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Stuart C. Althorpe - One of the best experts on this subject based on the ideXlab platform.
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An alternative derivation of ring-polymer molecular dynamics Transition-state theory
Journal of Chemical Physics, 2016Co-Authors: Stuart C. AlthorpeAbstract:In a previous article [T. J. H. Hele and S. C. Althorpe, J. Chem. Phys. 138, 084108 (2013)], we showed that the t → 0+ limit of ring-polymer molecular dynamics (RPMD) rate-theory is also the t → 0+ limit of a new type of Quantum flux-side time-correlation function, in which the dividing surfaces are invariant to imaginary-time translation; in other words, that RPMD Transition-state theory (RMPD-TST) is a t → 0+ Quantum Transition-state theory (QTST). Recently, Jang and Voth [J. Chem. Phys. 144, 084110 (2016)] rederived this Quantum t → 0+ limit and claimed that it gives instead the centroid-density approximation. Here we show that the t → 0+ limit derived by Jang and Voth is in fact RPMD-TST.
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an alternative derivation of ring polymer molecular dynamics Transition state theory
arXiv: Chemical Physics, 2016Co-Authors: Timothy J H Hele, Stuart C. AlthorpeAbstract:In a previous article [J. Chem. Phys. 138, 084108 (2013)], we showed that the $t\to 0_+$ limit of ring-polymer molecular dynamics (RPMD) rate-theory is also the $t\to 0_+$ limit of a new type of Quantum flux-side time-correlation function, in which the dividing surfaces are invariant to imaginary-time translation; in other words, that RPMD Transition-state theory (RPMD-TST) is a $t\to 0_+$ Quantum Transition-state theory (QTST). Recently, Jang and Voth [J. Chem. Phys. 144, 084110 (2016)] rederived this Quantum $t\to 0_+$ limit, and claimed that it gives instead the centroid-density approximation. Here we show that the $t\to 0_+$ limit derived by Jang and Voth is in fact RPMD-TST.
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shallow tunnelling correction factor for use with wigner eyring Transition state theory
Physical Chemistry Chemical Physics, 2014Co-Authors: Yanchuan Zhang, Judith B Rommel, Marko T Cvitas, Stuart C. AlthorpeAbstract:We obtain a shallow-tunnelling correction factor for use with Wigner–Eyring Transition-state theory (TST). Our starting point is Quantum Transition state theory (QTST), which approximates the accurate Quantum rate as the instantaneous flux through a delocalised Transition-state ensemble of ring-polymers. Expanding the ring-polymer potential to second order gives the well-known Wigner tunnelling-factor which diverges at the cross-over temperature between deep and shallow tunnelling. Here, we show how to remove this divergence by integrating numerically over the two softest ring-polymer normal modes. This results in a modified Wigner correction factor involving a one-dimensional integral evaluated along a straight line on the potential energy surface. Comparisons with accurate Quantum calculations indicate that the newly derived correction factor gives realistic estimates of Quantum rate coefficients in the shallow-tunnelling regime.
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derivation of a true t 0 Quantum Transition state theory ii recovery of the exact Quantum rate in the absence of recrossing
Journal of Chemical Physics, 2013Co-Authors: Stuart C. Althorpe, Timothy J H HeleAbstract:In Paper I [T. J. H. Hele and S. C. Althorpe, J. Chem. Phys. 138, 084108 (2013)]10.1063/1.4792697 we derived a Quantum Transition-state theory (TST) by taking the t → 0+ limit of a new form of Quantum flux-side time-correlation function containing a ring-polymer dividing surface. This t → 0+ limit appears to be unique in giving positive-definite Boltzmann statistics, and is identical to ring-polymer molecular dynamics (RPMD) TST. Here, we show that Quantum TST (i.e., RPMD-TST) is exact if there is no recrossing (by the real-time Quantum dynamics) of the ring-polymer dividing surface, nor of any surface orthogonal to it in the space describing fluctuations in the polymer-bead positions along the reaction coordinate. In practice, this means that RPMD-TST gives a good approximation to the exact Quantum rate for direct reactions, provided the temperature is not too far below the cross-over to deep tunnelling. We derive these results by comparing the t → ∞ limit of the ring-polymer flux-side time-correlation f...
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derivation of a true t 0 Quantum Transition state theory ii recovery of the exact Quantum rate in the absence of recrossing
Journal of Chemical Physics, 2013Co-Authors: Stuart C. Althorpe, Timothy J H HeleAbstract:In Paper I [T. J. H. Hele and S. C. Althorpe, J. Chem. Phys. 138, 084108 (2013)] we derived a Quantum Transition-state theory (TST) by taking the t → 0+ limit of a new form of Quantum flux-side time-correlation function containing a ring-polymer dividing surface. This t → 0+ limit appears to be unique in giving positive-definite Boltzmann statistics, and is identical to ring-polymer molecular dynamics (RPMD) TST. Here, we show that Quantum TST (i.e., RPMD-TST) is exact if there is no recrossing (by the real-time Quantum dynamics) of the ring-polymer dividing surface, nor of any surface orthogonal to it in the space describing fluctuations in the polymer-bead positions along the reaction coordinate. In practice, this means that RPMD-TST gives a good approximation to the exact Quantum rate for direct reactions, provided the temperature is not too far below the cross-over to deep tunnelling. We derive these results by comparing the t → ∞ limit of the ring-polymer flux-side time-correlation function with that of a hybrid flux-side time-correlation function (containing a ring-polymer flux operator and a Miller-Schwarz-Tromp side function), and by representing the resulting ring-polymer momentum integrals as hypercubes. Together with Paper I, the results of this article validate a large number of RPMD calculations of reaction rates.
Uwe Manthe - One of the best experts on this subject based on the ideXlab platform.
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full dimensional Quantum dynamics calculations for h chd3 h2 cd3 the effect of multiple vibrational excitations
Journal of Chemical Physics, 2018Co-Authors: Roman Ellerbrock, Uwe MantheAbstract:Initial state-selected reaction probabilities for the H + CHD3 → H2 + CD3 reaction starting from various different ro-vibrational states of CHD3 are studied by accurate full-dimensional (12D) Quantum dynamics calculation for vanishing total angular momentum (J = 0). The calculations employ the Quantum Transition state concept and the multi-layer multi-configurational time-dependent Hartree approach. First results focusing on fundamental excitations and the reactivity borrowing effect were communicated recently [R. Ellerbrock and U. Manthe, J. Chem. Phys. 147, 241104 (2017)]. In the present work, all vibrational states of the methane reactant are considered. It is found that energy deposited in overtones and combination bands is less efficient in promoting reactivity than expected from separable or sudden models. Furthermore, the effects of rotational excitation on the reactivity are studied in detail.
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communication reactivity borrowing in the mode selective chemistry of h chd3 h2 cd3
Journal of Chemical Physics, 2017Co-Authors: Roman Ellerbrock, Uwe MantheAbstract:Quantum state-resolved reaction probabilities for the H + CHD3 → H2 + CD3 reaction are calculated by accurate full-dimensional Quantum dynamics calculations using the multi-layer multi-configurational time-dependent Hartree approach and the Quantum Transition state concept. Reaction probabilities of various ro-vibrational states of the CHD3 reactant are investigated for vanishing total angular momentum. While the reactivity of the different vibrational states of CHD3 mostly follows intuitive patterns, an unusually large reaction probability is found for CHD3 molecules triply excited in the CD3 umbrella-bending vibration. This surprising reactivity can be explained by a Fermi resonance-type mixing of the single CH-stretch excited and the triple CD3 umbrella-bend excited vibrational states of CHD3. These findings show that resonant energy transfer can significantly affect the mode-selective chemistry of CHD3 and result in counter-intuitive reactivity patterns.
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s matrix decomposition natural reaction channels and the Quantum Transition state approach to reactive scattering
Journal of Chemical Physics, 2016Co-Authors: Uwe Manthe, Roman EllerbrockAbstract:A new approach for the Quantum-state resolved analysis of polyatomic reactions is introduced. Based on the singular value decomposition of the S-matrix, energy-dependent natural reaction channels and natural reaction probabilities are defined. It is shown that the natural reaction probabilities are equal to the eigenvalues of the reaction probability operator [U. Manthe and W. H. Miller, J. Chem. Phys. 99, 3411 (1993)]. Consequently, the natural reaction channels can be interpreted as uniquely defined pathways through the Transition state of the reaction. The analysis can efficiently be combined with reactive scattering calculations based on the propagation of thermal flux eigenstates. In contrast to a decomposition based straightforwardly on thermal flux eigenstates, it does not depend on the choice of the dividing surface separating reactants from products. The new approach is illustrated studying a prototypical example, the H + CH4 → H2 + CH3 reaction. The natural reaction probabilities and the contributions of the different vibrational states of the methyl product to the natural reaction channels are calculated and discussed. The relation between the thermal flux eigenstates and the natural reaction channels is studied in detail.
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loss of memory in h ch4 h2 ch3 state to state reactive scattering
Journal of Physical Chemistry Letters, 2015Co-Authors: Ralph Welsch, Uwe MantheAbstract:State-to-state reaction probabilities for the H + CH4→ H2 + CH3 reaction are calculated by accurate full-dimensional Quantum dynamics calculations employing the multilayer multiconfigurational time-dependent Hartree approach and the Quantum Transition-state concept. Reactions starting from different vibrational and rotational states of the methane reactant are investigated for vanishing total angular momentum. The vibrational state distributions of the products are found to be essentially independent of the initial rovibrational state of the reactants. The reaction products only show vibrational excitation in the methyl umbrella mode. No excitation in H2 vibration or another CH3 vibration is observed. Analyzing the results, the observed loss of vibrational memory can be explained by a Transition-state-based view of the reaction process.
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communication ro vibrational control of chemical reactivity in h ch4 h2 ch3 full dimensional Quantum dynamics calculations and a sudden model
Journal of Chemical Physics, 2014Co-Authors: Ralph Welsch, Uwe MantheAbstract:The mode-selective chemistry of the title reaction is studied by full-dimensional Quantum dynamics simulation on an accurate ab initio potential energy surface for vanishing total angular momentum. Using a rigorous Transition state based approach and multi-configurational time-dependent Hartree wave packet propagation, initial state-selected reaction probabilities for many ro-vibrational states of methane are calculated. The theoretical results are compared with experimental trends seen in reactions of methane. An intuitive interpretation of the ro-vibrational control of the chemical reactivity provided by a sudden model based on the Quantum Transition state concept is discussed.
Timothy J H Hele - One of the best experts on this subject based on the ideXlab platform.
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thermal Quantum time correlation functions from classical like dynamics
Molecular Physics, 2017Co-Authors: Timothy J H HeleAbstract:ABSTRACTThermal Quantum time-correlation functions are of fundamental importance in Quantum dynamics, allowing experimentally measurable properties such as reaction rates, diffusion constants and vibrational spectra to be computed from first principles. Since the exact Quantum solution scales exponentially with system size, there has been considerable effort in formulating reliable linear-scaling methods involving exact Quantum statistics and approximate Quantum dynamics modelled with classical-like trajectories. Here, we review recent progress in the field with the development of methods including centroid molecular dynamics , ring polymer molecular dynamics (RPMD) and thermostatted RPMD (TRPMD). We show how these methods have recently been obtained from ‘Matsubara dynamics’, a form of semiclassical dynamics which conserves the Quantum Boltzmann distribution. We also apply the Matsubara formalism to reaction rate theory, rederiving t → 0+ Quantum Transition-state theory (QTST) and showing that Matsubara-...
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an alternative derivation of ring polymer molecular dynamics Transition state theory
arXiv: Chemical Physics, 2016Co-Authors: Timothy J H Hele, Stuart C. AlthorpeAbstract:In a previous article [J. Chem. Phys. 138, 084108 (2013)], we showed that the $t\to 0_+$ limit of ring-polymer molecular dynamics (RPMD) rate-theory is also the $t\to 0_+$ limit of a new type of Quantum flux-side time-correlation function, in which the dividing surfaces are invariant to imaginary-time translation; in other words, that RPMD Transition-state theory (RPMD-TST) is a $t\to 0_+$ Quantum Transition-state theory (QTST). Recently, Jang and Voth [J. Chem. Phys. 144, 084110 (2016)] rederived this Quantum $t\to 0_+$ limit, and claimed that it gives instead the centroid-density approximation. Here we show that the $t\to 0_+$ limit derived by Jang and Voth is in fact RPMD-TST.
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derivation of a true t 0 Quantum Transition state theory ii recovery of the exact Quantum rate in the absence of recrossing
Journal of Chemical Physics, 2013Co-Authors: Stuart C. Althorpe, Timothy J H HeleAbstract:In Paper I [T. J. H. Hele and S. C. Althorpe, J. Chem. Phys. 138, 084108 (2013)]10.1063/1.4792697 we derived a Quantum Transition-state theory (TST) by taking the t → 0+ limit of a new form of Quantum flux-side time-correlation function containing a ring-polymer dividing surface. This t → 0+ limit appears to be unique in giving positive-definite Boltzmann statistics, and is identical to ring-polymer molecular dynamics (RPMD) TST. Here, we show that Quantum TST (i.e., RPMD-TST) is exact if there is no recrossing (by the real-time Quantum dynamics) of the ring-polymer dividing surface, nor of any surface orthogonal to it in the space describing fluctuations in the polymer-bead positions along the reaction coordinate. In practice, this means that RPMD-TST gives a good approximation to the exact Quantum rate for direct reactions, provided the temperature is not too far below the cross-over to deep tunnelling. We derive these results by comparing the t → ∞ limit of the ring-polymer flux-side time-correlation f...
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derivation of a true t 0 Quantum Transition state theory ii recovery of the exact Quantum rate in the absence of recrossing
Journal of Chemical Physics, 2013Co-Authors: Stuart C. Althorpe, Timothy J H HeleAbstract:In Paper I [T. J. H. Hele and S. C. Althorpe, J. Chem. Phys. 138, 084108 (2013)] we derived a Quantum Transition-state theory (TST) by taking the t → 0+ limit of a new form of Quantum flux-side time-correlation function containing a ring-polymer dividing surface. This t → 0+ limit appears to be unique in giving positive-definite Boltzmann statistics, and is identical to ring-polymer molecular dynamics (RPMD) TST. Here, we show that Quantum TST (i.e., RPMD-TST) is exact if there is no recrossing (by the real-time Quantum dynamics) of the ring-polymer dividing surface, nor of any surface orthogonal to it in the space describing fluctuations in the polymer-bead positions along the reaction coordinate. In practice, this means that RPMD-TST gives a good approximation to the exact Quantum rate for direct reactions, provided the temperature is not too far below the cross-over to deep tunnelling. We derive these results by comparing the t → ∞ limit of the ring-polymer flux-side time-correlation function with that of a hybrid flux-side time-correlation function (containing a ring-polymer flux operator and a Miller-Schwarz-Tromp side function), and by representing the resulting ring-polymer momentum integrals as hypercubes. Together with Paper I, the results of this article validate a large number of RPMD calculations of reaction rates.
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on the uniqueness of t 0 Quantum Transition state theory
Journal of Chemical Physics, 2013Co-Authors: Timothy J H Hele, Stuart C. AlthorpeAbstract:It was shown recently that there exists a true Quantum Transition-state theory (QTST) corresponding to the t → 0+ limit of a (new form of) Quantum flux-side time-correlation function. Remarkably, this QTST is identical to ring-polymer molecular dynamics (RPMD) TST. Here, we provide evidence which suggests very strongly that this QTST (≡ RPMD-TST) is unique, in the sense that the t → 0+ limit of any other flux-side time-correlation function gives either non-positive-definite Quantum statistics or zero. We introduce a generalized flux-side time-correlation function which includes all other (known) flux-side time-correlation functions as special limiting cases. We find that the only non-zero t → 0+ limit of this function that contains positive-definite Quantum statistics is RPMD-TST.
Jeremy O Richardson - One of the best experts on this subject based on the ideXlab platform.
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nonadiabatic Quantum Transition state theory in the golden rule limit ii overcoming the pitfalls of the saddle point and semiclassical approximations
Journal of Chemical Physics, 2019Co-Authors: Wei Fang, Manish Thapa, Jeremy O RichardsonAbstract:We describe a path-integral molecular dynamics implementation of our recently developed golden-rule Quantum Transition-state theory (GR-QTST). The method is applied to compute the reaction rate in various models of electron transfer and benchmarked against the exact results. We demonstrate that for systems exhibiting two or more Transition states, rates computed using Wolynes theory [P. G. Wolynes, J. Chem. Phys. 87, 6559 (1987)] can be overestimated by orders of magnitude, whereas the GR-QTST predictions are numerically accurate. This is the case both at low temperature, where nuclear tunneling makes a considerable contribution, and also in the classical limit, where only GR-QTST rigorously tends to the correct result. Analysis shows that the saddle-point approximation employed by Wolynes theory is not valid in this case, which results in the predictions of unphysical reaction pathways, while the energy constraint employed by GR-QTST resolves this problem. The GR-QTST method is also seen to give accurate results for a strongly anharmonic system by sampling configurations around the instanton pathway without making the semiclassical approximation. These promising results indicate that the GR-QTST method could be an efficient and accurate approach for simulating electron-transfer reactions in complex molecular systems.We describe a path-integral molecular dynamics implementation of our recently developed golden-rule Quantum Transition-state theory (GR-QTST). The method is applied to compute the reaction rate in various models of electron transfer and benchmarked against the exact results. We demonstrate that for systems exhibiting two or more Transition states, rates computed using Wolynes theory [P. G. Wolynes, J. Chem. Phys. 87, 6559 (1987)] can be overestimated by orders of magnitude, whereas the GR-QTST predictions are numerically accurate. This is the case both at low temperature, where nuclear tunneling makes a considerable contribution, and also in the classical limit, where only GR-QTST rigorously tends to the correct result. Analysis shows that the saddle-point approximation employed by Wolynes theory is not valid in this case, which results in the predictions of unphysical reaction pathways, while the energy constraint employed by GR-QTST resolves this problem. The GR-QTST method is also seen to give accurate...
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nonadiabatic Quantum Transition state theory in the golden rule limit ii overcoming the pitfalls of the saddle point and semiclassical approximations
Journal of Chemical Physics, 2019Co-Authors: Wei Fang, Manish J Thapa, Jeremy O RichardsonAbstract:We describe a path-integral molecular dynamics implementation of our recently developed golden-rule Quantum Transition-state theory (GR-QTST). The method is applied to compute the reaction rate in various models of electron transfer and benchmarked against the exact results. We demonstrate that for systems exhibiting two or more Transition states, rates computed using Wolynes theory [P. G. Wolynes, J. Chem. Phys. 87, 6559 (1987)] can be overestimated by orders of magnitude, whereas the GR-QTST predictions are numerically accurate. This is the case both at low temperature, where nuclear tunneling makes a considerable contribution, and also in the classical limit, where only GR-QTST rigorously tends to the correct result. Analysis shows that the saddle-point approximation employed by Wolynes theory is not valid in this case, which results in the predictions of unphysical reaction pathways, while the energy constraint employed by GR-QTST resolves this problem. The GR-QTST method is also seen to give accurate results for a strongly anharmonic system by sampling configurations around the instanton pathway without making the semiclassical approximation. These promising results indicate that the GR-QTST method could be an efficient and accurate approach for simulating electron-transfer reactions in complex molecular systems.
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nonadiabatic Quantum Transition state theory in the golden rule limit ii overcoming the pitfalls of the saddle point and semiclassical approximations
arXiv: Chemical Physics, 2019Co-Authors: Wei Fang, Manish J Thapa, Jeremy O RichardsonAbstract:We describe a path-integral molecular dynamics implementation of our recently developed golden-rule Quantum Transition-state theory (GR-QTST). The method is applied to compute the reaction rate in various models of electron transfer and benchmarked against exact results. We demonstrate that for systems exhibiting two or more Transition states, rates computed using Wolynes theory [P. G. Wolynes, J.\ Chem.\ Phys.\ 87, 6559 (1987)] can be overestimated by orders of magnitude, whereas the GR-QTST predictions are numerically accurate. This is the case both at low temperature, where nuclear tunneling makes a considerable contribution, and also in the classical limit, where only GR-QTST rigorously tends to the correct result. Analysis shows that the saddle-point approximation employed by Wolynes theory is not valid in this case, which results in predictions of unphysical reaction pathways, whilst the energy constraint employed by GR-QTST resolves this problem. The GR-QTST method is also seen to give accurate results for a strongly anharmonic system by sampling configurations around the instanton pathway without making the semiclassical approximation. These promising results indicate that the GR-QTST method could be an efficient and accurate approach for simulating electron-transfer reactions in complex molecular systems.
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nonadiabatic Quantum Transition state theory in the golden rule limit i theory and application to model systems
Journal of Chemical Physics, 2019Co-Authors: Manish Thapa, Wei Fang, Jeremy O RichardsonAbstract:We propose a new Quantum Transition-state theory for calculating Fermi’s golden-rule rates in complex multidimensional systems. This method is able to account for the nuclear Quantum effects of delocalization, zero-point energy, and tunneling in an electron-transfer reaction. It is related to instanton theory but can be computed by path-integral sampling and is thus applicable to treat molecular reactions in solution. A constraint functional based on energy conservation is introduced which ensures that the dominant paths contributing to the reaction rate are sampled. We prove that the theory gives exact results for a system of crossed linear potentials and show numerically that it is also accurate for anharmonic systems. There is still a certain amount of freedom available in generalizing the method to multidimensional systems, and the suggestion we make here is exact in the classical limit but not rigorously size consistent in general. It is nonetheless seen to perform well for multidimensional spin-boson models, where it even gives good predictions for rates in the Marcus inverted regime.We propose a new Quantum Transition-state theory for calculating Fermi’s golden-rule rates in complex multidimensional systems. This method is able to account for the nuclear Quantum effects of delocalization, zero-point energy, and tunneling in an electron-transfer reaction. It is related to instanton theory but can be computed by path-integral sampling and is thus applicable to treat molecular reactions in solution. A constraint functional based on energy conservation is introduced which ensures that the dominant paths contributing to the reaction rate are sampled. We prove that the theory gives exact results for a system of crossed linear potentials and show numerically that it is also accurate for anharmonic systems. There is still a certain amount of freedom available in generalizing the method to multidimensional systems, and the suggestion we make here is exact in the classical limit but not rigorously size consistent in general. It is nonetheless seen to perform well for multidimensional spin-boso...
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nonadiabatic Quantum Transition state theory in the golden rule limit i theory and application to model systems
arXiv: Chemical Physics, 2018Co-Authors: Manish J Thapa, Wei Fang, Jeremy O RichardsonAbstract:We propose a new Quantum Transition-state theory for calculating Fermi's golden-rule rates in complex multidimensional systems. This method is able to account for the nuclear Quantum effects of delocalization, zero-point energy and tunnelling in an electron-transfer reaction. It is related to instanton theory but can be computed by path-integral sampling and is thus applicable to treat molecular reactions in solution. A constraint functional based on energy conservation is introduced which ensures that the dominant paths contributing to the reaction rate are sampled. We prove that the theory gives exact results for a system of crossed linear potentials and also the correct classical limit for any system. In numerical tests, the new method is also seen to be accurate for anharmonic systems, and even gives good predictions for rates in the Marcus inverted regime.
Ralph Welsch - One of the best experts on this subject based on the ideXlab platform.
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loss of memory in h ch4 h2 ch3 state to state reactive scattering
Journal of Physical Chemistry Letters, 2015Co-Authors: Ralph Welsch, Uwe MantheAbstract:State-to-state reaction probabilities for the H + CH4→ H2 + CH3 reaction are calculated by accurate full-dimensional Quantum dynamics calculations employing the multilayer multiconfigurational time-dependent Hartree approach and the Quantum Transition-state concept. Reactions starting from different vibrational and rotational states of the methane reactant are investigated for vanishing total angular momentum. The vibrational state distributions of the products are found to be essentially independent of the initial rovibrational state of the reactants. The reaction products only show vibrational excitation in the methyl umbrella mode. No excitation in H2 vibration or another CH3 vibration is observed. Analyzing the results, the observed loss of vibrational memory can be explained by a Transition-state-based view of the reaction process.
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communication ro vibrational control of chemical reactivity in h ch4 h2 ch3 full dimensional Quantum dynamics calculations and a sudden model
Journal of Chemical Physics, 2014Co-Authors: Ralph Welsch, Uwe MantheAbstract:The mode-selective chemistry of the title reaction is studied by full-dimensional Quantum dynamics simulation on an accurate ab initio potential energy surface for vanishing total angular momentum. Using a rigorous Transition state based approach and multi-configurational time-dependent Hartree wave packet propagation, initial state-selected reaction probabilities for many ro-vibrational states of methane are calculated. The theoretical results are compared with experimental trends seen in reactions of methane. An intuitive interpretation of the ro-vibrational control of the chemical reactivity provided by a sudden model based on the Quantum Transition state concept is discussed.
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communication ro vibrational control of chemical reactivity in h ch h ch full dimensional Quantum dynamics calculations and a sudden model
Journal of Chemical Physics, 2014Co-Authors: Ralph Welsch, Uwe MantheAbstract:The mode-selective chemistry of the title reaction is studied by full-dimensional Quantum dynamics simulation on an accurate ab initio potential energy surface for vanishing total angular momentum. Using a rigorous Transition state based approach and multi-configurational time-dependent Hartree wave packet propagation, initial state-selected reaction probabilities for many ro-vibrational states of methane are calculated. The theoretical results are compared with experimental trends seen in reactions of methane. An intuitive interpretation of the ro-vibrational control of the chemical reactivity provided by a sudden model based on the Quantum Transition state concept is discussed.
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correlation functions for fully or partially state resolved reactive scattering calculations
Journal of Chemical Physics, 2014Co-Authors: Uwe Manthe, Ralph WelschAbstract:Flux correlation functions and the Quantum Transition state concept are important tools for the accurate description of polyatomic reaction processes. Combined with the multi-configurational time-dependent Hartree approach, they facilitate rigorous full-dimensional calculations of cumulative and initial-state selected reaction probabilities for six atom reactions. In recent work [R. Welsch, F. Huarte-Larranaga, and U. Manthe, J. Chem. Phys. 136, 064117 (2012)], an approach which allows one to calculate also state-to-state reaction probabilities within the Quantum Transition state concept has been introduced. This article presents further developments. Alternative generalized flux correlation functions are introduced and discussed. Equations for the calculation of fully state-resolved differential cross section using arbitrary definitions of the body fixed frame are derived. An approach for the efficient calculation of partially state-resolved observables as a function of the collision energy is introduced. Finally, numerical test studying the D + H2 reaction illustrate important aspects of the formalism.
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state to state reaction probabilities within the Quantum Transition state framework
Journal of Chemical Physics, 2012Co-Authors: Ralph Welsch, Fermin Huartelarranaga, Uwe MantheAbstract:Rigorous Quantum dynamics calculations of reaction rates and initial state-selected reaction probabilities of polyatomic reactions can be efficiently performed within the Quantum Transition state concept employing flux correlation functions and wave packet propagation utilizing the multi-configurational time-dependent Hartree approach. Here, analytical formulas and a numerical scheme extending this approach to the calculation of state-to-state reaction probabilities are presented. The formulas derived facilitate the use of three different dividing surfaces: two dividing surfaces located in the product and reactant asymptotic region facilitate full state resolution while a third dividing surface placed in the Transition state region can be used to define an additional flux operator. The eigenstates of the corresponding thermal flux operator then correspond to vibrational states of the activated complex. Transforming these states to reactant and product coordinates and propagating them into the respective asymptotic region, the full scattering matrix can be obtained. To illustrate the new approach, test calculations study the D + H(2)(ν, j) → HD(ν', j') + H reaction for J = 0.