Simulation of vibrational structure of photoelectron and electronic spectra of selected triatomic molecules using anharmonic potential functions

Abstract

Photoelectron (PE) spectroscopy and electronic spectroscopy, notably absorption, emission and fluorescence spectroscopy, are some primary experimental tools used in studying the electronic structure of molecules and radicals in the gas phase. From the observed spectra, information on the geometries, vibrational frequencies, bonding properties and thermochemical values of the species involved in the corresponding electronic transitions can be either obtained directly, or extracted with the aid of appropriate analyses of the spectra. When vibrational structure is observed in an electronic band, one of the techniques useful for spectral analysis is the Franck-Condon (FC) analysis method with the consideration of the associated vibrational intensity distribution. The aim of this project is to apply the technique together wiih the iterative Franck-Condon analysis (IFCA) procedure to study the vibrational structures of photoelectron (PE) and electronic spectra of selected triatomic molecules of SiCl2, BrO2, AlCN, Cl2O, ClO2 and F2O using harmonic and/or anharmonic potential energy functions (PEFs). A multidimensional FC method (Chen, 1994) with the combination of ab initio molecular orbital calculations has been employed in these studies with the inclusion of Duschinsky effect. The Chen's FC model (Chen, 1994) was adopted in this work for spectral simulation. In this model, the Cartesian coordinates instead of internal coordinates for both the neutral molecules and ions and/or excited molecules were used in the FC analysis procedure for the photoionization process and electronic transition. The Duschinsky effect, which arises from the rotation of the normal modes of the two electronic states involved in these processes, was also formulated in Cartesian coordinates. The major advantage of this approach is that it describes accurately the vibrational intensities even for electronic transition and photoionization process with large geometric changes but still assumes a harmonic force field. In the present work, we have extended the generating function method of Sharp and Rosenstock (Sharp and Rosenstock, 1964) to evaluate FC integrals for up to eight and four vibrational modes for transitions arising from the 'vibrationless' states and 'hot' bands, respectively. The software package CART-FCF for the multidimensional harmonic Franck-Condon factor (FCF) calculation was coded in the MATLAB (Bangert et al., 1993) environment. The commonly used harmonic oscillator model, might be inadequate in cases, where anharmonicity effects are important, such as for vibronic transitions involving vibrational levels of high quantum numbers and also species containing H atom. This work has also developed a multi-dimensional anharmonic FCF method for non-linear polyatomics. It is based on the Watson's Hamiltonian (Watson, 1968) and includes the Duschinsky effect, through employing multi-dimensional anharmonic potential energy functions (PEFs). The anharmonic vibrational wavefunctions are expressed as linear combinations of the products of harmonic oscillator functions (Botschwina, 1989, 1997). A software package AN-FCF in the FORTRAN environment (Microsoft, 1993) has been coded based on this anharmonic FCF method. The IFCA procedure which involves a systematic adjustment of the ionic or excited molecular geometry based on a computed ab initio geometry was also developed in the present works, in order to obtain the best experimentally fitted geometry for the ionic or excited molecular state involved. In the IFCA treatment, the experimental structural parameters of the neutral molecules available in the literature were utilized and fixed while those of the excited molecules or ions were varied systematically to give the best match between the computed and observed vibrational intensity distributions of the photoelectron, emission or absorption spectrum under study. The simulated spectra were produced by employing a Gaussian shape function for each vibrational component with its relative intensity given by the computed Franck-Condon factors, with an appropriate full-width-at-half-maximum (FWHM) as estimated from the corresponding experimental. The above proposed harmonic IFCA method with the combination of ab initio calculations and multidimensional Franck-Condon (FC) analysis has been applied to investigate the emission or the single vibrational level (SVL) dispersed fluorescence spectra of SiCli and A1CN and the He I PE spectra of C12O and BrO2, respectively. Comparison between the simulated and the observed spectra gave, for the first time, the experimentally derived geometries of the molecular excited states and the cationic states involved. The adiabatic ionization energy (AIE) position and the vibrational assignments of the Cl2O+ A2B2 ← Cl2O X1A1 band as reported in the literature were revised, based on spectral simulations, which included "hot" bands. There are different theoretical and practical advantages and disadvantages associated with the above proposed harmonic and anharmonic FCF methods. The method chosen for simulation depends on the problem under consideration, the quality of the experimental information in PE and electronic spectrum, and the available computational resources. The He I PE spectra of CIO2 and F2O, which are of the importance in atmospheric chemistry, have been selected as a testing case for spectral simulation, employing both the above developed harmonic FCF code CART-FCF and anharmonic FCF code AN-FCF. The highly accurate CASSCF/MRCI PEFs of the neutral ground state and low-lying cationic states of ClO2 available in literatures and the CCSD(T) anharmonic PEFs of the neutral ground state and cationic states of F2O obtained in his work have been used for anharmonic FCF spectral simulations. For the first PE band of ClO2 and F2O, the harmonic FCF model was shown to be inadequate and the anharmonic FCF simulation gave a much-improved agreement with the observed spectrum. The experimentally derived geometries of the ground cationic states of ClO2 and F2O were obtained, for the first time, via the anharmonic IFCA procedure. The spectral simulations reported here led also to re-assignments of the observed overlapping second PE band of ClO2 and the experimental overlapping second and third PE bands of F2O. The adiabatic ionizantion energy position of the F2O+ A2B2 ← F2O X1A1 in the observed He I PE spectrum (Brundle et al., 1972) was also revised. In investigations of different molecular systems using the FCF methods, ab initio calculations of the states involved in the electronic transitions of the selected molecules at the different levels of theory were performed to provide a reliable input of harmonic force constants, vibrational frequencies and minimum-energy geometries for the subsequent FCF simulation. Also, the ab initio single point energies of F2O at the levels of the CCSD(T)/aug-cc-pVQZ for the neutral ground state and cationic ground state and of the CCSD(T)/aug-cc-pVTZ for the lowest three cationic excited states were computed for the fittings of their anharmonic potential energy functions.