Single Potential Surface Research Articles

One and Two Dimensional Vibronic Spectra for an Exciton Dimer from Classical Trajectories.

We extend the semiclassical optimized mean trajectory (OMT) procedure to calculate electronic spectra for a dimer with excitonic and vibronic interactions. The electronic part of the quantum Hamiltonian is expressed in the Miller-Meyer-Stock-Thoss form with one fictitious harmonic oscillator per electronic state, and the classical limit is taken, transforming a quantum Hamiltonian governing discrete states to an equivalent classical form. The ad hoc addition of classical nuclear degrees of freedom and electron-nuclear coupling yields a classical Hamiltonian with one degree of freedom per each electronic state and also per each nuclear motion. Semiclassical quantization is applied to this Hamiltonian through the OMT, originally developed to describe nuclear dynamics on a single potential surface and subsequently generalized to include electronic transitions. The accuracy and practicality of this trajectory-based method is assessed for an excitonically coupled dimer. The semiclassical one- and two-dimensional spectra are shown to compare well with quantum dynamical calculations performed with the hierarchical equations of motion method.

A classical ride through a conical intersection

Regarding the correlated electron-nuclear motion in a model system, we investigate the dynamics in the vicinity of a conical intersection (CoIn) between two excited state potential surfaces. It is documented that an ensemble of classical trajectories which move in the complete electronic-nuclear phase space tracks the quantum wave-packet motion through the CoIn which is accompanied by a non-adiabatic population transfer. On the contrary, for an adiabatic circular motion around the position of the CoIn, the quantum mechanical and classical densities deviate substantially. In the latter case, the Born-Oppenheimer classical nuclear motion on a single potential surface is able to track the quantum dynamics.

A plastic-damage model for concrete under compression

A phenomenological model for plain concrete under compression is formulated within the framework of the coupled elastoplastic-damage theory. Phenomenological elastoplastic-damage models have been widely used for concrete because of their capability of representing both the permanent inelastic deformations and the degradation of material moduli beyond the elastic range. The essential contribution introduced in this paper is the proposed partitioning of the strain tensor within the coupled elastoplastic-damage framework which simplifies the selection of the failure surface and the potential function. Proposed partitioning permits the use of single failure criterion and single potential surface that are effective for both damage and plasticity models during inelastic deformations. Therefore, the coupled elastoplastic-damage model can be easily calibrated to fit the observed concrete behaviour based on well-established non-associated plasticity rules for concrete. The proposed approach also simplifies the numerical procedure by eliminating iterations that is required to equilibrate the stresses in plastic and damage components of the model. The numerical implementation is explained, and the results predicted by the model are compared with experimental data provided in the literature.

The Ehrenfest method with fully quantum nuclear motion (Qu-Eh): Application to charge migration in radical cations.

An algorithm is described for quantum dynamics where an Ehrenfest potential is combined with fully quantum nuclear motion (Quantum-Ehrenfest, Qu-Eh). The method is related to the single-set variational multi-configuration Gaussian approach (vMCG) but has the advantage that only a single quantum chemistry computation is required at each time step since there is only a single time-dependent potential surface. Also shown is the close relationship to the "exact factorization method." The quantum Ehrenfest method is compared with vMCG for study of electron dynamics in a modified bismethylene-adamantane cation system. Illustrative examples of electron-nuclear dynamics are presented for a distorted allene system and for HCCI+ where one has a degenerate Π system.

Vibronic eigenstates and the geometric phase effect in the 2E″ state of NO3.

The 2E″ state of NO3, a prototype for the Jahn-Teller effect, has been an enigma and a challenge for a long time for both experiment and theory. We present a detailed theoretical study of the vibronic quantum dynamics in this electronic state, uncovering the effects of tunnelling, geometric phase, and symmetry. To this end, 45 vibronic levels of NO3 in the 2E″ state are determined accurately and analyzed thoroughly. The computation is based on a high quality diabatic potential representation of the two-sheeted surface of the 2E″ state developed by us [W. Eisfeld et al., J. Chem. Phys. 140, 224109 (2014)] and on the multi-configuration time dependent Hartree approach. The vibrational eigenstates of the NO3- anion are determined and analyzed as well to gain a deeper understanding of the symmetry properties of such D3h symmetric systems. To this end, 61 eigenstates of the NO3- anion ground state are computed using the single sheeted potential surface of the 1A1 state published in the same reference quoted above. The assignments of both the vibrational and vibronic levels are discussed. A simple model is proposed to rationalize the computed NO3 spectrum strongly influenced by the Jahn-Teller couplings, the associated geometric phase effect, and the tunnelling. Comparison with the available spectroscopic data is also presented.

Nuclear Dynamics at Molecule-Metal Interfaces: A Pseudoparticle Perspective.

We discuss nuclear dynamics at molecule-metal interfaces including nonequilibrium molecular junctions. Starting from the many-body states (pseudoparticle) formulation of the molecule-metal system in the molecular vibronic basis, we introduce gradient expansion to reduce the adiabatic nuclear dynamics (that is, nuclear dynamics on a single molecular potential surface) into its semiclassical form while maintaining the effect of the nonadiabatic electronic transitions between different molecular charge states. This yields a set of equations for the nuclear dynamics in the presence of these nonadiabatic transitions, which reproduce the surface-hopping formulation in the limit of small metal-molecule coupling (where broadening of the molecular energy levels can be disregarded) and Ehrenfest dynamics (motion on the potential of mean force) when information on the different charging states is traced out.

From roaming atoms to hopping surfaces: mapping out global reaction routes in photochemistry.

The photodissociation of small molecules occurs upon irradiation by ultraviolet or visible light, and it is a very important chemical process in Earth's atmosphere, in the atmospheres of other planets, and in interstellar media. Photodissociation is an important method used to thoroughly investigate the fundamental issues of chemical reactivity. Photodissociation involves molecules and reaction fragments moving over ground- and excited-state potential surfaces (PESs). Molecules can move on a single PES (adiabatic pathway) or can cross over from one PES to another (nonadiabatic pathways). For a full theoretical understanding of a photodissociation mechanism, all of the important nonadiabatic and adiabatic pathways must be determined. This is not an easy task. We have developed an efficient computational method, called the global reaction route mapping (GRRM) strategy, that allows a theoretical exploration of ground- and excited-state PESs and their crossing seams in an automatic manner. In this Perspective, we summarize our approaches and present examples of their application together with newly determined chemical insights. These include the complex photodissociation mechanism of the formaldehyde molecule, the exclusive excited-state roaming dynamics of the nitrate radical, and all product channels and conformational memory in the photodissociation of the formic acid molecule. Finally, perspectives for the theoretical design of photofunctional molecules are discussed.

Dipole-Resonance Assisted Isomerization in the Electronic Ground State Using Few-Cycle Infrared Pulses

A computational investigation of HCN → HNC isomerization in the electronic ground state by one- and few-cycle infrared pulses is presented. Starting from a vibrationally pre-excited reagent state, isomerization yields of more than 50% are obtained using single one- to five-cycle pulses. The principal mechanism includes two steps of population transfer by dipole-resonance (DR), and hence, the success of the method is closely linked to the polarity of the system and, in particular, the stepwise change of the dipole moment from reactant to transition state and on to products. The yield drops massively if the diagonal dipole matrix elements are artificially set to zero. In detail, the mechanism includes DR-induced preparation of a delocalized vibrational wavepacket, which traverses the barrier region and is finally trapped in the product well by DR-dominated de-excitation. The excitation and de-excitation steps are triggered by pulse lobes of opposite field direction. As the number of optical cycles is increased, the leading field lobes prepare a vibrational superposition state by off-resonant ladder climbing, which is then subjected to the three steps of the principal isomerization mechanism. DR excitation is more efficient from a preformed vibrational wavepacket than from a molecular eigenstate. The entire process can be loosely described as Tannor-Kosloff-Rice type transfer mechanism on a single potential surface effected by a single pulse, individual field lobes assuming the roles of pump- and dump-pulses. Pre-excitation to a transient wavepacket can be enhanced by applying a separate, comparatively weak few-cycle prepulse, in which the prepulse prepares a vibrational wavepacket. The two-pulse setup corresponds to a double Tannor-Kosloff-Rice control scheme on a single potential surface.

Tailoring of motional states in double-well potentials by time-dependent processes

We show that the vibrational state tailoring method developed for molecular systems can be applied for cold atoms in optical lattices. The original method is based on a three-level model interacting with two strong laser pulses in a counterintuitive sequence [M. Rodriguez et al., Phys. Rev. A 62, 053413 (2000)]. Here we outline the conditions for achieving similar dynamics with single time-dependent potential surfaces. It is shown that guided switching between diabatic and adiabatic evolution has an essential role in this system. We also show that efficient and precise tailoring of motional states in optical lattices can be achieved, for instance, simply by superimposing two lattices and moving them with respect to each other.

Importance of the Single Amino Acid Potential in Water for Secondary and Tertiary Structures of Proteins

The structure of a protein molecule is considered to be primarily determined by the inter-amino-acid nonbonded interactions, such as hydrogen bonds. However, the conformational space of the polypeptide chain should be simultaneously restricted by the intrinsic conformational preferences of the individual amino acids. We present here precise single amino acid potential (SAAP) surfaces for glycine (For-Gly-NH(2)) and alanine (For-Ala-NH(2)) in water (epsilon = 78.39) and ether (epsilon = 4.335), which were calculated at the HF/6-31+G(d,p) level applying the self-consistent isodensity polarizable continuum model (SCIPCM) reaction field with geometry optimization in the corresponding solvents. The obtained Ramachandran potential surfaces in water showed distinct potential wells in the alpha- and beta-regions. The profiles were in almost perfect agreement with the Ramachandran plots of glycine and alanine residues in folded proteins, suggesting the Boltzmann distributions on the SAAP surfaces. Molecular simulations of polyalanines (For-Ala(n)-NH(2); n = 3-5) by using the SAAP force field equipped with the SCIPCM potentials revealed that the polyalanines readily form 3(10)-helical structures in water but not in vacuo. In ether (hydrophobic environments), the helical structures were relatively stable, but the most stable structure was assigned to a different one. These results indicated that the intrinsic conformational preferences of the individual amino acids (i.e., the SAAPs) in water are of significant importance not only for describing conformations of a polypeptide chain in the random coil state but also for understanding the folding to the secondary and tertiary structures.

Wave packet movements near the conical intersection between two excited potential surfaces may create observable molecular oscillations.

A femtosecond pump-probe experiment is performed on tetrakis(dimethylamino)ethylene. The evolution resulting from the pi-pi(*) excitation of the CC double bond corresponds to movement along a single adiabatic potential surface with deformation along several coordinates and passage near a conical intersection. Surprisingly, this movement excites the umbrella mode of the amino groups, resulting in a measurable oscillation regime.

Trajectory surface hopping study of the C + CH reaction

The influence of electronically nonadiabatic transitions in the C(3Pg) + CH(X 2Π) → C2(X 1Σ+g, a 3Πu) + H(2Sg) reaction is investigated by using Tully's fewest-switches version of the trajectory surface hopping method. A diabatic model of the first two 2A′ potential energy surfaces coupled by a conical intersection is used. The diatomic CH has the internal state (ν = 0, j = 0) and batches of 20 000 trajectories are computed for four collision energies, E = 0.1, 0.3, 0.5 and 0.7 eV. We find that the reaction dynamics does not exhibit a statistical character, despite the existence of deep wells along the reaction path. Only the distribution of scattering angle shows a good agreement between trajectories and phase space theory results. A strong excess of vibrational energy is disposed on both electronic products C2(X 1Σ+g) and C2(a 3Πu), correlated with a lack of recoil energy. With all trajectories starting on a single potential surface, we obtain an electronic branching ratio X : a close to 2 : 3, only slightly dependent on the collision energy.

Finite deformation analysis of geomaterials

AbstractThe mathematical structure and numerical analysis of classical small deformation elasto–plasticity is generally well established. However, development of large deformation elastic–plastic numerical formulation for dilatant, pressure sensitive material models is still a research area.In this paper we present development of the finite element formulation and implementation for large deformation, elastic–plastic analysis of geomaterials. Our developments are based on the multiplicative decomposition of the deformation gradient into elastic and plastic parts. A consistent linearization of the right deformation tensor together with the Newton method at the constitutive and global levels leads toward an efficient and robust numerical algorithm. The presented numerical formulation is capable of accurately modelling dilatant, pressure sensitive isotropic and anisotropic geomaterials subjected to large deformations. In particular, the formulation is capable of simulating the behaviour of geomaterials in which eigentriads of stress and strain do not coincide during the loading process.The algorithm is tested in conjunction with the novel hyperelasto–plastic model termed the B material model, which is a single surface (single yield surface, affine single ultimate surface and affine single potential surface) model for dilatant, pressure sensitive, hardening and softening geomaterials. It is specifically developed to model large deformation hyperelasto–plastic problems in geomechanics.We present an application of this formulation to numerical analysis of low confinement tests on cohesionless granular soil specimens recently performed in a SPACEHAB module aboard the Space Shuttle during the STS‐89 mission. We compare numerical modelling with test results and show the significance of added confinement by the thin hyperelastic latex membrane undergoing large stretching. Copyright © 2001 John Wiley & Sons, Ltd.

A semiclassical limit for the mapping Hamiltonian approach to electronically nonadiabatic dynamics

In this paper we derive a semiclassical limit of dynamics corresponding to the mapping Hamiltonian formulation of the electronically nonadiabatic problem originally proposed by Stock and co-workers, and Miller and his group. We show results comparing the approach described here with the alternative semiclassical scheme previously used by these workers in applications of this formulation. For simplicity the calculations presented here are for single potential surface models but the approach is generally applicable to many coupled surfaces. We demonstrate by comparison with exact numerical solution that the results obtained with the approach presented here are accurate for arbitrary potential forms but that the alternative semiclassical implementation only apparently converges when repulsive walls in the model surfaces are unimportant.

The gas-phase reaction between hydroxide ion and methyl formate: a theoretical analysis of the energy surface and product distribution.

The potential energy surface for the prototype solvent-free ester hydrolysis reaction: OH- +HCOOCH3 --> products has been characterized by high level ab initio calculations of MP4/6-311 + G(2df,2p)//MP2/6-31 + G(d) quality. These calculations reveal that the approach of an OH- ion leads to the formation of two distinct ion-molecule complexes: 1) the MS1 species with the hydroxide ion hydrogen bonded to the methyl group of the ester, and 2) the MS4 moiety resulting from proton abstraction of the formyl hydrogen by the hydroxide ion and formation of a three-body complex of water, methoxide ion and carbon monoxide. The first complex reacts to generate formate anion and methanol products through the well known B(AC)2 and S(N)2 mechanisms. RRKM calculations predict that these pathways will occur with a relative contribution of 85% and 15% at 298.15 K, in excellent agreement with experimentally measured values of 87% and 13%, respectively. The second complex reacts by loss of carbon monoxide to yield the water-methoxide complex through a single minimum potential surface and is the preferred pathway in the gas-phase. This water-methoxide adduct can further dissociate if the reactants have excess energy. These results provide clear evidence that the preferred pathways for ester hydrolysis in solution are dictated by solvation of the hydroxide ion.

Rovibrational structures of the pseudorotating lithium trimer Li321: Rotationally resolved spectroscopy and ab initio calculations of the A 2E″←X 2E′ system

Based on resonant two-photon ionization of Li321 with cw lasers and mass-selective detection of Li3+21 ions by a quadrupole mass spectrometer, isotope-selective rotationally resolved spectra of vibronic bands in the electronic A 2E″←X 2E′ system have been recorded. The complex but completely resolved spectra could be analyzed using optical–optical double resonance techniques in combination with accurate ab initio calculations which provide potential energy surfaces and rovibronic term values for both electronic states. A detailed comparison between experimental and theoretical results for the (vs′=0, vb′=0, va′=0)←(vs″=0, vb″=0, va″=0) band demonstrates excellent agreement. The coupling between pseudorotation and rotational motion is shown to produce complex level patterns which, however, can be accurately represented by an effective pseudo/rotation Hamiltonian in terms of rotational and coupling constants that directly provide structural information. For both electronic states the nuclear dynamics is adequately described as a motion on a single adiabatic potential surface with a geometric phase π for closed loops around the conical intersection at D3h geometries.

Lattice Relaxation Dynamics of Excitons and Elementary Nonlinear Processes in Photoinduced Structural Phase Transitions - Aggregation, Growth and Proliferation -

We theoretically study the lattice relaxation dynamics of a photogenerated single exciton which finally results in a macroscopic domain in insulating solids. Especially, we focus on three elementary nonlinear processes of this domain formation, which we call aggregation, growth and proliferation. This domain formation phenomenon is usually called `photoinduced structural phase transition' (PSPT). In these three elementary processes, the exciton does not stay within a single adiabatic potential surface but transits diabatically between the different potential ones. Hence, the full-quantum-mechanical treatment is indispensable. As one of the models for this type of phase transition, we consider a strongly coupled many exciton-Einstein phonon system. This is our relevant system. We also assume this system to interact with even and odd reservoir modes as well as photons. The even modes couple linearly with Einstein phonons and dissipate their energies, while the odd modes couple linearly with excitons and non...

Electronic nonadiabaticity in highly vibrationally excited O2(X 3Σg−): Spin-orbit coupling between X 3Σg− and b 1Σg+

We report full quantum-state-resolved spectra of highly vibrationally excited O2(X 3Σg−,v=26–31). In addition to providing high precision molecular constants for several new vibrational levels, we observe a local spectral perturbation of X 3Σg−(v=28). We present a deperturbation analysis of the observed spectra and assign the perturber to b 1Σg+(v=19). We predict a crossing between the b 1Σg+ and X 3Σg− state at an internuclear separation R=2.45±0.1 Å, somewhat further extended and higher in energy than the outer classical turning point of O2(X 3Σg−,v=28). Using the appropriate vibrational overlap integral, we are able to determine the spin–orbit interaction between these two electronic states, which is 200±20 cm−1 in the vicinity of the crossing. These results suggest that the collision dynamics of highly vibrationally excited O2(X 3Σg−) may involve excited potential surfaces. Furthermore, they imply that present theoretical approaches to the O4 problem, which use a single potential surface, may not be adequate. Possible implications regarding nonequilibrium models of stratospheric ozone formation and the dynamics of the O+O3→2O2 reaction are discussed.

Calculation of reduced partial cross sections of molecules photodesorbing from a cold crystal surface with internal vibrations: Inclusion of curve-crossing effects

A Gaussian wave packet/path integral (GWD/PI) method is used to compute final internal state distributions for a molecule photodesorbing from the surface of a zero-temperature crystal with internal vibrations in the situation where nonadiabatic coupling between two excited state potential surfaces is significant. The internal state distributions of the desorbed molecule are influenced by vast numbers of internal vibrational state transitions in the crystal which are not resolved in the calculation (or in experiment). A correlation function technique, introduced previously for the case of direct photodissociation on a single excited potential surface, is generalized to systems where two or more excited potential surfaces are nonadiabatically coupled. The accuracy of the method is successfully tested on a two-dimensional model for which numerically exact results can be computed. The method is then applied to a collinear model of a diatomic molecule photodesorbing from a chain of atoms coupled by Hooke’s law springs. While exact results cannot be obtained in this case, sum rule checks suggest that the results of the GWD/PI are of acceptable accuracy (fractional error of several percent). It is found that for the class of problems under study, which feature nonadiabatic coupling that decays to zero along the photodesorption coordinate, only a few paths through the electronic state space have significant weight. This suggests that the method can be utilized to treat more complicated problems.

On the B←X transitions of expansion cooled silver halides

Fluorescence excitation and mass-resolved excitation spectroscopy of jet-cooled silver halide (AgX) bare molecules are explored for the B←X systems of AgCl, AgBr, and AgI. These spectra are compared to those from static gas measurements. The continuous-wave expansion molecular beam of Ar–He with AgX species is generated at a temperature of 1100 °C. For AgI two types of progressions are shown to appear in 31 000–33 000 cm−1 range. The first set of transitions is attributed to the B state and is quite similar to the other AgX molecule’s B←X transitions. The second set has been previously observed for high-temperature AgI vapor as a partly resolved series of features on a broad absorption. The nature of this state and whether it arises from a level crossing between the B surface and an unobserved state is not clear. We analyze two different possible explanations for the newly resolved B′ progression: The B and B′ progressions involve two different excited electronic states; and both progressions belong to one excited electronic state with a complicated single adiabatic potential surface. Computation of vibrational harmonic and anharmonic constants suggests that the potential shape of the B/B′ state is substantially different from that of a common anharmonic oscillator. The nature of the B/B′ surface must be resolved through detailed and accurate ab initio calculations. Ag ions produced by 1+2 photoionization of AgX at longer wavelengths are not fragmentation products of AgX ions, but rather arise from the dissociation of a neutral AgX in a highly excited state. This intermediate state at ∼62 000 cm−1 is accessed from the B state by absorption of a photon of approximately the same energy as required for the B←X AgX transition.