On Invariance of Localized Hamiltonians Under Feasible Elements of the Nuclear Permutation‐Inversion Group

Natanson, G. A.

doi:10.1002/9780470142820.ch2

Cited by 25 publications

(1 citation statement)

References 224 publications

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“…Some ambiguous aspects arising from the difference between a geometrical symmetry operation and a permutational symmetry operation, have been discussed, 42,43 and the existence of a symmetry group paradox for non‐rigid molecules has been recently pointed out 44 …”

Section: Introductionmentioning

confidence: 99%

Physical achirality in geometrically chiral rotamers of hydrazine and boranylborane molecules

et al. 2021

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The diagonal components and the trace of tensors which account for chiroptical response of the hydrazine molecule N2H4, that is, static anapole magnetizability and frequency‐dependent electric dipole‐magnetic dipole polarisability, are a function of the ϕ≡∠ H─N─N─H dihedral angle. They vanish for symmetry reasons at ϕ = 0° and ϕ = 180°, corresponding respectively to C2v and C2h point group symmetries, that is, cis and trans conformers characterized by the presence of molecular symmetry planes. Nonetheless, vanishing diagonal components have been observed also in the proximity of ∠ H─N─N─H = 90°, in which the point group symmetry is C2 and hydrazine is unquestionably chiral. In the boranylborane molecule B2H4, assuming the B─B bond in the y direction, the ayy component of the anapole magnetizability tensor approximately vanishes for dihedral angles ∠ H─B─B─H corresponding to chiral rotamers which belong to D2 symmetry. Such anomalous effects have been ascribed to physical achirality of these conformers, that is, to their inability to sustain electronic current densities inducing either anapole moments, or electric and magnetic dipole moments, about the chiral axis connecting heavier atoms, as well as perpendicular directions. In other terms, the structure of certain geometrically chiral rotamers may be such that neither toroidal nor helical flow, which determine chiroptical phenomenology, can take place in the presence of perturbing fields parallel or orthogonal to the chiral axis.

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Section: Introductionmentioning

confidence: 99%

Physical achirality in geometrically chiral rotamers of hydrazine and boranylborane molecules

et al. 2021

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On the numerical solution of the multidimensional vibrational time‐independent Schroedinger equation

Collado

Buenker

1992

J Comput Chem

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A preliminary study of the capability of the finite difference and finite element methods (FDM, FEM) to evaluate eigenvalues of one-, two-, and three-dimensional self-adjoint operators is reported with reference to applications dealing with the description of vibrational levels. Results of harmonic oscillator model potentials and ab initio PES for the water molecule are obtained by using the FDM. In spite of the large matrices used, low accuracy, nonvariational results are found. A different method, based on FEM and normal coordinates, is therefore proposed. Two nearly harmonic cases are studied and it is shown that variational results with higher accuracy can be obtained with a moderate cost. The vibrational levels of the water molecule are also calculated in order to compare the results with those of the FDM treatment.

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Normal coordinates–finite elements calculation of 3D vibrational energy levels: Henon—Heiles and Eckart potentials, H molecule

Collado

1994

J Comput Chem

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Theoretical and numerical results related to the calculation of multidimensional vibrational levels are presented. A description of the methodological details of a very general method (normal coordinates-finite elements, NC-FEM) is provided. Several representative three-dimensional (3D) systems (Henon-Heiles and Eckart potentials, and the H3+ molecule) are studied, and NC-FEM results are compared with those published by other authors. For the H3+, a vibrational Hamiltonian expressed in terms of the three internuclear distances is integrated. and the results obtained are compared with the experimental oKes 0

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On Invariance of Localized Hamiltonians Under Feasible Elements of the Nuclear Permutation‐Inversion Group

Cited by 25 publications

References 224 publications

Physical achirality in geometrically chiral rotamers of hydrazine and boranylborane molecules

Physical achirality in geometrically chiral rotamers of hydrazine and boranylborane molecules

On the numerical solution of the multidimensional vibrational time‐independent Schroedinger equation

Normal coordinates–finite elements calculation of 3D vibrational energy levels: Henon—Heiles and Eckart potentials, H molecule

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