A numerical application of linear-molecule symmetry properties, described by the D∞h point group, is formulated in terms of lower-order symmetry groups Dnh with finite n. Character tables and irreducible representation transformation matrices are presented for Dnh groups with arbitrary n-values. These groups are subsequently used in the construction of symmetry-adapted ro-vibrational basis functions for solving the Schrödinger equations of linear molecules as part of the variational nuclear motion program TROVE. The TROVE symmetrisation procedure is based on a set of "reduced" vibrational eigenvalue problems with simplified Hamiltonians. The solutions of these eigenvalue problems have now been extended to include the classification of basis-set functions using ℓ, the eigenvalue (in units of ℏ) of the vibrational angular momentum operator L ^ z . This facilitates the symmetry adaptation of the basis set functions in terms of the irreducible representations of Dnh. 12C2H2 is used as an example of a linear molecule of D∞h point group symmetry to illustrate the symmetrisation procedure.
MetaXL: Meta Representation Transformation for Low-resource Cross-lingual Learning
