Efficient Fourth-Order Split Operator for Solving the Triatomic Reactive Schrödinger Equation in the Time-Dependent Wavepacket Approach

Higher-Order Split Operator Schemes for Solving Tetratomic Reactions Using the Time-Dependent Wave Packet Method

In this work, using the time-dependent quantum wave packet method, quite a few typical higher-order split operators (HOSOs) were for the first time applied to calculate the tetratomic reactive scattering processes in the hyperspherical coordinate. It was found that the HOSOs were hardly efficient for a tetratomic reaction calculation, unlike those for a triatomic reactive scattering calculation. We proposed an efficient HOSO with a force gradient (denoted as 2G1 in the main text) for efficiently and accurately calculating a tetratomic reaction using the quantum wave packet method. Several typical tetratomic reactions, such as H2 + OH, HF + OH, and H2 + OH+, are calculated for demonstrating the effectiveness of the proposed 2G1 in terms of (product state-resolved) reaction probability and inelastic probability, by comparing with the performance of the previously reported various HOSOs. We suggest that the 2G1 propagator could be applied to efficiently calculate a general tetratomic reaction.

Reactant-Product Decoupling Technique Using the Intermediate Coordinate Method

Although the reactant-product decoupling (RPD) technique was proposed over two decades ago, it remains an efficient approach for calculating product state-resolved information on some simple direct reactions using the quantum wave packet method. In the past, usually the RPD technique employed the collocation method to transform the wave function between reactant and product arrangements, which requires quite large computational efforts. In this work, the intermediate coordinate (IC) method is employed to realize the RPD technique. Numerical examples demonstrate that this new IC RPD (IRPD) technique has superior computational efficiency compared with the original method employing the collocation method. Especially, the new IRPD technique significantly saves disk space and computer memory. To illustrate the features of our new method, the total reaction probabilities of the H + H2, H + Br2, and F + H2 reactions with J = 0 and the differential cross sections of the H + H2 and F + H2 reactions at a series of collision energy are calculated and presented. With this efficient and effective new RPD technique, the Li + HF reaction, which involves sharp resonances with long-range wave functions in the van der Waals wells in both the reactant and product arrangements, is also calculated with several J at the product state-resolved level to reveal the ability of the RPD technique for describing resonance wave functions. With these numerical examples, it is found that, for the reaction with resonances, the RPD approach should be applied carefully. Otherwise, it is very possible that the resonances could disappear with the application of the RPD technique.

Interaction-Asymptotic Region Decomposition Method for an Insertion Reaction: Application to the S(1D) + H2 Reaction

With adjusting principal axes hyperspherical (APH) coordinate in the interaction region, and the Jacobi coordinates in the asymptotic regions, an efficient multidomain interaction-asymptotic region decomposition (IARD) method has been developed to solve the "coordinate problem" in a product-state-resolved reactive scattering calculation using the quantum wave packet method. Although the APH coordinate treats with all three channels equally, and is efficient for describing the interaction region for some direct reactions, it is inefficient for describing the insertion-type reaction due to the singularity problem, such as the S(¹D) + H₂ reaction. To deal with this issue, in this work, the channel-dependent Delves hyperspherical (DH) coordinate is proposed to describe the interaction region using the IARD method. The proposed DH-IARD method was applied to calculate the product-state-resolved reaction probabilities of the H + HD reaction, and the differential and integral cross sections of the typical insertion reaction S(¹D) + H₂. It is found that the new DH-IARD method is much more efficient than the previous APH-IARD method for dealing with insertion reactions. The partial wave resonance structures were observed in the integral cross section. It is found that at a low collision energy, the position of the initial wave packet has to be put far away. Otherwise, the partial wave resonance structures could not be correctly reproduced due to the reef well arising with a large total angular momentum J.

High Order Split Operators for the Time-Dependent Wavepacket method of Triatomic Reactive Scattering in Hyperspherical Coordinates

Since the introduction of a series of methods for solving the time-dependent Schrödinger equation (TDSE) in the 80s of the last centry, such as the Fourier transform, the split operator (SO), the Chebyshev polynomial propagator, and complex absorbing potential, investigation of the molecular dynamics within quantum mechanics principle have become popular. In this paper, the application of the time-dependent wave packet (TDWP) method using high-order SO propagators in hyperspherical coordinates for solving triatomic reactive scattering was investigated. The fast sine transform was applied to calculate the derivatives of the wave function of the radial degree of freedom. These high-order SO propagators are examined in different forms, i.e., TVT (Kinetic–Potential–Kinetic) and VTV (Potential–Kinetic–Potential) forms with three typical triatomic reactions, H + H 2, O + O 2 and F + HD. A little difference has been observed among the performances of high-order SO propagators in the TVT and VTV representations in the hyperspherical coordinate. For obtaining total reaction probabilities with 1% error, some of the S class high-order SO propagators, which have symmetric forms, are more efficient than second order SO for reactions involving long lived intermediate states. High order SO propagators are very efficient for obtaining total reaction probabilities.

Time-Dependent Wave Packet Dynamics Calculations of Cross Sections for Ultracold Scattering of Molecules

Because the de Broglie wavelength of ultracold molecules is very large, the cross sections for collisions of molecules at ultracold temperatures are always computed by the time-independent quantum scattering approach. Here, we report the first accurate time-dependent wave packet dynamics calculation for reactive scattering of ultracold molecules. Wave packet dynamics calculations can be applied to molecular systems with more dimensions and provide real-time information on the process of bond rearrangement and/or energy exchange in molecular collisions. Our work thus makes possible the extension of rigorous quantum calculations of ultracold reaction properties to polyatomic molecules and adds a new powerful tool for the study of ultracold chemistry.

Solvent-free synthesis of monodisperse Cu nanoparticles by thermal decomposition of an oleylamine-coordinated Cu oxalate complex

Monodisperse Cu nanoparticles are synthesized via the thermal decomposition of an oleylamine-coordinated Cu oxalate complex in high yield (∼90%).