Effective rotational Hamiltonian for molecules with two periodic large-amplitude motions

Abstract

Starting from a general Hamiltonian for a molecule with two periodic large-amplitude motions, an effective rotational Hamiltonian is developed for bound states of the internal motions. It contains two types of matrix elements: (i) The internal motion energy, expressed as two-dimensional Fourier series, and transformed to a reference axes system. (ii) Matrix elements of rotational operators in the reference axes system multiplied by two-dimensional Fourier series. The spectroscopic parameters are the coefficients of the Fourier series (integrals of localized functions), the internal motion parameters ρ, and the angles between the vectors ρ and the reference axes. Expressions are given for cases with higher symmetry. The effectiveness of the Hamiltonian is demonstrated by fitting the rotational spectrum of the ground state of dimethylether (356 frequencies involving levels up to J=25) to experimental precision. The data of five vibrational excited states can be fit to almost the same precision.

Rotational spectrum of13C2-methyl formate (HCOO13CH3) and detection of the two13C-methyl formate in Orion

“…In Table 3, we also present the values obtained by Maeda et al (2008b) for 13 C 1 -methyl formate species, using the ErHam procedure (Groner 1992(Groner , 1997Groner et al 1998), and the values obtained in this work by a global fit of the available data for the ground torsional state of this species. These 4954 lines were refitted using 24 parameters up to J max = 59 with a standard deviation of 66.9 kHz.…”

“…In 2006 around 500 measurements for 13 C 1 methyl formate, H 13 COOCH 3 , were carried out in the 7-62 GHz, 300-322 GHz and 570-610 GHz spectral range by Willaert et al (2006). Very recently, the spectrum of H 13 COOCH 3 was also recorded between 110 and 377 GHz using the FASSST spectrometer and more than 4900 transitions belonging to v t = 0, 910 transitions belonging to v t = 1 and 231 transitions belonging to v t = 2 (Maeda et al 2008a,b) were fitted separately using the ErHam procedure in the principal axis system (Groner 1992(Groner , 1997Groner et al 1998). Lately new spectroscopic measurements of monodeuterated species HCOOCH 2 D were carried out by Margules et al (2009).…”

Dimethyl ether: laboratory spectra up to 2.1 THz

“…They measured and assigned another 1800 transitions and accessed frequencies up to 550 GHz and J quantum numbers up to 49. Their analysis was based on an effective Hamiltonian proposed by Groner (1997). The experimental dataset including all previously published rotational transition frequencies was reproduced within experimental uncertainties and accurate frequency predictions up to 600 GHz were calculated.…”

“…For this study, additional spectra were recorded and analyzed from 38 GHz up to 2.1 THz accessing J and K values up to 70 and 30, respectively. The assigned transitions have been modeled using the same effective Hamiltonian model as in Groner (1997) and frequency predictions up to 2.5 THz have been derived.…”

CCSD(T) study of the far-infrared spectrum of ethyl methyl ether

“…We would like to remark that the few previous theoretical studies of EME have been performed at lower levels of theory dealing with a reduced number of geometries. Furthermore, simpler one-dimensional model ͑for ethyl group torsion͒ 14 or two-dimensional models ͑for the two methyl groups͒ 3,19 were employed. In the current work, we include interactions among the three internal rotations.…”