Modified Bond Eigenfunction Method of Constructing Potential Energy Surface of Reaction. II. Application to the Hydrogen Atom-Molecule Reaction

Yasumori, Iwao

doi:10.1246/bcsj.32.1110

Cited by 11 publications

(4 citation statements)

References 23 publications

(1 reference statement)

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“…In Figure 7, we plot the geometry dependence of the Mu + H 2 BODC, relative to the reactant value, along the reaction path; there is a very significant variation in the BODC as one varies the reaction coordinate s, with low values being observed in the region of high reaction path curvature in the entrance channel, a peak of 16.1 meV near the saddle point on the PES, and then a monotonic decrease with values of about 8 meV at the maximum in the v = 0 vibrationally adiabatic potential (Figure 1), and a value of about −2.4 meV at the products. One would expect such a large variation because simple considerations show that the BODC should be largest, where the energy gap between the ground and first excited electronic state is smallest, and this gap is smallest near the saddle point, larger near the variational transition state, and even larger at reactants and products [71][72][73]. Given this large variation, together with the sensitivity of the Mu + H 2 (v = 1) reaction to two disparate regions on the PES, a simple BODC barrier correction approximation for the Mu + H 2 (v = 1) reaction is invalid.…”

Section: Quantitative Assessmentsmentioning

confidence: 99%

Zero-point energy, tunnelling, and vibrational adiabaticity in the Mu + H₂reaction

et al. 2014

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Isotopic substitution of muonium for hydrogen provides an unparalleled opportunity to deepen our understanding of quantum mass effects on chemical reactions. A recent topical review in this journal of the thermal and vibrationally state-selected reaction of Mu with H 2 raises a number of issues that are addressed here. We show that some earlier quantum mechanical calculations of the Mu + H 2 reaction, which are highlighted in this review, and which have been used to benchmark approximate methods, are in error by as much as 19% in the low-temperature limit. We demonstrate that an approximate treatment of the Born-Oppenheimer diagonal correction that was used in some recent studies is not valid for treating the vibrationally state-selected reaction. We also discuss why vibrationally adiabatic potentials that neglect bend zero-point energy are not a useful analytical tool for understanding reaction rates, and why vibrationally non-adiabatic transitions cannot be understood by considering tunnelling through vibrationally adiabatic potentials. Finally, we present calculations on a hierarchical family of potential energy surfaces to assess the sensitivity of rate constants to the quality of the potential surface. IntroductionTwo recent experiments [1-3] and comparison of these new measurements with earlier thermal rate constants [4] have prompted new theoretical calculations [1-3,5-10] for the Mu + H 2 reaction. The reaction of Mu, the lightest isotope of the H atom (with a mass of 0.114 amu), with H 2 has received significant attention because it exhibits a large inverse isotope effect for the thermal reaction and an extremely large enhancement of the rate when H 2 is in its first excited vibrational state. Much of this recent interest has been motived by a desire to understand the causes of these unusual features, particularly as they relate to approximate methods that may be useful for the study of larger systems. Benchmarks of these methods against accurate quantum mechanical (QM) results for this very challenging test system are important to understand why some approximations work well whereas others fail badly. In a recent review, which is based partly on earlier work [5,7] but also containing new analysis for this reaction, Aldegunde et al. [8] use the concepts of tunnelling, zero-point energy (ZPE), and vibrationally adiabatic potentials in an attempt to understand the accurate results and analyse the behaviour of approximate treatments. Although the results from their computed QM calculations are in semi-quantitative agreement with ours, their interpretations of these results differ

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Section: Quantitative Assessmentsmentioning

confidence: 99%

Zero-point energy, tunnelling, and vibrational adiabaticity in the Mu + H₂reaction

et al. 2014

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“…In contrast to previous methods which have utilized isolated diatomic wave functions to construct composite triatomic states, this approach restricts the wave function to two-atom interactions By neglecting the influence of the third atom on the individual diatomic wave functions, eq 19 is able to account for each contributing component without adiabatizing the overall system…”

Section: Constructing the Diabatic Statesmentioning

confidence: 99%

Near-Field Influence on Barrier Evolution in Symmetric Atom Transfer Reactions: A New Model for Two-State Mixing

2000

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We here consider the fundamental interactions which drive barrier evolution in atom transfer reactions. By applying the functional behavior predicted by second-order nondegenerate perturbation theory to a symmetric linear curve crossing model, we are able to derive a simple formula for two-state mixing in the near-field. It becomes readily apparent that the system property most critically responsible for governing the magnitude of coupling is the diabatic state-to-state overlap. In order to explore this parameter in depth, we outline a basic strategy for diabatic state construction in the near-field and use the imposed symmetry requirements and phase relations to derive a functional form which relates the state-to-state overlap to molecular orbital properties of the isolated reactants and the interatomic overlap matrix. Finally, we show how trends in barrier heights may be analyzed in the context of combined far-field and near-field effects and how these effects may be separated in order to provide insight into the underlying physics and broadly applicable mechanistic information.

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“…However, previous work on diabatization (e.g., work on ammonia, phenol, and thioanisole) has shown that one can often identify the diabatic–adiabatic connections at key points by looking at the orbitals and configuration interaction vectors at critical and asymptotic geometries, especially, geometries where the adiabatic surfaces are well separated. One can also use analogies to valence bond calculations. ,− …”

Section: Pr-ddnnmentioning

confidence: 99%

“…The noninvariance of a DPEM to permutations of identical nuclei is most simply illustrated by the H 2 + H → H + H 2 reaction, − and we will use this protype problem as the test case for our new procedure. The H 3 system has a conical intersection seam that is an example of Jahn–Teller intersection .…”

Section: Introductionmentioning

confidence: 99%

Permutationally Restrained Diabatization by Machine Intelligence

Shu

Varga

Oliveira-Filho

et al. 2021

J. Chem. Theory Comput.

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Simulations of electronically nonadiabatic processes may employ either the adiabatic or diabatic representation. Direct dynamics calculations are usually carried out in the adiabatic basis because the energy, force, and state coupling can be evaluated directly by many electronic structure methods. However, although its straightforwardness is appealing, direct dynamics is expensive when combined with quantitatively accurate electronic structure theories. This generates interest in analytically fitted surfaces to cut the expense, but the cuspidal ridges of the potentials and the singularities and vector nature of the couplings at high-dimensional, nonsymmetry-determined intersections in the adiabatic representation make accurate fitting almost impossible. This motivates using diabatic representations, where the surfaces are smooth and the couplings are also smooth andimportantlyscalar. In a recent previous work, we have developed a method called diabatization by deep neural network (DDNN) that takes advantage of the smoothness and nonuniqueness of diabatic bases to obtain them by machine learning. The diabatic potential energy matrices (DPEMs) learned by the DDNN method yield not only diabatic potential energy surfaces (PESs) and couplings in an analytic form useful for dynamics calculations, but also adiabatic surfaces and couplings in the adiabatic representation can be calculated inexpensively from the transformation. In the present work, we show how to extend the DDNN method to produce good approximations to global permutationally invariant adiabatic PESs simultaneously with DPEMs. The extended method is called permutationally restrained DDNN.

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Modified Bond Eigenfunction Method of Constructing Potential Energy Surface of Reaction. II. Application to the Hydrogen Atom-Molecule Reaction

Cited by 11 publications

References 23 publications

Zero-point energy, tunnelling, and vibrational adiabaticity in the Mu + H₂reaction

Zero-point energy, tunnelling, and vibrational adiabaticity in the Mu + H₂reaction

Near-Field Influence on Barrier Evolution in Symmetric Atom Transfer Reactions: A New Model for Two-State Mixing

Permutationally Restrained Diabatization by Machine Intelligence

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Modified Bond Eigenfunction Method of Constructing Potential Energy Surface of Reaction. II. Application to the Hydrogen Atom-Molecule Reaction

Cited by 11 publications

References 23 publications

Zero-point energy, tunnelling, and vibrational adiabaticity in the Mu + H2reaction

Zero-point energy, tunnelling, and vibrational adiabaticity in the Mu + H2reaction

Near-Field Influence on Barrier Evolution in Symmetric Atom Transfer Reactions: A New Model for Two-State Mixing

Permutationally Restrained Diabatization by Machine Intelligence

Contact Info

Product

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Zero-point energy, tunnelling, and vibrational adiabaticity in the Mu + H₂reaction

Zero-point energy, tunnelling, and vibrational adiabaticity in the Mu + H₂reaction