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Ma D, Ma J. Full-dimensional quantum mechanical calculations for the tunneling behavior of HOCO dissociation to H + CO 2. Phys Chem Chem Phys 2022; 24:15321-15329. [PMID: 35703166 DOI: 10.1039/d1cp04269f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The tunneling behavior during HOCO dissociation to H + CO2 was investigated by full-dimensional quantum mechanical calculations based on an accurate global potential energy surface. The tunneling lifetimes for the low-lying 1500 vibrational states were calculated using the low-storage filter diagonalization method after a 1 million-step Chebyshev propagation. In the calculated energy range, the lifetimes of different vibrational states with similar energy are found to differ by 3-4 orders of magnitude, and the lower limit for these tunneling lifetimes is consistent with the experimental results reported by Continetti et al. For the given vibrational progressions, the lifetime of the vibrational states decreases with the increasing energy level, which is consistent with the results of 1D simulation calculations reported by Bowman, but the declining curve obviously fluctuates, and the declining slope is significantly different from that obtained by 1D simulation. Due to a difference in the effective barrier width, the mode-specific behavior of the tunneling effect is manifested in that the O-C-O' and H-O-C bend modes lead to the largest enhancement and an inhibitory effect on the tunneling process, respectively.
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Affiliation(s)
- Dandan Ma
- Institute of Atomic and Molecular Physics, Sichuan University, Chengdu, Sichuan, 610065, China.
| | - Jianyi Ma
- Institute of Atomic and Molecular Physics, Sichuan University, Chengdu, Sichuan, 610065, China.
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Wang J, Li J, Ma J, Guo H. Full-dimensional characterization of photoelectron spectra of HOCO−and DOCO−and tunneling facilitated decay of HOCO prepared by anion photodetachment. J Chem Phys 2014; 140:184314. [DOI: 10.1063/1.4874975] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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MANDELSHTAM VLADIMIRA, NEUMAIER ARNOLD. FURTHER GENERALIZATION AND NUMERICAL IMPLEMENTATION OF PSEUDO-TIME SCHRÖDINGER EQUATIONS FOR QUANTUM SCATTERING CALCULATIONS. JOURNAL OF THEORETICAL & COMPUTATIONAL CHEMISTRY 2012. [DOI: 10.1142/s0219633602000142] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
We review and further develop the recently introduced numerical approach [Phys. Rev. Lett. 86, 5031, (2001)] for scattering calculations based on a so called pseudo-time Schrödinger equation, which is in turn a modification of the damped Chebyshev polynomial expansion scheme [J. Chem. Phys. 103, 2903, (1995)]. The method utilizes a special energy-dependent form for the absorbing potential in the time-independent Schrödinger equation, in which the complex energy spectrum is mapped inside the unit disk Ek → uk, where uk are the eigenvalues of some explicitly known sparse matrix U. Most importantly for the numerical implementation, all the physical eigenvalues uk are the extreme eigenvalues of U (i.e. |uk| ≈ 1 for resonances and |uk| = 1 for the bound states), which allows one to extract these eigenvalues very efficiently by harmonic inversion of a pseudo-time autocorrelation function y(t) = ϕ T Ut ϕ using the filter diagonalization method. The computation of y(t) up to time t = 2T requires only T sparse real matrix-vector multiplications. We describe and compare different schemes, effectively corresponding to different choices of the energy-dependent absorbing potential, and test them numerically by calculating resonances of the HCO molecule. Our numerical tests suggest an optimal scheme that provide accurate estimates for most resonance states using a single autocorrelation function.
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Affiliation(s)
| | - ARNOLD NEUMAIER
- Institut für Mathematik, Universität Wien Strudlhofgasse 4, A-1090 Wien, Austria
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Recursive Solutions to Large Eigenproblems in Molecular Spectroscopy and Reaction Dynamics. REVIEWS IN COMPUTATIONAL CHEMISTRY 2007. [DOI: 10.1002/9780470189078.ch7] [Citation(s) in RCA: 49] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/21/2023]
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Lin SY, Xie D, Guo H. Revelation of non-statistical behavior in HO2 vibration by a newab initiopotential energy surface. J Chem Phys 2006; 125:091103. [PMID: 16965065 DOI: 10.1063/1.2349476] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The hydroperoxyl radical (HO2) has long been considered as a prototype for statistical vibrational dynamics. In this work, however, it is shown that the bound state energy levels (up to the dissociation threshold) and low-lying resonances of the HO2 system (J=0) obtained on a new ab initio potential energy surface exhibit surprisingly large regularity. The implications of the non-statistical behavior of the HO2 system in unimolecular and bimolecular reactions are discussed.
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Affiliation(s)
- Shi Ying Lin
- Department of Chemistry, University of New Mexico, Albuquerque, New Mexico 87131, USA
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Zhang H, Smith SC. HO2 Ro-Vibrational Bound-State Calculations for Large Angular Momentum: J = 30, 40, and 50. J Phys Chem A 2006; 110:3246-53. [PMID: 16509649 DOI: 10.1021/jp0582336] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The Lanczos homogeneous filter diagonalization method and the real Chebyshev filter diagonalization scheme incorporating doubling of the autocorrelation functions have been employed to compute the HO2 ro-vibrational states for high total angular momenta, J = 30, 40, and 50. For such computationally challenging calculations, we have adopted a parallel computing strategy to perform the matrix-vector multiplications. Low-lying bound states and high-lying bound states close to the dissociation threshold are reported. For low-lying bound states, a spectroscopic assignment has been attempted and the widely used approximate J-shifting method has been tested for this deep-well system. For high-lying bound states, the attempted spectroscopic assignments as well as the J-shifting approximation fail because of very strong Coriolis mixing, indicating that the Coriolis couplings are important for this system.
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Affiliation(s)
- Hong Zhang
- Centre for Computational Molecular Science, Chemistry Building (#68), The University of Queensland, Qld 4072, Brisbane, Australia
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Zhang H, Smith SC. Unimolecular rovibrational bound and resonance states for large angular momentum: J=20 calculations for HO2. J Chem Phys 2005; 123:014308. [PMID: 16035836 DOI: 10.1063/1.1949609] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We explore the calculation of unimolecular bound states and resonances for deep-well species at large angular momentum using a Chebychev filter diagonalization scheme incorporating doubling of the autocorrelation function as presented recently by Neumaier and Mandelshtam [Phys. Rev. Lett. 86, 5031 (2001)]. The method has been employed to compute the challenging J=20 bound and resonance states for the HO2 system. The methodology has firstly been tested for J=2 in comparison with previous calculations, and then extended to J=20 using a parallel computing strategy. The quantum J-specific unimolecular dissociation rates for HO2-->H+O2 in the energy range from 2.114 to 2.596 eV have been reported for the first time, and comparisons with the results of Troe and co-workers [J. Chem. Phys. 113, 11019 (2000) Phys. Chem. Chem. Phys. 2, 631 (2000)] from statistical adiabatic channel method/classical trajectory calculations have been made. For most of the energies, the reported statistical adiabatic channel method/classical trajectory rate constants agree well with the average of the fluctuating quantum-mechanical rates. Near the dissociation threshold, quantum rates fluctuate more severely, but their average is still in agreement with the statistical adiabatic channel method/classical trajectory results.
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Affiliation(s)
- Hong Zhang
- Centre for Computational Molecular Science, Chemistry Building (No. 68), The University of Queensland, Qld 4072, Brisbane, Australia
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Tremblay JC, Carrington T. Computing resonance energies, widths, and wave functions using a Lanczos method in real arithmetic. J Chem Phys 2005; 122:244107. [PMID: 16035746 DOI: 10.1063/1.1942494] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2023] Open
Abstract
We introduce new ideas for calculating resonance energies and widths. It is shown that a non-Hermitian-Lanczos approach can be used to compute eigenvalues of H+W, where H is the Hamiltonian and W is a complex absorbing potential (CAP), without evaluating complex matrix-vector products. This is done by exploiting the link between a CAP-modified Hamiltonian matrix and a real but nonsymmetric matrix U suggested by Mandelshtam and Neumaier [J. Theor. Comput. Chem. 1, 1 (2002)] and using a coupled-two-term Lanczos procedure. We use approximate resonance eigenvectors obtained from the non-Hermitian-Lanczos algorithm and a very good CAP to obtain very accurate energies and widths without solving eigenvalue problems for many values of the CAP strength parameter and searching for cusps. The method is applied to the resonances of HCO. We compare properties of the method with those of established approaches.
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Lin SY, Guo H, Farantos SC. Resonances of CH2(ãA11) and their roles in unimolecular and bimolecular reactions. J Chem Phys 2005; 122:124308. [PMID: 15836379 DOI: 10.1063/1.1866094] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Low-lying resonances of the CH2(a 1A1) system (J=0) in an accurate ab initio potential energy surface are studied using a filter-diagonalization method. The width of these resonances fluctuates by more than two orders of magnitude and on average increases with the energy. Analysis of the resonance states concludes that the unimolecular decay of the excited molecular system near the dissociation threshold is neither mode specific nor statistical state specific. This is apparently due to remnant regularity embedded in the largely chaotic classical phase space, as evidenced by periodic orbit analysis. As a result, the Rice-Ramsperger-Kassel-Marcus and statistical adiabatic channel models overestimate the average unimolecular decay rate. The implications of the resonances for the bimolecular C(1D)+H2 reaction are also discussed.
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Affiliation(s)
- Shi Ying Lin
- Department of Chemistry, University of New Mexico, Albuquerque, New Mexico 87131, USA
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Zhang H, Smith SC. Converged quantum calculations of HO2 bound states and resonances for J=6 and 10. J Chem Phys 2004; 120:9583-93. [PMID: 15267970 DOI: 10.1063/1.1711811] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Bound and resonance states of HO(2) are calculated quantum mechanically using both the Lanczos homogeneous filter diagonalization method and the real Chebyshev filter diagonalization method for nonzero total angular momentum J=6 and 10, using a parallel computing strategy. For bound states, agreement between the two methods is quite satisfactory; for resonances, while the energies are in good agreement, the widths are in general agreement. The quantum nonzero-J specific unimolecular dissociation rates for HO(2) are also calculated.
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Affiliation(s)
- Hong Zhang
- Centre for Computational Molecular Science, Chemistry Building 68, The University of Queensland, Qld 4072, Brisbane, Australia
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Mussa HY, Tennyson J. Calculating quasi-bound rotation-vibrational states of HOCl using massively parallel computers. Chem Phys Lett 2002. [DOI: 10.1016/s0009-2614(02)01554-3] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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Zhang H, Smith SC. Chebyshev real wave packet propagation: H+O2 (J=0) state-to-state reactive scattering calculations. J Chem Phys 2002. [DOI: 10.1063/1.1499123] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Poirier B, Carrington T. A preconditioned inexact spectral transform method for calculating resonance energies and widths, as applied to HCO. J Chem Phys 2002. [DOI: 10.1063/1.1428752] [Citation(s) in RCA: 71] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Li G, Guo H. Efficient calculation of resonance positions and widths using doubled Chebyshev autocorrelation functions. Chem Phys Lett 2001. [DOI: 10.1016/s0009-2614(01)01045-4] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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Zhang H, Smith SC. A comparison of low-storage strategies for spectral analysis in dissipative systems: filter diagonalisation in the Lanczos representation and harmonic inversion of the Chebychev-order-domain autocorrelation function. Chem Phys Lett 2001. [DOI: 10.1016/s0009-2614(01)01000-4] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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Neumaier A, Mandelshtam VA. Pseudotime Schrödinger equation with absorbing potential for quantum scattering calculations. PHYSICAL REVIEW LETTERS 2001; 86:5031-5034. [PMID: 11384413 DOI: 10.1103/physrevlett.86.5031] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/04/2001] [Indexed: 05/23/2023]
Abstract
The Schrödinger equation (Hpsi) (r) = [E+u(E)W(r)]psi(r) with an energy-dependent complex absorbing potential -u(E)W(r), associated with a scattering system, can be reduced for a special choice of u(E) to a harmonic inversion problem of a discrete pseudotime correlation function y(t) = phi(T)U(t)phi. An efficient formula for Green's function matrix elements is also derived. Since the exact propagation up to time 2t can be done with only approximately t real matrix-vector products, this gives an unprecedently efficient scheme for accurate calculations of quantum spectra for possibly very large systems.
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Affiliation(s)
- A Neumaier
- Institut für Mathematik, Universität Wien Strudlhofgasse 4, A-1090 Wien, Austria.
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