Accurate Quantum Dynamics Study on the Resonance Decay of Vinylidene

Abstract

Hydrogen (H) migration/proton transfer is widely regarded as being of paramount importance in different fields. [1,2] As H migration processes involve hydrogen, the most "quantum" of atoms, quantum dynamical (QD) effects such as tunneling often play a significant role, and the understanding of the nature of these processes thus requires that accurate full-dimensional QD calculations be performed. However, such calculations are very challenging, even for the benchmark vinylidene-acetylene system. Herein, we propose a simple functional form for the isomerization coordinate of 1,2-H migration, and by combining this with a complex absorbing potential and Hamiltonian in Jacobi coordinates, we achieve the first accurate QD calculations of resonance decay (RD) lifetimes of vinylidene, providing a probe to the vibrationally resolved rate of H migration. Our calculational results provide new insights at the quantum-state level, and the findings are important for acquiring a deeper understanding of H migration processes.Vinylidene (H 2 C=C:) is a vital reactive intermediate in the combustion of hydrocarbon. The isomerization between vinylidene and acetylene is an important prototype of intramolecular H migration, and has attracted much attention; [3][4][5][6][7][8][9][10][11][12][13][14][15] however, the key issue related to the lifetime of vinylidene has not been resolved so far. For example, the lifetime of vinylidene was estimated to be 0.04-0.2 ps based on a simulation of line shapes by the Lineberger group using photoelectron spectroscopy of vinylidene anion;[4] while a very long lifetime of at least 3.5 ms was claimed by Vager et al. in their coulomb explosion imaging (CEI) experiments.[5] Approximate QD calculations [7,8,10,15] also yielded lifetimes with large discrepancies. The present QD calculations also make it possible to clarify the inconsistency among previous studies on the lifetime of vinylidene. We use CC-HH Jacobi coordinates (see Figure 1 a) to represent the nuclear motion, and the Hamiltonian with a complex absorbing potential (CAP) can be written as [Eq. (1) In Equation (1),ĵ i (i = 1,2) is the angular momentum operator associated with r i ;ĵ 12 is the vector addition ofĵ 1 andĵ 2 ; and s is the isomerization coordinate. To compute the RD lifetime of vinylidene, the introduction of V CAP is essential. The CAP is a kind of useful theoretical tool, with which the resonance states could be directly computed using methods similar to those for bound-state problems; [16,17] the eigenvalue of a CAP-modified Hamiltonian takes a complex form [Eq. (2)]:

Mode-Specific Tunneling Splittings for a Sequential Double-Hydrogen Transfer Case: An Accurate Quantum Mechanical Scheme

“…In terms of the basis expansion, we separate the basis functions into the inner (r 1 and r 2 ) and outer (θ 1 , θ 2 , ϕ, and r 0 ) groups, and the expression of Hamiltonian matrix elements is given in eq S2 (Supporting Information), resulting in a large, sparse, and well-structured matrix. Herein, the PIST method combined with an optimal separable basis plus Wyatt (OSBW) preconditioner 31,35,36 is employed to solve its eigenvalue problem. To make large-scale computations possible, message passing interface (MPI) is utilized to parallelize the most timeconsuming parts of this scheme, which include the evaluation of Hamiltonian matrix elements, block Jacobi diagonalization and quasi-minimal residual iterations, and very good scalability is achieved.…”

“…The mode-specific isomerization lifetimes obtained in this way are also presented in Table 1, in comparison with the "resonance decay" (RD) lifetimes calculated before. 36 The RD lifetime actually involves an ideal physical model, which presumes that vibrationally highly excited acetylene levels can be dealt with as a quasicontinuum. The computed RD lifetimes thus provide us with useful lower bounds to the realistic isomerization lifetimes.…”

Efficient Quantum Mechanical Calculations of Mode-Specific Tunneling Splittings upon Fundamental Excitation in the Dimer of Formic Acid

“…Total wave function is expanded by the direct product of 1D discrete variable representation (DVR) basis functions where π i kj ( Q k j ) is the 1D DVR basis function for Q k j with a basis size of N k j , and obtained by taking a unitary transformation to the truncated eigenfunctions of a designed 1D effective Hamiltonian. where V ( Q k j ) is the 1D EP. ,, By using the PBFC strategy, we customize the 1D EPs for the H-tunneling process, and several representative 1D EPs used in the present calculations are shown in Figure . In particular, for the Q 1 , Q 9 , and Q 3 SP coordinates, the 1D EP is obtained by following the steepest descending path starting from the SP on 2D ( Q 1 , Q 9 ) (or ( Q 1 , Q 3 )) PES, which are produced by minimizing the potential with all the remaining 22 coordinates; for the other Q i coordinates, the 1D EP is generated from the full-dimensional ab initio PES by minimizing the potential with all the remaining degrees of freedom.…”

Double Proton Transfer in the Dimer of Formic Acid: An Efficient Quantum Mechanical Scheme

“…where V ( Q j ) is the 1D EP (Li et al, 2011; Ren et al, 2011; Zhang et al, 2012). The two protons in FAD transfer between the two equivalent wells results in ground-state tunneling splitting (Figure 1), and in normal coordinates at the saddle point, Q 1 is identified as the proton transfer reaction coordinate as shown in Table 1.…”