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

TL;DR: In this paper, the authors investigated the topological effects of Renner-Teller conical interactions in slightly bent N2H2+ and HBNH+ and found that the appearance of JT-CIs is in molecular plane while for N 2H2+, in certain nonplanar configuration, in sharp contrast to th...

Abstract: 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 th...

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TL;DR: In this article, the authors investigate the relationship between JTCI and RTPI in the linear tetra-atomic molecular system with slightly bent HCNOplus, a motivated choice of tetraatomic with all four different atoms.

Abstract: Search for configuration space with welldefined topological (Berry) phases corresponding to Jahn Teller (JT) conical intersection (CI) and Renner Teller(RT) parabolic intersection (PI) in the linear tetra-atomic molecular system on introduction of bending, reveal the interesting aspect that these potential intersections may appear in molecular plane as well as out of the molecular plane. While understanding this aspect is important for following the class of phenomena led by potential intersections, till date studies on molecular systems including pairs like (C2H2plus , HCNH) as well as (N2H2plus , HBNHplus ), have not been able to clarify the issue. The present paper embodies calculation of non-adiabatic coupling terms (NACTs) involving four low lying states of slightly bent HCNOplus , a motivated choice of tetra-atomic with all four different atoms, to study this aspect associated with JTCI and RTPI in slightly bent linear system. The plane of appearance of these effects, has been advocated to be related to electronic configuration of the concerned states of the molecular system.

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TL;DR: In this paper, the authors investigate the relationship between JTCI and RTPI in the linear tetra-atomic molecular system with slightly bent HCNOplus, a motivated choice of tetraatomic with all four different atoms.

Abstract: Search for configuration space with welldefined topological (Berry) phases corresponding to Jahn Teller (JT) conical intersection (CI) and Renner Teller(RT) parabolic intersection (PI) in the linear tetra-atomic molecular system on introduction of bending, reveal the interesting aspect that these potential intersections may appear in molecular plane as well as out of the molecular plane. While understanding this aspect is important for following the class of phenomena led by potential intersections, till date studies on molecular systems including pairs like (C2H2plus , HCNH) as well as (N2H2plus , HBNHplus ), have not been able to clarify the issue. The present paper embodies calculation of non-adiabatic coupling terms (NACTs) involving four low lying states of slightly bent HCNOplus , a motivated choice of tetra-atomic with all four different atoms, to study this aspect associated with JTCI and RTPI in slightly bent linear system. The plane of appearance of these effects, has been advocated to be related to electronic configuration of the concerned states of the molecular system.

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01 Jan 1954

TL;DR: Born and Huang's classic work on the dynamics of crystal lattices was published over thirty years ago, and it remains the definitive treatment of the subject as mentioned in this paper. But it is not the most complete work on crystal lattice dynamics.

Abstract: Although Born and Huang's classic work on the dynamics of crystal lattices was published over thirty years ago, the book remains the definitive treatment of the subject. It begins with a brief introduction to atomic forces, lattice vibrations and elasticity, and then breaks off into four sections. The first section deals with the general statistical mechanics of ideal lattices, leading to the electric polarizability and to the scattering of light. The second section deals with the properties of long lattice waves, the third with thermal properties, and the fourth with optical properties.

7,756 citations

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TL;DR: In this article, it was shown that the Aharonov-Bohm effect can be interpreted as a geometrical phase factor and a general formula for γ(C) was derived in terms of the spectrum and eigen states of the Hamiltonian over a surface spanning C.

Abstract: A quantal system in an eigenstate, slowly transported round a circuit C by varying parameters R in its Hamiltonian Ĥ(R), will acquire a geometrical phase factor exp{iγ(C)} in addition to the familiar dynamical phase factor. An explicit general formula for γ(C) is derived in terms of the spectrum and eigenstates of Ĥ(R) over a surface spanning C. If C lies near a degeneracy of Ĥ, γ(C) takes a simple form which includes as a special case the sign change of eigenfunctions of real symmetric matrices round a degeneracy. As an illustration γ(C) is calculated for spinning particles in slowly-changing magnetic fields; although the sign reversal of spinors on rotation is a special case, the effect is predicted to occur for bosons as well as fermions, and a method for observing it is proposed. It is shown that the Aharonov-Bohm effect can be interpreted as a geometrical phase factor.

7,425 citations

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TL;DR: In der Anwendung der Quantentheorie auf die Molekeln kann man folgende Entwicklungsstufen unterscheiden: Das erste Stadium1) ersetzt die zweiatomige Molekel durch das Hantelmodell, das als einfacher „Rotator“ behandelt wird as discussed by the authors.

Abstract: In der Anwendung der Quantentheorie auf die Molekeln kann man folgende Entwicklungsstufen unterscheiden: Das erste Stadium1) ersetzt die zweiatomige Molekel durch das Hantelmodell, das als einfacher „Rotator“ behandelt wird. Mehratomige Molekeln werden in entsprechender Weise als starre „Kreisel“ angesehen.2) Dieser Standpunkt erlaubt es, die einfachsten Gesetze der Bandenspektren und der spezifischen Warme mehratomiger Gase zu erklaren. Das nachste Stadium1) last die Annahme starrer Verbindungen zwischen den Atomen fallen und berucksichtigt die Kernschwingungen, zunachst als harmonische Schwingungen; dabie ergenben sich nach Sponer3) und Kratzer4) Zusammenhange zwischen den einzelnen Banden eines Bandensystems.

4,131 citations

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TL;DR: In this paper, it was shown that if the total electronic state of orbital and spin motion is degenerate, then a non-linear configuration of the molecule will be unstable unless the degeneracy is the special twofold one (discussed by Kramers 1930) which can occur only when the molecule contains an odd number of electrons.

Abstract: In a previous paper (Jahn and Teller 1937) the following theorem was established: A configuration of a polyatomic molecule for an electronic state having orbital degeneracy cannot be stable with respect to all displacements of the nuclei unless in the original configuration the nuclei all lie on a straight line. The proof given of this theorem took no account of the electronic spin, and in the present paper the justification of this is investigated. An extension of the theorem to cover additional degeneracy arising from the spin is established, which shows that if the total electronic state of orbital and spin motion is degenerate, then a non-linear configuration of the molecule will be unstable unless the degeneracy is the special twofold one (discussed by Kramers 1930) which can occur only when the molecule contains an odd number of electrons. The additional instability caused by the spin degeneracy alone, however, is shown to be very small and its effect for all practical purposes negligible. The possibility of spin forces stabilizing a non-linear configuration which is unstable owing to orbital degeneracy is also investigated, and it is shown that this is not possible except perhaps for molecules containing heavy atoms for which the spin forces are large. Thus whilst a symmetrical nuclear configuration in a degenerate orbital state might under exceptional circumstances be rendered stable by spin forces, it is not possible for the spin-orbit interaction to cause instability of an orbitally stable state. 1—General theorem for molecules with spin Just as before we must see how the symmetry of the molecular framework determines whether the energy of a degenerate electronic state with spin depends linearly upon nuclear displacements. This is again determined by the existence of non-vanishing perturbation matrix elements which are linear in the nuclear displacements. These matrix elements are integrals involving the electronic wave functions with spin and the nuclear displacements, and we deduce as before from their transformation properties whether for a given molecular symmetry they can be different from zero.

2,539 citations

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TL;DR: In this article, a contracted Gaussian basis set capable of describing about 63% of the correlation energy of N2 has been used in a detailed configuration-interaction calculation, and second-order perturbation theory overestimated the correlated energy by 23-50% depending on how H0 was chosen.

Abstract: A contracted Gaussian basis set capable of describing about 63% of the correlation energy of N2 has been used in a detailed configuration-interaction calculation. Second-order perturbation theory overestimated the correlation energy by 23–50% depending on how H0 was chosen. Pair-pair interaction affects the correlation energy by about 20% while quadruple excitations have an 8% effect.

2,374 citations