Strong Nonadiabatic Coupling Research Articles

Direct Signature of Light-Induced Conical Intersections in Diatomics.

Nonadiabatic effects are ubiquitous in physics, chemistry, and biology. They are strongly amplified by conical intersections (CIs), which are degeneracies between electronic states of triatomic or larger molecules. A few years ago it was revealed that CIs in molecular systems can be formed by laser light, even in diatomics. Because of the prevailing strong nonadiabatic couplings, the existence of such laser-induced conical intersections (LICIs) may considerably change the dynamical behavior of molecular systems. By analyzing the photodissociation process of the D2+ molecule carefully, we found a robust effect in the angular distribution of the photofragments that serves as a direct signature of the LICI, providing undoubted evidence of its existence.

Ab initio multiple cloning algorithm for quantum nonadiabatic molecular dynamics.

We present a new algorithm for ab initio quantum nonadiabatic molecular dynamics that combines the best features of ab initio Multiple Spawning (AIMS) and Multiconfigurational Ehrenfest (MCE) methods. In this new method, ab initio multiple cloning (AIMC), the individual trajectory basis functions (TBFs) follow Ehrenfest equations of motion (as in MCE). However, the basis set is expanded (as in AIMS) when these TBFs become sufficiently mixed, preventing prolonged evolution on an averaged potential energy surface. We refer to the expansion of the basis set as "cloning," in analogy to the "spawning" procedure in AIMS. This synthesis of AIMS and MCE allows us to leverage the benefits of mean-field evolution during periods of strong nonadiabatic coupling while simultaneously avoiding mean-field artifacts in Ehrenfest dynamics. We explore the use of time-displaced basis sets, "trains," as a means of expanding the basis set for little cost. We also introduce a new bra-ket averaged Taylor expansion (BAT) to approximate the necessary potential energy and nonadiabatic coupling matrix elements. The BAT approximation avoids the necessity of computing electronic structure information at intermediate points between TBFs, as is usually done in saddle-point approximations used in AIMS. The efficiency of AIMC is demonstrated on the nonradiative decay of the first excited state of ethylene. The AIMC method has been implemented within the AIMS-MOLPRO package, which was extended to include Ehrenfest basis functions.

Influence of light-induced conical intersection on the photodissociation dynamics of D2(+) starting from individual vibrational levels.

Previous works have shown that dressing of diatomic molecules by standing or by running laser waves gives rise to the appearance of so-called light-induced conical intersections (LICIs). Because of the strong nonadiabatic couplings, the existence of such LICIs may significantly change the dynamical properties of a molecular system. In our former paper (J. Phys. Chem. A 2013, 117, 8528), the photodissociation dynamics of the D(2)(+) molecule were studied in the LICI framework starting the initial vibrational nuclear wave packet from the superposition of all the vibrational states initially produced by ionizing D(2). The present work complements our previous investigation by letting the initial nuclear wave packets start from different individual vibrational levels of D(2)(+), in particular, above the energy of the LICI. The kinetic energy release spectra, the total dissociation probabilities, and the angular distributions of the photofragments are calculated and discussed. An interesting phenomenon has been found in the spectra of the photofragments. Applying the light-induced adiabatic picture supported by LICI, explanations are given for the unexpected structure of the spectra.

Coherence penalty functional: a simple method for adding decoherence in Ehrenfest dynamics.

We present a new semiclassical approach for description of decoherence in electronically non-adiabatic molecular dynamics. The method is formulated on the grounds of the Ehrenfest dynamics and the Meyer-Miller-Thoss-Stock mapping of the time-dependent Schrödinger equation onto a fully classical Hamiltonian representation. We introduce a coherence penalty functional (CPF) that accounts for decoherence effects by randomizing the wavefunction phase and penalizing development of coherences in regions of strong non-adiabatic coupling. The performance of the method is demonstrated with several model and realistic systems. Compared to other semiclassical methods tested, the CPF method eliminates artificial interference and improves agreement with the fully quantum calculations on the models. When applied to study electron transfer dynamics in the nanoscale systems, the method shows an improved accuracy of the predicted time scales. The simplicity and high computational efficiency of the CPF approach make it a perfect practical candidate for applications in realistic systems.

Dynamical Outcomes of Quenching: Reflections on a Conical Intersection

This review focuses on experimental studies of the dynamical outcomes following collisional quenching of electronically excited OH A(2)Σ(+) radicals by molecular partners. The experimental observables include the branching between reactive and nonreactive decay channels, kinetic energy release, and quantum state distributions of the products. Complementary theoretical investigations reveal regions of strong nonadiabatic coupling, known as conical intersections, which facilitate the quenching process. The dynamical outcomes observed experimentally are connected to the local forces and geometric properties of the nuclei in the conical intersection region. Dynamical calculations for the benchmark OH-H2 system are in good accord with experimental observations, demonstrating that the outcomes reflect the strong coupling in the conical intersection region as the system evolves from the excited electronic state to quenched products.

Dynamical Steps that Bridge Piecewise Adiabatic Shapes in the Exact Time-Dependent Potential Energy Surface

We study the exact time-dependent potential energy surface (TDPES) in the presence of strong nonadiabatic coupling between the electronic and nuclear motion. The concept of the TDPES emerges from the exact factorization of the full electron-nuclear wave function [A. Abedi, N. T. Maitra, and E. K. U. Gross, Phys. Rev. Lett. 105, 123002 (2010)]. Employing a one-dimensional model system, we show that the TDPES exhibits a dynamical step that bridges between piecewise adiabatic shapes. We analytically investigate the position of the steps and the nature of the switching between the adiabatic pieces of the TDPES.

Manifestation of phonons in the optical spectra of pseudo Jahn-Teller systems

The system under consideration is a molecule or an impurity center in a crystal with a two-fold quasi-degenerate electronic state (pseudo Jahn-Teller system) in strong interaction with one main mode and in weak interaction with continuum of secondary modes of phonons. This system exhibits strong non-adiabatic couplings which have been demonstrated to be detectable in absorption and Raman excitation spectra. By choosing an appropriate axis of polarization the non-adiabatic transitions become directly observable.

Reactive quenching of OH A 2Σ+ by O2 and CO: Experimental and nonadiabatic theoretical studies of H- and O-atom product channels

The outcomes following collisional quenching of electronically excited OH A (2)Σ(+) by O(2) and CO are examined in a combined experimental and theoretical study. The atomic products from reactive quenching are probed using two-photon laser-induced fluorescence to obtain H-atom Doppler profiles, O ((3)P(J)) atom fine structure distributions, and the relative yields of these products with H(2), O(2), and CO collision partners. The corresponding H-atom translational energy distributions are extracted for the H + O(3) and H + CO(2) product channels, in the latter case revealing that most of the available energy is funneled into internal excitation of CO(2). The experimental product branching ratios show that the O-atom producing pathways are the dominant outcomes of quenching: the OH A (2)Σ(+) + O(2) → O + HO(2) channel accounts for 48(3)% of products and the OH A (2)Σ(+) + CO → O + HCO channel yields 76(5)% of products. In addition, quenching of OH A (2)Σ(+) by O(2) generates H + O(3) products [12(3)%] and returns OH to its ground X (2)Π electronic state [40(1)%; L. P. Dempsey, T. D. Sechler, C. Murray, and M. I. Lester, J. Phys. Chem. A 113, 6851 (2009)]. Quenching of OH A (2)Σ(+) by CO also yields H + CO(2) reaction products [26(5)%]; however, OH X (2)Π (v" = 0,1) products from nonreactive quenching are not observed. Theoretical studies characterize the properties of energy minimized conical intersections in four regions of strong nonadiabatic coupling accessible from the OH A (2)Σ(+) + CO asymptote. Three of these regions have the O-side of OH pointing toward CO, which lead to atomic H and vibrationally excited CO(2) products and/or nonreactive quenching. In the fourth region, energy minimized points are located on a seam of conical intersection from the OH A (2)Σ(+) + CO asymptote to an energy minimized crossing with an extended OH bond length and the H-side of OH pointing toward CO in a bent configuration. This region, exoergic with respect to the reaction asymptote, is likely to be the origin of the dominant O + HCO product channel.

Fingerprints of Adiabatic versus Diabatic Vibronic Dynamics in the Asymmetry of Photoelectron Momentum Distributions.

When the Born–Oppenheimer approximation is valid, electrons adiabatically follow the nuclear motion in molecules. For strong nonadiabatic coupling between electronic states, one encounters a diabatic motion where the electrons remain local and do not adapt to molecular geometry changes. We show that the mentioned limiting cases are reflected differently in the asymmetry of time-resolved photoelectron momentum distributions. Whereas for adiabatic dynamics, the asymmetry directly maps the time-dependent average nuclear momentum, in the diabatic case, the asymmetry is determined by a nonclassical interference effect arising from the mixing of wave function components in different electronic states, which is present at times nonadiabatic transitions take place.

Photophysics of fluorinated benzene. III. Hexafluorobenzene

A theoretical study of the photoabsorption spectroscopy of hexafluorobenzene (HFBz) is presented in this paper. The chemical effect due to fluorine atom substitution on the electronic structure of benzene (Bz) saturates in HFBz. State- of-the-art quantum chemistry calculations are carried out to establish potential energy surfaces and coupling surfaces of five energetically low-lying electronic (two of them are orbitally degenerate) states of HFBz. Coupling of these electronic states caused by the Jahn-Teller (JT) and pseudo-Jahn-Teller (PJT) type of interactions are examined. The impact of these couplings on the nuclear dynamics of the participating electronic states is thoroughly investigated by quantum mechanical methods and the results are compared with those observed in the experiments. The complex structure of the S(1) ← S(0) absorption band is found to originate from a very strong nonadiabatic coupling of the S(2) (of πσ* origin) and S(1) (of ππ* origin) state. While S(2) state is orbitally degenerate and JT active, the S(1) state is nondegenerate. These states form energetically low-lying conical intersections (CIs) in HFBz. These CIs are found to be the mechanistic bottleneck of the observed low quantum yield of fluorescence emission, non overlapping absorption, and emission bands of HFBz and contribute to the spectral width. Justification is also provided for the observed two peaks in the second absorption (the unassigned "c band") band of HFBz. The peaks observed in the third, fourth, and fifth absorption bands are also identified and assigned.

Theoretical study of electronic absorption spectroscopy of propadienylidene molecule vis-â-vis the observed diffuse interstellar bands

Observation of broad and diffuse interstellar bands (DIBs) at 4881Å and 5440Å assigned to the optical absorption spectrum of Y-shaped propadienylidene (H2CCC:) molecule is theoretically examined in this paper. This molecule apparently absorbs in the same wavelength region as the observed DIBs and was suggested to be a potential carrier of these DIBs. This assignment mostly relied on the experimental data from radioastronomy and laboratory measurements. Motivated by these available experimental data we attempt here a theoretical study and investigate the detailed electronic structure and nuclear dynamics underlying the electronic absorption bands of propadienylidene molecule. Our results show that this molecule indeed absorbs in the wavelength region of the recorded DIBs. Strong nonadiabatic coupling between its energetically low-lying electronic states plays major role, initiates ultrafast internal conversion and contributes to the spectral broadening. Theoretical findings are finally compared with the available experimental and theoretical data and discussed in connection with the recorded DIBs.

The dissociative chemisorption of methane on Ni(100): Reaction path description of mode-selective chemistry

We derive a model for the dissociative chemisorption of methane on a Ni(100) surface, based on the reaction path Hamiltonian, that includes all 15 molecular degrees of freedom within the harmonic approximation. The total wavefunction is expanded in the adiabatic vibrational states of the molecule, and close-coupled equations are derived for wave packets propagating on vibrationally adiabatic potential energy surfaces, with non-adiabatic couplings linking these states to each other. Vibrational excitation of an incident molecule is shown to significantly enhance the reactivity, if the molecule can undergo transitions to states of lower vibrational energy, with the excess energy converted into motion along the reaction path. Sudden models are used to average over surface impact site and lattice vibrations. Computed dissociative sticking probabilities are in good agreement with experiment, with respect to both magnitude and variation with energy. The ν(1) vibration is shown to have the largest efficacy for promoting reaction, due to its strong non-adiabatic coupling to the ground state, and a significant softening of the vibration at the transition state. Most of the reactivity at 475 K is shown to result from thermally assisted over-the-barrier processes, and not tunneling.

Ab initiostudy of charge-transfer dynamics in collisions of C2+ions with hydrogen chloride

Ab initio quantum chemistry molecular calculations followed by a semiclassical dynamical treatment in the keV collision energy range have been developed for the study of the charge-transfer process in collisions of ${\mathrm{C}}^{2+}$ ions with hydrogen chloride. The mechanism has been investigated in detail in connection with avoided crossings between states involved in the reaction. A simple mechanism driven by a strong nonadiabatic coupling matrix element has been pointed out for this process. A comparative analysis with the halogen fluoride target corresponding to a similar electronic configuration shows a quite different charge-transfer mechanism leading to a very different behavior of the cross sections. Such behavior may be correlated to specific nonadiabatic interactions observed in these collision systems.

Born–Oppenheimer breakdown and non-adiabatic lifetimes of rovibrational levels of D2 lying near the n=2 dissociation limit: Experiment and theory

Abstract The singlet gerade states of the hydrogen molecule are strongly affected by the breakdown of the Born–Oppenheimer approximation. This leads to strong non-adiabatic coupling resulting in large changes of the energies and lifetimes of the quantum levels compared to the values obtained in the Born–Oppenheimer or even the adiabatic levels of approximation. The non-adiabatic calculations of Quadrelli, Dressler, and Wolniewicz (1990) [7] (hereinafter QDW) for the three highest vibrational levels (υ = 44, 45, and 46) of the EF 1Σg+ state of D2 predicted an enormous increase of the lifetimes upon excitation of just one quantum of rotational motion. However, although our experimental results for these levels just below the n = 2 dissociation limit do show a strong increase in lifetime, the non-adiabatic lifetimes calculated by QDW are longer than experiment by as much as three orders of magnitude. In their work on isotopomers of hydrogen QDW and Yu and Dressler (1994) [5] published extensive summary tables of ab initio non-adiabatic coupling data. We present a technique which allows us to use their summary data to calculate approximate non-adiabatic ab initio lifetimes. The results reconcile our observed lifetimes with the non-adiabatic coupling from those previous ab initio calculations and also provide a detailed quantitative and qualitative understanding of the unusual rotational dependence of the lifetimes of these very highly excited levels. We also test the current technique by calculating the lifetimes of other levels involved in interactions with these EF levels and by calculating the lifetimes of the EF υ = 33 level of H2, for which no corresponding level exists in the Born–Oppenheimer or adiabatic approximations.

Phase-space surface hopping: Nonadiabatic dynamics in a superadiabatic basis

In this paper, we construct a phase-space surface hopping algorithm for use in systems that exhibit strong nonadiabatic coupling. The algorithm is derived from a representation of the electronic basis which is a function of the nuclear phase-space coordinates rather than the nuclear position coordinates. This phase-space adiabatic basis can be understood in the context of Berry's superadiabatic basis formalism as the first-order superadiabatic correction to the conventional position-space adiabatic basis. This superadiabatic representation leads to nuclear dynamics described not by Newton's equations of motion but by generalized Hamilton's equations of motion. The phase-space surface hopping algorithm captures physical effects that cannot be described by traditional algorithms. For a simple model problem, we show that phase-space surface hopping is more accurate than position-space surface hopping, especially when the nonadiabatic coupling is strong.

Study on Photodissociation Dynamics of n-Pentyliodide Using Velocity Map Ion Imaging

Photodissociation dynamics of n-C5H11I at 266 and 277 nm was investigated using velocity map ion imaging. Speed and angular distributions of the corresponding photofragments were obtained by detecting ion images of I*(5p(2)P(1/2)) and I (5p(2)P(3/2)). Quantum yields of I* and I were also obtained. The contribution of parallel and perpendicular transitions and the relative fraction of each potential surface at different excitation wavelengths were determined. These determinations were based on the relative quantum yield and the angular distribution. It is found that a very strong nonadiabatic coupling exists between the two excited states (3)Q(0) and (1)Q(1), and the curve crossing probability rises gradually with a decrease in the excitation wavelength. Additionally, analysis of the angular distributions for the I* channel and the I channel at the same excitation wavelength revealed that the population of (3)Q(0) was the main pathway following excitation. However, when compared to the situation that the I* channel mainly results from the direct dissociation of the (3)Q(0) state, the I channel originates mostly from the nonadiabatic coupling between (3)Q(0) and (1)Q(1).

Mixed quantum-classical equilibrium: Surface hopping

We re-examine the analysis of the equilibrium limits of the fewest switches surface hopping algorithm for mixed quantum-classical dynamics. In contrast with previously reported results, we show that surface hopping does not, in general, exactly yield Boltzmann equilibrium, but that in practice the observed deviations are quite small. We also demonstrate that surface hopping does approach the exact equilibrium distribution in both the limits of small adiabatic splitting and/or strong nonadiabatic coupling. We verify these analytical results with numerical simulations for a simple two-level quantum system connected to a bath of classical particles.

Algorithmic decoherence time for decay-of-mixing non–Born–Oppenheimer dynamics

The performance of an analytical expression for algorithmic decoherence time is investigated for non-Born-Oppenheimer molecular dynamics. There are two terms in the function that represents the dependence of the decoherence time on the system parameters; one represents decoherence due to the quantum time-energy uncertainty principle and the other represents a back reaction from the decoherent force on the classical trajectory. We particularly examine the question of whether the first term should dominate. Five one-dimensional two-state model systems that represent limits of multidimensional nonadiabatic dynamics are designed for testing mixed quantum-classical methods and for comparing semiclassical calculations with exact quantum calculations. Simulations are carried out with the semiclassical Ehrenfest method (SE), Tully's fewest switch version (TFS) of the trajectory surface hopping method, and the decay-of-mixing method with natural switching, coherent switching (CSDM), and coherent switching with reinitiation (CSDM-D). The CSDM method is demonstrated to be the most accurate method, and it has several desirable features: (i) It behaves like the representation-independent SE method in the strong nonadiabatic coupling regions; (ii) it behaves physically like the TFS method in noninteractive region; and (iii) the trajectories are continuous with continuous momenta. The CSDM method is also demonstrated to balance coherence well with decoherence, and the results are nearly independent of whether one uses the adiabatic or diabatic representation. The present results provide new insight into the formulation of a physically correct decoherence time to be used with the CSDM method for non-Born-Oppenheimer molecular dynamic simulations.

Reclassifying exciton-phonon coupling in molecular aggregates: Evidence of strong nonadiabatic coupling in oligothiophene crystals

Exciton-phonon (EP) coupling in molecular aggregates is reexamined in cases where extended intermolecular interactions result in low-energy excitons with high effective masses. The analysis is based on a single intramolecular vibrational mode with frequency omega0 and Huang-Rhys factor lambda2. When the curvature Jc at the exciton band bottom is much smaller than the free-exciton Davydov splitting W, the strength of the EP coupling is determined by comparing the nuclear relaxation energy lambda2omega0 with the curvature. In this way, weak (lambda2omega0<<4piJc), intermediate I (lambda2omega0 approximately 4piJc), and strong I (lambda2omega0>>4piJc) coupling regimes are introduced. The conventional intermediate (lambda2omega0 approximately W) and strong (lambda2omega0>>W) EP coupling regimes originally defined by Simpson and Peterson [J. Chem. Phys. 26, 588 (1957)] are based solely on the Davydov splitting and are referred to here as intermediate II and strong II regimes, respectively. Within the intermediate I and strong I regimes the near degeneracy of the low-energy excitons allows efficient nonadiabatic coupling, resulting in a spectral splitting between the b- and ac-polarized first replicas in the vibronic progression characterizing optical absorption. Such spectral signatures are clearly observed in OT4 thin films and crystals, where splittings for the lowest energy mode with omega0=161 cm(-1) are as large as 30 cm(-1) with a small variation due to sample disorder. Numerical calculations using a multiphonon BO basis set and a Hamiltonian including linear EP coupling yield excellent agreement with experiment.

Conical intersections and strong nonadiabatic coupling effects in singlet-excited acetylene: An ab initio quantum dynamical study

The conically intersecting potential energy surfaces of the S 1 and S 2 excited states of acetylene and the resulting strong nonadiabatic couplings are investigated theoretically. The adiabatic potential energy surfaces are obtained from high-level MRCI calculations. They are diabatized using the concept of regularized diabatic states and then used as a basis for the subsequent wave-packet dynamical treatment of the nuclear motion. All three angular degrees of freedom are included in the present study, while the bond lengths are kept frozen. The importance of the nonadiabatic interactions for the fine structure of the VUV spectrum of acetylene in the 6.5–8 eV excitation energy range is established. The electronic populations display an S 2 → S 1 internal conversion process on the order of 50 fs, which is, however, incomplete owing to the relatively small S 2–S 1 energy gap and the present reduced-dimensionality treatment. Snapshots of the wave-packet as well as angular probability densities are analyzed and reveal, for the first time, an incipient excited-state cis–trans isomerization in this system.