Product State Distributions Research Articles

Matrix product state approximations to quantum states of low energy variance

We show how to efficiently simulate pure quantum states in one dimensional systems that have both finite energy density and vanishingly small energy fluctuations. We do so by studying the performance of a tensor network algorithm that produces matrix product states whose energy variance decreases as the bond dimension increases. Our results imply that variances as small as ∝1/log⁡N can be achieved with polynomial bond dimension. With this, we prove that there exist states with a very narrow support in the bulk of the spectrum that still have moderate entanglement entropy, in contrast with typical eigenstates that display a volume law. Our main technical tool is the Berry-Esseen theorem for spin systems, a strengthening of the central limit theorem for the energy distribution of product states. We also give a simpler proof of that theorem, together with slight improvements in the error scaling, which should be of independent interest.

A comparative study on adiabatic and nonadiabatic dynamics of the H(2S) + NaH(X1Σ+) reaction

To reveal the influence of nonadiabatic couplings on the H(2S) + NaH(X1Σ+) reaction, a comparative study on adiabatic and nonadiabatic dynamics is conducted by using the time-dependent wave packet method. The dynamics results show that nonadiabatic couplings reduce the reactivity of H2(X1Σg+) forming channel and vibrational state density of the product, while the exchange reaction channel is almost unaffected. Although the nonadiabatic couplings have a great influence on the product state distribution, it has little influence on the scattering direction of the product. For the H2(X1Σg+) forming channels, products tend to forward scattering. For the exchange reaction channel, the NaH(X1Σ+) product exhibits a maximum scattering peak in the backward direction. The study reveals that the effect of nonadiabatic couplings on the ro-vibration distribution of the H2(X1Σg+) forming channel in the H(2S) + NaH(X1Σ+) reaction is significantly different from the effect in the H(2S) + LiH(X1Σ+) reaction.

Isotope Effects on State-to-State Photodissociation Dynamics of D2S in Its First Absorption Band.

State-to-state photodissociation dynamics of D2S in its first absorption band were explored by utilizing recently developed diabatic potential energy surfaces (PESs). Quantum dynamics calculations, involving the first two strongly coupled 1A″ states, were executed employing a Chebyshev real wavepacket method. The nonadiabatic channel via the conical intersection (CI) is facile, direct, and fast, leading to the production of rotationally and vibrationally cold SD(X̃2Π). The calculated absorption spectrum, product state distributions, and angular distributions are in reasonable agreement with the experimental results, although some discrepancies exist at 193.3 nm. Compared with H2S, there are obvious isotope effects on rotational state distributions for D2S photodissociation in its first absorption band. Moreover, we scrutinize the variation of product state distributions as a function of photon energy and the vibrational mediated photodissociation of the parent molecule. Due to the diverse shapes of the three fundamental vibrational wave functions, photoexcited wavepackets access distinct segments of the upper-state PES, resulting in a disparate absorption spectrum and ro-vibrational distributions via the nonadiabatic transition. This study provides a comprehensive figure of the isotopic effect and wavelength dependence on the photofragmentation behaviors from D2S photodissociation, which should attract more experimental and theoretical attention to this prototypical system.

Automated potential energy surface development and comprehensive dynamics for the F + CH3NH2 reaction.

This work is an extensive investigation of the F + CH3NH2 reaction dynamics using a newly-developed potential energy surface (PES). The full-dimensional spin-orbit (SO) corrected (MRCI+Q/aug-cc-pwCVDZ) PES is developed by the Robosurfer program package and the ManyHF method is used in order to fix the Hartree-Fock (HF) convergence issues in the entrance channel. On the surface, retrieved by the fitting of the iteratively extended set of the ManyHF-CCSD(T)-F12a/triple-zeta-quality and SO-corrected energy points, quasi-classical trajectory (QCT) simulations are run. By analyzing the opacity functions and integral cross sections (ICSs) of six reaction channels, the dynamics of the two most reactive hydrogen-abstraction reactions resulting in HF + CH2NH2/CH3NH products are selected for a thorough examination. Despite the statistically and thermodynamically expected results, the kinetically preferred amino hydrogen-abstraction is the dominant mechanism at low collision energies. The initial attack angle and scattering angle distributions are investigated as well. The post-reaction energy distributions show that the collision energy mostly converts into the translational energy of the products, while the reaction energy excites the vibration of the products. The computed vibrationally resolved rotational distributions and vibrational state distributions of the HF product are compared to experimental data, and the theory and experiment are found to be in good agreement.

Theoretical study of the O(3P) + CN(X2Σ+) → CO(X1Σ+) + N(2D)/N(4S) reactions.

The barrierless exothermic reactions between atomic oxygen and the cyano radical, O(3P) + CN(X2Σ+) → CO(X1Σ+) + N(2D)/N(4S), play a significant role in combustion, astrochemistry, and hypersonic environments. In this work, their dynamics and kinetics are investigated using both wave packet (WP) and quasi-classical trajectory (QCT) methods on recently developed potential energy surfaces of the 12A', 12A,″ and 14A″ states. The product state distributions in the doublet pathway obtained with the WP method for a few partial waves show extensive internal excitation in the CO product. This observation, combined with highly oscillatory reaction probabilities, signals a complex-forming mechanism. The statistical nature of the reaction is confirmed by comparing the WP results with those from phase space theory. The calculated rate coefficients using the WP (with a J-shifting approximation) and QCT methods exhibit agreement with each other near room temperature, 1.77 × 10-10 and 1.31 × 10-10cm3molecule-1s-1, but both are higher than the existing experimental results. The contribution of the quartet pathway is small at room temperature due to a small entrance channel bottleneck. The QCT rate coefficients are further compared with experimental results above 3000K, and the agreement is excellent.

Infrared-driven dynamics and scattering mechanisms of NO radicals with propane and butane: impacts of pseudo Jahn-Teller effects.

The topology of multidimensional potential energy surfaces defines the bimolecular collision outcomes of open-shell radicals with molecular partners. Understanding these surfaces is crucial for predicting the inelastic scattering and chemical transformations of increasingly complex radical-molecule collisions. To characterize the inelastic scattering mechanisms of nitric oxide (NO) radicals with large alkanes, we generated the collision complexes comprised of NO with propane or n-butane. The infrared action spectroscopy and infrared-driven dynamics of NO-propane and NO-(n-butane) collision complexes in the CH stretch region were recorded, while also comparing the results to the analogous experiments carried out for NO-CH4 and NO-ethane. The infrared spectroscopy is analyzed using rovibrational simulations to characterize the transition bands and to determine the vibrational predissociation lifetimes of NO-propane and NO-(n-butane). Due to pseudo Jahn-Teller dynamics, the NO-propane and NO-(n-butane) decay mechanisms from IR activation appear similar to those for NO-ethane previously reported from this laboratory (J. P. Davis et al. Faraday Discuss., 2024, 251, 262-278). Furthermore, the NO (X2Π, v'' = 0, J'', Fn, Λ) product state distributions from NO-alkane fragmentation reveal a strong electron-spin polarization and a propensity for NO products to rotate in the plane of the π* molecular orbital, yielding mechanistic insights into the inelastic scattering outcomes. We hypothesize that a geometric phase may be present, impacting the relative population distributions, in addition to the accessible pathway timescales.

Reaction interferometry with ultracold molecules.

We propose to coherently control the ultracold 2KRb → K2 + Rb2 reaction product state distribution via quantum interference. By leveraging that the nuclear spin degrees of freedom in the reaction maintain coherence, which was demonstrated in Liu, Zhu et al., arXiv, 2023, arXiv:2310.07620, https://doi.org/10.48550/arXiv.2310.07620, we explore the concept of a "reaction interferometer". Such an interferometer involves splitting one KRb molecular cloud into two, imprinting a well-defined relative phase between them, recombining the clouds for reactions, and measuring the product state distribution. We show that the interference patterns provide a mechanism to coherently control the product states, and specific product channels also serve as an entanglement witness of the atoms in the reactant KRb molecule.

Photodissociation dynamics of acetaldehyde at 267 nm: A computational study of the CO‐forming channels

AbstractA recent experiment on the 267 nm photolysis of gaseous acetaldehyde reveals that the molecular products (CO + CH4) present product state distributions with computation –experiment discrepancy. This work aims to provide solution to such issue. The direct dynamics simulation of classical trajectories and the generalized multi‐center impulsive model (GMCIM) are both utilized to predict the product state distributions of CO and CH4 from 267 nm photolysis of acetaldehyde. Comparison with the experimental observation provides an assessment of the conventional approach of minimum energy path within the framework of three‐center transition state (TS) and CH3‐roaming pathways. The result shows that the high‐speed products observed in experiment are likely formed via the three‐center TS pathway. The reasons that lead to the discrepancy between computation and experiments in previous studies are also investigated. A better agreement between computational and state‐resolved experimental results can be achieved by selecting specific internal states of CO product from the computational data.

Energy scaling of the product state distribution for three-body recombination of ultracold atoms

Three-body recombination is a chemical reaction where the collision of three atoms leads to the formation of a diatomic molecule. In the ultracold regime it is expected that the production rate of a molecule generally decreases with its binding energy ${E}_{b}$, however, its precise dependence and the physics governing it have been left unclear so far. Here we present a comprehensive experimental and theoretical study of the energy dependency for three-body recombination of ultracold Rb. For this, we determine production rates for molecules in a state-to-state resolved manner, with the binding energies ${E}_{b}$ ranging from 0.02 to 77 $\mathrm{GHz}\ifmmode\times\else\texttimes\fi{}h$. We find that the formation rate approximately scales as ${E}_{b}^{\ensuremath{-}\ensuremath{\alpha}}$, where $\ensuremath{\alpha}$ is in the vicinity of 1. The formation rate typically varies only within a factor of two for different rotational angular momenta of the molecular product, apart from a possible centrifugal barrier suppression for low binding energies. In addition to numerical three-body calculations we present a perturbative model which reveals the physical origin of the energy scaling of the formation rate. Furthermore, we show that the scaling law potentially holds universally for a broad range of interaction potentials.

State-to-State Dynamics in Mode-Specific Reactions of Cl + CH3D(v1-I, v1-II, and v4 = 1; |10⟩): Loss of Memory or Not

Several decades of the study of reaction dynamics culminate in the concept of mode specificity and bond selectivity in polyatomic systems. Until very recently, the main concern of those studies has been total reactivity and little attention has been paid to the mode-specific effects on the more detailed product-state and angular distributions. Conventional wisdom would anticipate that the fine detail should reveal a more pronounced mode dependency. However, a few recent studies showed that the product distributions could appear to be surprisingly insensitive to the modes of internal excitation of reagents. This counterintuitive finding led to a concept of loss of memory. Here, we present detailed experimental results in the reactions of the Cl atom with three distinct stretching-excited CH3D(vCH3 = 1) reagents. In conjunction with the previous reports on various aspects of this reaction, such a comprehensive set of data enables us to perform an in-depth examination of the validity of this new concept.

New accurate diabatic potential energy surfaces for the two lowest 1A'' states of H2S and photodissociation dynamics in its first absorption band.

In this work, state-to-state photodissociation dynamics of H2S in its first absorption band has been studied quantum mechanically with a new set of coupled potential energy surfaces (PESs) for the first two 1A'' excited states, which were developed at the explicitly correlated internally contracted multi-reference configuration interaction level with the cc-pVQZ-F12 basis set and a large active space. The calculated absorption spectrum, product state distributions, and angular distributions are in excellent agreement with available experimental data, validating the accuracy of the PESs and the non-adiabatic couplings. Detailed analysis of the dynamics reveals that there are strong non-adiabatic couplings between the bound 11B1 and dissociative 11A2 states around the Franck-Condon region, leading to very fast predissociation to ro-vibrationally cold SH(X̃) fragments, during which marginal angular anisotropy of the PESs is involved. This study provides quantitatively accurate characterization of the electronic structure and detailed fragmentation dynamics of this prototypical photodissociation system, which is desirable for improving astrochemical modelling.

POPTARTS: A New Method to Determine Quantum Yields in a Molecular Beam.

A new technique is reported to determine absolute photodissociation quantum yields, ϕdiss, in a molecular beam. The technique relies on a molecule having two available product channels, where a species in channel A can be converted photolytically to a species in channel B. The relative decrease in the species from channel A and the relative increase in species from B provide a direct measure of the relative product yield of each channel, with no external calibration required. In the event that only channels A and B exist, or at least dominate, then the sum rule ϕA + ϕB = 1 can be used to convert relative quantum yields into absolute yields. The technique is demonstrated using the well-understood and characterized photochemistry of HCHO. Formaldehyde photolysis at wavelengths near 310 nm produces either H + HCO (channel A) or H2 + CO (channel B). HCO can then be photolyzed with high efficiency into H + CO. The product state distributions for HCO from channel A, CO from channel B, and CO from the secondary HCO photolysis event are all well-known; this is not a requirement but is utilized here to demonstrate the veracity of the technique. The zero-pressure quantum yields of HCO from HCHO photolysis via the 2341 and 2151 states of HCHO are determined to be 0.66 and 0.74, respectively, which are in excellent agreement with the established quantum yields at atmospheric pressure and support the conclusion that HCHO quantum yields at these photolysis energies are not pressure dependent.

Probing the Dependence of Long-Range, Four-Atom Interactions on Intermolecular Orientation. 4. The Dissociation Dynamics of H2/D2···ICl(B,v'=3) and the Observation of Efficient Vibrational-Rotational Energy Transfer.

The vibrational predissociation dynamics of H2/D2···I35Cl(B,v'=3) complexes containing both para- and ortho-hydrogen prepared in different intermolecular vibrational levels were investigated. The Δv = -1 I35Cl(B,v = 2,j) rotational product-state distributions measured for excitation to the lowest-energy T-shaped levels of these complexes are mostly bimodal. The rotational distributions measured for excitation of the H2···I35Cl(B,v'=3) complexes are colder than those of the D2···I35Cl(B,v'=3) complexes, and there are only slight differences between those measured for the para- and ortho-hydrogen containing complexes. Excitation of the delocalized bending levels results in slightly colder rotational product-state distributions. The distributions suggest the dynamics result from more than impulsive dissociation off of the inner repulsive wall of the lower-energy H2/D2 + I35Cl(B,v = 2) potential surfaces of the products. The depths of these potentials and the energies available to these products also contribute to the dynamics. The formation of the Δv = -2, I35Cl(B,v = 1) product channel was only identified for excitation of levels within the ortho(j = 0)-D2 + I35Cl(B,v'=3) potential. The formation of this channel occurs via I35Cl(B,v'=3) vibrational to D2 rotational energy transfer forming the ortho(j = 2)-D2 + I35Cl(B,v = 1,j) products.

Electronically Nonadiabatic Effects on the Quantum Dynamics of the Ha + BeHb+ → Be+ + HaHb; Hb + BeHa+ Reactions.

Nonadiabatic effects are ubiquitous and play an important role in many chemical processes. Here, the adiabatic and nonadiabatic quantum scattering calculations of the H + BeH+ reaction are performed using the time-dependent wave packet method based on an accurate diabatic potential energy matrix that includes the lowest two electronic states and their couplings. The resulting integral cross sections reveal that the nonadiabatic effect significantly inhibits the reactivity of the BeH+-depletion channel but enhances that of the H-exchange channel. The vibrational excitation is suppressed, but the translational excitation is promoted for the H2 product in the BeH+-depletion channel when the nonadiabatic coupling is included. However, the nonadiabatic coupling has a mild effect on the H-exchange product-state distribution. When the nonadiabatic effect is considered, the differential cross sections of the H2 product become less polarized because of the formation of an excited-state complex, whereas the corresponding results of the H-exchange channel only present an increase in the magnitude at the backward region.

Ultracold state-to-state chemistry for three-body recombination in realistic 3He2-alkaline-earth-metal systems.

The ultracold state-to-state chemistry for three-body recombination (TBR) in realistic systems has recently been experimentally investigated with full quantum state resolution. However, many detected phenomena remain challenging to be explored and explained from the theoretical viewpoints because this generally requires computational powers beyond state of the art. Here, the product-state distributions after TBR of 3He2-alkaline-earth-metal systems, i.e., after the processes of 3He + 3He + X → 3HeX + 3He with X being 9Be, 24Mg, 40Ca, 88Sr, or 138Ba, in the zero-collision-energy limit are theoretically studied. Two propensity rules for the distribution of the products found in current experiments have been checked, and the mechanism underlying these product-state distributions is explored. Particularly, two main intriguing transition pathways are identified, which may be responsible for the nonlinear distribution of the products vs their respective rotational quantum number. In addition, the TBR rates of these systems are also influenced by details of the interaction potential and relevant nonadiabatic couplings.

Rotational state specific dissociation dynamics of D2O via the C̃(010) state: The effect of bending vibrational excitation.

The rotational state resolved photodissociation dynamics of D2O via the C̃(010) state has been investigated by using the D-atom Rydberg tagging time-of-flight technique combined with a tunable vacuum ultraviolet light source. The D-atom action spectrum of the C̃(010) ← X̃(000) band and the corresponding time-of-flight (TOF) spectra of D-atom photoproducts formed following the excitation of D2O to individual rotational transition have been measured. By comparison with the action spectrum of the C̃(000) ← X̃(000) band, the bending vibrational constant of the C̃ state for D2O can be determined to be v2 = 1041.37 ± 0.71cm-1. From the TOF spectra, the product kinetic energy spectra, the vibrational state distributions of OD products, and the state resolved anisotropy parameters have been determined. The experimental results indicate a dramatic variation in the OD product state distributions for different rotational excitations. This illuminates that there are two distinctive coupling channels from the C̃(010) state to the low-lying electronic states: the homogeneous electronic coupling to the Ã1B1 state, resulting in vibrationally hot OD(X) products, and the Coriolis-type coupling to the B̃1A1 state, producing vibrationally cold but rotationally hot OD(X) and OD(A) products. Furthermore, the three-body dissociation channel is confirmed, which is attributed to the C̃ → 1A2 or C̃ → Ã pathway. In comparison with the previous results of D2O photolysis via the C̃(000) state, it is found that the v2 vibration of the parent molecule enhances both the vibrational and rotational excitations of OD products.

Machine learning product state distributions from initial reactant states for a reactive atom-diatom collision system.

A machine-learned model for predicting product state distributions from specific initial states (state-to-distribution or STD) for reactive atom-diatom collisions is presented and quantitatively tested for the N(4S) + O2(X3Σg -) → NO(X2Π) + O(3P) reaction. The reference dataset for training the neural network consists of final state distributions determined from quasi-classical trajectory (QCT) simulations for ∼2000 initial conditions. Overall, the prediction accuracy as quantified by the root-mean-squared difference (∼0.003) and the R2 (∼0.99) between the reference QCT and predictions of the STD model is high for the test set, for off-grid state-specific initial conditions, and for initial conditions drawn from reactant state distributions characterized by translational, rotational, and vibrational temperatures. Compared with a more coarse grained distribution-to-distribution (DTD) model evaluated on the same initial state distributions, the STD model shows comparable performance with the additional benefit of the state resolution in the reactant preparation. Starting from specific initial states also leads to a more diverse range of final state distributions, which requires a more expressive neural network compared with DTD. A direct comparison between QCT simulations, the STD model, and the widely used Larsen-Borgnakke (LB) model shows that the STD model is quantitative, whereas the LB model is qualitative at best for rotational distributions P(j') and fails for vibrational distributions P(v'). As such, the STD model can be well-suited for simulating nonequilibrium high-speed flows, e.g., using the direct simulation Monte Carlo method.

Effects of single quantum rotational excitation on reaction of F+D2 at collision energies between 44 and 164 cm−1

There is no general picture to describe the influences of reagent rotational excitation on the reaction, which proceeds via the tunnelling mechanism at collision energies far below the reaction barrier. Here we report a crossed beam study on the prototypical reaction of F + D2(v=0, j=0,1) → DF(v′) + D at collision energies between 44 and 164 cm−1 with the scheme of multichannel D-atom Rydberg tagging time-of-flight detection. Vibrational state resolved differential cross sections are obtained at v′=2, 3, 4 levels. The effects of reagent rotational excitation were investigated at an equivalent amount of total energy by precise tuning of translational energies. Compared with translation, the rotation of D2 is found to be more efficient to promote the title reaction. Profound differences introduced by rotation of D2 are also observed on the angular distribution and quantum state distribution of DF products. We hope the present work could provide an example for understanding the effects of reagent rotational excitation on the chemical reaction at energies that are much lower than the reaction barrier.

Spectroscopic Properties Relevant to Astronomical and Laboratory Detection of MCH and MCH+ (M = Al, Mg)

Abstract New spectroscopic parameters have been calculated to aid in the laboratory and observational detection of AlCH, AlCH+, MgCH, MgCH+, and their deuterated analogs. All species exist in linear geometry except for AlCH+, which exhibits a bent structure. Rotational frequencies have been calculated and the transition with maximum intensity is discussed for three temperature regions present in space: 100 K for a central circumstellar envelope (CSE), 30 K for an outer CSE, and 3 K indicative of the interstellar medium. Pertinent frequencies range from 25 to 250 GHz, depending on the species. At 30 K, the most intense transition is expected to be J = 4 → 3 for all species. The vibrational spectrum of each molecule is expected to be complicated due to the flat nature of the potential energy surface along the bending angle and the presence of anharmonic resonances. Deuteration produces a decrease in vibrational frequency, which may be utilized in experiments to confirm detection of these molecules. The electronic absorption spectrum of both AlCH and MgCH is predicted to be congested and broad. Various high-oscillator-strength transitions are predicted. Upon photoexcitation in the 220–300 nm region, facile dissociation on a repulsive excited state along the Al–C coordinate is predicted to be a source of Al in the colder regions of space. Photodissociation of MgCH requires several nonradiative processes that will control the product state distribution of the fragments.

Model for nuclear spin product-state distributions of ultracold chemical reactions in magnetic fields

Based on a theoretical model where the nuclear spins remain unchanged during a collision, we provide an analytical and general expression for the nuclear spin state-to-state distribution of an ultracold chemical reaction in a magnetic field, for given rotational transitions of the molecules. It simply requires knowledge of the field-dependent eigenfunctions of the molecular reactants and products of the chemical reaction. The final state-to-state distribution drastically changes with the magnetic field. When the distribution is summed over all the final products, a simplified expression is found where only the knowledge of the eigenfunctions of the molecular reactants is required. The present theoretical formalism has been successfully used to explain the magnetic field behavior of the product-state distribution in chemical reactions of ultracold KRb molecules [Hu et al., Nat. Chem. 13, 435 (2021)].