We perform ab initio calculation using MOLPRO on the 22E ′ and 12A1′ states of Na3 cluster and explore for locating the point of conical intersections (CIs) in the configuration space (CS). The functional form of Non-Adiabatic Coupling Term (NACT) between the 22E′ states indicates the presence of singularity at four points in the CS. While performing Adiabatic-to-Diabatic Transformation (ADT) [Chem. Phys. Lett. 35 (1975) 112] by employing three state NACTs, two diagonal elements of ADT matrix display four sign changes as a signature of four CIs. Moreover, the locations of those CIs are confirmed by Longuet-Higgins' theorem. © 2011 Elsevier B.V. All rights reserved.

DEBASIS MUKHOPADHYAY

Chemistry

A K PAUL

S RAY

S ADHIKARI

University of Calcutta (informally known as Calcutta University or CU) is a collegiate public state university located in Kolkata, West Bengal, India.&nbsp;Within India it is recognized as a &quot;Five-Star University&quot; and accredited &quot;A&quot; Grade by National Assessment and Accreditation Council.

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The University of Calcutta has secured the Fifth position among the Universities of India in the prestigious &quot;Indian University Ranking 2019&quot; list, released by the NIRF of the Ministry of Human Resource Development, Government of India.

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It was established on 24 January 1857, and was one of the first institutions in Asia to be established as a multidisciplinary and Western-style university. Its alumni and faculty include several heads of state, heads of government, social reformers, prominent artists, only academy award winner and Dirac medal winner in India, many Fellows of the Royal Society and five Nobel laureates as of 2019 which is highest in South Asia.

University Of Calcutta

Chemical Physics Letters

The current decade has seen illuminating and extensive study of interplay of topological effects such as Renner–Teller and Jahn–Teller (JT) effects in small molecules. Study of such effects in HCNH molecule showed an interesting feature that for slightly bent system, a pair of JT conical interactions (CIs) appear only for certain nonplanar configuration, in contrast to its appearance in CS configuration (molecular plane) for C2H2 +. Moreover, since the feature of appearance of JT-CIs in two 2Σ+ states of HCNH in some bent configuration may be critically associated to the abundance of HNC in interstellar spaces, as advocated recently by Das and Mukhopadhyay (J. Phys. Chem. 117, 8680 (2013)), the interest in such topological studies have remained relevant. In this article we have investigated such topological effects for slightly bent N2H2 + and HBNH+. Interestingly, the appearance of JT-CIs are, for HBNH+, in molecular plane while for N2H2 +, in certain nonplanar configuration, in sharp contrast to the effect in the otherwise similar pair of molecular systems, C2H2 + and HCNH. © 2018, © 2018 Informa UK Limited, trading as Taylor & Francis Group.

Molecular Physics

Topological effects in low-lying electronic states of linear N2H2 + and HBNH+ associated with onset of bending

Demonstration of onset of Jahn-Teller (JT) intersections, characterized by a topological phase of π, on introduction of bending in the collinear tetra-atomic C 2H 2 + cation, originally a Renner-Teller (RT) system, has raised interest in the study of the generality of this phenomenon. This interest has initiated similar study by shifting one external light atom from the collinear molecular axes of systems such as HCNH and HC 2O. Recent studies have revealed that slightly bent HCNH poses a specialty in this regard and thus demands focused attention. In the present work we performed a combined study using both the potential intersections and the angular nonadiabatic coupling terms (NACTs) and report two new results: (i) The first result is the appearance of the JT conical intersections (ci's) between the two lowest states of a slightly bent HCNH molecule (1 2A′ and 1 2A-3, originated from collinear X 2Π state) only with certain nonplanar configurations, in contrast to its appearance in C S configuration space (molecular plane) for slightly bent C 2H 2 +, HC 2O, or some other tetra-atomics. This is also associated with the first time demonstration of Berry phase for such a single isolated ci for HCNH molecule. (ii) For energetically higher potentials of slightly bent HCNH, the present study reveals the existence of the intersection of the state 1 2A-3 with the state 2 2A′ (originated from the collinear 1 2Σ + state); in contrast to the (1,2) ci this appears in the molecular plane. The search for ci's has been performed by varying the distances of the two H-atoms (designated as H C and H N) from the C-N axis as well as the dihedral angle φ between the two planes (H C,C,N) and (C,N,H N). Existence of these JT ci's results in deterioration of a two-state Hilbert subspace (HSS) model in diabatization, while the proper choice of an n (&gt;2)-state HSS circumvents this problem. © 2012 American Chemical Society.

Journal of Physical Chemistry A

Jahn-Teller intersections induced by introduction of bending in linear polyatomics: Study with HCNH, a selected molecular system

We perform ab initio calculation using quantum chemistry package (MOLPRO) on the excited states of Na3 cluster and present the adiabatic PESs for the electronic states 22E′ and 12A1′, and the non-adiabatic coupling (NAC) terms among those states. Since the ab initio calculated NAC elements for the states 22E′ and 12 A1′ demonstrate the numerical validity of so called Curl Condition, such states closely form a sub-Hilbert space. For this subspace, we employ the NAC terms to solve the adiabatic-diabatic transformation (ADT) equations to obtain the functional form of the transformation angles and pave the way to construct the continuous and single valued diabatic potential energy surface matrix by exploiting the existing first principle based theoretical means on beyond Born-Oppenheimer treatment. Nuclear dynamics has been carried out on those diabatic surfaces to reproduce the experimental spectrum for system B of Na3 cluster and thereby, to explore the numerical validity of the theoretical development on beyond Born-Oppenheimer approach for adiabatic to diabatic transformation. © 2011 American Institute of Physics.

Fulltext

Journal of Chemical Physics

Ab initio calculations on the excited states of Na3 cluster to explore beyond Born-Oppenheimer theories: Adiabatic to diabatic potential energy surfaces and nuclear dynamics

The tetra-atomic C2 H2+ cation is known to form Renner-Teller-type intersections along its collinear axis. Not too long ago, we studied the nonadiabatic coupling terms (NACTs) of this molecule [G. J. Halász, J. Chem. Phys. 126, 154309 (2007)] and revealed two kinds of intersections. (i) By employing one of the hydrogens as a test particle, we revealed the fact that indeed the corresponding (angular) NACTs produce topological (Berry) phases that are equal to 2π , which is a result anticipated in the case of Renner-Teller intersections. (ii) However, to our big surprise, repeating this study when one of the atoms (in this case a hydrogen) is shifted from the collinear arrangement yields for the corresponding topological phase a value that equals π (and not 2π ). In other words, shifting (even slightly) one of the atoms from the collinear arrangement causes the intersection to change its character and become a Jahn-Teller intersection. This somewhat unexpected novel result was later further analyzed and confirmed by other groups [e.g., T. Vertesi and R. Englman, J. Phys. B 41, 025102 (2008)]. The present article is devoted to another tetra-atomic molecule, namely, the H2 CN molecule, which just like the C2 H2+ ion, is characterized by Renner-Teller intersections along its collinear axis. Indeed, we revealed the existence of Renner-Teller intersections along the collinear axis, but in contrast to the C2 H2+ case a shift of one atom from the collinear arrangement did not form Jahn-Teller intersections. What we found instead is that the noncollinear molecule was not affected by the shift and kept its Renner-Teller character. Another issue treated in this article is the extension of (the two-state) Berry (topological) phase to situations with numerous strongly interacting states. So far the relevance of the Berry phase was tested for systems characterized by two isolated interacting states, although it is defined for any number of interacting states [M. V. Berry, Proc. R. Soc. London, Ser. A 392, 45 (1984)]. We intend to show how to overcome this limitation and get a valid, fully justified definition of a Berry phase for an isolated system of any number of interacting states (as is expected). © 2010 American Institute of Physics.

Renner-Teller intersections along the collinear axes of polyatomic molecules: H2 CN as a case study

Hans Hellmann: Einführung in die Quantenchemie

Einführung in die Quantenchemie

Astrophysics and Space Science Proceedings

Recent Advances in Spectroscopy

The Journal of Chemical Physics

Single surface beyond Born–Oppenheimer equation for a three-state model Hamiltonian of Na3 cluster

International Journal of Quantum Chemistry

A rigorous approach to the formulation of extended Born-Oppenheimer equation for a three-state system

Conical intersections in 22Eâ€² states of Na 3 cluster

Journal	Chemical Physics Letters
Publisher	-
ISSN	0009-2614
Open Access	No