The excited states of K3 cluster: The molecular symmetry adapted non-adiabatic coupling terms and diabatic Hamiltonian matrix

Mukherjee, Saikat; Adhikari, Satrajit

doi:10.1016/j.chemphys.2014.05.022

Cited by 22 publications

(13 citation statements)

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“…At this stage it is important to emphasize that drawing the (angular) NACTs along the contours as a function of φ, has to be done with care: in particular, the plots have to be continuous and fulfill symmetry with respect the φ-axis, which implies flipping the sign of the corresponding NACTs while intersecting the φ-axis (for details see refs and ).…”

Section: Resultsmentioning

confidence: 99%

“…In the present article we consider a well established approach, introduced some time ago, , that yields rigorous diabatic potential energy surfaces (PES) with high accuracy for large regions in configuration space. It is based on numerous interacting Born–Oppenheimer (adiabatic) PESs and therefore requires deriving a set of mixing angles, γ ij ( s ), to form the required adiabatic-to-diabatic transformations (ADT). − It is well-known that these angles are formed by the Born–Oppenheimer nonadiabatic coupling terms (NACT) that have their origin either in the Jahn–Teller (JT) conical intersections (ci) − or in the Renner–Teller (RT) degeneracy. − ...…”

Section: Introductionmentioning

confidence: 99%

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Study of Topological Effects Concerning the Lowest A″ and the Three A′ States for the CO₂⁺ Ion

2015

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A study of the topological effects, viz., the Jahn-Teller (JT) and Renner-Teller (RT) effects, in CO2(+) has been carried out by calculating nonadiabatic coupling terms (NACTs) at the state-averaged CASSCF level using the cc-pVTZ basis set for the lowest three A' states and one A″ state along a circular contour. Using the NACTs, the privileged adiabatic-to-diabatic transformation (ADT) angles (γ12) for 1A' and 2A' states of CO2(+) have been calculated along various circular contours. Employing one of the oxygen atoms as the test particle exposed two conical intersections (ci) located on each side of the CO diatom. The main purpose of this study is to explore the possibility of forming reliable diabatic potential energy surfaces for this system. Success in achieving this goal is guaranteed by the ability to calculate quantized privileged ADT angles along closed contours covering large regions in configuration space (see, e.g., J. Phys. Chem. A 2014 , 118 , 6361 ). The calculations were carried out for two and three JT states. In most cases very nice quantization has been achieved although the calculations were frequently done, as required, for large regions in configuration space (sometimes ≥18 Å(2)). In one case, for which the quantization was not gratifying, the inclusion of the RT effect modified it considerably.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Study of Topological Effects Concerning the Lowest A″ and the Three A′ States for the CO₂⁺ Ion

2015

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“…So far several theoretical developments took place on Beyond Born–Oppenheimer (BBO) theories, and many calculations were performed on quantum dynamics, where the inclusion of appropriate number of coupled electronic states to constitute a sub-Hilbert space is highly relevant to derive the ADT equations and expressions of τ. In the context of non-adiabatic chemistry, ADT equations for two, , three, − and four states have already been deduced to construct diabatic PESs for several real molecular systems on which dynamics has been performed thoroughly with utmost care. On the other hand, various molecules still exist where more than four electronic states are highly coupled, and such coupling must be taken into account while understanding their spectral features, scattering cross section, and also other experimental quantities.…”

Section: Discussionmentioning

confidence: 99%

“…In other words, this quantization rule is obeyed only when all electronic states constituting the sub-Hilbert space are taken into account . Adhikari et al have generalized the BO treatment for three as well as four coupled electronic states in terms of electronic basis functions or the ADT matrix elements, where the explicit forms of the NACTs, their Curl-Divergence equations, Curl conditions, and the diabatic PESs in terms of the ADT angles have been formulated. − Not only this approach paves a practical way of handling NACTs with singularities at the CI point(s) in the nuclear CS but also has been quite successfully implemented on model − as well as realistic − systems in constructing smooth, continuous, and single-valued diabatic PESs. Later on, ADT equations for four-state sub-Hilbert space have been successfully implemented to investigate the non-adiabatic interactions in HCNH molecule. , In this regard, it is worthwhile to mention that till now no extensive formalism of ADT for five-state sub-Hilbert space has been developed.…”

Section: Introductionmentioning

confidence: 99%

Five Electronic State Beyond Born–Oppenheimer Equations and Their Applications to Nitrate and Benzene Radical Cation

Mukherjee

Adhikari

2017

J. Phys. Chem. A

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We present explicit form of Adiabatic to Diabatic Transformation (ADT) equations and expressions of non-adiabatic coupling terms (NACTs) for a coupled five-state electronic manifold in terms of ADT angles between electronic wave functions. ADT matrices eliminate the numerical instability arising from singularity of NACTs and transform the adiabatic Schrödinger equation to its diabatic form. Two real molecular systems NO and CH (Bz) are selectively chosen for the demonstration of workability of those equations. We examine the NACTs among the lowest five electronic states of the NO radical [X̃A (1B), ÃE″ (1A and 1B) and B̃E' (1A and 2B)], in which all types of non-adiabatic interactions, that is, Jahn-Teller (JT) interactions, Pseudo Jahn-Teller (PJT) interactions, and accidental conical intersections (CIs) are present. On the other hand, lowest five electronic states of Bz [X̃E (1B and 1B), B̃E (1A and 1B), and C̃A (1B)] depict similar kind of complex feature of non-adiabatic effects. For NO radical, the two components of degenerate in-plane asymmetric stretching mode are taken as a plane of nuclear configuration space (CS), whereas in case of Bz, two pairs are chosen: One is the pair of components of degenerate in-plane asymmetric stretching mode, and the other one is constituted with one of the components each from out-of-plane degenerate bend and in-plane degenerate asymmetric stretching modes. We calculate ab initio adiabatic potential energy surfaces (PESs) and NACTs among the lowest five electronic states at the CASSCF level using MOLPRO quantum chemistry package. Subsequently, the ADT is performed using those newly developed equations to validate the positions of the CIs, evaluate the ADT angles and construct smooth, symmetric, and continuous diabatic PESs for both the molecular systems.

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“…Previous theoretical studies on alkali trimers [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39]43] were essentially restricted to either the doublet or quartet ground state or they investigated selected JT distorted excited states. Furthermore, we calculate the electronic dipole transition matrix elements between states.…”

Section: Introductionmentioning

confidence: 99%

Towards photoassociation processes of ultracold rubidium trimers

Schnabel,

Kampschulte,

Rupp

et al. 2021

Preprint

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We theoretically investigate the prospects for photoassociation (PA) of Rb3, in particular at close range. We provide an overview of accessible states and possible transitions. The major focus is placed on the calculation of equilibrium structures, the survey of spin-orbit effects and the investigation of transition dipole moments. Furthermore we discuss Franck-Condon overlaps and special aspects of trimers including the (pseudo) Jahn-Teller effect and the resulting topology of adiabatic potentialenergy surfaces. With this we identify concrete and suitable PA transitions to potentially produce long-lived trimer bound states. Calculations are performed using the multireference configurationinteraction method together with a large-core effective core potential and a core-polarization potential with a large uncontracted even-tempered basis set.

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The excited states of K3 cluster: The molecular symmetry adapted non-adiabatic coupling terms and diabatic Hamiltonian matrix

Cited by 22 publications

References 53 publications

Study of Topological Effects Concerning the Lowest A″ and the Three A′ States for the CO₂⁺ Ion

Study of Topological Effects Concerning the Lowest A″ and the Three A′ States for the CO₂⁺ Ion

Five Electronic State Beyond Born–Oppenheimer Equations and Their Applications to Nitrate and Benzene Radical Cation

Towards photoassociation processes of ultracold rubidium trimers

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The excited states of K3 cluster: The molecular symmetry adapted non-adiabatic coupling terms and diabatic Hamiltonian matrix

Cited by 22 publications

References 53 publications

Study of Topological Effects Concerning the Lowest A″ and the Three A′ States for the CO2+ Ion

Study of Topological Effects Concerning the Lowest A″ and the Three A′ States for the CO2+ Ion

Five Electronic State Beyond Born–Oppenheimer Equations and Their Applications to Nitrate and Benzene Radical Cation

Towards photoassociation processes of ultracold rubidium trimers

Contact Info

Product

Resources

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Study of Topological Effects Concerning the Lowest A″ and the Three A′ States for the CO₂⁺ Ion

Study of Topological Effects Concerning the Lowest A″ and the Three A′ States for the CO₂⁺ Ion