Theoretical high-resolution spectroscopy for reactive molecules in astrochemistry and combustion processes

Abstract

Rovibrational spectroscopy is a prime tool for the indirect investigation of molecular potential energy surfaces (PES). Naturally, theoretical predictions of molecular spectra have been the focus of numerous works since the early days of quantum chemistry. With the formulation of modern ab initio methods and ever increasing computing power of modern high-performance computing facilities it has become possible to calculate the PES with unprecedented accuracy. On the other hand, such a high-level PES requires also an accurate treatment of the rovibrational problem. For molecules with up to 3 atoms such methods have been know for quite some time and are available in different formulations but going beyond that still poses a challenge. In this thesis, methods for calculating rovibrational spectra of linear molecules with up to four atoms are presented, rivaling with experimental lab accuracy. As a first step towards a general procedure for high-level theoretical spectroscopy of linear molecules a composite ab initio approach to the construction of a PES is presented. The method is tested on two experimentally well known triatomic linear molecules hydrogen cyanide (HCN) and tricarbon (C3). For HCN, the composite PES reproduces the experimental results with standard deviations of 0.33 cm-1 and 0.00009 cm-1 in the vibrational term energies and rotational constants, respectively, considering all 113 vibrational states up to about 6500 cm-1 above the ground state. A new electric dipole moment function, which has been constructed also in a composite manner, yields accurate rovibrational intensities for a large variety of HCN transitions ranging form the strong CH stretching and bending fundamentals to very weak overtone transitions. The intensity of the peculiar CN stretching fundamental of HCN is in much better agreement with experiment than previous theoretical results. For the very flexible C3 molecule the presented composite PES yields fundamental vibrational transition frequencies which are within 1 cm-1 compared to experiment. The rovibrational calculations on C3 highlight the necessity of an accurate rovibrational treatment. Common perturbational approaches based on contact transformation of the Hamiltonian fail to describe the strong rovibrational couplings in C3. Employing the variational ground state rotational constants a mixed experimental/theoretical equilibrium geometry is determined and shown to be superior to results obtained from experimental results only. In cooperation with the Linnartz group for laboratory astrophysics a joint experimental/theoretical investigation of highly excited stretching state is presented. In order to increase the size of linear molecules which can be studied by such composite approaches a new method (C8v4) has been developed. C8v4 is based on the exact kinetic energy operator formulated in normal coordinates and the rovibrational term energies and wave functions of linear tetra atomic molecules are calculated by a variational ansatz. Products of harmonic oscillator and rigid-rotor functions are used to expand the rovibrational wave function. Intricacies related to the vibrational angular momentum in linear molecules require a careful study of symmetry properties to set up a symmetry adapted basis set. Kinetic energy matrix elements can be evaluated in a fast mixed numerical/analytical fashion. The main computational bottlenecks are the integration of the potential energy matrix and the diagonalisation of the Hamiltonian. These can be overcome by exploiting the block structure of the Hamiltonian. Benchmark calculations on acetylene (HCCH) and boranimine (HBNH) are presented which perfectly reproduce previous variational calculations based on a different Hamiltonian formulated in internal coordinates. Using the C8v4 program and a composite quartic force field obtained earlier, variational rovibrational calculations for the interesting astromolecule propynylidynium (l-C3H+) are carried out. The results of these calculations rectify long standing discrepancies between theory and experiment. The need for high-order correlation contributions to the composite force field is clearly highlighted. The new composite PES yields a ground state rotational constant based on C8v4 variational term energies which is within 5 MHz of the experimental result and a quartic centrifugal distortion constant in virtual agreement with experiment. Spectroscopic parameters for low-lying excited vibrational states are presented which should provide a starting point in forthcoming experimental studies on l-C3H+. A close relationship can be established by comparing the properties of the l-C3H+ composite PES with the composite PES of C3. An analysis of differences in rotational parameters calculated variationally and by perturbation theory confirms the assumption that l-C3H+ behaves like a protonated, albeit more rigid, C3.