2 Linear Polyatomic Molecules: Introduction

Wlodarczak, G.

doi:10.1007/978-3-540-44926-3_2

Cited by 2 publications

(3 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[18,27,28]). The maximum value for L max = K max is specified as an input into the TROVE numerical routine.…”

Section: Symmetrization Of the Basis Set Formentioning

confidence: 99%

“…We therefore refer to this as the deciding factor in what n for D nh to use. However, it is also dependent on K max , the maximum value required for the z-projection of rotational angular momentum quantum number J, which would ideally be limited by J max (working under the assumption that K = L for the (3N − 5)-approach to dealing with linear molecules; see [18] and, for example, [27,28]). …”

Section: Even Vs Odd D ∞N Symmetriesmentioning

confidence: 99%

“…For a linear molecule, only combinations with k = are physically meaningful, where k is the z-axis-projection of the rotational angular momentum quantum number and is the vibrational angular momentum quantum number (see, for example, Refs. [1,18,[26][27][28]). With the extended symmetrization procedure of the present work, the vibrational basis functions can be labelled by their -values and it becomes straightforward to construct the meaningful combinations.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Symmetry Adaptation of the Rotation-Vibration Theory for Linear Molecules

2018

View full text Add to dashboard Cite

Abstract:A numerical application of linear-molecule symmetry properties, described by the D ∞h point group, is formulated in terms of lower-order symmetry groups D nh with finite n. Character tables and irreducible representation transformation matrices are presented for D nh groups with arbitrary n-values. These groups can subsequently be used in the construction of symmetry-adapted ro-vibrational basis functions for solving the Schrödinger equations of linear molecules. Their implementation into the symmetrisation procedure based on a set of "reduced" vibrational eigenvalue problems with simplified Hamiltonians is used as a practical example. It is shown how the solutions of these eigenvalue problems can also be extended to include the classification of basis-set functions using , the eigenvalue (in units ofh) of the vibrational angular momentum operatorL z . This facilitates the symmetry adaptation of the basis set functions in terms of the irreducible representations of D nh . 12 C 2 H 2 is used as an example of a linear molecule of D ∞h point group symmetry to illustrate the symmetrisation procedure of the variational nuclear motion program Theoretical ROVibrational Energies (TROVE).

show abstract

“…[18,27,28]). The maximum value for L max = K max is specified as an input into the TROVE numerical routine.…”

Section: Symmetrization Of the Basis Set Formentioning

confidence: 99%

Section: Even Vs Odd D ∞N Symmetriesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Symmetry Adaptation of the Rotation-Vibration Theory for Linear Molecules

2018

View full text Add to dashboard Cite

show abstract

Treating linear molecule HCCH in calculations of rotation-vibration spectra

Chubb

Yachmenev

Tennyson

et al. 2018

The Journal of Chemical Physics

View full text Add to dashboard Cite

Special treatment is required for ro-vibrational calculations involving polyatomic molecules of linear geometry in order to avoid singularities in the kinetic energy operator. Here we present a variational approach which allows calculations involving such configurations, with a set of 3N-5 linearized coordinates used to represent the vibrations. This approach has been implemented as part of the variational nuclear motion program TROVE (Theoretical ROVibrational Energies). A symmetry adapted basis set based on the D symmetry point group is used. As an illustration of the 3N-5 model presented, TROVE has been used to compute an ab initio room temperature line list for C212H using symmetry-adapted ab initio potential energy (CCSD(T)-F12c/cc-pVQZ-F12) and dipole moment surfaces for the ground electronic state. Line positions and intensities (J ≤ 58, l < 8, covering the wavenumbers up to 10 000 cm) are compared against HITRAN-2016 and ASD-1000. Alternative methods for treating linear molecules and future work are discussed.

show abstract

2 Linear Polyatomic Molecules: Introduction

Cited by 2 publications

References 21 publications

Symmetry Adaptation of the Rotation-Vibration Theory for Linear Molecules

Symmetry Adaptation of the Rotation-Vibration Theory for Linear Molecules

Treating linear molecule HCCH in calculations of rotation-vibration spectra

Contact Info

Product

Resources

About