Quantum Dynamics Study on D+OD+ Reaction: Competition between Exchange and Abstraction Channels

Quantum dynamics for the D+OD⁺ reaction at the collision energy range of 0.0-1.0 eV was studied on an accurate ab initio potential energy surface. Both of the endothermic abstrac-tion (D+OD⁺→O⁺+D₂) and thermoneutral exchange (D+OD⁺→D+OD⁺) channels were investigated from the same set of time-dependent quantum wave packets method under cen-trifugal sudden approximation. The reaction probability dependence with collision energy, the integral cross sections, and the thermal rate constant of the both channels are calculated. It is found that there is a convex structure in the reaction path of the exchange reaction. The calculated time evolution of the wave packet distribution at J=0 clearly indicates that the convex structure significantly influences the dynamics of the exchange and abstraction channels of title reaction.     

Electronic quantum motions in hydrogen molecule ion

The hydrogen molecule ion is a two‐center force system expressed under the prolate spheroidal coordinates, whose quantum motions and quantum trajectories have never been addressed in the literature before. The momentum operators in this coordinate system are derived for the first time from the Hamilton equations of motion and used to construct the Hamiltonian operator. The resulting Hamiltonian comprises a kinetic energy T and a total potential V_Total consisting of the Coulomb potential and a quantum potential. It is shown that the participation of the quantum potential and the accompanied quantum forces in the force interaction within H₂⁺ is essential to develop an electronic motion consistent with the prediction of the probability density function |Ψ|². The motion of the electron in H₂⁺ can be either described by the Hamilton equations derived from the Hamiltonian H = T_K + V_Total or by the Lagrange equations derived from the Lagrangian H = T_K ? V_Total. Solving the equations of motion with different initial positions, we show that the solutions yield an assembly of electronic quantum trajectories whose distribution and concentration reconstruct the σ and π molecular orbitals in H₂⁺. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Ab initio potential energy surface and vibration‐rotation energy levels of sulfur dioxide

An accurate potential energy surface of sulfur dioxide, SO₂, in its ground electronic state has been determined from ab initio calculations using the coupled‐cluster approach in conjunction with the correlation‐consistent basis sets up to septuple‐zeta quality. The results obtained with the conventional and explicitly correlated coupled‐cluster methods are compared. The role of the core–electron correlation, higher‐order valence–electron correlation, scalar relativistic, and adiabatic effects in determining the structure and dynamics of the SO₂ molecule is discussed. The vibration‐rotation energy levels of the ³²SO₂ and ³⁴SO₂ isotopologues were predicted using a variational approach. It was shown that the inclusion of the aforementioned effects was mandatory to attain the “spectroscopic” accuracy. © 2017 Wiley Periodicals, Inc.     

Current‐density functional study of the HeH+ molecular ion under a strong ultrashort magnetic field

The HeH⁺ molecular ion under an ultrashort magnetic field on the order of 10⁹ G is investigated through quantum fluid dynamics and a current‐density functional theory (CDFT) based approach, employing a vector exchange–correlation (XC) potential which depends on the electronic charge‐density as well as on the current‐density. The behavior of the exchange and correlation energies of the HeH⁺ ion is analyzed and compared with those obtained using an approach based on the time‐dependent density functional theory (TD‐DFT) under similar computational constraints but employing a scalar XC potential dependent only on the electronic charge‐density. The CDFT‐based approach yields exchange and correlation energies as well as TD electronic charge‐densities drastically different from those obtained using the TD‐DFT‐based approach particularly, at typical TD magnetic field strengths. This is attributed to the nonadiabatic effects induced by the vector XC potential of the CDFT in the oscillating charge‐density of the HeH⁺ ion, which are further explained in the terminology of quantum fluid dynamics. The vector XC potential of the CDFT‐based approach is observed to augment the magnetic interactions in the H₂ molecule and in the He ion, whereas it opposes the magnetic interactions in the HeH⁺ ion particularly, at the intermediate magnetic field strengths. © 2012 Wiley Periodicals, Inc.     

Quasi-classical Trajectory Study of the Intramolecular Isotope Effect in the Reaction O（3p）＋H2/HD

Theoretical studies of the dynamics of the reactions O（3p）＋H2/HD（ν=0, j=0）→OH＋H have been performed with quasi-classical trajectory method （QCT） on an ab initio potential surface for the lowest triplet electronic state of H2O（aA＂）. The QCT-calculated integral cross sections are in good agreement with the earlier time-dependent quantum mechanics results. The state-resolved rotational distributions reveal that the product OH rotational distributions for O＋HD have a preference for populating highly internally excited states compared with the O＋H2 reaction. Distributions of differential cross sections show that directions of scattering are strongly dependent on the choice of quantum state. The polarization dependent generalized differential cross-sections and the distributions were calculated and a pronounced isotopic effect is revealed. The calculated results indicate that the product polarization is very sensitive to the mass factor.     

Low‐Temperature Thermal Rate Constants for the Water Formation Reaction H2+OH from Rigorous Quantum Dynamics Calculations

Thermal rate constants for the prototypical water‐forming reaction H₂+OH→H+H₂O were obtained for temperatures between 150 K and 600 K by rigorous quantum dynamics calculations including all degrees of freedom. Results are reported for a recent, highly accurate neural network potential (NN1) and compared to results obtained on a previous, semi‐empirical potential (SE). The rate constants computed on both potentials significantly differ in their temperature dependence, and differences of over one order of magnitude in the rates were found. The rate constants computed for the NN1 potential compare very well to experimental work. Furthermore, the influence of overall rotation is discussed for the title reaction. While previous close‐coupling simulations were limited to thermal rate constants above room temperature, we report rate constants for temperatures as low as 250 K. The high‐level results reported here provide an accurate benchmark for the development of approximate methods for the calculation of thermal as well as microcanonical rate constants.     

Quantum mechanics and quasiclassical study of the H/D+FO → OH/OD+F,HF/DF+O reactions: Chemical stereodynamics

The time‐dependent quantum wave packet and the quasi‐classical trajectory (QCT) calculations for the title reactions are carried out using three recent‐developed accurate potential energy surfaces of the 1¹A′, 1³A′, and 1³A″ states. The two commonly used polarization‐dependent differential cross sections, dσ₀₀/dω_t, dσ₂₀/dω_t, with ω_t being the polar coordinates of the product velocity ω′, and the three angular distributions, P(θ_r), P(Φ_r), and P(θ_r,Φ_r), with θ_r, Φ_r being the polar angles of the product angular momentum, are generated in the center‐of‐mass frame using the QCT method to gain insight into the alignment and the orientation of the product molecules. Influences of the potential energy surface, the collision energy, and the isotope mass on the stereodynamics are shown and discussed. Validity of the QCT calculation has been examined and proved in the comparison with the quantum wave packet calculation. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

A “classical” trajectory driven nuclear dynamics by a parallelized quantum‐classical approach to a realistic model Hamiltonian of benzene radical cation

We explore the workability of a parallelized algorithm of time‐dependent discrete variable representation (TDDVR) methodology formulated by involving “classical” trajectories on each DOF of a multi‐mode multi‐state Hamiltonian to reproduce the population dynamics, photoabsorption spectra and nuclear dynamics of the benzene radical cation. To perform such dynamics, we have used a realistic model Hamiltonian consists of five lowest electronic states (X²E_1g, B²E_2g, C²A_2u, D²E_1u, and E²B_2u) which are interconnected through several conical intersections with nine vibrational modes. The calculated nuclear dynamics and photoabsorption spectra with the advent of our parallelized TDDVR approach show excellent agreement with the results obtained by multiconfiguration time‐dependent Hartree method and experimental findings, respectively. The major focus of this article is to demonstrate how the “classical” trajectories for the different modes and the “classical” energy functional for those modes on each surface can enlight the time‐dependent feature of nuclear density and its' nodal structure. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Systematic calculation of molecular vibrational spectra through a complete Morse expansion

We propose an accurate and efficient method to compute vibrational spectra of molecules, based on exact diagonalization of an algebraically calculated matrix based on powers of Morse coordinate. The present work focuses on the 1D potential of diatomic molecules: as typical examples, we apply this method to the standard Lennard‐Jones oscillator, and to the ab initio potential of the H₂ molecule. Global cm^?1 accuracy is exhibited through the H₂ spectrum, obtained through the diagonalization of a 30 × 30 matrix. This theory is at the root of a new method to obtain globally accurate vibrational spectral data in the context of the multi‐dimensional potential of polyatomic molecules, at an affordable computational cost. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Multicomponent Molecular Orbital–Climbing Image–Nudged Elastic Band Method to Analyze Chemical Reactions Including Nuclear Quantum Effect

To analyze the H/D isotope effects on hydrogen transfer reactions in XHCHCHCHY?XCHCHCHYH (X, Y=O, NH, or CH₂) including the nuclear quantum effect of proton and deuteron, we propose a multicomponent molecular orbital‐climbing image‐nudged elastic band (MC_MO–CI–NEB) method. We obtain not only transition state structures but also minimum‐energy paths (MEPs) on the MC_MO effective potential energy surface by using MC_MO–CI–NEB method. We find that nuclear quantum effect affects not only stationary‐point geometries but also MEPs and electronic structures in the reactions. We clearly demonstrate the importance of including nuclear quantum effects for H/D isotope effect on rate constants (k_H/k_D).     

Could an anisotropic molecular mechanics/dynamics potential account for sigma hole effects in the complexes of halogenated compounds?

Halogenated compounds are gaining an increasing importance in medicinal chemistry and materials science. Ab initio quantum chemistry (QC) has unraveled the existence of a “sigma hole” along the C? X (X = F, Cl, Br, I) bond, namely, a depletion of electronic density prolonging the bond, concomitant with a build‐up on its sides, both of which are enhanced along the F < Cl < Br < I series. We have evaluated whether these features were intrinsically built‐in in an anisotropic, polarizable molecular mechanics (APMM) procedure such as SIBFA (sum of interactions between fragments ab initio computed). For that purpose, we have computed the interaction energies of fluoro‐, chloro‐, and bromobenzene with two probes: a divalent cation, Mg(II), and water approaching X through either one H or its O atom. This was done by parallel QC energy‐decomposition analyses (EDA) and SIBFA computations. With both probes, the leading QC contribution responsible for the existence of the sigma hole is the Coulomb contribution E_c. For all three halogenated compounds, and with both probes, the in‐ and out‐of‐plane angular features of E_c were closely mirrored by the SIBFA electrostatic multipolar contribution (E_MTP). Resorting to such a contribution thus dispenses with empirically‐fitted “extra”, off‐centered partial atomic charges as in classical molecular mechanics/dynamics. © 2013 Wiley Periodicals, Inc.     

Photodissociation Spectroscopy and Dynamics of Weakly Bonded Metal Ion—Ethylene Complexes

The photodissociation spectroscopy of weakly bonded bimolecular complexes can give important insight into fundamental molecular interactions and dynamics. We have applied these techniques to a study of metal ion‐ethylene interactions in the Mg⁺(3s)‐C₂H₄ and Al⁺(3s²)‐C₂H₄ π‐bonded complexes. Experimental work is supported by ab‐initio electronic structure calculations. These experiments allow us to explore and compare the chemical binding, electronic structure, and nonadiabatic dissociation dynamics of these complexes.     

Influences of Quantum Mechanically Mixed Electronic and Vibrational Pigment States in 2D Electronic Spectra of Photosynthetic Systems: Strong Electronic Coupling Cases

In 2D electronic spectroscopy studies, long‐lived quantum beats have recently been observed in photosynthetic systems, and several theoretical studies have suggested that the beats are produced by quantum mechanically mixed electronic and vibrational states. Concerning the electronic‐vibrational quantum mixtures, the impact of protein‐induced fluctuations was examined by calculating the 2D electronic spectra of a weakly coupled dimer with the Franck‐Condon active vibrational modes in the resonant condition [Fujihashi et al., J. Chem. Phys.­ 2015 , 142, 212403.]. This analysis demonstrated that quantum mixtures of the vibronic resonance are rather robust under the influence of the fluctuations at cryogenic temperatures, whereas the mixtures are eradicated by the fluctuations at physiological temperatures. However, this conclusion cannot be generalized because the magnitude of the coupling inducing the quantum mixtures is proportional to the inter‐pigment electronic coupling. In this study, we explore the impact of the fluctuations on electronic‐vibrational quantum mixtures in a strongly coupled dimer with an off‐resonant vibrational mode. Toward this end, we calculate energy transfer dynamics and 2D electronic spectra of a model dimer that corresponds to the most strongly coupled bacteriochlorophyll molecules in the Fenna‐Matthews‐Olson complex in a numerically accurate manner. The quantum mixtures are found to be robust under the exposure of protein‐induced fluctuations at cryogenic temperatures, irrespective of the resonance. At 300 K, however, the quantum mixing is disturbed more strongly by the fluctuations, and therefore, the beats in the 2D spectra become obscure even in a strongly coupled dimer with a resonant vibrational mode. Further, the overall behaviors of the energy transfer dynamics are demonstrated to be dominated by the environment and coupling between the 0 0 vibronic transitions as long as the Huang‐Rhys factor of the vibrational mode is small. The electronic‐vibrational quantum mixtures do not necessarily play a significant role in electronic energy transfer dynamics despite contributing to the enhancement of long‐lived quantum beating in the 2D spectra.     

Theoretical study of the dehydrogenate reaction of H2S by Sc+(1D)

The reaction Sc⁺(¹D)+H₂S→Sc⁺S+H₂ is theoretically investigated by ab initio MO methods. Two possible reaction channels on the singlet potential surface (PES) and the reaction mechanism are examined and discussed. Three regions of the potential surface were studied, the molecular complex, the S‐H insertion products and the transition states for the reaction. In addition the singlet and triplet PESs of this reaction system are compared in an investigation the chemistry of excited electronic state. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 82: 60–64, 2001     

Time‐dependent quantum study of H(2S) + FO(2Π) → OH(2Π) + F(2P) reaction on the 13A′ and 13A″ states

The dynamics of the H(²S) + FO(²Π) → OH(²Π) + F(²P) reaction on the adiabatic potential energy surface of the 1³A′ and 1³A″ states is investigated. The initial state selected reaction probabilities for total angular momentum J = 0 have been calculated by using the quantum mechanical real wave packet method. The integral cross sections and initial state selected reaction rate constants have been obtained from the corresponding J = 0 reaction probabilities by means of the simple J‐Shifting technique. The initial state‐selected reaction probabilities and reaction cross section do not manifest any sharp oscillations and the initial state selected reaction rate constants are sensitive to the temperature. © 2010 Wiley Periodicals, Inc. J Comput Chem 2010     

Nonadiabatic relaxation dynamics of water anion cluster and its isotope effects by ring‐polymer molecular dynamics simulation

We have applied a recently developed hybrid quantum ring‐polymer molecular dynamics method to the nonadiabatic p → s relaxation dynamics in water anion clusters to understand the isotope effects observed in previous experiments. The average relaxation times for (H₂O)₅₀^? and (D₂O)₅₀^? were calculated at 120 and 207 fs, respectively, and are comparable to the experimental results. Therefore, we conclude that nuclear quantum effects play an essential role in understanding the observed isotope effects for water anion cluster nonadiabatic dynamics. The nonadiabatic relaxation mechanisms are also discussed in detail. © 2014 Wiley Periodicals, Inc.     

Chemical Solutions in a Quantum Solvent: Anionic Electrolytes in 4He Nanodroplets

Variational and diffusion Monte Carlo (VMC and DMC) calculations are presented for anionic electrolytes solvated in ⁴He. The electrolytes have the general structure X^?(He)_N, with X=F, Cl, Br and I, and N varying up to 40 (41 for I^?). The overall interaction potential is obtained from accurate ab initio data for the two‐body components and then using the sum‐of‐potentials approximation. Our computational scheme is a robust procedure, giving us accurate trial wavefunctions that can be used to perform high‐quality DMC calculations. The results indicate very marked delocalization and permanence of the liquid‐like quantum features of the solvent adatoms surrounding the anionic impurities. This finding stands in contrast to the more structured, solid‐like behavior of the quantum solutions with alkali metal cations embedded in He nanodroplets. While other negatively charged species such as H^? have shown an overall repulsive interaction with He, the present calculations clearly indicate that the halogen anions remain solvated within liquid‐like solvent “bubbles” of species‐dependent size.     

A Novel Method for Fixed‐node Quantum Monte Carlo

In this paper, a novel method for fixed‐node quantum Monte Carlo is given. By comparing this method with the traditional fixed‐node one, this novel method can be applied to calculate molecular energy more exactly. An expansion of the eigenvalue of the energy for a system has been derived. It is proved that the value of the energy calculated using the traditional fixed‐node method is only the zeroth order approximation of the eigenvalue of the energy. But when using this novel method, in the case of only increasing less computing amounts ( < 1%), the first order approximation, the second order approximation, and so on can be obtained conveniently with the detailed equations and steps in the practical calculation to calculate the values of the zeroth, first and second approximation of the energies of 1 ¹A, state of CH₂, ¹A₂(C_4h, acet) state of C₈ and the ground‐states of H₂, LiH, Li₂, and H₂O The results indicate that for these states it needs only the second order approximation to obtain over 97% of electronic correlation energy, which demonstrates that this novel method is very excellent in both the computing accuracy and the amount of calculation required.     

多原子反应体系的高精度拟合势能面

本文介绍了近几年来我们组构建多原子反应体系的高精度拟合势能面的进展。我们基于神经网络(NN)方法,成功构建了多原子气相分子体系和气相分子在金属表面解离的一系列势能面。这些势能面的拟合精度相当高,并且经过了严格的量子动力学测试,能广泛应用到动力学研究中。我们还提出了一种新的置换不变势能面的拟合方法,即基本不变量神经网络方法(FI-NN)。基本不变量的使用极大地减少了神经网络输入层多项式的个数,有效提高了势能面的计算速度。     

Ab initio excited states calculations of Kr 3 + , probing semi-empirical modelling

The accuracy of the diatomics-in-molecules (DIM) model for the krypton ionic trimer is examined in a series of ab initio calculations. In the C_2v symmetry, the ground states of irreducible representations B₂ and A₁ were calculated using partially spin restricted open-shell coupled cluster method with perturbative triple connections (RHF-RCCSD-T), the relativistic effective core potential (RECP) and an extended basis set of atomic orbitals. Internally contracted multireference configuration interaction method (icMRCI) with the extended and restricted basis set was used to generate the potential energy surfaces (PESs) of the nine electronic states of Kr ₃ ⁺ corresponding to Kr(¹S) + Kr(¹S) + Kr⁺(²P) dissociation limit in a wide interval of nuclear geometries. The overall agreement of the accurate ab initio PESs and the diatomics-in-molecules PESs confirms the quality of the DIM Hamiltonian for the Kr ₃ ⁺ clusters and justifies its use in dynamical and spectroscopic studies of the Kr _n ⁺ clusters. Inclusion of the spin–orbit coupling into the ab initio PESs through a semi-empirical scheme is proposed.