Full-dimensional Quantum Dynamics Calculations Research Articles

Spin-Dependent Stereochemistry: A Nonadiabatic Quantum Dynamics Case Study of S + H2 → SH + H Reaction.

We study the spin-dependent stereodynamics of the S + H2 → SH + H reaction by using full-dimensional quantum dynamics calculations with zero total nuclear angular momentum along the triplet 3A″ states and singlet 1A' states. We find that the interplay between the electronic spin direction and the molecular geometry has a measurable influence on the singlet-triplet intersystem crossing reaction probabilities. Our results show that for some incident scattering angles in the body-fixed frame, the relative difference in intersystem crossing reaction probabilities (as determined between spin up and spin down initial states) can be as large as 15%. Our findings are an ab initio demonstration of spin-dependent nonadiabatic dynamics, which we hope will shine light as far as understanding the chiral-induced spin selectivity effect.

The Li + CaF → Ca + LiF chemical reaction under cold conditions.

The calcium monofluoride (CaF) molecule has emerged as a promising candidate for precision measurements, quantum simulation, and ultracold chemistry experiments. Inelastic and reactive collisions of laser cooled CaF molecules in optical tweezers have recently been reported and collisions of cold Li atoms with CaF are of current experimental interest. In this paper, we report ab initio electronic structure and full-dimensional quantum dynamical calculations of the Li + CaF → LiF + Ca chemical reaction. The electronic structure calculations are performed using the internally contracted multi-reference configuration-interaction method with Davidson correction (MRCI + Q). An analytic fit of the interaction energies is obtained using a many-body expansion method. A coupled-channel quantum reactive scattering approach implemented in hyperspherical coordinates is adopted for the scattering calculations under cold conditions. Results show that the Li + CaF reaction populates several low-lying vibrational levels and many rotational levels of the product LiF molecule and that the reaction is inefficient in the 1-100 mK regime allowing sympathetic cooling of CaF by collisions with cold Li atoms.

Multilayer Multiconfiguration Time-Dependent Hartree Study on the Mode-/Bond-Specific Quantum Dynamics of Water Dissociation on Cu(111).

In this work, full-dimensional (9D) quantum dynamics calculations on mode-/bond-specific surface scattering of a water molecule on a copper (111) rigid surface are performed through the multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) method. To easily perform the ML-MCTDH calculations on such a triatomic molecule-surface system, we first choose specific Jacobi coordinates as a set of coordinates of water. Next, to efficiently perform the 9D ML-MCTDH wavepacket propagation, the potential energy surface is transferred to a canonical polyadic decomposition form with the aid of a Monte Carlo-based method. Excitation-specific dissociation probabilities of H2O on Cu(111) are computed, and mode-/bond-specific dynamics are demonstrated by comparison with a probability curve computed for a water molecule in the ground state. The dependence of the dissociation probability of the initial state of H2O is studied, and it is found that the excitation-specific dissociation probabilities can be divided into three groups. We find that the vibrationally excited states enhance the dissociation reactivity of H2O, while the rotationally excited states hardly influence it.

Full-dimensional quantum stereodynamics of the non-adiabatic quenching of OH(A2\u03a3+) by H2

The Born–Oppenheimer approximation, assuming separable nuclear and electronic motion, is widely adopted for characterizing chemical reactions in a single electronic state. However, the breakdown of the Born–Oppenheimer approximation is omnipresent in chemistry, and a detailed understanding of the non-adiabatic dynamics is still incomplete. Here we investigate the non-adiabatic quenching of electronically excited OH(A2Σ+) molecules by H2 molecules using full-dimensional quantum dynamics calculations for zero total nuclear angular momentum using a high-quality diabatic-potential-energy matrix. Good agreement with experimental observations is found for the OH(X2Π) ro-vibrational distribution, and the non-adiabatic dynamics are shown to be controlled by stereodynamics, namely the relative orientation of the two reactants. The uncovering of a major (in)elastic channel, neglected in a previous analysis but confirmed by a recent experiment, resolves a long-standing experiment–theory disagreement concerning the branching ratio of the two electronic quenching channels.

Neural Network Representation of Three-State Quasidiabatic Hamiltonians Based on the Transformation Properties from a Valence Bond Model: Three Singlet States of H3+

A neural network (NN) approach was recently developed to construct accurate quasidiabatic Hamiltonians for two-state systems with conical intersections. Here, we derive the transformation properties of elements of 3 × 3 quasidiabatic Hamiltonians based on a valence bond (VB) model and extend the NN-based method to accurately diabatize the three lowest electronic singlet states of H3+, which exhibit the avoided crossing between the ground and first excited states and the conical intersection between the first and second excited states for equilateral triangle configurations (D3h). The current NN framework uses fundamental invariants (FIs) as the input vector and appropriate symmetry-adapted functions called covariant basis to account for the special symmetry of complete nuclear permutational inversion (CNPI). The resulting diabatic potential energy matrix (DPEM) can reproduce the ab initio adiabatic energies, energy gradients, and derivative couplings between adjacent states as well as the particular symmetry. The accuracy of DPEM is further validated by full-dimensional quantum dynamics calculations. The flexibility of the FI-NN approach based on the VB model shows great potential to resolve diabatization problems for many extended and multistate systems.

Quantum dynamics calculations reveal temperature independence of kinetic isotope effect of the OH + HBr/DBr reaction.

The reaction of OH radicals with HBr plays a key role in atmospheric chemistry as the reaction, OH + HBr → Br + H2O, produces Br atoms that destroy ozone. The experimental measurements of the kinetic isotope effect of k(OH + HBr)/k(OH + DBr) found that the kinetic isotope effects are temperature-independent. However, previous quasi-classical trajectory calculations on an accurate ab initio potential energy surface showed that the kinetic isotope effect is temperature-dependent. By contrast, the present full-dimensional time-dependent quantum dynamics calculations on the same potential energy surface find that the kinetic isotope effect is temperature-independent, agreeing well with the experimental studies both qualitatively and quantitatively. Furthermore, the rate constants from both quantum dynamics and quasi-classical trajectory calculations have a peak at around 15 K whereas the experimental data are not available in this low temperature range. The good agreement of the temperature-dependence of kinetic isotope effects between the present quantum dynamics calculations and the experimental measurements indicates that the kinetic isotope effect of k(OH + HBr)/k(OH + DBr) should be temperature-independent and the peak of the rate constants from the theoretical calculations call for experimental measurements at a very low temperature range.

Accurate integral cross sections for the H + CO2 → OH + CO reaction

A full-dimensional quantum dynamics calculation has been carried out to yield the coupled-channel reaction probabilities with total angular momentum J up to 60 for the H + CO2 → OH + CO reaction on the PIP-NN PES potential energy surface. Well converged integral cross section (ICSs) for collision energy up to 2.4 eV were obtained for the ground initial state. As compared with previous study, it is found that the CS approximation substantially underestimated ICSs, which is inadequate for the title reaction. In addition, the agreement between QM and QCT ICSs is quite satisfactory, indicating that the QCT method is rather accurate on describing dynamics of this complex-forming reaction.

Full-dimensional quantum dynamics calculations for H + CHD3 → H2 + CD3: The effect of multiple vibrational excitations

Initial state-selected reaction probabilities for the H + CHD3 → H2 + CD3 reaction starting from various different ro-vibrational states of CHD3 are studied by accurate full-dimensional (12D) quantum dynamics calculation for vanishing total angular momentum (J = 0). The calculations employ the quantum transition state concept and the multi-layer multi-configurational time-dependent Hartree approach. First results focusing on fundamental excitations and the reactivity borrowing effect were communicated recently [R. Ellerbrock and U. Manthe, J. Chem. Phys. 147, 241104 (2017)]. In the present work, all vibrational states of the methane reactant are considered. It is found that energy deposited in overtones and combination bands is less efficient in promoting reactivity than expected from separable or sudden models. Furthermore, the effects of rotational excitation on the reactivity are studied in detail.

Communication: Reactivity borrowing in the mode selective chemistry of H + CHD3 → H2 + CD3.

Quantum state-resolved reaction probabilities for the H + CHD3 → H2 + CD3 reaction are calculated by accurate full-dimensional quantum dynamics calculations using the multi-layer multi-configurational time-dependent Hartree approach and the quantum transition state concept. Reaction probabilities of various ro-vibrational states of the CHD3 reactant are investigated for vanishing total angular momentum. While the reactivity of the different vibrational states of CHD3 mostly follows intuitive patterns, an unusually large reaction probability is found for CHD3 molecules triply excited in the CD3 umbrella-bending vibration. This surprising reactivity can be explained by a Fermi resonance-type mixing of the single CH-stretch excited and the triple CD3 umbrella-bend excited vibrational states of CHD3. These findings show that resonant energy transfer can significantly affect the mode-selective chemistry of CHD3 and result in counter-intuitive reactivity patterns.

A full-dimensional time-dependent wave packet study of the H + CO2 → OH + CO reaction

A full dimensional quantum dynamics calculation has been carried out to study the prototypical complex forming H+CO2→OH+CO reaction. The total reaction probability is converged with a propagation time much shorter than the reverse reaction, and only exhibits very small oscillatory structures, indicating the reaction proceeds mainly through a direct mechanism. The strong Fermi resonance between the (020) and (100) vibrationally excited states makes it hard to define their efficacy for reactivity, although it is conceivable that the bending excitation is much more effective than the symmetric excitation according to the geometry of the transition state in the entrance channel.

Quasi-Bound States of the F·CH4 Complex

The F + CH4 → HF + CH3 reaction is an intensively studied prototypical example of a polyatomic reaction showing an early transition state. Prereactive complexes are assumed to play an important role in the dynamics of the reaction. In this work, the long-living resonance states resulting from the formation of a metastable F·CH4 complex are investigated in detail. Full-dimensional quantum dynamics calculations employing the multiconfigurational time-dependent Hartree (MCTDH) approach and a single adiabatic potential energy surface are used to study the low-lying quasi-bound states of the F·CH4 complex for vanishing total (nuclear) angular momentum. The computed dissociation energy of the F·CH4 complex with respect to the reactant asymptote is 170 cm(-1). About 60 resonance states with energies below the reactant asymptote are found. A detailed analysis of the computed wave function of the low-lying states shows an almost free relative rotation of F and CH4 and an approximately separable F-CH4 stretching vibration. The present results are compared with transition state spectroscopy experiments which study the photodetachment spectrum of the CH4F(-) anion.

Full-Dimensional Quantum Dynamical Studies of the Cl + HOD → HCl/DCl + OD/OH Reaction: Bond Selectivity and Isotopic Branching Ratio.

Full-dimensional quantum dynamical calculations are carried out to study the mode specificity, bond selectivity, and isotopic branching ratio of the Cl + HOD reaction on an accurate global potential energy surface. Total reaction cross sections have been computed for several low-lying vibrational states of HOD. Our results confirm the experimental observed vibrationally promoted bond cleavage, in which the breaking of the OH(OD) bond is strongly enhanced by the OH(OD) excitation. These results are rationalized by the recently proposed sudden vector projection model. In addition, the OH/OD branching ratio as a function of energy is investigated and rationalized by a reorientation effect.

Loss of Memory in H + CH4 → H2 + CH3 State-to-State Reactive Scattering.

State-to-state reaction probabilities for the H + CH4→ H2 + CH3 reaction are calculated by accurate full-dimensional quantum dynamics calculations employing the multilayer multiconfigurational time-dependent Hartree approach and the quantum transition-state concept. Reactions starting from different vibrational and rotational states of the methane reactant are investigated for vanishing total angular momentum. The vibrational state distributions of the products are found to be essentially independent of the initial rovibrational state of the reactants. The reaction products only show vibrational excitation in the methyl umbrella mode. No excitation in H2 vibration or another CH3 vibration is observed. Analyzing the results, the observed loss of vibrational memory can be explained by a transition-state-based view of the reaction process.

Communication: Ro-vibrational control of chemical reactivity in H+CH₄→ H₂+CH₃: full-dimensional quantum dynamics calculations and a sudden model.

The mode-selective chemistry of the title reaction is studied by full-dimensional quantum dynamics simulation on an accurate ab initio potential energy surface for vanishing total angular momentum. Using a rigorous transition state based approach and multi-configurational time-dependent Hartree wave packet propagation, initial state-selected reaction probabilities for many ro-vibrational states of methane are calculated. The theoretical results are compared with experimental trends seen in reactions of methane. An intuitive interpretation of the ro-vibrational control of the chemical reactivity provided by a sudden model based on the quantum transition state concept is discussed.

Permutation invariant polynomial neural network approach to fitting potential energy surfaces. II. Four-atom systems

A rigorous, general, and simple method to fit global and permutation invariant potential energy surfaces (PESs) using neural networks (NNs) is discussed. This so-called permutation invariant polynomial neural network (PIP-NN) method imposes permutation symmetry by using in its input a set of symmetry functions based on PIPs. For systems with more than three atoms, it is shown that the number of symmetry functions in the input vector needs to be larger than the number of internal coordinates in order to include both the primary and secondary invariant polynomials. This PIP-NN method is successfully demonstrated in three atom-triatomic reactive systems, resulting in full-dimensional global PESs with average errors on the order of meV. These PESs are used in full-dimensional quantum dynamical calculations.

Coupled potential energy surface for the F(2P) + CH4 → HF + CH3 entrance channel and quantum dynamics of the CH4 · F− photodetachment

An approach to construct vibronically and spin-orbit coupled diabatic potential energy surfaces (PESs) which describe all three relevant electronic states in the entrance channels of the X(P) + CH4 →HX + CH3 reactions (with X=F((2)P), Cl((2)P), or O((3)P)) is introduced. The diabatization relies on the permutational symmetry present in the methane molecule and results in diabatic states which transform as the three p orbitals of the X atom. Spin-orbit coupling is easily and accurately included using the atomic spin-orbit coupling matrix of the isolated X atom. The method is applied to the F + CH4 system obtaining an accurate PES for the entrance channel based on ab initio multi-reference configuration interaction (MRCI) calculations. Comparing the resulting PESs with spin-orbit MRCI calculations, excellent agreement is found for the excited electronic states at all relevant geometries. The photodetachment spectrum of CH4·F(-) is investigated via full-dimensional (12D) quantum dynamics calculations on the coupled PESs using the multi-layer multi-configurational time-dependent Hartree approach. Extending previous work [J. Palma and U. Manthe, J. Chem. Phys. 137, 044306 (2012)], which was restricted to the dynamics on a single adiabatic PES, the contributions of the electronically excited states to the photodetachment spectrum are calculated and compared to experiment. Considering different experimental setups, good agreement between experiment and theory is found. Addressing questions raised in the previous work, the present dynamical calculations show that the main contribution to the second peak in the photodetachment spectrum results from electron detachment into the electronically excited states of the CH4F complex.

Theoretical Investigation of the He4Br2 Conformers

Full dimensional quantum dynamics calculations of the three lowest isomers of the He(4)Br(2) van der Waals molecule in its ground electronic state are reported. The calculations are performed using the multiconfiguration time-dependent Hartree (MCTDH) method and a realistic potential form that includes the sum of three body ab initio coupled-cluster single double triple [CCSD(T)] He-Br(2) interactions plus the He-He and Br-Br interactions. This potential exhibits several multiple minima, with the three lowest ones lying very close in energy, just within 2 cm(-1). Such small differences are also found in the calculated binding energies of the three most stable conformers, indicating the floppiness of the system and, thus, the need of accurate potential forms and quantum full dynamics methods to treat this kind of complexes. The 12 dimensional results reported in this work present benchmark data and, thus, can serve to evaluate approximate methods aiming to describe higher order rare gas-dihalogen (N > 4) complexes. A comparison with previous studies using different potential forms and approaches to the energetics for the He(4)Br(2) cluster is also presented.

Rovibrational energy transfer in collisions of H2 with D2: a full-dimensional wave packet propagation study

We present full-dimensional quantum dynamics calculations for the process of rovibrational energy transfer in collisions between H2 and D2 molecules, specifically H2(ν = 1) + D2(ν = 0) → H2(ν = 0) + D2(ν = 1). Rotationally resolved state-to-state cross-sections are obtained for collision energies up to 0.5 eV. From these we calculate rotationally averaged thermal rate coefficients in the temperature range from 100 to 500 K, and compare them with available experimental data. For some transitions, we found it numerically advantageous to compute cross-sections of the reverse collision process and then use microscopic reversibility to obtain the originally sought cross-sections. We employ the Multi-Configuration Time-Dependent Hartree (MCTDH) method for propagating wave packets, and calculate the cross-sections from transition probabilities obtained by the correlation function formalism introduced by Tannor and Weeks. Computations are performed with a potential energy surface that is based on the six-dimensional surface from Boothroyd et al. but reduced in anisotropy, as suggested by Pogrebnya and Clary. The expression of the kinetic energy operator in terms of internal curvilinear coordinates allows us to treat the kinematics of the system exactly, without any decoupling approximations.

Photodissociation of methyl iodide embedded in a host-guest complex: A full dimensional (189D) quantum dynamics study of CH3I@resorc[4]arene

Accurate full dimensional quantum dynamics calculations studying the photodissociation of CH(3)I@resorc[4]arene on an ab initio based potential energy surface (PES) model are reported. The converged 189D quantum dynamics calculations are facilitated by the multilayer multi-configurational time-dependent Hartree (ML-MCTDH) approach combined with the correlation discrete variable representation (CDVR) for the evaluation of potential energy matrix elements. The potential employed combines an established ab initio PES describing the photodissociation of methyl iodide in the A band with a harmonic description of the resorc[4]arene host and a bilinear modeling of the host-guest interaction. All potential parameters required in the description of the vibrations of the host molecule and the host-guest interaction are derived from ab initio calculations on the host-guest complex. Absorption spectra at 0 K and 300 K are calculated and the electronic population dynamics during the bond breaking process occurring in the first 20-30 fs after the photoexcitation is investigated. Weak but significant effects resulting from the host-guest interaction on this time scale are found and interpreted. The present study demonstrates that accurate fully quantum mechanical dynamics calculations can be preformed for systems consisting of more than 50 atoms using the ML-MCTDH/CDVR approach. Utilizing an efficient statistical approach for the construction of the ensemble of initial wavepackets, these calculations are not restricted to zero temperature but can also study the dynamics at 300 K.

Full-dimensional quantum dynamics study of vinylidene–acetylene isomerization: a scheme using the normal mode Hamiltonian

Full-dimensional quantum dynamics calculations of vinylidene-acetylene isomerization are performed and the state-specific resonance decay lifetimes of vinylidene(-d(2)) are computed. The theoretical scheme is a combination of several methods: normal coordinates are chosen to describe the nuclear motion of vinylidene, with both the parity and permutation symmetry exploited; phase space optimization in combination with physical considerations is used to generate an efficient discrete variable representation; the reaction coordinate is defined by us according to the three most relevant normal coordinates, along which a kind of optimal complex absorbing potential is imposed; the preconditioned inexact spectral transform method combined with an efficient preconditioner is employed to extract the energies and lifetimes of vinylidene. The overall computation is efficient. The computed energy levels generally agree with experiment well, and several state-specific lifetimes are reported for the first time.