Exploring dynamical electron theory beyond the Born-Oppenheimer framework: from chemical reactivity to non-adiabatically coupled electronic and nuclear wavepackets on-the-fly under laser field

Chemical theory and its application to dynamical electrons in molecules under intense electromagnetic fields is explored, in which we take an explicit account of nuclear nonadiabatic (kinematic) interactions along with simultaneous coupling with intense optical interactions. All the electronic wavefunctions studied here are necessarily time-dependent, and thereby beyond stationary state quantum chemistry based on the Born-Oppenheimer framework. As a general and tractable alternative framework with which to track the electronic and nuclear simultaneous dynamics, we propose an on-the-fly method to calculate the electron and nuclear wavepackets coupled along the branching non-Born-Oppenheimer paths, through which their bifurcations, strong quantum entanglement between nuclear electronic motions, and coherence and decoherence among the phases associated with them are properly represented. Some illustrative numerical examples are also reported, which are aimed at our final goals; real time tracking of nonadiabatic electronic states, chemical dynamics in densely degenerate electronic states coupled with nuclear motions and manipulation and/or creation of new electronic states in terms of intense lasers, and so on. Other examples are also presented as to how the electron wavepacket dynamics can be used to analyze chemical reactions, shedding a new light on some typical and conventional chemical reactions such as proton transfer followed by tautomerization.     

Semiclassical study of quantum coherence and isotope effects in ultrafast electron transfer reactions coupled to a proton and a phonon bath

The linearized semiclassical initial value representation is employed to describe ultrafast electron transfer processes coupled to a phonon bath and weakly coupled to a proton mode. The goal of our theoretical investigation is to understand the influence of the proton on the electronic dynamics in various bath relaxation regimes. More specifically, we study the impact of the proton on coherences and analyze if the coupling to the proton is revealed in the form of an isotope effect. This will be important in distinguishing reactions in which the proton does not undergo significant rearrangement from those in which the electron transfer is accompanied by proton transfer. Unlike other methodologies widely employed to describe nonadiabatic electron transfer, this approach treats the electronic and nuclear degrees of freedom consistently. However, due to the linearized approximation, quantum interference effects are not captured accurately. Our study shows that at small phonon bath reorganization energies, coherent oscillations and isotope effect are observed in both slow and fast bath regimes. The coherences are more substantially damped by deuterium in comparison to the proton. Further, in contrast to the dynamics of the spin-boson model, the coherences are not long-lived. At large bath reorganization energies, the decay is incoherent in the slow and fast bath regimes. In this case, the extent of the isotope effect depends on the relative relaxation timescales of the proton mode and the phonon bath. The isotope effect is magnified for baths that relax on picosecond timescales in contrast to baths that relax in femtoseconds.     

Nonadiabatic sudden increase of the cooperative kinetic effect at lattice energy stabilization—Microscopic mechanism of superconducting state transition: Model study of MgB2

The theory of the nonadiabatic electron–vibration interactions has been applied to the study of MgB₂ superconducting state transition. It has been shown that at nonadiabatic conditions in which the Born–Oppenheimer approximation is not valid and electronic motion is dependent not only on the nuclear coordinates but also on the nuclear momenta, the fermionic ground‐state energy of the studied system can be stabilized by nonadiabatic electron–phonon interactions at broken translation symmetry. Moreover, the new arising state is geometrically degenerate; i.e., there are an infinite number of different nuclear configurations with the same fermionic ground‐state energy. The model study of MgB₂ yields results that are in a good agreement with the experimental data. For distorted lattice, with 0.016 Å/atom of in‐plane out‐of‐phase B? B atoms displacements out of the equilibrium (E_2g phonon mode) when the nonadiabatic interactions are most effective, it has been calculated that the new arising state is 87 meV/unit cell more stable than the equilibrium–high symmetry clumped nuclear structure at the level of the Born–Oppenheimer approximation. The calculated T_c is 39.5 K. The resulting density of states exhibits two‐peak character, in full agreement with the tunneling spectra. The peaks are at ±4 meV, corresponding to the change of the π band density of states, and at ±7.6 meV, corresponding to the σ band. The superconducting state transition can be characterized as a nonadiabatic sudden increase of the cooperative kinetic effect at lattice energy stabilization (NASICKELES). © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Theoretical study on the lowest-frequency mode of the flavin ring

The dynamic aspects along the normal vibrational motions of the lowest frequencies in the oxidized, radical, and reduced states of flavin (isoalloxazine) have been studied. In comparison with the twist motions in the oxidized state, the butterfly motions in the radical and reduced states turned out to bring more significant variations to the frontier molecular orbital energies and to the charge distributions on the atoms of the pyrazine ring in isoalloxazine. It can be considered that the electron transfers from and to the isoalloxazine ring can be adjusted or controlled by these variations. In the reduced states the electron release from the molecule, and in the radical states the electron release from or acceptance by the molecule, could be impelled by the butterfly motions, while in the oxidized state the electron acceptance by the molecule could be accelerated slightly by the twist motion. Received: 30 September 1998 / Accepted: 20 January 1999 / Published online: 7 June 1999     

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.     

Modulated Structure Calculated for Superconducting Hydrogen Sulfide

Compression of hydrogen sulfide using first principles metadynamics and molecular dynamics calculations revealed a modulated structure with high proton mobility which exhibits a diffraction pattern matching well with experiment. The structure consists of a sublattice of rectangular meandering SH⁻ chains and molecular‐like H₃S⁺ stacked alternately in tetragonal and cubic slabs forming a long‐period modulation. The novel structure offers a new perspective on the possible origin of the superconductivity at very high temperatures in which the conducting electrons in the SH chains are perturbed by the fluxional motions of the H₃S resulting in strong electron‐phonon coupling.     

Surface phonons in quasicrystals

Phonons describe the excitations and eigenstates of atomic motions in solids. Since atomic motions are easily visualized, phonons often serve as an introduction to the less tangible electronic states. In this article, we will review results from surface phonon measurements and present calculations for simple spring models to discuss the impact of quasicrystallinity on the interpretation of phonon measurements. Through this, some fundamental aspects of phonons as well electronic states in quasicrystals are illustrated.     

Conductance switching in an organic material: from bulk to monolayer

Fluorescein sodium, which does not exhibit electrical bistability in thin films, can be switched to a high conducting state by the introduction of carbon nanotubes as channels for carrier transport. Thin films based on fluorescein sodium/carbon nanotubes display memory switching phenomenon among a low conducting state and several high conducting states. Read-only and random-access memory applications between the states resulted in multilevel memory in these systems. Results in thin films and in a monolayer (deposited via layer-by-layer assembly) show that instead of different molecular conformers, multilevel conducting states arise from the different density of high conducting fluorescein molecules.     

Slow Molecular Motions in Ionic Liquids Probed by Cross‐Relaxation of Nuclear Spins During Overhauser Dynamic Nuclear Polarization

Solution‐state Overhauser dynamic nuclear polarization (ODNP) at moderate fields, performed by saturating the electron spin resonance (ESR) of a free radical added to the sample of interest, is well known to lead to significant NMR signal enhancements in the steady state, owing to electron–nuclear cross‐relaxation. Here it is shown that under conditions which limit radical access to the molecules of interest, the time course of establishment of ODNP can provide a unique window into internuclear cross‐relaxation, and reflects relatively slow molecular motions. This behavior, modeled mathematically by a three‐spin version of the Solomon equations (one unpaired electron and two nuclear spins), is demonstrated experimentally on the ¹⁹F/¹H system in ionic liquids. Bulky radicals in these viscous environments turn out to be just the right setting to exploit these effects. Compared to standard nuclear Overhauser effect (NOE) work, the present experiment offers significant improvement in dynamic range and sensitivity, retains usable chemical shift information, and reports on molecular motions in the sub‐megahertz (MHz) to tens of MHz range—motions which are not accessed at high fields.     

Ultrafast Exciton Self‐Trapping and Delocalization in Cycloparaphenylenes: The Role of Excited‐State Symmetry in Electron‐Vibrational Coupling

Upon photon absorption, π‐conjugated organics are apt to undergo ultrafast structural reorganization via electron‐vibrational coupling during non‐adiabatic transitions. Ultrafast nuclear motions modulate local planarity and quinoid/benzenoid characters within conjugated backbones, which control primary events in the excited states, such as localization, energy transfer, and so on. Femtosecond broadband fluorescence upconversion measurements were conducted to investigate exciton self‐trapping and delocalization in cycloparaphenylenes as ultrafast structural reorganizations are achieved via excited‐state symmetry‐dependent electron‐vibrational coupling. By accessing two high‐lying excited states, one‐photon and two‐photon allowed states, a clear discrepancy in the initial time‐resolved fluorescence spectra and the temporal dynamics/spectral evolution of fluorescence spectra were monitored. Combined with quantum chemical calculations, a novel insight into the effect of the excited‐state symmetry on ultrafast structural reorganization and exciton self‐trapping in the emerging class of π‐conjugated materials is provided.     

Resonant coupling of bound excitons with LO phonons in ZnO: excitonic polaron states and Fano interference

We report on a photoluminescence observation of robust excitonic polarons due to resonant coupling of exciton and longitudinal optical (LO) phonon as well as Fano-type interference in high quality ZnO crystal. At low enough temperatures, resonant coupling of excitons and LO phonons leads to not only traditional Stokes lines (SLs) but also up to second-order anti-Stokes lines (ASLs) besides the zero-phonon line (ZPL). The SLs and ASLs are found to be not mirror symmetric with respect to the ZPL, strongly suggesting that they are from different coupling states of exciton and phonons. Besides these spectral features showing the quasiparticle properties of exciton-phonon coupling system, the first-order SL is found to exhibit characteristic Fano lineshape, caused by quantum interference between the LO components of excitonic polarons and the continuous phonon bath. These findings lead to a new insight into fundamental effects of exciton-phonon interactions.     

Excess electron relaxation dynamics at water/air interfaces

We have performed mixed quantum-classical molecular dynamics simulations of the relaxation of a ground state excess electron at interfaces of different phases of water with air. The investigated systems included ambient water/air, supercooled water/air, Ih ice/air, and amorphous solid water/air interfaces. The present work explores the possible connections of the examined interfacial systems to finite size cluster anions and the three-dimensional infinite, fully hydrated electron. Localization site analyses indicate that in the absence of nuclear relaxation the electron localizes in a shallow potential trap on the interface in all examined systems in a diffuse, surface-bound (SB) state. With relaxation, the weakly bound electron undergoes an ultrafast localization and stabilization on the surface with the concomitant collapse of its radius. In the case of the ambient liquid interface the electron slowly (on the 10 ps time scale) diffuses into the bulk to form an interior-bound state. In each other case, the excess electron persists on the interface in SB states. The relaxation dynamics occur through distinct SB structures which are easily distinguishable by their energetics, geometries, and interactions with the surrounding water bath. The systems exhibiting the most stable SB excess electron states (supercooled water/air and Ih ice/air interfaces) are identified by their characteristic hydrogen-bonding motifs which are found to contain double acceptor-type water molecules in the close vicinity of the electron. These surface states correlate reasonably with those extrapolated to infinite size from simulated water cluster anions.     

Nonadiabatic quantum dynamics of Br2 in solid Ar: A four-dimensional study of the B to C state predissociation

Quantum dynamics simulations are performed for a diatomics-in-molecules based model of Br₂ in solid Ar which incorporates four nuclear degrees of freedom and four electronic states. The nuclear motions comprise two large amplitude coordinates describing the Br₂ bond distance and an effective symmetry-preserving matrix mode. Two symmetry-lowering harmonic modes are added in the spirit of linear vibronic coupling theory. Initiating the dynamics on the B state by means of an ultrafast laser pulse, nonadiabatic transitions to the two degenerate C states are monitored and the effect of vibrational preexcitation in the electronic ground state is investigated.     

Studies of magnetic resonance phenomena in polymers. I. The effects of free volume and segmental mobility on the motion of nitroxide spin probes and labels in poly(methyl methacrylate)

Thin films of spin-probed and spin-labeled poly(methyl methacrylate) (PMMA) have been examined by electron spin resonance (ESR) at X-band frequency (9.2 GH_z) and at various temperatures. Direct spectral evidence is presented to indicate that the composite ESR spectra observed in a certain temperature range originate from two states of distinctly different mobility, one with slow motions corresponding to a glassy state and the other with fast motions corresponding to a liquidlike state. The coexistence of these two states at temperatures considerably below the glass transition temperature can be explained as a result of the effect of free volume in a solid polymeric glass.     

Effects of complex-valued electronic wave functions on nuclear motions

Moleculer species and colliding groups of atoms are considered for which the electronic wave functions are complex-valued, having arguments that depend parametrically on the nuclear coordinates. The effective Hamiltonian for nuclear motions in the adiabatic approximation that arises in the present case differs from the ordinary Born–Oppeneheimer Hamiltonian, the latter being obtained when restriction to real-valued electronic functions is made. The asymptotic boundary conditions imposed in collision theory lead to in- and out- states [8], and hence to complex-valued wave functions in the coordinate representation. The study of the influence of electron–molecule scattering on nuclear motions therefore necessitates the use of the new effective Hamiltonian, which leads to results differing from those predicted on the basis of the Born–Oppenheimer operator. It is shown that momentum-dependent potentials occurring in the new Hamiltonian might cause “distortions” to the vibrational patterns of some electron–molecule metastable states. Also, these terms can give rise to non-Born–Oppenheimer resonances when motions in an internuclear coordinate become unbounded. We derive expressions for the relevant level widths and line shapes, showing them to be subject to an isotope effect. Even when real-valued electronic functions may be used, the selections of complex-valued functions in their linear span is still optional. Although exact treatments lead to the same results in both real and complex cases we show how the choice of the argument of the electronic function to be non-zero and dependent on nuclear coordinates may be useful for the application of certain approximation schemes. It is demonstrated that for certain systems a suitable choice of the argument assures convergence when the related Lippmann–Schwinger Equation is iterated. It is also shown that in this way an nth order term in the series expansion of the T matrix [8] for moleculer systems can be made negligibly small.     

Theoretical analysis of proton relays in electrochemical proton-coupled electron transfer

The coupling of long-range electron transfer to proton transport over multiple sites plays a vital role in many biological and chemical processes. Recently the concerted proton-coupled electron transfer (PCET) reaction in a molecule with a hydrogen-bond relay inserted between the proton donor and acceptor sites was studied electrochemically. The standard rate constants and kinetic isotope effects (KIEs) were measured experimentally for this double proton transfer system and a related single proton transfer system. In the present paper, these systems are studied theoretically using vibronically nonadiabatic rate constant expressions for electrochemical PCET. Application of this approach to proton relays requires the calculation of multidimensional proton vibrational wave functions and the incorporation of multiple proton donor-acceptor motions. The decrease in proton donor-acceptor distances due to thermal fluctuations and the contributions from excited electron-proton vibronic states play important roles in these systems. The calculated KIEs and the ratio of the standard rate constants for the single and double proton transfer systems are in agreement with the experimental data. The calculations indicate that the standard PCET rate constant is lower for the double proton transfer system because of the smaller overlap integral between the ground state reduced and oxidized proton vibrational wave functions, resulting in greater contributions from excited electron-proton vibronic states with higher free energy barriers. The theory predicts that this rate constant may be increased by modifying the molecule in a manner that decreases the equilibrium proton donor-acceptor distances or alters the molecular thermal motions to facilitate the concurrent decrease of these distances. These insights may guide the design of more efficient catalysts for energy conversion devices.     

Quantum fluctuation of electronic wave-packet dynamics coupled with classical nuclear motions

An ab initio electronic wave-packet dynamics coupled with the simultaneous classical dynamics of nuclear motions in a molecule is studied. We first survey the dynamical equations of motion for the individual components. Reflecting the nonadiabatic dynamics that electrons can respond to nuclear motions only with a finite speed, the equations of motion for nuclei include a force arising from the kinematic (nuclear momentum) coupling from electron cloud. To materialize these quantum effects in the actual ab initio calculations, we study practical implementation of relevant electronic matrix elements that are related to the derivatives with respect to the nuclear coordinates. Applications of the present scheme are performed in terms of the configuration state functions (CSF) using the canonical molecular orbitals as basis functions without transformation to particular diabatic basis. In the CSF representation, the nonadiabatic interaction due to the kinematic coupling is anticipated to be rather small, and instead it should be well taken into account through the off-diagonal elements of the electronic Hamiltonian matrix. Therefore it is expected that the nonadiabatic dynamics based on this CSF basis neglecting the kinematic coupling may work. To verify this anticipation and to quantify the actual effects of the kinematic coupling, we compare the dynamics with and without the kinematic-coupling terms using the same CSF set. Applications up to the fifth electronically excited states in a nonadiabatic collision between H(2) and B(+) shows that the overall behaviors of these two calculations are surprisingly similar to each other in an average sense except for a fast fluctuation reflecting the electronic time scale. However, at the same time, qualitative differences in the collision events are sometimes observed. Therefore it turns out after all that the kinematic-coupling terms cannot be neglected in the CSF-basis representation. The present applications also demonstrate that the nonadiabatic electronic wave-packet dynamics within ab initio quantum chemical calculation is feasible.     

Non-Born-Oppenheimer approximation for very weakly bound states of molecular anions

The influence of nuclear rotation on weak electron binding in the long range field of a linear polar molecule is treated in a way that leads ultimately, with suitable approximation, to the familiar equations for close coupling of electron-nuclear-rotational motions. Subsequently, a conventional pseudopotential approximation is invoked to examine the rotational spectra of HCN and DCN anions. It is shown that the number of rotationally excited anion states cannot be reliably predicted by assuming that zero binding occurs when the rotational energy equals the electron affinity obtained in the Born-Oppenheimer approximation. A method is suggested for combining accurate molecular orbital and parameterized pseudopotential methods to provide accurate electron affinities for very weakly bound anionic states.     

On the role of nuclear motions in electron and excitation transfer rates: Importance of transfer-integral dependence upon nuclear coordinate

The role of nuclear degrees of freedom in modifying the electron or exciton transfer rates between molecules is investigated. In addition to the usual Franck-Condon overlap factors which arise from the overlaps of initial and final vibrational states, we discuss a dependence of the transfer integral upon nuclear motions, a dependence which has been often cited, but nearly always ignored, in the usual dynamical theories of transfer processes. We show, within a Bom-Oppenheimer treatment, that the transfer integral dependence upon librational, rotational and vibrational modes can profoundly change both the rate itself and its functional dependences (upon temperature, upon orientation, etc.). Using a simple cosine form for the dependence of the transfer integral upon the modifying nuclear mode and a simple displaced-oscillator transformation, we obtain a closed-form solution for the transfer rate, which includes a new overlap factor arising from the dependence of the transfer integral upon nuclear coordinates. Some general remarks about the role of this dependence are made, and applications to particular transfer systems are briefly discussed.