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Kroes GJ. Computational approaches to dissociative chemisorption on metals: towards chemical accuracy. Phys Chem Chem Phys 2021; 23:8962-9048. [PMID: 33885053 DOI: 10.1039/d1cp00044f] [Citation(s) in RCA: 42] [Impact Index Per Article: 14.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We review the state-of-the-art in the theory of dissociative chemisorption (DC) of small gas phase molecules on metal surfaces, which is important to modeling heterogeneous catalysis for practical reasons, and for achieving an understanding of the wealth of experimental information that exists for this topic, for fundamental reasons. We first give a quick overview of the experimental state of the field. Turning to the theory, we address the challenge that barrier heights (Eb, which are not observables) for DC on metals cannot yet be calculated with chemical accuracy, although embedded correlated wave function theory and diffusion Monte-Carlo are moving in this direction. For benchmarking, at present chemically accurate Eb can only be derived from dynamics calculations based on a semi-empirically derived density functional (DF), by computing a sticking curve and demonstrating that it is shifted from the curve measured in a supersonic beam experiment by no more than 1 kcal mol-1. The approach capable of delivering this accuracy is called the specific reaction parameter (SRP) approach to density functional theory (DFT). SRP-DFT relies on DFT and on dynamics calculations, which are most efficiently performed if a potential energy surface (PES) is available. We therefore present a brief review of the DFs that now exist, also considering their performance on databases for Eb for gas phase reactions and DC on metals, and for adsorption to metals. We also consider expressions for SRP-DFs and briefly discuss other electronic structure methods that have addressed the interaction of molecules with metal surfaces. An overview is presented of dynamical models, which make a distinction as to whether or not, and which dissipative channels are modeled, the dissipative channels being surface phonons and electronically non-adiabatic channels such as electron-hole pair excitation. We also discuss the dynamical methods that have been used, such as the quasi-classical trajectory method and quantum dynamical methods like the time-dependent wave packet method and the reaction path Hamiltonian method. Limits on the accuracy of these methods are discussed for DC of diatomic and polyatomic molecules on metal surfaces, paying particular attention to reduced dimensionality approximations that still have to be invoked in wave packet calculations on polyatomic molecules like CH4. We also address the accuracy of fitting methods, such as recent machine learning methods (like neural network methods) and the corrugation reducing procedure. In discussing the calculation of observables we emphasize the importance of modeling the properties of the supersonic beams in simulating the sticking probability curves measured in the associated experiments. We show that chemically accurate barrier heights have now been extracted for DC in 11 molecule-metal surface systems, some of which form the most accurate core of the only existing database of Eb for DC reactions on metal surfaces (SBH10). The SRP-DFs (or candidate SRP-DFs) that have been derived show transferability in many cases, i.e., they have been shown also to yield chemically accurate Eb for chemically related systems. This can in principle be exploited in simulating rates of catalyzed reactions on nano-particles containing facets and edges, as SRP-DFs may be transferable among systems in which a molecule dissociates on low index and stepped surfaces of the same metal. In many instances SRP-DFs have allowed important conclusions regarding the mechanisms underlying observed experimental trends. An important recent observation is that SRP-DFT based on semi-local exchange DFs has so far only been successful for systems for which the difference of the metal work function and the molecule's electron affinity exceeds 7 eV. A main challenge to SRP-DFT is to extend its applicability to the other systems, which involve a range of important DC reactions of e.g. O2, H2O, NH3, CO2, and CH3OH. Recent calculations employing a PES based on a screened hybrid exchange functional suggest that the road to success may be based on using exchange functionals of this category.
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Affiliation(s)
- Geert-Jan Kroes
- Leiden Institute of Chemistry, Gorlaeus Laboratories, Leiden University, P.O. Box 9502, 2300 RA Leiden, The Netherlands.
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Sathyamurthy N, Mahapatra S. Time-dependent quantum mechanical wave packet dynamics. Phys Chem Chem Phys 2020; 23:7586-7614. [PMID: 33306771 DOI: 10.1039/d0cp03929b] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Starting from a model study of the collinear (H, H2) exchange reaction in 1959, the time-dependent quantum mechanical wave packet (TDQMWP) method has come a long way in dealing with systems as large as Cl + CH4. The fast Fourier transform method for evaluating the second order spatial derivative of the wave function and split-operator method or Chebyshev polynomial expansion for determining the time evolution of the wave function for the system have made the approach highly accurate from a practical point of view. The TDQMWP methodology has been able to predict state-to-state differential and integral reaction cross sections accurately, in agreement with available experimental results for three dimensional (H, H2) collisions, and identify reactive scattering resonances too. It has become a practical computational tool in predicting the observables for many A + BC exchange reactions in three dimensions and a number of larger systems. It is equally amenable to determining the bound and quasi-bound states for a variety of molecular systems. Just as it is able to deal with dissociative processes (without involving basis set expansion), it is able to deal with multi-mode nonadiabatic dynamics in multiple electronic states with equal ease. We present an overview of the method and its strength and limitations, citing examples largely from our own research groups.
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Nihill KJ, Hund ZM, Muzas A, Díaz C, Del Cueto M, Frankcombe T, Plymale NT, Lewis NS, Martín F, Sibener SJ. Experimental and theoretical study of rotationally inelastic diffraction of H2(D2) from methyl-terminated Si(111). J Chem Phys 2016; 145:084705. [PMID: 27586939 DOI: 10.1063/1.4961257] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Fundamental details concerning the interaction between H2 and CH3-Si(111) have been elucidated by the combination of diffractive scattering experiments and electronic structure and scattering calculations. Rotationally inelastic diffraction (RID) of H2 and D2 from this model hydrocarbon-decorated semiconductor interface has been confirmed for the first time via both time-of-flight and diffraction measurements, with modest j = 0 → 2 RID intensities for H2 compared to the strong RID features observed for D2 over a large range of kinematic scattering conditions along two high-symmetry azimuthal directions. The Debye-Waller model was applied to the thermal attenuation of diffraction peaks, allowing for precise determination of the RID probabilities by accounting for incoherent motion of the CH3-Si(111) surface atoms. The probabilities of rotationally inelastic diffraction of H2 and D2 have been quantitatively evaluated as a function of beam energy and scattering angle, and have been compared with complementary electronic structure and scattering calculations to provide insight into the interaction potential between H2 (D2) and hence the surface charge density distribution. Specifically, a six-dimensional potential energy surface (PES), describing the electronic structure of the H2(D2)/CH3-Si(111) system, has been computed based on interpolation of density functional theory energies. Quantum and classical dynamics simulations have allowed for an assessment of the accuracy of the PES, and subsequently for identification of the features of the PES that serve as classical turning points. A close scrutiny of the PES reveals the highly anisotropic character of the interaction potential at these turning points. This combination of experiment and theory provides new and important details about the interaction of H2 with a hybrid organic-semiconductor interface, which can be used to further investigate energy flow in technologically relevant systems.
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Affiliation(s)
- Kevin J Nihill
- The James Franck Institute and Department of Chemistry, The University of Chicago, 929 E. 57th Street, Chicago, Illinois 60637, USA
| | - Zachary M Hund
- The James Franck Institute and Department of Chemistry, The University of Chicago, 929 E. 57th Street, Chicago, Illinois 60637, USA
| | - Alberto Muzas
- Departamento de Química, Módulo 13, Universidad Autónoma de Madrid, 28049 Madrid, Spain
| | - Cristina Díaz
- Departamento de Química, Módulo 13, Universidad Autónoma de Madrid, 28049 Madrid, Spain
| | - Marcos Del Cueto
- Departamento de Química, Módulo 13, Universidad Autónoma de Madrid, 28049 Madrid, Spain
| | - Terry Frankcombe
- School of Physical, Environmental and Mathematical Sciences, University of New South Wales, Canberra ACT 2610, Australia
| | - Noah T Plymale
- Division of Chemistry and Chemical Engineering, Beckman Institute and Kavli Nanoscience Institute, California Institute of Technology, 210 Noyes Laboratory, 127-72, Pasadena, California 91125, USA
| | - Nathan S Lewis
- Division of Chemistry and Chemical Engineering, Beckman Institute and Kavli Nanoscience Institute, California Institute of Technology, 210 Noyes Laboratory, 127-72, Pasadena, California 91125, USA
| | - Fernando Martín
- Departamento de Química, Módulo 13, Universidad Autónoma de Madrid, 28049 Madrid, Spain
| | - S J Sibener
- The James Franck Institute and Department of Chemistry, The University of Chicago, 929 E. 57th Street, Chicago, Illinois 60637, USA
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NEUHAUSER DANIEL, BAER ROI. A TWO-GRID TIME-DEPENDENT FORMALISM FOR THE MAXWELL EQUATION. JOURNAL OF THEORETICAL & COMPUTATIONAL CHEMISTRY 2011. [DOI: 10.1142/s0219633603000781] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
We develop a formalism for efficient iterative solutions of scattering problems involving the Maxwell equations. The methods, borrowed from recent advancements in chemical reaction dynamics, represent the scattering wavefunctions on two grids; one used for the initial wave and is one-dimensional; the other is a small three-dimensional grid padded with absorbing-potentials on which the scattered function is represented. The formalism is automatically suitable for scattering studies of transmission, reflection and scattering components of a wave. The simulations can be done with time-dependent wavepackets or direct iterative solution for the Green's function, but the results are rigorous time-independent (frequency-dependent) scattering amplitudes. Model time-dependent simulations involving up to a 100×100×100 grid for the inner wavefunction were numerically done on a simple PC.
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Affiliation(s)
- DANIEL NEUHAUSER
- Department of Chemistry and Biochemistry, UCLA, Los Angeles, CA 90095-1569, USA
| | - ROI BAER
- Institute of Chemistry, Lisa Meitner Center, Hebrew University of Jerusalem, Jerusalem 91904, Israel
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KROES GEERTJAN, SOMERS MARKF. SIX-DIMENSIONAL DYNAMICS OF DISSOCIATIVE CHEMISORPTION OF H2 ON METAL SURFACES. JOURNAL OF THEORETICAL & COMPUTATIONAL CHEMISTRY 2011. [DOI: 10.1142/s0219633605001647] [Citation(s) in RCA: 73] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
The theory of time-dependent quantum dynamics of dissociative chemisorption of hydrogen on metal surfaces is reviewed, in the framework of electronically adiabatic scattering from static surfaces. Four implementations of the time-dependent wave packet (TDWP) method are discussed. In the direct product pseudo-spectral and the spherical harmonics pseudo-spectral methods, no use is made of the symmetry associated with the surface unit cell. This symmetry is exploited by the symmetry adapted wave packet and the symmetry adapted pseudo-spectral (SAPS) method, which are efficient for scattering at normal incidence. The SAPS method can be employed for potential energy surfaces of general form. Comparison to experiment shows that the TDWP method yields good, but not yet excellent, quantitative accuracy for dissociation of (ν = 0, j = 0) H 2 if the calculations are based on accurately fitted density functional theory calculations that are performed using the generalized gradient approximation. The influence of the molecule's vibration (rotation) is well (reasonably well) described. The theory does not yet yield quantitatively accurate results for rovibrationally inelastic scattering. The theory has helped with the interpretation of existing experimental results, for instance, by solving a parodox regarding the corrugation of Pt(111) as seen by reacting and scattering H 2. The theory has also provided some exciting new predictions, for instance, concerning where on the surface of Cu(100) H2 reacts depending on its vibrational state. Future theoretical studies of H 2 reacting on metal surfaces will likely be aimed at validating GGAs for molecule-surface interactions, and understanding trends in collisions of H 2 with complex metal surfaces.
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Affiliation(s)
- GEERT-JAN KROES
- Leiden Institute of Chemistry, Gorlaeus Laboratories, Leiden, University, P. O. Box 9502, 2300 RA Leiden, The Netherlands
| | - MARK F. SOMERS
- Leiden Institute of Chemistry, Gorlaeus Laboratories, Leiden, University, P. O. Box 9502, 2300 RA Leiden, The Netherlands
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Korolkov MV, Manz J, Schild A. The Cl + H2 --> HCl + H reaction induced by IR + UV irradiation of Cl2 in solid para-H2: quantum model simulation. J Phys Chem A 2009; 113:7630-46. [PMID: 19378981 DOI: 10.1021/jp9003455] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Recent experimental investigations by the group of D. T. Anderson (Kettwich, S. C.; Raston, P. L.; Anderson, D. T. J. Phys. Chem. A 2009, 113, DOI 10.1021/jp811206a) show that the reaction Cl + H(2) --> HCl + H in the para-H(2) crystal can be induced by infrared (IR) + ultraviolet (UV) coirradiations causing vibrational pre-excitation of the molecular reactant, H(2)(v=1), and generation of the atomic reactant, Cl((2)P(3/2)), by near-resonant photodissociation of a matrix-isolated Cl(2) molecule in the C (1)Pi(u) state, respectively. The corresponding reaction probability P(v=1) for the reactants Cl + H(2)(v=1) is approximately 0.15; this is approximately 25 times larger than P(v=0) for Cl + H(2)(v=0) (as initiated by pure UV irradiation). We present a simple three-step quantum model which accounts for some important parts of the experimental results and allows predictions for other scenarios, for example, UV photodissociation of the Cl(2) molecule by a laser pulse. The first step, vibrational pre-excitation of H(2), yields the molecular initial state which is described using the Einstein model of the para-H(2) crystal. The second step, photodissociation of Cl(2), generates the Cl((2)P(3/2)) atom approaching H(2)(v=1). In the third step, Cl reacts with H(2)(v=1) much more efficiently than with H(2)(v=0) close to threshold. The ultrashort time domains (approximately 100 fs) of steps 2 plus 3 support one- and then two-dimensional models of photodissociation of Cl(2) by short laser pulses and of the subsequent reaction of the system Cl-H-H embedded in frozen environments. The widths of the corresponding wave function describing the translational motion of the reactants is revealed as a significant parameter which is determined not only by the duration of the laser pulse but, even more importantly, by the width of the Gaussian-type distribution of the center of mass of the H(2) molecule in its Einstein cell. As a consequence, the resulting P(v) are quite robust versus variations of the UV pulse durations, allowing extrapolations to continuous wave irradiation. Quantum dynamics simulations of the reaction reveal that the experimental results are due to energetic and dynamical effects.
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Affiliation(s)
- M V Korolkov
- Institut für Chemie and Biochemie, Freie Universität Berlin, 14195 Berlin, Germany
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Ndong M, Tal-Ezer H, Kosloff R, Koch CP. A Chebychev propagator for inhomogeneous Schrödinger equations. J Chem Phys 2009; 130:124108. [DOI: 10.1063/1.3098940] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Crespos C, Meyer HD, Mowrey RC, Kroes GJ. Multiconfiguration time-dependent Hartree method applied to molecular dissociation on surfaces: H2+Pt(111). J Chem Phys 2006; 124:74706. [PMID: 16497069 DOI: 10.1063/1.2171246] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Four-dimensional quantum dynamics calculations are performed on the dissociative chemisorption of H(2) on Pt(111) using the multiconfiguration time-dependent Hartree method. The aim of this work is to study the performance of the multiconfiguration time-dependent Hartree method for a gas-surface reaction by comparison with the standard time-dependent wave-packet propagation method. The initial-state resolved dissociation probability of H(2) is calculated within two four-dimensional models. The first four-dimensional model treats explicitly the rotational motion of the molecule and the H(2) dissociation is studied above two different sites of the Pt(111). For this model, only a potential-energy surface of general form was available. This potential was refitted to a sum of product form to allow efficient calculations with the multiconfiguration time-dependent Hartree method. The second model focuses on the description of the center-of-mass motion parallel to the surface, the rotational motion of the molecule being frozen. These four-dimensional quantum dynamics calculations yield important insights which can help with performing full six-dimensional calculations on H(2) dissociating on Pt(111). The multiconfiguration time-dependent Hartree method is shown to be particularly efficient for computing initial-state selective dissociation probabilities for the system studied, with a good accuracy and a reduced amount of memory and computational time when compared to the standard time-dependent wave-packet method.
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Affiliation(s)
- C Crespos
- Laboratoire de Physico-Chimie Moléculaire, UMR 5803 CNRS, Université Bordeaux 1, 351 Course de la Liberation, Talence, France.
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van Harrevelt R, Manthe U. Off-normal incidence dissociative sticking of H2 on Cu(100) studied using six-dimensional quantum calculations. J Chem Phys 2005; 123:124706. [PMID: 16392510 DOI: 10.1063/1.2043027] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Six-dimensional quantum calculations of the sticking probability for H2 hitting a Cu(100) surface with off-normal incidence are presented. The multiconfiguration time-dependent Hartree approach is employed for an efficient wave-packet propagation. The sticking probability is calculated for different initial momenta parallel to the surface. In contrast with the picture described in the literature, the sticking probability was found to depend on the parallel momentum. The results are explained by the topology of the potential-energy surface, which shows significant corrugation with a moderate variation of the barrier height with the surface site.
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Affiliation(s)
- Rob van Harrevelt
- Theoretische Chemie, Universität Bielefeld, Postfach 100131, D-33501 Bielefeld, Germany.
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van Harrevelt R, Manthe U. Degeneracy in discrete variable representations: General considerations and application to the multiconfigurational time-dependent Hartree approach. J Chem Phys 2004; 121:5623-8. [PMID: 15366985 DOI: 10.1063/1.1782811] [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
Problems appear in discrete variable representations (DVRs) based on general basis sets when the coordinate matrix has degenerate eigenvalues. Then the DVR is not uniquely defined. This paper shows that this problem can be caused by symmetry. Taking the symmetry into account when constructing the DVR solves the problem. The symmetry effect can be particularly important for the time-dependent DVR used in multiconfigurational time-dependent Hartree calculations employing the correlation DVR (CDVR) approach. Problems reported previously for the initial-state selected treatment of the H+H(2) reaction can be attributed to this symmetry effect. They can be solved by using a symmetry-adapted approach to construct the time-dependent DVR. Thus, the present paper shows that the CDVR scheme can be employed also in initial-state selected scattering calculations if the symmetry of the system is properly taken into account in the construction of the time-dependent DVR.
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Affiliation(s)
- Rob van Harrevelt
- Technische Universität München, Lichtenbergstrasse 4, 85747 Garching, Germany
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Somers M, Lemoine D, Kroes G. Performance and application of a symmetry adapted pseudo spectral method for scattering of a diatomic molecule from a square surface: H2+Cu(100). Chem Phys 2004. [DOI: 10.1016/j.chemphys.2004.06.011] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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van Harrevelt R, Manthe U. Multiconfigurational time-dependent Hartree calculations for dissociative adsorption of H2 on Cu(100). J Chem Phys 2004; 121:3829-35. [PMID: 15303951 DOI: 10.1063/1.1775785] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The efficiency of the multiconfigurational time-dependent Hartree (MCTDH) method for calculating the initial-state selected dissociation probability of H(2)(v=0,j=0) on Cu(100) is investigated. The MCTDH method is shown to be significantly more efficient than standard wave packet methods. A large number of single-particle functions is required to converge the initial-state selected reaction probability for dissociative adsorption. Employing multidimensional coordinates in the MCTDH ansatz (mode combination) is found to be crucial for the efficiency of these MCTDH calculations. Perspectives towards the application of the MCTDH approach to study dissociative adsorption of polyatomic molecules on surfaces are discussed.
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Affiliation(s)
- Rob van Harrevelt
- Theoretische Chemie, Technische Universitat Munchen, Lichtenbergstrasse 4, 85747 Garching, Germany
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van Harrevelt R, van Hemert MC, Schatz GC. The CH+H reaction studied with quantum-mechanical and classical trajectory calculations. J Chem Phys 2002. [DOI: 10.1063/1.1459416] [Citation(s) in RCA: 31] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022] Open
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Affiliation(s)
- Erasmo Buonomo
- Department of Chemistry, University College London, 20 Gordon Street, London, WC1H 0AJ, U.K
| | - David C. Clary
- Department of Chemistry, University College London, 20 Gordon Street, London, WC1H 0AJ, U.K
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Skokov S, Bowman JM. State-to-State Reactive Scattering via Real L2 Wave Packet Propagation for Reduced Dimensionality AB + CD Reactions. J Phys Chem A 2000. [DOI: 10.1021/jp0022151] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Sergei Skokov
- Department of Chemistry and Cherry L. Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322
| | - Joel M. Bowman
- Department of Chemistry and Cherry L. Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322
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Skokov S, Bowman JM. A reduced dimensionality quantum calculation of the reaction of H2 with diamond (111) surface. J Chem Phys 2000. [DOI: 10.1063/1.481852] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Meijer AJ, Goldfield EM, Gray SK, Balint-Kurti GG. Flux analysis for calculating reaction probabilities with real wave packets. Chem Phys Lett 1998. [DOI: 10.1016/s0009-2614(98)00743-x] [Citation(s) in RCA: 112] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/16/2022]
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Kroes GJ, Snijders JG, Mowrey RC. Performance of close‐coupled wave packet methods for molecule‐corrugated surface scattering. J Chem Phys 1995. [DOI: 10.1063/1.470599] [Citation(s) in RCA: 27] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Moiseyev N. Cumulative reaction probability from time independent scattering theory. J Chem Phys 1995. [DOI: 10.1063/1.470484] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022] Open
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Mowrey RC, Kroes GJ. Application of an efficient asymptotic analysis method to molecule–surface scattering. J Chem Phys 1995. [DOI: 10.1063/1.469831] [Citation(s) in RCA: 46] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Katz G, Baer R, Kosloff R. A new method for numerical flux calculations in quantum molecular dynamics. Chem Phys Lett 1995. [DOI: 10.1016/0009-2614(95)00499-t] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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Wall MR, Neuhauser D. Extraction, through filter‐diagonalization, of general quantum eigenvalues or classical normal mode frequencies from a small number of residues or a short‐time segment of a signal. I. Theory and application to a quantum‐dynamics model. J Chem Phys 1995. [DOI: 10.1063/1.468999] [Citation(s) in RCA: 463] [Impact Index Per Article: 16.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Mandelshtam VA, Taylor HS. Spectral projection approach to the quantum scattering calculations. J Chem Phys 1995. [DOI: 10.1063/1.469051] [Citation(s) in RCA: 271] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Kroes GJ, Snijders JG, Mowrey RC. Performance of a fully close‐coupled wave packet method for the H2+LiF(001) model problem. J Chem Phys 1995. [DOI: 10.1063/1.469281] [Citation(s) in RCA: 30] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Makarov AA, Taylor HS, Pont M. Application of the scrL2 box-stabilization method to time-periodic systems. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1994; 50:3276-3284. [PMID: 9911274 DOI: 10.1103/physreva.50.3276] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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