Vincent Pouthier

Two-vibron bound states in α-helix proteins: The interplay between the intramolecular anharmonicity and the strong vibron–phonon coupling

The influence of the intramolecular anharmonicity and the strong vibron-phonon coupling on the two-vibron dynamics in an alpha-helix protein is studied within a modified Davydov model. The intramolecular anharmonicity of each amide-I vibration is considered, and the vibron dynamics is described according to the small polaron approach. A unitary transformation is performed to remove the intramolecular anharmonicity, and a modified Lang-Firsov transformation is applied to renormalize the vibron-phonon interaction. Then a mean field procedure is realized to obtain the dressed anharmonic vibron Hamiltonian. It is shown that the anharmonicity modifies the vibron-phonon interaction, which results in an enhancement of the dressing effect. In addition, both the anharmonicity and the dressing favor the occurrence of two different bound states whose properties strongly depend on the interplay between the anharmonicity and the dressing. This dependence was summarized in a phase diagram which characterizes the number and the nature of the bound states as a function of the relevant parameters of the problem. For a significant anharmonicity, the low-frequency bound states describe two vibrons trapped onto the same amide-I vibration, whereas the high-frequency bound states refer to the trapping of the two vibrons onto nearest neighbor amide-I vibrations.

Relaxation channels of two-vibron bound states in α-helix proteins

Relaxation channels for two-vibron bound states in an anharmonic alpha-helix protein are studied. According to a recently established small polaron model [V. Pouthier, Phys. Rev. E 68, 021909 (2003)], it is shown that the relaxation originates in the interaction between the dressed anharmonic vibrons and the remaining phonons. This interaction is responsible for the occurrence of transitions between two-vibron eigenstates mediated by both phonon absorption and phonon emission. At biological temperature, the relaxation rate does not significantly depend on the nature of the two-vibron states involved in the process. The lifetime for both bound and free states is of the same order of magnitude and ranges between 0.1 and 1.0 ps for realistic parameter values. By contrast, the relaxation channels strongly depend on the nature of the two-vibron states which is a consequence of the breatherlike behavior of the two-vibron bound states.

Amide-I relaxation-induced hydrogen bond distortion: An intermediate in electron capture dissociation mass spectrometry of α-helical peptides?

Electron capture dissociation (ECD) of peptides and proteins in the gas phase is a powerful tool in tandem mass spectrometry whose current description is not sufficient to explain many experimental observations. Here, we attempt to bridge the current understanding of the vibrational dynamics in alpha-helices with the recent experimental results on ECD of alpha-helical peptides through consideration of amide-I relaxation-induced hydrogen bond distortion. Based on a single spine of H-bonded peptide units, we assume that charge neutralization upon electron capture by a charged alpha-helix excites a nearby amide-I mode, which relaxes over a few picoseconds due to Fermi resonances with intramolecular normal modes. The amide-I population plays the role of an external force, which drives the displacements of each peptide unit. It induces a large immobile contraction of the H bonds surrounding the excited site whose lifetime is about the amide-I lifetime. In addition, it creates two lattice deformations describing H bond stretchings, which propagate from the excited region toward both termini of the alpha-helix, get reflected at the termini and yield H bond contractions which move back to the excited region. Consequently, we show that H bonds experience rather large contractions whose amplitude depends on general features such as the position of the amide-I mode, the peptide length and the H bond force constants. When an H bond contraction is sufficiently large, it may promote a hydrogen atom transfer between two neighboring peptide units leading to the formation of a radical at charge site remote carbonyl carbon which is known to be a precursor to the rupture of the corresponding N[Single Bond]C(alpha) bond. The introduced here way of excitation energy generation and transfer may significantly advance ECD understanding and complement existing ECD mechanisms.

Quantum transport theory of vibrons in a molecular monolayer

We establish a quantum kinetic equation describing the transport properties of the vibrons in a molecular monolayer adsorbed on a dielectric substrate. A renormalization procedure is applied to the Hamiltonian of the system which is then separated in a vibron Hamiltonian, a bath Hamiltonian connected the external motions and a coupling Hamiltonian between the vibrons and the external modes. A perturbative analysis based on the projector method allows us to eliminate the irrelevant information related to the bath dynamics. The use of conventional approximations (Markov limit and Wick theorem) leads us to write the kinetic equation in a form exhibiting linear and nonlinear contributions. The linear term characterizes irreversible processes connected to the bath fluctuations whereas the nonlinear term represents a self-modulation of the dynamical matrix with respect to the vibron distribution. An application of the transport of CO vibrons on NaCl(100) illustrates the method.

Infrared and infrared-visible sum frequency generation spectroscopic response of harmonic monolayer vibrons: Homogeneous profile

We determine the profile of the vibrational band of an ordered monolayer adsorbed on a clean surface corresponding to the infrared spectrum and to the resonant infrared-visible sum frequency generation spectrum. The theoretical model is based on the renormalization of the monolayer and substrate Hamiltonians. The harmonic dynamics of the effective vibrons characterizing the collective internal vibrations of the admolecules is written in terms of a complex dynamical matrix whose elements can be expressed as correlation functions of the external libron and phonon modes. The dephasing broadening is obtained by solving a master equation for the time evolution of the vibron modes while the external dynamics of the layer is described by using molecular dynamics simulation. An application to the calculation of the profile of the vibrational band of the low temperature (2×1) CO monolayer adsorbed on NaCl(100) is performed without any adjustable parameter by considering a well established semiempirical potential t...

Two-vibron bound states lifetime in a one-dimensional molecular lattice coupled to acoustic phonons

The lifetime of two-vibron bound states in the overtone region of a one-dimensional anharmonic molecular lattice is investigated. The anharmonicity, introduced within an attractive Hubbard Hamiltonian for bosons, is responsible for the formation of bound states which belong to a finite linewidth band located below the continuum of two-vibron free states. The decay of these bound states into either bound or free states is described by considering the coupling between the vibrons and a thermal bath formed by a set of low-frequency acoustic phonons. The relaxation rate is expressed in terms of the spectral distribution of the vibron/phonon coupling and of the two-vibron Green operator which is calculated exactly by using the number states method. The behavior of the two-vibron bound states relaxation rate is analyzed with a special emphasis on the influence of the anharmonicity. It is shown that the rate exhibits two distinct regimes depending on the thermal bath dimension. When the bath dimension is equal to unity, the rate increases with the anharmonicity and the decay of the two-vibron bound states into the other bound states appears as the main contribution of the rate. By contrast, when the bath dimension is equal to 2 and 3, the rate decreases as the anharmonicity increases, indicating that the two-vibron bound states decay into the two-vibron free states continuum.

Surface self-diffusion of hydrogen on Cu(100): A quantum kinetic equation approach

The self-diffusion of hydrogen on the (100) copper surface is investigated using a quantum kinetic equation approach. The dynamics of the adatom is described with a multiple-band model and the surface phonons represent the thermal bath responsible for the diffusion mechanism. Using the Wigner distribution formalism, the diffusive motion of the adatom is characterized in terms of the correlation functions of the adatom–phonon interaction. The diffusion coefficient exhibits two terms related to phonon mediated tunneling (incoherent part) and to dephasing limited coherent motion (coherent part). The competition between these two contributions induced a transition from a thermally activated regime to an almost temperature independent regime at a crossover temperature T*. A numerical analysis is performed using a well-established semiempirical potential to describe the adatom–surface interaction and a slab calculation to characterize the surface phonons. These calculations show that two-phonon processes repres...

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).

Vibrons in finite size molecular lattices: a route for high-fidelity quantum state transfer at room temperature

A communication protocol is proposed in which vibron-mediated quantum state transfer takes place in a molecular lattice. We consider two distant molecular groups grafted on each side of the lattice. These groups form two quantum computers where vibrational qubits are implemented and received. The lattice defines the communication channel along which a vibron delocalizes and interacts with a phonon bath. Using quasi-degenerate perturbation theory, vibron-phonon entanglement is taken into account through the effective Hamiltonian concept. A vibron is thus dressed by a virtual phonon cloud whereas a phonon is clothed by virtual vibronic transitions. It is shown that three quasi-degenerate dressed states define the relevant paths followed by a vibron to tunnel between the computers. When the coupling between the computers and the lattice is judiciously chosen, constructive interference takes place between these paths. Phonon-induced decoherence is minimized and a high-fidelity quantum state transfer occurs over a broad temperature range.