Higher order dipole moments for pure rotational transitions of methane-type molecules

Permanent Dipole Moments of Methane-Type Molecules: Calculation of the ΔJ= 0 Matrix Elements in thel= 1 Vibrational State

“…The first two mechanisms were theoretically predicted by Mizushima and Venkateswarlu The molecule-fixed PDM m a can be expanded in the usual way (2-5, 8, 13, 14, 17) into a series of terms which are the (2), and by Watson (3), Fox (4), and Aliev (5), and were experimentally verified by Uehara et al (6) and Ozier (7) products of the dimensionless normal coordinate operator q ta , the dimensionless total angular momentum operator J a , and more than 20 years ago. Very recently the last mechanism, proposed by Aliev et al (8), was confirmed in sub-Doppler the dimensionless vibrational angular momentum operator l ta Å (q tb p tg 0 q tg p tb ), where a Å x, y, z are the S 4 axes, p ta resolution spectroscopy of the 2n 3 band of methane (9).…”

“…In the pioneering theoretical works (2)(3)(4)(5)8), the PDMs is the dimensionless vibrational momentum operator, and t designates the triply degenerate vibrational modes. Three were described as quantum mechanical operators even though their matrix elements are required to analyze Stark effects components of the q ta , J a , and l ta operators transform as the F 2 , F 1 , and F 1 irreducible representations of the tetrahedral and rotational transition intensity.…”

“…Explicit numerical quadratic J a l s term, where l s Å (q s 1 p s 2 0 q s 2 p s 1 ) is the vibra- tional-angular momentum operator for the s mode of the E tum quantum numbers, respectively (10). Thus, the four terms giving rise to the PDMs are expressed as species, and 1 and 2 represent the two degenerate normal modes (8). However, we do not consider the term, because its contribution to the PDM of the…”

“…tx ,ty , and W are parameters with the dimension of a dipole moment, and the first three are as defined by previous works (3,6,8). The summations are carried out for any cyclic permutation of (x, y, z).…”

High-order contact transformations of molecular Hamiltonians: general approach, fast computational algorithm and convergence of ro-vibrational polyad models

“…In practical terms, the CT method provides links between PES and effective constants involved in empirical EH models. CTs also apply to other molecular properties relating for example dipole moment surfaces (DMS) with effective transition moment band parameters [7,8,[145][146][147][148][149][150][151][152][153][154][155]. Though basic framework of CT is well-established and widely used in molecular physics, a further development will be beneficial in order to achieve a spectroscopic accuracy and to consider vibrational polyads in higher energy range.…”