Lowest Potential Energy Surface Research Articles

Electronic nonadiabatic effects in the state-to-state dynamics of the H + H2 → H2 + H exchange reaction with a vibrationally excited reagent.

Out of the many major breakthroughs that the hydrogen-exchange reaction has led to, electronic nonadiabatic effects that are mainly due to the geometric phase has intrigued many. In this work we investigate such effects in the state-to-state dynamics of the H + H2 (v = 3, 4, j = 0) → H2 (v', j') + H reaction with a vibrationally excited reagent at energies corresponding to thermal conditions. The dynamical calculations are performed by a time-dependent quantum mechanical method both on the lower adiabatic potential energy surface (PES) and also using a two-states coupled diabatic theoretical model to explicitly include all the nonadiabatic couplings present in the 1E' ground electronic manifold of the H3 system. The nonadiabatic couplings are considered here up to the quadratic term; however, the effect of the latter on the reaction dynamics is found to be very small. Adiabatic population analysis showed a minimal participation of the upper adiabatic surface even for the vibrationally excited reagent. A strong nonadiabatic effect appears in the state-to-state reaction probabilities and differential cross sections (DCSs). This effect is manifested as "out-of-phase" oscillations in the DCSs between the results of the uncoupled and coupled surface situations. The oscillations persist as a function of both scattering angle and collision energy in both the backward and forward scattering regions. The origins of these oscillations are examined in detail. The oscillations that appear in the forward direction are found to be different from those due to glory scattering, where the latter showed a negligibly small nonadiabatic effect. The nonadiabatic effects are reduced to a large extent when summed over all product quantum states, in addition to the cancellation due to integration over the scattering angle and partial wave summation.

Strong Exciton-Vibrational Coupling in Molecular Assemblies. Dynamics Using the Polaron Transformation in HEOM Space.

In Frenkel exciton dynamics of aggregated molecules, the polaron transformation (PT) technique leads to decoupling of diagonal elements in the subspace of excited electronic states from vibrations. In this article we describe for the first time how PT becomes applicable in the framework of the "Hierarchical Equations of Motion" (HEOM) approach for treatment of open quantum systems. We extend the concept of formulating operators in HEOM space by deriving hierarchical equations of PT which lead to a shift in the excited state potential energy surface to compensate its displacement. While the assumption of thermal equilibration of the vibrational oscillators, introduced by PT, results in a stationary state in a monomer, in a dimer under the same assumption nonequilibrium dynamics appears because of the interplay of the transfer process and vibrational equilibration. Both vertical transitions generating a vibrationally hot state and initially equilibrated vibrational oscillators evolve toward the same stationary asymptotic state associated with polaron formation. The effect of PT on the dynamics of this process depends on initial excitation and basis representation of the electronic system. The developed approach facilitates a generic formulation of quantum master equations involving perturbative treatment of polaron dynamics.

Gas phase Elemental abundances in Molecular cloudS (GEMS)

Context. Carbon monosulphide (CS) is among the most abundant gas-phase S-bearing molecules in cold dark molecular clouds. It is easily observable with several transitions in the millimeter wavelength range, and has been widely used as a tracer of the gas density in the interstellar medium in our Galaxy and external galaxies. However, chemical models fail to account for the observed CS abundances when assuming the cosmic value for the elemental abundance of sulfur. Aims. The CS+O → CO + S reaction has been proposed as a relevant CS destruction mechanism at low temperatures, and could explain the discrepancy between models and observations. Its reaction rate has been experimentally measured at temperatures of 150−400 K, but the extrapolation to lower temperatures is doubtful. Our goal is to calculate the CS+O reaction rate at temperatures <150 K which are prevailing in the interstellar medium. Methods. We performed ab initio calculations to obtain the three lowest potential energy surfaces (PES) of the CS+O system. These PESs are used to study the reaction dynamics, using several methods (classical, quantum, and semiclassical) to eventually calculate the CS + O thermal reaction rates. In order to check the accuracy of our calculations, we compare the results of our theoretical calculations for T ~ 150−400 K with those obtained in the laboratory. Results. Our detailed theoretical study on the CS+O reaction, which is in agreement with the experimental data obtained at 150–400 K, demonstrates the reliability of our approach. After a careful analysis at lower temperatures, we find that the rate constant at 10 K is negligible, below 10−15 cm3 s−1, which is consistent with the extrapolation of experimental data using the Arrhenius expression. Conclusions. We use the updated chemical network to model the sulfur chemistry in Taurus Molecular Cloud 1 (TMC 1) based on molecular abundances determined from Gas phase Elemental abundances in Molecular CloudS (GEMS) project observations. In our model, we take into account the expected decrease of the cosmic ray ionization rate, ζH2, along the cloud. The abundance of CS is still overestimated when assuming the cosmic value for the sulfur abundance.

Visible‐light‐stimulated Alkalis‐triggered Platinum Cocatalyst with Electron Deficient Interface for Hydrogen Evolution

AbstractSolid–liquid interface engineering has recently emerged as a promising technique to optimize the activity. Here, the cation identity and induced interfacial electronic structure of Pt have been shown to have a particularly significant impact on the activity of desired photocatalytic hydrogen evolution. The behavior of Pt aggregation synergistically induced by photo‐electron accumulation on Pt surface and the ionic potential of alkalis was logically elucidated. X‐ray photoelectron spectroscopy (XPS) and photoconductive atomic force microscopy (pcAFM) results revealed that the surface of alkali‐triggered Pt nanoparticles (Pt NPs) aggregates are electron‐deficient, which favors photo‐induced charge separation, leading to improved reaction kinetics. Based on the density functional theory (DFT) calculation, alkalis‐triggered Pt NPs has lower Gibbs free energy and potential energy surface of H2 formation for hydrogen evolution in thermodynamics. As a result, K+ triggered Pt cocatalyst displays the highest activity (3306.6 μmol h−1 g−1) on pure CN, almost 4‐fold increase compared to the reference without the addition of alkalis, showing high utilization efficiency of Pt.

The kinetics and dynamics of the multichannel multiwell reaction of CO(1Σ+) with OH(2Π): theoretical investigation

The kinetics and mechanism of the gas-phase reaction between carbon monoxide and hydroxyl radical have been theoretically investigated on the lowest potential energy surface. The dynamics of the reaction of CO(1Σ+) with OH(2Π) is studied by stochastic one-dimensional chemical master equation (CEM) simulation method. The role of the energized intermediates on the kinetics of the reaction was investigated by determination the fraction of different intermediates and products at the early stages of the reaction. The temperature dependence of the rate constants of the each individual channels of the reaction over a wide range of temperature (200–2000 K) was studied. The calculated rate constants from the CEM simulation were compared with those obtained from the RRKM–SSA [Rice–Ramsperger–Kassel–Marcus (RRKM) theory and Steady State Approximation (SSA)] method based on strong collision assumption. At lower temperatures, the calculated RRKM–SSA rate constant was found to be twice of the calculated by CEM, although the results are in good agreement with experimental values.

Up to a Sign. The Insidious Effects of Energetically Inaccessible Conical Intersections on Unimolecular Reactions.

It is now well established that conical intersections play an essential role in nonadiabatic radiationless decay where their double-cone topography causes them to act as efficient funnels channeling wave packets from the upper to the lower adiabatic state. Until recently, little attention was paid to the effect of conical intersections on dynamics on the lower state, particularly when the total energy involved is significantly below that of the conical intersection seam. This energetic deficiency is routinely used as a sufficient condition to exclude consideration of excited states in ground state dynamics. In this account, we show that, this energy criterion notwithstanding, energy inaccessible conical intersections can and do exert significant influence on lower state dynamics. The origin of this influence is the geometric phase, a signature property of conical intersections, which is the fact that the real-valued electronic wave function changes sign when transported along a loop containing a conical intersection, making the wave function double-valued. This geometric phase is permitted by an often neglected property of the real-valued adiabatic electronic wave function; namely, it is determined only up to an overall sign. Noting that in order to change sign a normalized, continuous function must go through zero, for loops of ever decreasing radii, demonstrating the need for an electronic degeneracy (intersection) to accompany the geometric phase. Since the total wave function must be single-valued a compensating geometry dependent phase needs to be included in the total electronic-nuclear wave function. This Account focuses on how this consequence of the geometric phase can modify nuclear dynamics energetically restricted to the lower state, including tunneling dynamics, in directly measurable ways, including significantly altering tunneling lifetimes, thus confounding the relation between measured lifetimes and barrier heights and widths, and/or completely changing product rotational distributions. Some progress has been made in understanding the origin of this effect. It has emerged that for a system where the lower adiabatic potential energy surface exhibits a topography comprised of two saddle points separated by a high energy conical intersection, the effect of the geometric phase can be quite significant. In this case topologically distinct paths through the two adiabatic saddle points may lead to interference. This was pointed out by Mead and Truhlar almost 50 years ago and denoted the Molecular Aharonov-Bohm effect. Still, the difficulty in anticipating a significant geometric phase effect in tunneling dynamics due to energetically inaccessible conical intersections leads to the attribute insidious that appears in the title of this Account. Since any theory is only as relevant as the prevalence of the systems it describes, we include in this Account examples of real systems where these effects can be observed. The accuracy of the reviewed calculations is high since we use fully quantum mechanical dynamics and construct the geometric phase using an accurate diabatic state fit of high quality ab initio data, energies, energy gradients, and interstate couplings. It remains for future work to establish the prevalence of this phenomenon and its deleterious effects on the conventional wisdom discussed in this work.

On Estimation of Adhesive Strength of Implants Bioactive Coating with Titanium by Density Functional Theory and Molecular Dynamics Simulations

One of the ways to improve and accelerate osseointegration of a surgical implant with bone is application of biocompatible coatings, in particular, hydroxyapatite (HAp). Since the cases of delamination of the coating take place in dental practice, it is very important to estimate the adhesive strength of HAp with the implant. A measure of the coating-to-substrate bond strength is the energy of this bond. In this research, quantum chemistry is used to calculate the binding energy of functional groups (anions) of hydroxyapatite and titanium 2+, which is a standard implant material. First, using Density Functional Theory with Becke three-parameter Lee-Yang-Parr hybrid exchange-correlation functional, the lowest potential energy surface is calculated. Then, by ab initio molecular dynamics, the reaction path, the reaction products, frequencies of oscillations, the activation energies and binding energies between various combinations of component anions of HAp and Ti(II) are calculated.

NO3 full-dimensional potential energy surfaces and ground state vibrational levels revisited

A new full-dimensional (6D) diabatic potential energy surface (PES) model is presented representing the five lowest PESs corresponding to the X̃2A2′,Ã2E″, and B̃2E′ electronic states of the nitrate radical (NO3). It is based on high-level ab initio calculations of roughly 90000 energy data over a wide range of nuclear configurations and represents the energies with a root mean-squares (rms) error of about 100 cm−1. An accurate dipole surface was developed for the X̃ state as well. The new PES model is used to re-investigate the infra-red (IR) spectrum corresponding to the electronic ground state by full dimensional quantum dynamics simulations. Vibrational eigenstates, IR transition probabilities, and isotopic shifts are computed and analyzed. Levels up to 2000 cm−1 are obtained and show good to excellent agreement with known experimental values. Some larger deviations are observed and discussed as well. The new results are in agreement with previous theoretical studies that the disputed ν3 fundamental corresponds to a frequency of roughly 1022 cm−1 and that the prominent experimental feature observed at 1492 cm−1 is due to the 3141 (e′) combination mode. Observed discrepancies in the IR intensities may be explained by coupling to the B̃ state which is also analysed by diabatic decomposition of the eigenstates.

Theoretical investigation of rotationally inelastic collisions of CH(X2Π) with molecular hydrogen.

We report calculations of state-to-state cross sections for collision-induced rotational transitions of CH(X2Π) with molecular hydrogen. These calculations employed the diabatic matrix elements of the interaction potential determined by Dagdigian [J. Chem. Phys. 145, 114301 (2016)], which employed the multi-reference configuration-interaction method [MRCISD+Q(Davidson)]. Because of the presence of a deep well on the lower potential energy surface, the scattering calculations were carried out using the quantum statistical method of Manolopoulos and co-workers [Chem. Phys. Lett. 343, 356 (2001)]. The computed cross sections included contributions from direct scattering, as well as from the formation and decay of a collision complex. The magnitude of latter contribution was found to decrease significantly with increasing collision energy. Rotationally energy transfer rate constants were computed for this system since these are required for astrochemical modeling.

Characterizing a nonclassical carbene with coupled cluster methods: cyclobutylidene.

Carbenes represent a special class of reactive compounds that possess a lone pair of electrons on a carbon atom. Among the myriad examples of carbenes in the literature, cyclobutylidene stands out as a unique nonclassical compound that includes transannular interaction between opposing C1 and C3 carbon atoms within a four-membered ring. On its lowest potential energy surface (X[combining tilde](1)A'), cyclobutylidene quickly rearranges, following three reaction paths: (i) 1,2-H migration; (ii) 1,2-C migration; and, (iii) 1,3-H migration. Herein, this reactivity is examined with high-level coupled-cluster methods [up to CCSDT(Q)]. At this level of theory, combined with extrapolation techniques to obtain energies at the complete basis set (CBS) limit, the long-standing disparity between theoretical and experimental results is resolved. Specifically, cyclobutylidene is predicted to prefer 1,2-C migration rather than 1,2-H migration. Rate constants for the three reaction paths are obtained from canonical variational transition state theory (CVT) and yield reasonable agreement with existing experimental results. Further characterization of cyclobutylidene is also reported: the singlet-triplet gap (ΔES-T) is found to be -9.3 kcal mol(-1) at the CCSDT(Q)/CBS level of theory, and anharmonic vibrational frequencies are determined with second-order vibrational perturbation theory (VPT2).

Catalytic Mechanism for the Ruthenium-Complex-Catalyzed Synthesis of Amides from Alcohols and Amines: A DFT Study

Details of the reaction mechanism for the Ru–PNN pincer complex catalyzed amidation from an alcohol and an amine proposed by Milstein et al. was elucidated using M06 density functional theory calculations. In addition, the bifunctional double hydrogen transfer (BDHT) mechanism for the dehydrogenative oxidation step was investigated for comparison. Finally, the BDHT mechanism was found to be preferred over the β-H elimination pathway that was proposed by Milstein et al. On the basis of the analysis of NBO charges and orbital interactions of intermediates and transition states, we designed a new catalyst with the addition of an electron-donating substituent (−NEt2), which provided much reduced energy barriers and a lower potential energy surface along both mechanisms.

Vibrational quenching of excitonic splittings in H-bonded molecular dimers: Adiabatic description and effective mode approximation

The quenching of the excitonic splitting in hydrogen-bonded molecular dimers has been explained recently in terms of exciton coupling theory, involving Förster's degenerate perturbation theoretical approach [P. Ottiger, S. Leutwyler, and H. Köppel, J. Chem. Phys. 136, 174308 (2012)]. Here we provide an alternative explanation based on the properties of the adiabatic potential energy surfaces. In the proper limit, the lower of these surfaces exhibits a double-minimum shape, with an asymmetric distortion that destroys the geometric equivalence of the excitonically coupled monomers. An effective mode is introduced that exactly reproduces the energy gain and amount of distortion that occurs in a multi-dimensional normal coordinate space. This allows to describe the quenched exciton splitting as the energy difference of the two (S(1) and S(2)) vibronic band origins in a one-dimensional (rather than multi-dimensional) vibronic calculation. The agreement with the earlier result (based on Förster theory) is excellent for all five relevant cases studied. A simple rationale for the quenched exciton splitting as nonadiabatic tunneling splitting on the lower double-minimum potential energy surface is given.

Decoherence induced by conical intersections: Complexity constrained quantum dynamics of photoexcited pyrazine

Decoherence effects induced by conical intersecting potential energy surfaces are studied employing the correlation-based von Neumann (CvN) entropy which provides a measure of the complexity of the underlying wavefunction. As a prototypical example, the S(0) → S(2) excitation in pyrazine is investigated. The 24-dimensional wavepacket dynamics calculations presented utilize the multi-layer extension of the multi-configurational time-dependent Hartree (MCTDH) approach. An efficient numerical scheme is introduced which facilitates CvN entropy constrained wavepacket propagation within the multi-layer MCTDH approach. In unconstrained multi-layer MCTDH calculations, the CvN-entropy is found to provide a valuable analytical tool for studying the decoherence phenomena present. Investigating the CvN entropy after the S(0) → S(2) excitation as a function of time, a clear separation of time scales is obtained. It can be related to the different dynamical phenomena present: the initial transfer from the upper (S(2)) to the lower (S(1)) adiabatic electronic states rapidly generates vast amounts of CvN-entropy, while the subsequent motion on the anharmonic lower adiabatic potential energy surface only yields a slow increase of the CvN-entropy. Employing CvN-entropy constrained calculations, the sensitivity of the autocorrelation function, the absorption spectrum, and the diabatic electronic population dynamics to complexity constraints is analyzed in detail.

Acidification of three-dimensional emeraldine polymers: Search for minimum energy paths from base to salt

We present a numerical simulation of the HCl acidification process of a three-dimensional semiconducting emeraldine base (EB) polymer leading to the corresponding metallic emeraldine salt form. We have searched minimum energy paths connecting the initial configuration, composed of two EB polymer chains per cell each one attached by two HCl molecules, with the Pc2a polaronic configuration which is the final state of the acidification process. For this aim, the variational nudged elastic band method has been adopted. We provide a pictorial representation of the acidification process at T=0 K, monitoring the EB protonation and the evolution of the polymeric chains and of the positions of the Cl(-) counterions on the lowest potential energy surface. To include also temperature effects, we have explored the potential energy surface around the final equilibrium configuration, heating the system and following its dynamics by the Car-Parrinello procedure.

Microsolvation of LiH+ in Helium Clusters: Many-Body Effects and Additivity Models for the Interaction Forces

The ab initio calculation of the interaction forces between the LiH+ molecular ion, at its equilibrium geometry, and several He atoms is carried out in order to isolate and assess the importance of many-body contributions in the search for realistic energy and geometry data. The full potential energy surface (PES) with a single helium partner is obtained first by using an aug-cc-pVQZ basis set for He and higher quality ones for Li and H. The calculations were performed at the CAS-SCF plus MRCI level for the lowest potential energy surface over a total of 480 grid points of the two intermolecular Jacobi coordinates, whereas the excited state surface has also been examined in order to exclude the presence of any significant nonadiabatic interaction between the two PESs. A numerical fit of the lower surface is presented and the general physical changes of the ionic interaction when going from the lower to the upper of the two potentials are described and discussed. The fairly limited importance of many-body effects for such systems is seen from further ab initio calculations including several He atoms: our results suggest that, at least in the present case, no strong charge migration occurs after He attachment, and therefore, one could realistically model larger clusters by implementing a sum-of-potentials approach via the presently computed PES.

Influence of collision energy on the N(2D)+O2→O(3P)+NO reaction dynamics: A quasiclassical trajectory study involving four potential energy surfaces

The influence of collision energy (ET) on the dynamics of the N(2D)+O2→O(3P)+NO atmospheric reaction was studied by means of the quasiclassical trajectory method. The four lowest potential energy surfaces (PESs) involved in the process were used in the calculations (2 2A′, 3 2A′, 1 2A″, and 2 2A″ PESs), and the nonadiabatic couplings between them were neglected. The dependence of the scalar and two-vector properties of the reaction with ET was analyzed. Moreover, the different modes of reaction taking place were investigated. Although only one type of microscopic mechanism (abstraction) was found for the 2 2A′, 3 2A′, and 2 2A″ PESs, two different modes of reaction (abstraction and insertion) were observed to coexist for the 1 2A″ PES. For this PES, the abstraction mechanism is the most important one at room temperature, while the insertion mechanism increases its contribution to reactivity with ET (it accounts for about half of the reactivity above 0.5 eV).

Ab initio calculations and modeling of diabatic potential energy surfaces for the Van der Waals complex [formula omitted

The three lowest potential energy surfaces, Σ, Π x and Π y of the Van der Waals complex Cl( 2 P)+ CH 4( X 1 A 1) are derived from accurate ab initio calculations for the vertex, edge and face geometries. The restricted coupled cluster singles, doubles and non-iterative triples excitations [RCCSD(T)] level of theory is applied with a large basis set. The global Van der Waals minimum, which is 348 cm −1 deep, occurs at R=3.3 Å on the Σ surface and is located in the vicinity of the face arrangement.

Propagation of 3D Wave Packets for Nonzero Total Angular Momentum Using the Split Operator Method

Three-dimensional wave packet calculations for total angular momentum quantum number J ≥ 0 have been performed in Jacobi coordinates. To be able to use the split operator propagator together with the fast Fourier transform method, the wave function is transformed and a modified Hamiltonian obtained. The filter diagonalization method has been used to determine a few rovibrational eigenstates of the H2O molecule on the lowest potential energy surface. Good agreement with previous work is obtained.

The Photohydration ofN-Alkylpyridinium Salts: Theory and Experiment

Bicyclic aziridines formed by the irradiation of pyridinium salts in basic solution have recently been recognized to have great synthetic potential. We have undertaken a joint computational and experimental investigation of the mechanism of this photoreaction. We have computationally determined the structures and relative energies of the relevant stationary points on the lowest potential energy surface (PES) of the pyridinium and methylpyridinium ions. Two important intermediates are shown to be bound minima on the ground-state PES: azoniabenzvalene and a 6-aza[3.1.0]bicyclic ion with an exo-oriented substituent (analogous to prefulvene). We advance a mechanism which involves initial formation of this exo-bicyclic ion, followed by nitrogen migration around the ring via the azoniabenzvalene intermediate. Thus, the barrier separating the two intermediates is the factor that determines the degree of scrambling observed in the photoproducts when the carbon atoms are labeled with deuterium or substituted with additional methyl groups. For N-methylpyridinium, the exo-methyl bicyclic ion was computed to be approximately 1 kcalmol(-1) lower in energy than N-methyl-azoniabenzvalene. The transition state was computed to lie several kcal mol(-1) above the exo-methyl bicyclic ion (+8.4kcalmol(-1), 6-31G* RHF; +3.7kcalmol(-1), 6-31G* B3LYP), but still well below the energy available from the 254 nm excitation of the N-methylpyridinium ion. The computed relative energies correspond splendidly with several experimental findings which include the preference for exo products, the results of deuterium labeling, and the impact of additional substituent methyl groups on the product distribution.

Multiple lines of conical intersections and nondegenerate ground state in T⊗t2 Jahn–Teller systems

We have investigated the T⊗t2 Jahn–Teller problem with linear and quadratic vibronic coupling including a fourth-order term. First, numerical calculations of the lowest vibronic states were carried out by direct diagonalization of the Hamiltonian. The results show that the energy level of the ground vibronic state, which is triply degenerate T for small quadratic coupling g values, intersects the next A level with increasing g, thus realizing the nondegenerate ground state at sufficiently large g values. This result reverses the long-standing belief that the ground vibronic state for the T⊗t2 system has the same degeneracy and symmetry T as the initial electronic state. To explain these results in terms of Berry phase requirements and conical intersections, the adiabatic potential energy surface of the system is analyzed, and the relationships among the type and number of minima, conical intersections, and relevant tunneling paths are revealed. Depending on the vibronic coupling parameter values, there are four trigonal minima and six orthorhombic saddle points, which become minima at large g values, plus ten lines of conical intersections on the lowest potential energy surface. The barriers between the minima are significantly increased near the lines of conical intersections where the Born–Huang terms diverge. For small enough quadratic coupling, only four lines of conical intersections that originate from the highest symmetry point and proceed along the four trigonal directions are significant in determining the Berry phase, and the triply degenerate ground T state is obtained. By increasing the quadratic coupling parameter, the remaining six lines of conical intersections approach the point of highest symmetry, thus allowing for alternative tunneling paths and Berry phases which lead to the nondegenerate A ground state. This explanation of the origin of the nondegenerate ground state for some range of values of the vibronic coupling parameters is strengthened by model calculations of tunneling splitting.