrared (2D-IR) spectrum of dialanine exhibits the coupling between the amide oscillators and the correlations of the frequency fluctuations. An internally hydrogen-bonded conformation exists in CCl(4) but not in H(2)O where two externally hydrogen-bonded forms are preferred. Simulations of solvated dialanine show how the 2D-IR spectra expose the underlying structural distributions and dynamics that are not deducible from linear-infrared spectra. In H(2)O the 2D-IR shows cross-peaks from large coupling in the alpha-helical conformer and an elongated higher frequency diagonal peak, reflecting the broader distribution of structures for the more flexible acetyl end. In CCl(4), the computed cross-peak portion of the 2D-IR shows evidence of two amide-I transitions in the high-frequency region which are not apparent from the diagonal peak profile. The vibrational frequency inhomogeneity of the amide-I band arises from fluctuations of the instantaneous normal modes of these conformers rather than the shifts induced by hydrogen bonding. The simulation shows that there are correlations between fluctuations of the acetyl and amino end frequencies in H(2)O that arise from mechanical coupling and not from hydrogen bonding at the two ends of the molecule. The angular relationships between the two amide units which also show up in 2D-IR were computed, and spectral manifestations of them are discussed. The simulations also permit a calculation of the rate of energy transfer from one side of the molecule to the other. From these calculations, 2D-IR spectroscopy in conjunction with simulations is seen to be a promising tool for determining dynamics of structure changes in dipeptides.     

Vibronic fine structure in the absorption spectrum of oligothiophene thin films

A multimode Holstein Hamiltonian is used to describe optical excitations in quaterthiophene pinwheel aggregates. The Hamiltonian includes the coupling of excitons originating from the 1A(g)-->1B(u) electronic transition to phonons originating from the five intramolecular vibrational modes known from oligothiophene solution absorption/emission spectroscopy. The resulting eigenstates with lowest energy are best described as hybrid polaron phonons. The polarons are formed by coupling excitons with the higher frequency (688, 1235, and 1551 cm(-1)) vibrational modes, while the (optical) phonons arise from the lower frequency (161 and 333 cm(-1)) modes. The polaron phonons are responsible for the fine structure defining the A(1) band in the low-energy region of the absorption spectrum, ranging from the band origin to approximately 1500 cm(-1) beyond. The calculated A(1) band of quaterthiophene aggregates agrees favorably with that observed from thin films.     

Effects of disordered interchain interactions on polaron dynamics in semiconducting polymers

Polaron dynamics in a system of two randomly coupled polymer chains is simulated using a nonadiabatic evolution method. The simulations are performed within the framework of the Su-Schrieffer-Heeger model modified to include disordered interchain interactions and an external electric field. By analysing the polaron velocity statistically, we find that the polaron motion is determined by the competition between the electric field and the disordered interchain interactions. Polaron dynamics are classified into two types, weak-coupling dynamics and strong-coupling dynamics. It is found that the strength of interchain interactions is the dominant factor controlling charge propagation in weak-coupling dynamics, whereas the effects of disorder are dominant in strong-coupling dynamics. The charge carriers tend to have higher mobility for stronger interchain coupling, and interchain coupling disorder can be favorable for charge transport depending on the coupling strength and the electric field.     

Quasi‐classical fluctuation–dissipation description of dielectric loss in oxides with implications for quantum information processing

One of the most important problems in developing devices for quantum computation is the coupling and dissipation of states by thermal noise. We present a study of a two‐state electric dipole in a crystal coupling to noise from a reservoir. As a realization of such an energy‐dissipating dipole, we report and analyze dielectric loss measurements in single crystal and polycrystalline Al₂O₃ over the temperature range 70–300 K. We are able to model the dielectric loss in terms of a quasi‐classical model that uses the fluctuation–dissipation theorem. Two key parameters in this model are the crystal oscillator energy and reservoir–lattice coupling constant. In polycrystalline samples, it is assumed that the main effect of structural disorder is a modification of the spectrum of the thermal phonons, so that acoustical vibrations acquire some optical mode character. The temperature dependence of the linewidth of the high dielectric strength infrared (IR) mode at 438 cm^?1 and the quasi‐degenerate Raman mode of the k = 0 (418 cm^?1) transition are also investigated and are shown to be related simply to the dielectric loss. The model reproduces the unusual temperature dependence of the dielectric loss observed experimentally. The implications for the coupling of quantum mechanical objects to noise and quantum information processing are discussed. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Anharmonicity of amide modes

The principal contributions to the anharmonic coupling of amide vibrations are explored with the objective of comparing recent experiments with density functional theory and evaluating simple models of mode coupling. Experimental information obtained by means of two-dimensional infrared spectroscopy (2D IR) is reasonably well predicted by the computed one- and two-quantum anharmonic modes of amide-A, -I, and -II types in mono-, di- and tripeptides. The expansion of the vibrational energy up to the cubic and quartic coupling of harmonic modes suggested criteria to assess how localized are the forces determining the anharmonicity. The off-diagonal anharmonicity between an amide-A and one other amide mode was shown to be mainly determined by forces involving only these two modes, whereas the off-diagonal anharmonicity of two amide-I modes in peptides depended significantly on forces due to motions other than those of the amide-I type. Both the diagonal and off-diagonal anharmonicities exhibit sensitivity to peptide structures. These results should prove useful in linking 2D IR experimental results to secondary structure. Further, the results are used to evaluate the vibrational exciton model for the mixed-mode anharmonicities of the amide-I transitions.     

The exciton—phonon interaction for triplet exciton bands of organic solids: An experimental and theoretical study

Very high resolution optical data on the temperature dependences of the Davydov component absorption profiles and polarization dependent one-phonon structures associated with the lowest triplet exciton band of anthracene are presented along with a theoretical framework for their interpretation. The interpretation of the one-particle exciton—phonon transitions involving both one-phonon creation and annihilation (cold and hot phonon transitions) is entirely consistent with the analysis of the T-dependent dephasing of the lowest zero-phonon Davydov transition in terms of two mechanisms: delocalized exciton—delocalized phonon scattering operative for the low frequency (< 30 cm^?) phonons which undergo no lattice distortion and: Raman like phonon scattering operative for the higher frequency phonons which do. It is the latter which leads to the identical T² linewidth dependences of the two Davydov components in the high T limit. The former scattering is dominant at the lowest temperatures. In addition, the, marked and polarization dependent mirror symmetry breakdown between the hot and cold one-particle transitions can be nicely understood in terms of interferences occurring between the Condon and phononic (from the dependence of the pure exciton transition dipoles on phonon coordinate displacement) contributions to the one-particle transition dipoles. It is argued that our findings for anthracene should prove useful for triplet exciton bands in other organic solids.     

On the origin of temperature dependent band width of the out-of-plane hydrogen bonded NH group in simple amides.

We have previously shown that both OH librations and NH out-of-plane motions of simple organic molecules exhibit unusual breadth which is strongly temperature dependent. Among the possible mechanisms the modulation model and/or the anharmonic coupling with one and two low-frequency phonons can account for the experimental observations.     

Polaronic discontinuities induced by off-diagonal coupling

In this paper, we study a form of the Holstein molecular crystal model in which the influence of lattice vibrations on the transfers of electronic excitations between neighboring sites (off-diagonal coupling) is taken into account. Using the Toyozawa Ansatz and the Lanczos algorithm, the Holstein Hamiltonian with two types of off-diagonal coupling is studied focusing on a number of analyticity issues in the ground state. For finite-sized lattices and antisymmetric coupling, a sequence of discontinuities are found in the polaron energy dispersion, the size of the ground-state phonon cloud, and the linearized von Neumann entropy used to quantify the quantum entanglement between the exciton and the phonons in the ground state. Such behavior is accompanied by a shift of the ground-state crystal momentum from zero to nonzero values as the coupling strength is increased. In the thermodynamic limit, all discontinuities associated with antisymmetric coupling vanish except the one corresponding to the initial departure of the ground-state wavevector from the Brillouin zone center. For the case of symmetric off-diagonal coupling, a smooth crossover is found to exist in all parameters regimes.     

Correlation between large polarons in molecular chains

We studied few extra electrons in a molecular chain with respect of electron-phonon coupling in the adiabatic approximation. It is shown that the lowest state of two extra electrons in a chain corresponds to the singlet bisoliton state with one deformational potential well. Two electrons with parallel spins form a localised triplet state, which corresponds to the two-hump charge distribution function. Three extra electrons form an almost independent nonlinear superposition of a soliton and bisoliton states. In the case of four electrons, the two almost independent bisolitons are formed. These two states tend to separate in the chain at the maximal distance due to the Fermi repulsion, accounted for in the zero-order adiabatic approximation. This repulsion is partly compensated by the attraction between the solitons due to their exchange with virtual phonons, described by the non-adiabatic part of the Hamiltonian. The formation of solitons is characterised by the appearance of the bound soliton and bisoliton levels in the forbidden energy band. This constitutes the qualitative difference of the large polaron (soliton) states from the almost free electron states and small polaron states.     

Spin dephasing in impurity induced states in molecular solids

Spin coherence experiments are used to determine the energy level structure, physical geometry, and exciton dynamics of a series of impurity-induced traps in 1,2,4,5-tetrachlorobenzene. The trap, a pertubed host molecule, is shown to be caused by an adjacent, translationally equivalent chemical impurity whose triplet energy may lie above or below the host exciton, but above the trap. The slow rates of thermal processes within the trap are interpreted as weak coupling between the lattice phonons and localized phonons induced at the trap by the impurity.     

The geometrical-classical limit of algebraic Hamiltonians for molecular vibrotational spectra

A classical limit, which is amenable to a geometrical interpretation, is discussed for the vibron model of molecular vibrotational spectra. Both diatomic and triatomic molecules are considered. An example of a coupling between the two stretching modes of a linear triatomic is examined in detail.