Extension of the fourfold way for calculation of global diabatic potential energy surfaces of complex, multiarrangement, non-Born–Oppenheimer systems: Application to HNCO(S,S1)

Nakamura, Hisao; Truhlar, Donald G.

doi:10.1063/1.1540622

Cited by 112 publications

(127 citation statements)

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“…We particularly single out for discussion a new approach called the fourfold way. 43,55,56 The fourfold way allows for the direct calculation of diabatic states and their couplings using the conventional variational and perturbational methods of quantum chemistry. This is particularly important because diabatic representations used for dynamics calculations should not be based on an arbitrary selection of configurations.…”

Section: General Theoretical Considerations and Definitionsmentioning

confidence: 99%

Introductory lecture: Nonadiabatic effects in chemical dynamics

et al. 2004

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Recent progress in the theoretical treatment of electronically nonadiabatic processes is discussed. First we discuss the generalized Born-Oppenheimer approximation, which identifies a subset of strongly coupled states, and the relative advantages and disadvantages of adiabatic and diabatic representations of the coupled surfaces and their interactions are considered. Ab initio diabatic representations that do not require tracking geometric phases or calculating singular nonadiabatic nuclear momentum coupling will be presented as one promising approach for characterizing the coupled electronic states of polyatomic photochemical systems. Such representations can be accomplished by methods based on functionals of the adiabatic electronic density matrix and the identification of reference orbitals for use in an overlap criterion. Next, four approaches to calculating or modeling electronically nonadiabatic dynamics are discussed: (1) accurate quantum mechanical scattering calculations, (2) approximate wave packet methods, (3) surface hopping, and (4) self-consistent-potential semiclassical approaches. The last two of these are particularly useful for polyatomic photochemistry, and recent refinements of these approaches will be discussed. For example, considerable progress has been achieved in making the surface hopping method more applicable to the study of systems with weakly coupled electronic states. This includes introducing uncertainty principle considerations to alleviate the problem of classically forbidden surface hops and the development of an efficient sampling algorithm for low-probability events. A topic whose central importance in a number of quantum mechanical fields is becoming more widely appreciated is the introduction of decoherence into the quantal degrees of freedom to account for the effect of the classical treatment on the other degrees of freedom, and we discuss how the introduction of such decoherence into a self-consistent-potential approximation leads to a reasonably accurate but very practical trajectory method for electronically nonadiabatic processes. Finally, the performances of several dynamical methods for Landau-Zener-type and Rosen-Zener-Demkov-type reactive scattering problems are compared.

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Section: General Theoretical Considerations and Definitionsmentioning

confidence: 99%

Introductory lecture: Nonadiabatic effects in chemical dynamics

et al. 2004

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“…[92][93][94] In general, the diabatic states generated by the fourfold way are linear combinations of more than one valence-bond structure, so one should expect a somewhat larger variation of the spin-orbit matrix elements expressed in the diabatic basis set than for a pure valence-bond treatment. Hamiltonian.…”

Section: 93mentioning

confidence: 99%

“…The V-diabatic potential energy matrix for the singlet states was obtained using the fourfold way [92][93][94] as implemented in HONDOPLUS, version 5.1.…”

Section: Application To the Two-channel Brch 2 CL Systemmentioning

confidence: 99%

A Diabatic Representation Including Both Valence Nonadiabatic Interactions and Spin−Orbit Effects for Reaction Dynamics

Valero

Truhlar

2007

J. Phys. Chem. A

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A diabatic representation is convenient in the study of electronically nonadiabatic chemical reactions because the diabatic energies and couplings are smooth functions of the nuclear coordinates and the couplings are scalar quantities. A method called the fourfold way was devised in our group to generate diabatic representations for spin-free electronic states. One drawback of diabatic states computed from the spin-free Hamiltonian, called a valence diabatic representation, for systems in which spin-orbit coupling cannot be ignored is that the couplings between the states are not zero in asymptotic regions, leading to difficulties in the calculation of reaction probabilities and other properties by semiclassical dynamics methods. Here we report an extension of the fourfold way to construct diabatic representations suitable for spincoupled systems. In this article we formulate the method for the case of even-electron systems that yield pairs of fragments with doublet spin multiplicity. For this type of system, we introduce the further simplification of calculating the triplet diabatic energies in terms of the singlet diabatic energies via Slater's rules and assuming constant ratios of Coulomb to exchange integrals. Furthermore, the valence diabatic couplings in the triplet manifold are taken equal to the singlet ones. An important feature of the method is the introduction of scaling functions, as they allow one to deal with multibond reactions without having to include Comparison of the spin-coupled adiabatic energies obtained from the spin-valence diabatics with those obtained by ab initio calculations with geometry-dependent spin-orbit matrix elements shows that the new method is sufficiently accurate for practical purposes. The method formulated here should be most useful for systems with a large number of atoms, especially heavy atoms, and/or a large number of spin-coupled electronic states.

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“…The fourfold way 18,19,21,29 is a general diabatization scheme based on configurational uniformity that generates diabatic states spanning the same model space as the selected adiabatic states; the diabatic states and the adiabatic states are related by an orthogonal transformation. The fourfold way was first formulated at the CASSCF level 18 and then extended to the MC-QDPT level 19 and to include spin-orbit coupling.…”

Section: A Review Of the Fourfold Waymentioning

confidence: 99%

“…Examples of such methods are the state-averaged complete active space self-consistent field method (SA-CASSCF) followed by second-order multiconfigurational quasi-degenerate perturbation theory (MC-QDPT), 37 extended MC-QDPT (XMC-QDPT), 38 multistate complete active space second-order perturbation theory (MS-CASPT2), 39 extended MS-CASPT2 (XMS-CASPT2), 42 and quasidegenerate second-order n-electron valence state perturbation theory (QD-NEVPT2). 40 The fourfold way 18,19,21,29 is a diabatization method that enforces the smoothness of wave functions by first construct-ing diabatic molecular orbitals (DMOs) by a threefold density criterion and a sometimes employed fourth criterion based on reference orbitals and then applying a configurational uniformity step originally proposed by Atchity and Ruedenberg. 13,15 The fourfold way was developed to have general applicability to diverse types of electronic states and electronic excitation problems.…”

Section: Introductionmentioning

confidence: 99%

Model space diabatization for quantum photochemistry

Truhlar

Schmidt

et al. 2015

The Journal of Chemical Physics

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Diabatization is a procedure that transforms multiple adiabatic electronic states to a new representation in which the potential energy surfaces and the couplings between states due to the electronic Hamiltonian operator are smooth, and the couplings due to nuclear momentum are negligible. In this work, we propose a simple and general diabatization strategy, called model space diabatization, that is applicable to multiconfiguration quasidegenerateperturbation theory (MC-QDPT) or its extended version (XMC-QDPT). An advantage over previous diabatization schemes is that dynamical correlation calculations are based on standard post-multi-configurational self-consistent field (MCSCF) multi-state methods even though the diabatization is based on state-averaged MCSCF results. The strategy is illustrated here by applications to LiH, LiF, and thioanisole, with the fourfold-way diabatization and XMC-QDPT, and the results illustrate its validity. KeywordsWave functions, Monte Carlo methods, Potential energy surfaces, Quasicrystals, Eigenvalues Disciplines Chemistry CommentsThe following article appeared in Journal of Chemical Physics 142 (2015) (Received 11 November 2014; accepted 19 January 2015; published online 11 February 2015) Diabatization is a procedure that transforms multiple adiabatic electronic states to a new representation in which the potential energy surfaces and the couplings between states due to the electronic Hamiltonian operator are smooth, and the couplings due to nuclear momentum are negligible. In this work, we propose a simple and general diabatization strategy, called model space diabatization, that is applicable to multi-configuration quasidegenerate perturbation theory (MC-QDPT) or its extended version (XMC-QDPT). An advantage over previous diabatization schemes is that dynamical correlation calculations are based on standard post-multi-configurational self-consistent field (MCSCF) multi-state methods even though the diabatization is based on state-averaged MCSCF results. The strategy is illustrated here by applications to LiH, LiF, and thioanisole, with the fourfoldway diabatization and XMC-QDPT, and the results illustrate its validity. C 2015 AIP Publishing LLC. [http://dx

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Extension of the fourfold way for calculation of global diabatic potential energy surfaces of complex, multiarrangement, non-Born–Oppenheimer systems: Application to HNCO(S,S1)

Cited by 112 publications

References 65 publications

Introductory lecture: Nonadiabatic effects in chemical dynamics

Introductory lecture: Nonadiabatic effects in chemical dynamics

A Diabatic Representation Including Both Valence Nonadiabatic Interactions and Spin−Orbit Effects for Reaction Dynamics

Model space diabatization for quantum photochemistry

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