An efficient route to thermal rate constants in reduced dimensional quantum scattering simulations: applications to the abstraction of hydrogen from alkanes

We present an efficient approach to the determination of two-dimensional potential energy surfaces for use in quantum reactive scattering simulations. Our method involves first determining the minimum energy path (MEP) for the reaction by means of an ab initio intrinsic reaction coordinate calculation. This one-dimensional potential is then corrected to take into account the zero point energies of the spectator modes. These are determined from Hessians in curvilinear coordinates after projecting out the modes to be explicitly treated in quantum scattering calculations. The final (1+1)-dimensional potential is constructed by harmonic expansion about each point along the MEP before transforming the whole surface to hyperspherical coordinates for use in the two-dimensional scattering simulations. This new method is applied to H-atom abstraction from methane, ethane and propane. For the latter, both reactive channels (producing i-C(3)H(7) or n-C(3)H(7)) are investigated. For all reactions, electronic structure calculations are performed using an efficient, explicitly correlated, coupled cluster methodology (CCSD(T)-F12). Calculated thermal rate constants are compared to experimental and previous theoretical results.     

Multidimensional reactive scattering with quantum trajectories: dynamics with 50-200 vibrational modes

The dynamics of ensembles containing thousands of quantum trajectories are studied for multidimensional systems undergoing reactive scattering. The Hamiltonian and equations of motion are formulated in curvilinear reaction path coordinates, for the case of a planar (zero-torsion) reaction path. In order to enhance the computational efficiency, an improved least squares fitting procedure is introduced. This scheme involves contracted basis sets and the use of inner and outer stencils around points where fitting is performed. This method is applied to reactive systems with 50-200 harmonic vibrational modes which are coupled to motion along the reaction coordinate. Dynamical results, including trajectory evolution and time-dependent reaction probabilities, are presented and power law scaling of computation time with the number of vibrational modes is described.     

Quantum theory of chemical reactions in the presence of electromagnetic fields

We present a theory for rigorous quantum scattering calculations of probabilities for chemical reactions of atoms with diatomic molecules in the presence of an external electric field. The approach is based on the fully uncoupled basis set representation of the total wave function in the space-fixed coordinate frame, the Fock-Delves hyperspherical coordinates, and the adiabatic partitioning of the total Hamiltonian of the reactive system. The adiabatic channel wave functions are expanded in basis sets of hyperangular functions corresponding to different reaction arrangements, and the interactions with external fields are included in each chemical arrangement separately. We apply the theory to examine the effects of electric fields on the chemical reactions of LiF molecules with H atoms and HF molecules with Li atoms at low temperatures and show that electric fields may enhance the probability of chemical reactions and modify reactive scattering resonances by coupling the rotational states of the reactants. Our preliminary results suggest that chemical reactions of polar molecules at temperatures below 1 K can be selectively manipulated with dc electric fields and microwave laser radiation.     

超球坐标下共线三原子反应散射的一阶Magnus数值传播法计算

使用一阶Magnus数值传播积分法计算了超球坐标描述下的共线三原子反应散射问题。应用于共线H+H_2和F+H_2体系得到了较好的结果。     

Classical theory of collisional entropy production

A classical dynamical theory of elementary collision processes is formulated in analogy to the quantum theory of the dynamical scattering matrix, which can be defined for a pure quantum stationary scattering state. The elements of this matrix are probability amplitudes for transitions between internal states defined for given values of a reaction coordinate. The squared magnitudes of these amplitudes, modeled in the proposed classical theory, define normalized internal state population distributions suitable for information theoretical analysis. Statistical entropy and surprisal are defined as dynamical functions of a reaction coordinate. This formalism differs fundamentally from concepts based on the classical Liouville equation.     

A general treatment of vibration-rotation coordinates for triatomic molecules

An exact, within the Born–Oppenheimer approximation, body-fixed Hamiltonian for the nuclear motions of a triatomic system is presented. This Hamiltonian is expressed in terms of two arbitrarily defined internal distances and the angle between them. The body-fixed axis system is related to these coordinates in a general fashion. Problems with singularities and the domain of the Hamiltonian are discussed using specific examples of axis embedding. A number of commonly used coordinate systems including Jacobi, bond-length-bond-angle, and Radau coordinates are special cases of this Hamiltonian. Sample calculations on the H₂S molecule are presented using all these and other coordinate systems. The possibility of using this Hamiltonian for reactive scattering calculations is also discussed.     

Proton dynamics in an extended array of hydrogen bonds: normal coordinates, proton transfer and macroscopic quantum entanglement in the ground state

After a brief introduction to neutron scattering techniques, illustrated with the scattering function for harmonic oscillators, some new aspects of proton dynamics in the KHCO₃ crystal are presented. The full scattering function for the proton modes measured on single crystals provides a graphic view of proton dynamics. Vibrational states are fully characterized with three quantum numbers. The effective oscillator mass of 1 amu confirms the decoupling of protons from the lattice. Combining infrared, Raman and inelastic neutron scattering techniques, the double minimum potential for the transfer of a single proton along hydrogen bonds is totally determined. Elastic neutron scattering techniques probe dynamics in the fully degenerate ground state. Quantum entanglement arising from normal coordinates gives rise to quantum interference. With diffraction techniques, the dynamical structure arising from large-scale quantum coherence is observed as ridges of intensity, well separated from Bragg's peaks. The vibrational wave function in the ground state must be regarded as a superposition of non-factorable macroscopic wave function.     

Ab initio potential energy surface of CH and reaction dynamics of H + CH+

This work presents a new ground state potential energy surface (PES) for CH. The potential is tested using quasi classical trajectory (QCT) and quantum reactive scattering methods for the H + CH(+) reaction. Cross sections and rate coefficients for all reaction channels up to 300 K are calculated. The abstraction rate coefficients follow the expected slightly decreasing behaviour above 90 K, but have a positive gradient with lower temperatures. The inelastic collision and exchange reaction rate constants are increasing monotonically with temperature. The rate coefficients of the exchange reaction differ significantly between QCT and quantum reactive scattering, due to intrinsic shortcomings of the QCT final state distributions.     

Time-dependent quantum dynamics of reactive scattering and the calculation of product quantum state distributions — A study of the collinear F+H2(v=0) → HF(v′)+H reaction

Summary A new method for the calculation of partial cross sections in the time-dependent quantum theory of molecular reactive scattering processes is discussed. Preliminary calculations are presented which clearly illustrate the power of the method. They show how all the partial cross sections associated with a single initial quantum state may be computed over a very wide energy range from a single propagation of a prepared wavepacket. The resonance behaviour is obtained without difficulty and the energies of the reactive scattering resonances are exactly reproduced.     

Hyperspherical coordinates in quantum mechanical collinear reactive scattering

A new hyperspherical coordinate method for performing atom—diatom quantum mechanical collinear reactive scattering calculations is described. The method is applicable at energies for which breakup channels are open. Comparison with previous results and new results at high energies for H H₂ are given. The usefulness of this approach is discussed.     

二维凝聚体系中单轴取向分子的偏振Raman散射强度

分析了薄膜体系几种常用测量坐标下的偏振Raman散射强度表达式,发现当测量坐标与膜坐标重叠对,各种偏振Raman散射强度只需用膜坐标中的Raman散射活性来表达。如果这两个坐标不重叠,需进一步求出膜坐标中Raman张量元二次交叉项的平均值。本文给出了单轴唯一角取向模型下这些二次交叉项的平均值表达式及取向分布模型下膜坐标中所有Raman张量元二次项平均值。     

Exact quantum mechanical vibration-rotation kinetic energy operator of four-particle system in various coordinates

The vibration-rotational kinetic energy operators of four-particle system in various coordinates are derived using a new and simple angular momentum method. The operators are respectively suitable for studying the systems described by scattering coordinate, valence coordinate, Radau coordinate, Radau/Jacobi and Jacobi/valence hybrid coordinates and so on. Certain properties of these operators and their possible applications are discussed.     

A semiclassical adiabatic calculation of state densities for molecules exhibiting torsion: application to hydrogen peroxide and its isotopomers

A practical computational method is discussed for obtaining the rotational–vibrational molecular state densities of molecules with large amplitude torsional degrees of freedom (DoFs). This method goes beyond the traditional harmonic oscillator/rigid rotor or separable hindered rotor approximations in that it includes coupling between the torsion, the remaining vibrational modes, and the overall rotation. The method is based on the vibrationally adiabatic approximation whereby the torsional motion is assumed to be slow compared to the remaining vibrational DoFs although the nonseparability may be large. The torsional coordinate therefore parameterizes the rotational constants and the effective vibrational potential. A semiclassical method is then introduced to calculate the total state density in which the torsion is treated classically while the remaining coordinates are treated quantum mechanically. The method is also formulated for reactive problems in which the density of states is parameterized by a second large amplitude degree of freedom, the reaction coordinate. The performance of the method is assessed using the dissociation reaction of the hydrogen peroxide molecule and its isotopomers. It is found that the method performs well based on numerical tests. The torsional nonseparability is found to yield errors of factors of 2–3 in the statistical rate coefficient when compared with results of traditional separable models.     

Plane wave packet formulation of atom-plus-diatom quantum reactive scattering

We recently interpreted several reactive scattering experiments using a plane wave packet (PWP) formulation of quantum scattering theory [see, e.g., S. C. Althorpe, F. Fernandez-Alonso, B. D. Bean, J. D. Ayers, A. E. Pomerantz, R. N. Zare, and E. Wrede, Nature (London) 416, 67 (2002)]. This paper presents the first derivation of this formulation for atom-plus-diatom reactive scattering, and explains its relation to conventional time-independent reactive scattering. We generalize recent results for spherical-particle scattering [S. C. Althorpe, Phys. Rev. A 69, 042702 (2004)] to atom-rigid-rotor scattering in the space-fixed frame, atom-rigid-rotor scattering in the body-fixed frame, and finally A+BC rearrangement scattering. The reactive scattering is initiated by a plane wave packet, describing the A+BC reagents in center-of-mass scattering coordinates, and is detected by projecting onto a series of AC+B (or AB+C) plane wave "probe" packets. The plane wave packets are localized at the closest distance from the scattering center at which the interaction potential can be neglected. The time evolution of the initial plane wave packet provides a clear visualization of the scattering into space of the reaction products. The projection onto the probe packets yields the time-independent, state-to-state scattering amplitude, and hence the differential cross section. We explain how best to implement the PWP approach in a numerical computation, and illustrate this with a detailed application to the H+D2 reaction.     

一种计算Feshbach共振态寿命的新方法

在自然碰撞坐标下构建偏分势能面, 利用数值传播方法求解沿反应坐标的核运动方程, 然后用过渡态波函数的相移因子构造反应体系共振态寿命矩阵. 这是一种直接计算化学反应散射共振寿命的量子散射方法. 用此方法计算了I+HI(υ)→IH(υ’)+I体系的第一散射共振态寿命, 所得数值与Neumark 的高分辨阈值光分离光谱实验的结果相一致.     

Few-body quantum and many-body classical hyperspherical approaches to reactions and to cluster dynamics

The hyperspherical method is a widely used and successful approach for the quantum treatment of elementary chemical processes. It has been mostly applied to three-atomic systems, and current progress is here outlined concerning the basic theoretical framework for the extension to four-body bound state and reactive scattering problems. Although most applications only exploit the advantages of the hyperspherical coordinate systems for the formulation of the few-body problem, the full power of the technique implies representations explicitly involving quantum hyperangular momentum operators as dynamical quantities and hyperspherical harmonics as basis functions. In terms of discrete analogues of these harmonics one has a universal representation for the kinetic energy and a diagonal representation for the potential (hyperquantization algorithm). Very recently, advances have been made on the use of the approach in classical dynamics, provided that a hyperspherical formulation is given based on “classical” definitions of the hyperangular momenta and related quantities. The aim of the present paper is to offer a retrospective and prospective view of the hyperspherical methods both in quantum and classical dynamics. Specifically, regarding the general quantum hyperspherical approaches for three- and four-body systems, we first focus on the basis set issue, and then we present developments on the classical formulation that has led to applications involving the implementations of hyperspherical techniques for classical molecular dynamics simulations of simple nanoaggregates.     

Multidimensional reactive scattering with quantum trajectories: dynamics with Morse vibrational modes

The reactive scattering of a wave packet is studied by the quantum trajectory method for a model system with up to 25 Morse vibrational modes. The equations of motion are formulated in curvilinear reaction path coordinates with the restriction to a planar reaction path. Spatial derivatives are evaluated by the least squares method using contracted basis sets. Dynamical results, including trajectory evolution and time-dependent reaction probabilities, are presented and analyzed. For the case of one Morse vibrational mode, the results are in good agreement with those derived through direct numerical integration of the time-dependent Schrodinger equation.     

Ab initio calculations of the ultraviolet resonance Raman spectra of uracil

An equation been derived to calculate, ab initio, the frequencies and intensities of a resonant Raman spectrum from the transform theory of resonance Raman scattering. This equation has been used to calculate the intensities of the ultraviolet resonance Raman spectra from the first π-π* excited state of uracil and 1,3-dideuterouracil. The protocol for this calculation is as follows: (1) The force constant matrix elements in Cartesian coordinate space, the vibrational frequencies, and the minimum energy ground and excited state geometries of the molecule are calculated ab initio using the molecular orbital program Gaussian 92, (2) the force constants in Cartesian coordinates are transformed into force constants in the space of a set of 3N – 6 nonredundant symmetrized internal coordinates, (3) the G matrix is constructed from the energy minimized ground state Cartesian coordinates and the GFL = LΛ eigenvalue equation is solved in internal coordinate space, (4) the elements of the L and L^?1 matrices are calculated, (5) the changes in all of the internal coordinates in going from the ground to the excited state are calculated, and (6) these results are used in combination with the transform theory of resonance Raman scattering to calculate the relative intensities of each of the 3N – 6 vibrations as a function of the exciting laser frequency. There are no adjustable parameters in this calculation, which reproduces the experimental frequencies and intensities with remarkable fidelity. This indicates that the Dushinsky rotation of the modes in the excited state of these molecules is not important and that the simplest form of the transform theory is adequate. © 1995 John Wiley & Sons, Inc.     

基于量子波包方法的态-态分辨反应散射动力学计算

本文回顾了最近十几年利用量子波包方法研究气相分子反应散射动力学的工作进展,特别是在态-态分辨水平上的工作进展。比较详细地讨论了目前存在的利用量子波包方法计算态-态微分截面的几种方法。目前态-态分辨的波包动力学计算可以精确地预测三原子和四原子分子反应散射的各种信息,文章最后对几个典型的利用波包方法在态-态分辨水平上研究过的三原子和四原子反应散射体系做了讨论。