Initial Vibrational State Research Articles

Exhaustive State-to-State Cross Sections and Rate Coefficients for Inelastic N2-N2 Collisions using QCT Combined with Neural Network Models.

Using the quasi-classical trajectory method, we systematically studied the state-to-state vibrational relaxation process of N2(v1) + N2(v2) collisions over a wide temperature range (5000-30,000 K). Different temperature dependencies of the single- and multiquantum VV and VT events in various (v1,v2) collisions are captured, with the dominant channel being related to the initial vibrational energy levels (vmax = 50). At a specified relative translational energy, there is a monotonic relationship of the VT cross sections with the vibrational energy level, particularly in high-energy collisions. Additionally, we constructed well-trained neural network models (R-values reaching 0.99) using limited quasi-classical trajectory (QCT) data sets, which can be used to predict the state-to-state cross sections and rate coefficients of the VV processes N2(v1) + N2(v2) → N2(v1 - Δv) + N2(v2 + Δv) and VT processes N2(v1) + N2(v2) → N2(v1 - Δv) + N2(v2) (Δv = ±1, ±2, ±3) for collisions with arbitrary initial vibrational states. This work not only significantly reduces computational resources but also serves as a reference for the study of the state-to-state dynamics of all four-atom collision systems in hypersonic flows.

Product State-Resolved Reactive Scattering Studies of the H + Cl2 (v0 = 1-3, j0 = 0) → HCl + Cl Reaction by the Time-Dependent Wave Packet Method.

The typical hydrogen atom plus halogen molecule reaction H + Cl2 → HCl + Cl has implications across many fields. In this paper, product state-resolved quantum dynamics calculations for the vibrationally excited reaction H + Cl2 (v0 = 1-3, j0 = 0) → HCl + Cl were conducted using the time-dependent wave packet method on a newly developed accurate potential energy surface. Numerical results indicate that the initial vibrational excitation of Cl2 does enhance the reactivity for this early barrier reaction, although less than the enhancement of the translational energy. The calculated product vibrational state-resolved integral cross sections and rate constants reveal that the product vibrational state distribution and the initial vibrational state of Cl2 are highly correlated. The thermal rate constant in the temperature range from 100 to 1000 K was given and is found to be in reasonable agreement with the experimental measurements.

On the Statistical Regime, Coherence versus Incoherence and Ergodicity of Quantum Vibrational Trajectories in Soft Condensed Molecular Systems.

A theoretical-computational procedure, recently proposed for modelling Vibrational Energy Relaxation (VER) processes of a molecule (Quantum Center, QC) embedded in a complex atomic-molecular system, is extended and applied for analyzing in detail the features of the QC density matrix (DM) temporal evolution. The results, obtained using aqueous azide ion as a case study, show the total lack of coherence in the DM, when the system is prepared to be initially in a pure vibrational eigenstate. This finding is fully in line with the statistical interpretation of the process typically adopted also in the experimental studies where the relaxation processes are all described within the typical schemes of chemical kinetics. Consistently, when the initial vibrational state corresponds to an eigenstate mixture, although initially coherent, the DM relaxes to a fully incoherent condition with a mean lifetime related to the one of the diagonal elements relaxation. These specific DM features turn out to be essentially governed by the thermal equilibrium condition of the atomic-molecular classical coordinates which drive the ensemble of the quantum-trajectories toward the observed statistical regime. Finally, from the analysis of a single long timescale quantum vibrational trajectory it also clearly emerges its ergodic behaviour.

Strong Laser Field-Driven Coupled Electron-Nuclear Dynamics: Quantum vs Classical Description.

We have performed a coupled electron-nuclear dynamics study of H2+ molecular ions under the influence of an intense few-cycle 4.5 fs laser pulse with an intensity of 4 × 1014 W/cm2 and a central wavelength of 750 nm. Both quantum and classical dynamical methods are employed in the exact similar initial conditions with the aim of head-to-head comparison of two methodologies. A competition between ionization and dissociation channel is explained under the framework of quantum and classical dynamics. The origin of the electron localization phenomena is elucidated by observing the molecular and electronic wave packet evolution pattern. By probing with different carrier envelope phase (CEP) values of the ultrashort pulse, the possibility of electron localization on either of the two nuclei is investigated. The effects of initial vibrational states on final dissociation and ionization probabilities for several CEP values are studied in detail. Finally, asymmetries in the dissociation probabilities are calculated and mutually compared for both quantum and classical dynamical methodologies, whereas Franck-Condon averaging over the initial vibrational states is carried out in order to mimic the existing experimental conditions.

Inelastic N_2+H_2 collisions and quantum-classical rate coefficients: large datasets and machine learning predictions

Rate coefficients for vibrational energy transfer are calculated for collisions between molecular nitrogen and hydrogen in a wide range of temperature and of initial vibrational states (vle 40 for N_2 and wle 10 for H_2). These data are needed for the modelling of discharges in N_2/H_2 plasma or of atmospheric and interstellar medium chemistry in different temperature ranges. The calculations were performed by a mixed quantum-classical method, to recover quantum effects associated with the vibrational motion, on a refined potential energy surface. The obtained rates present striking discrepancies with those evaluated by first-order perturbation theories, like the SSH (Schwartz, Slavsky, Herzfeld) theory, which are often adopted in kinetic modelling. In addition, we present a detailed, though preliminary, analysis on the performance of different Machine Learning models based on the Gaussian Process or Neural Network techniques to produce complete datasets of inelastic scattering rate coefficients. Eventually, by using the selected models, we give the complete dataset (i.e., covering the whole vibrational ladder) of rate coefficients for the textrm{N}_2(v)+textrm{H}_2(0) longrightarrow textrm{N}_2(v-Delta v)+textrm{H}_2(0), Delta v=1,2,3 processes.Graphical abstract

Temperature Dependence of the Electronic Absorption Spectrum of NO2.

The nitrogen dioxide (NO2) radical is composed of the two most abundant elements in the atmosphere, where it can be formed in a variety of ways including combustion, detonation of energetic materials, and lightning. Relevant also to smog and ozone cycles, together these processes span a wide range of temperatures. Remarkably, high-resolution NO2 electronic absorption spectra have only been reported in a narrow range below about 300 K. Previously, we reported [ J. Phys. Chem. A 2021, 125, 5519-5533] the construction of quasi-diabatic potential energy surfaces (PESs) for the lowest four electronic states (X̃, Ã, B̃, and C̃) of NO2. In addition to three-dimensional PESs based on explicitly correlated MRCI(Q)-F12/VTZ-F12 ab initio data, the geometry dependence of each component of the dipoles and transition dipoles was also mapped into fitted surfaces. The multiconfigurational time-dependent Hartree (MCTDH) method was then used to compute the 0 K electronic absorption spectrum (from the ground rovibrational initial state) employing those energy and transition dipole surfaces. Here, in an extension of that work, we report an investigation into the effects of elevated temperature on the spectrum, considering the effects of the population of rotationally and vibrationally excited initial states. The calculations are complemented by new experimental measurements. Spectral contributions from hundreds of rotational states up to N = 20 and from 200 individually-characterized vibrational states were computed. A spectral simulation tool was developed that enables modeling the spectrum at various temperatures─by weighting individual spectral contributions via the partition function, or for pure excited initial states, which can be probed via transient absorption spectroscopy. We validate these results against experimental absorption spectroscopy data at high temperatures, as well as via a new measurement from the (1,0,1) initial vibrational state.

Modeling noise in global Mølmer-Sørensen interactions applied to quantum approximate optimization

Many-qubit Molmer-Sorensen (MS) interactions applied to trapped ions offer unique capabilities for quantum information processing, with applications including quantum simulation and the quantum approximate optimization algorithm (QAOA). Here, we develop a physical model to describe many-qubit MS interactions under four sources of experimental noise: vibrational mode frequency fluctuations, laser power fluctuations, thermal initial vibrational states, and state preparation and measurement errors. The model parameterizes these errors from simple experimental measurements, without free parameters. We validate the model in comparison with experiments that implement sequences of MS interactions on two and three $^{171}$Yb$^+$ ions. The model shows good agreement after several MS interactions as quantified by the reduced chi-squared statistic $\chi^2_\mathrm{red}< 2$. As an application we examine MaxCut QAOA experiments on three and six ions. The experimental performance is quantified by approximation ratios that are $91\%$ and $83\%$ of the optimal theoretical values. Our model predicts $0.93^{+0.03}_{-0.02}$ and $0.92^{+0.06}_{-0.06}$, respectively, with disagreement in the latter value attributable to secondary noise sources beyond those considered in our analysis. With realistic experimental improvements to reduce measurement error and radial trap frequency variations the model achieves approximation ratios that are 99$\%$ of the optimal. Incorporating these improvements into future experiments is expected to reveal new aspects of noise for future modeling and experimental improvements.

Electron scattering on molecular nitrogen: common gas, uncommon cross sections

We discuss peculiar features of electron scattering on the N2 molecule and the N2+ ion, that are important for modeling plasmas, Earth’s and other planets’ atmospheres. These features are, among others: the resonant enhancement of the vibrational excitation in the region of the shape resonance around 2.4 eV, the resonant character of some of electronic excitation channels (and high values of these cross sections, both for triplet and singlet states), high cross section for the dissociation into neutrals, high cross sections for elastic scattering (and electronic transitions) on metastable states. For the N2+ ion we discuss both dissociation and the dissociative ionization, leading to the formation of atoms in excited states, and dissociative recombination which depends strongly on the initial vibrational state of the ion. We conclude that the theory became an indispensable completion of experiments, predicting many of partial cross sections and their physical features. We hope that the data presented will serve to improve models of nitrogen plasmas and atmospheres.Graphical abstract

Theoretical study on photodissociation dynamics of vibrational excited states of H2S in the first absorption band

The photodissociation quantum dynamics for the first absorption band of H2S in different initial vibrational states have been investigated using Chebyshev real wave packet method. Because of the difference of the wave functions for the initial vibrational states, the calculated absorption spectra and the distributions of vibrational and rotational state of the products display different dynamic characteristics. The width and peak position of the absorption spectra for initial stretching excited states (1,0,0) and (0,0,1) are different from that of the vibrational ground state, while the (0,1,0) vibrational state has two almost equally high peaks in its absorption spectrum because of the change of wave function in angular coordinate. The product vibrational state distribution for (0,1,0) initial state weakly depends on the excitation energy and is dominated by the products of v=0, but SH(v=1) fragment is dominant at lower energy for (1,0,0) and (0,0,1) vibrational states. The rotational state distributions of products are very cold with the peak at j=l for these four states and weakly depend on the total energy. Besides, the rotational state distribution from (0,1,0) vibrational state displays strong oscillation, and its anisotropic parameter with rotational quantum numbers is also different from that of the other three vibrational states.

Scattering of N2 Molecules from Silica Surfaces: Effect of Polymorph and Surface Temperature

The inelastic scattering of N2 molecules from silica surfaces, taken at 100 K, has been investigated by adopting a semiclassical collision model in conjunction with the appropriate treatment of the long-range interaction forces. Such forces promote the formation of the precursor state that controls all basic elementary processes occurring at the gas-surface interphase. The probabilities for the different elementary surface processes triggered by quartz are determined and compared with those recently obtained for another silica polymorph (cristobalite). In addition, the final roto-vibrational distributions of N2 molecules undergoing inelastic scattering have been characterized. N2 molecules, impinging on both considered surfaces in low-medium vibrational states, preserve the initial vibrational state, while those inelastically scattered are rotationally excited and translationally colder. The surface temperature effect, investigated by raising the temperature itself from 100 K up to 1000 K, emerges more sharply for the cristobalite polymorph, mainly for the molecules impinging in the ground roto-vibrational state and with low collision energies.

Dipole-induced processes in HeH+ produced by an excited Li( 2p ) neighbor: From charge transfer to virtual photon dissociation, and formation of LiH and LiHe

Dipole interaction between neighbor systems is of importance in the behavior of atoms and molecules as it produces distortion in the electronic structure of the system. In this work, we study the dipole processes in a $\mathrm{He}{\mathrm{H}}^{+}$ molecule induced by an initially excited lithium atom placed at an ${R}_{0}$ distance from the center of mass of the molecule. The electronic and nuclear degrees of freedom are treated by the electron-nuclear dynamics approach as it allows a time-dependent description of the electronic and nuclear dynamics. The energy transferred from the neighbor excited lithium atom to the $\mathrm{He}{\mathrm{H}}^{+}$ molecule is distributed into several channels depending on the initial vibrational state of the $\mathrm{He}{\mathrm{H}}^{+}$ and initial ${R}_{0}$ separation. We find that several processes are induced by the dipole interaction. Among these, we find that the charge-transfer channel from the Li onto the ionic molecule $\mathrm{He}{\mathrm{H}}^{+}$ is the dominant outcome. Also, we find that a virtual photon dissociation process takes place via a dipole interaction that induces nuclear motion of the molecule through an electronic relaxation of the initial lithium $2p$ electron to the $2s$ state or to the $1s$ state of the He or H atom of the neighbor system, as well as vibrational intermolecular energy transfer. We report dissociation of the $\mathrm{He}{\mathrm{H}}^{+}$ molecule followed by chemical rearrangement leading to the formation of LiH and LiHe molecules and their respective charged ions. We find that deexcitation occurs on femtosecond while the molecular dissociation on picosecond time scales. Consequently, the dipole interaction between neighbors induces a richer dynamics.

Finite-Temperature, Anharmonicity, and Duschinsky Effects on the Two-Dimensional Electronic Spectra from Ab Initio Thermo-Field Gaussian Wavepacket Dynamics.

Accurate description of finite-temperature vibrational dynamics is indispensable in the computation of two-dimensional electronic spectra. Such simulations are often based on the density matrix evolution, statistical averaging of initial vibrational states, or approximate classical or semiclassical limits. While many practical approaches exist, they are often of limited accuracy and difficult to interpret. Here, we use the concept of thermo-field dynamics to derive an exact finite-temperature expression that lends itself to an intuitive wavepacket-based interpretation. Furthermore, an efficient method for computing finite-temperature two-dimensional spectra is obtained by combining the exact thermo-field dynamics approach with the thawed Gaussian approximation for the wavepacket dynamics, which is exact for any displaced, distorted, and Duschinsky-rotated harmonic potential but also accounts partially for anharmonicity effects in general potentials. Using this new method, we directly relate a symmetry breaking of the two-dimensional signal to the deviation from the conventional Brownian oscillator picture.

Full-dimensional quantum mechanical calculations of the reaction probability of the H + CH4 reaction based on a mixed Jacobi and Radau description.

A full-dimensional time-dependent wave packet study using mixed polyspherical Jacobi and Radau coordinates for the title reaction has been reported. The non-reactive moiety CH3 has been described using three Radau vectors, whereas two Jacobi vectors have been used for the bond breaking/formation process. A potential-optimized discrete variable representation basis has been employed to describe the vibrational coordinates of the reagent CH4. About one hundred billion basis functions have been necessary to achieve converged results. The reaction probabilities for some initial vibrational states are given. A comparison between the present approach and other methods, including reduced and full-dimensional ones, is also presented.

Effect of initial vibrational excitation on the methane cation sub-femtosecond photodynamics

An ab initio ab quantum dynamics study is attempted to understand the effect of initial vibrational state excitation on the sub-femtosecond photodynamics of the methane cation. A time-dependent wave packet (WP) propagation method is utilised where the WPs are prepared for each initial vibrational state of the neutral species of the title cation and its deuteriated isomer. The ratio of the squared of the nuclear autocorrelation functions (ACFs) of CD and CH on the lowest potential sheet of the state are calculated in full dimensionality, including nonadiabatic coupling of the three electronic sheets. The results predict the above ratio to start at unity and then increase with time before passing through a maximum, irrespective of the initial vibrational state. At the first maximum, such a ratio is found to decrease with the number of nodes of the vibrational wave function while the magnitudes of the ACFs of CD and CH diminish gradually with vibrational excitation. This is enhanced by inclusion of further excited vibrational modes. The present results indicate that nuclear motion on the lowest adiabatic sheet of the states of title cation can be slowed down by initial vibrational state excitation.

Vibrational shifts of absorption bands of linear molecules diluted in high-density rare gases: Measurements and modeling for CO2-Rg and OCS-Rg

Increase of buffer gas pressure causes redistribution of intensity in the IR absorption bands and, indicating the presence of vibrational perturbation, changes the first spectral moment value responsible for the band-origin position. Band-origin shift coefficients for the ν3, 2ν3 and ν2 bands of OCS and the ν3 band of CO2 diluted in high-density Ar, Kr and Xe are measured and calculated by two methods: directly with available in the literature vibrationally dependent potential-energy surfaces for both initial and final vibrational states and assuming that vibrational dependence arises from the interaction of the permanent /transient dipole moment of the absorbing molecule and the dipole moment induced on the perturber. A comparative analysis of results is given, showing a general underestimation of calculations with respect to measurements.

Neutral transport code for rovibrational population calculation of molecular hydrogen in large helical device plasmas

AbstractAn rovibrationally resolved collisional‐radiative model of molecular hydrogen (K. Sawada and M. Goto, Atoms 4: 29, 2016) is included in the authors' neutral transport code for large helical device (LHD) plasmas. The spatial distributions of the electron temperature and density, including the divertor and divertor leg regions, are given to the code. The molecules released from the graphite divertor target are tracked. The initial rotational and vibrational states of the released molecules are provided by simulation using a molecular dynamics model. The rovibrational population produced in an LHD plasma is evaluated.

Dynamical Study of the Dissociative Chemisorption of CHD3 on Pd(111).

The specific reaction parameter (SRP) approach to density functional theory has been shown to model reactions of polyatomic molecules with metal surfaces important for heterogeneous catalysis in the industry with chemical accuracy. However, transferability of the SRP functional among systems in which methane interacts with group 10 metals remains unclear for methane + Pd(111). Therefore, in this work, predictions have been made for the reaction of CHD3 on Pd(111) using Born–Oppenheimer molecular dynamics while also performing a rough comparison with experimental data for CH4 + Pd(111) obtained for lower incidence energies. Hopefully, future experiments can test the transferability of the SRP functional among group 10 metals also for Pd(111). We found that the reactivity of CHD3 on Pd(111) is intermediate between and similar to either Pt(111) or Ni(111), depending on the incidence energy and the initial vibrational state distribution. This is surprising because the barrier height and experiments performed at lower incidence energies than investigated here suggest that the reactivity of Pd(111) should be similar to that of Pt(111) only. The relative decrease in the reactivity of Pd(111) at high incidence energies is attributed to site specificity of the reaction and to dynamical effects such as the bobsled effect and energy transfer from methane to the surface.

A quantum-mechanical tier model for phonon-driven vibrational relaxation dynamics of adsorbates at surfaces.

We present a quantum-mechanical tier model for vibrational relaxation of low-lying excited states of an adsorbate vibrational mode (system), coupled to surface phonons (bath), at zero temperature. The tier model, widely used in studies of intramolecular vibrational energy redistribution in polyatomics, is adapted here to adsorbate-surface systems with the help of an embedded cluster approach, using orthogonal coordinates for the system and bath modes, and a phononic expansion of their interaction. The key idea of the model is to organize the system-bath zeroth-order vibrational space into a hierarchical structure of vibrational tiers and keep therein only vibrational states that are sequentially generated from the system-bath initial vibrational state. Each tier is generated from the previous one by means of a successor operator, derived from the system-bath interaction Hamiltonian. This sequential procedure leads to a drastic reduction of the dimension of the system-bath vibrational space. We notably show that for harmonic vibrational motion of the system and linear system-bath couplings in the system coordinate, the dimension of the tier-model vibrational basis scales as ∼Nl×υ. Here, N is the number of bath modes, l is the highest-order of the phononic expansion, and υ is the size of the system vibrational basis. This polynomial scaling is computationally far superior to the exponential scaling of the original zeroth-order vibrational basis, ∼MN, with M being the number of basis functions per bath mode. In addition, since each tier is coupled only to its adjacent neighbors, the matrix representation of the system-bath Hamiltonian in this new vibrational basis has a symmetric block-tridiagonal form, with each block being very sparse. This favors the combination of the tier-model with iterative Krylov techniques, such as the Lanczos algorithm, to solve the time-dependent Schrödinger equation for the full Hamiltonian. To illustrate the method, we study vibrational relaxation of a D-Si bending mode, coupled via two- and (mainly) one-phonon interactions to a fully D-covered Si(100)-(2 × 1) surface, using a recent first-principles system-bath Hamiltonian. The results of the tier model are compared with those obtained by the Lindblad formalism of the reduced density matrix. We find that the tier model provides much more information and insight into mechanisms of vibration-phonon couplings at surfaces, and gives more reliable estimates of the adsorbate vibrational lifetimes. Moreover, the tier model might also serve as a benchmark for other approximate quantum-dynamics methods, such as multiconfiguration wavefunction approaches.

The effect of the nuclear motion on harmonic spectral structure

The harmonic emissions from hydrogen molecular ion at different initial vibrational states have been simulated by numerically solving the time-dependent Schrödinger equation. The results show that the nuclear motion exhibits different effects on the spectral structure for different vibrational states. For lower vibrational state, the odd harmonics experience obvious harmonic shifting; however, for higher vibrational state, the even harmonics are emitted from the symmetric system due to the asymmetric electronic distribution in the coupling region of two lowest electronic states.

Full dimensional quantum mechanical calculations of the reaction probability of the H + NH3 collision based on a mixed Jacobi and Radau description.

The collision between hydrogen and ammonia is a benchmark system to study chemical elementary reactions with five atoms. In this work, we present a description of the system based on mixed Jacobi and Radau coordinates combined with the time-dependent wave packet method to study the H + NH3 reaction. The Radau coordinates are used to describe the reactive moiety NH2. A salient feature of this approach is that the present coordinates have a great advantage that a very small number of basis set functions can be used to describe the NH2 group. Potential-optimized discrete variable representation basis is applied for the vibrational coordinates of the reagent NH3. The reaction probabilities for several initial vibrational states are presented in this paper. The role of the different vibrational excitations on the reactivity is thoroughly described.