Hybrid variational–perturbation method for calculating ro-vibrational energy levels of polyatomic molecules

The Astrochemistry Implications of Quantum Chemical Normal Modes Vibrational Analysis

Understanding the molecular vibrations underlying each of the unknown infrared emission (UIE) bands (such as those found at 3.3, 3.4, 3.5, 6.2, 6.9, 7.7, 11.3, 15.8, 16.4, 18.9 μ m) observed in or towards astronomical objects is a vital link to uncover the molecular identity of their carriers. This is usually done by customary classifications of normal-mode frequencies such as stretching, deformation, rocking, wagging, skeletal mode, etc. A large literature on this subject exists and since 1952 ambiguities in classifications of normal modes via this empirical approach were pointed out by Morino and Kuchitsu New ways of interpretation and analyzing vibrational spectra were sought within the theoretical framework of quantum chemistry. Many of these methods cannot easily be applied to the large, complex molecular systems which are one of the key research interests of astrochemistry. In considering this demand, a simple and new method of analyzing and classifying the normal mode vibrational motions of molecular systems was introduced. This approach is a fully quantitative method of analysis of normal-mode displacement vector matrices and classification of the characteristic frequencies (fundamentals) underlying the observed IR bands. Outcomes of applying such an approach show some overlap with customary empirical classifications, usually at short wavelengths. It provides a quantitative breakdown of a complex vibration (at longer wavelengths) into the contributed fragments such as their aromatic or aliphatic components. In addition, in molecular systems outside the classical models of chemical bonds and structures where the empirical approach cannot be applied, this quantitative method enables an interpretation of vibrational motion(s) underlying the IR bands. As a result, further modifications in the structures (modeling) and the generation of the IR spectra (simulating) of the UIE carriers, initiated by proposing a PAH model, can be implemented in an efficient way. Here fresh results on the vibrational origin of the spectacular UIE bands based on astrochemistry molecular models, explored through the lens of the quantitative method applied to thousands of different vibrational motion matrices are discussed. These results are important in the context of protoplanetary nebulae and planetary nebulae where various molecular species have been uncovered despite their harsh environments.

Pruning the Hamiltonian Matrix in MULTIMODE: Test for C2H4 and Application to CH3NO2 Using a New Ab Initio Potential Energy Surface

We report vibrational self-consistent field/virtual state configuration interaction energies of nitromethane using the code MULTIMODE and a new full-dimensional potential energy surface (PES). The PES is a precise, permutationally invariant linear least-squares fit to 17,049 electronic energies, using the CCSD(T)-F12b method with HaDZ basis (cc-pVDZ basis for H atoms, and aug-cc-pVDZ basis for C, O, N atoms). Nitromethane has 15 vibrational degrees of freedom, including one that is a nearly free internal methyl torsion, which is accurately described by the PES. This torsional mode makes vibrational calculations very challenging and here we present the results of calculations without it. Nevertheless, 14-mode calculations are still challenging and can lead to very large Hamiltonian matrices. To address this issue, we apply a pruning scheme, suggested previously by Handy and Carter, that reduces the size of matrix without sacrificing accuracy in the eigenvalues. The method is briefly described here in the context of partitioning theory. A new and more efficient implementation of it, coded in the latest version of MULTIMODE program, is described. The accuracy and efficiency are demonstrated for 12-mode C2H4 and then applied to CH3NO2. Agreement with available experimental values of the CH3NO2 14 fundamentals is very good. Diffusion Monte Carlo calculations in full dimensionality are done for the zero-point energy and wavefuction. These indicate that the torisonal motion is nearly a free-rotor in this state.