High-Accuracy Spectral Lines for Radiation Transport in Stellar Atmospheres

The theory of radiative transfer is an important element for the understanding of the spectral signature and physical structure of stellar atmosphere. PHOENIX1 is a such, very general non-Local Thermodynamic Equilibrium(NLTE) stellar atmosphere computer code which can handle very large model atoms/molecules as well as line blanketing by hundreds of millions of atomic and molecular lines. The code is used to compute model atmospheres and synthetic spectra (solution of the radiative transport equations) for, e.g., novae, supernovae, M and brown dwarfs, O to M giants, white dwarfs and accretion disks in Active Galactic Nuclei (AGN). The radiative transfer in PHOENIX is solved in spherical geometry and includes the effects of special relativity (including advection and aberration) in the modeling. The code includes a large number of NLTE and LTE background spectral lines and solves transport equation for each of the lines. The numerical solution requires many wavelength points which arise in the non-LTE case by balancing all populating and de-populating processes from each molecular level (typically 150,000 to 300,000 points). Typically, HITRAN and GEISA are the computer accessible spectroscopic databases used by such transport codes. However, these spectroscopic databases are far from adequate and complete and there is constant demand for more complete and consistent spectral lines for the existing and newly observed molecules in space. We used the code MULTIMODE2 to obtain eigenvalues and eigenfunctions of the general so-called Watson Hamiltonian using variational methods. The procedure begins with a Hartree form for the wavefunction and then vibrational self-consistent field (VSCF) equations are solved for the given state (usually the ground vibrational state) The Hartree form for the wavefunction in the VSCF method is the representation of the vibrational wavefunction as a product of single-mode wavefunctions. From the converged single mode Hamiltonians a basis of virtual states is obtained and these are used in subsequent virtual space CI calculations. This is very much in the spirit of CI approaches taken in electronic structure theory. The application of this methodology for molecules with more than 4 atoms is made possible by the so-called n-mode representation of the potential3 VSCF method augmented by CI or perturbation theory results in improved vibrational frequencies. These methods can accurately solve the problem of coupled vibrations, which physically arise because the vibrationally excited states of polyatomic molecules exhibit displacements, so large that anharmonicities become important, causing the harmonic modes to mix. Following the (ro-)vibrational state calculations we compute Einstein coefficients and spectral intensities for all allowed transitions. However, a stringent requirement for these calculations is a highly accurate potential energy surface. Ab initio-based, full-dimensional potential energy surfaces (PES) are employed in this work. These potentials are global fits to of the order of 104 electronic energies using a basis of polynomials in Morse-like functions of all the internuclear distances. The polynomial basis is invariant with respect to all permutations of like atoms and, as a result, yield highly compact and accurate representations of the PES. Similar techniques are also employed to represent the dipole moment surface (DMS)4 for a polyatomic molecules in the normal coordinate space using full dimensional permutationally invariant potential energy surface. The VSCF, VCI and PES generation scheme, together, can consistently deliver high accuracy spectral lines for large number of molecules for radiation transport application in astrophysics. Chemically interesting singlet carbocation C2H + 5 , known as the ethyl cation, is of special interest in the field astrophysics, specially in the ionosphere of Titan, due to the recent observations by cassini spacecraft. Ethyl cation exhibits interesting structural minimum and transition state, namely the bridged structure (or non-classical) and the Y-shape (or classical) structure. The calculations performed at the Hartree-Fock level of theory found the classical form to be a real minimum and the bridged structure to be less stable than the classical form. However, as soon as correlation effects are taken into account the classical form turns out to be a first order saddle point and less stable than the non-classical form. In the lower-lying structure, referred to as the _bridged஠structure (or non-classical structure), one hydrogen forms a bridge with the two carbon nuclei and the other four hydrogen atoms (two hydrogen on each carbon nuclei) are nearly co-planar with the two carbon atoms. Semi-global potential energy surface is developed using the method described above with the electronic structure energy calculated using the fourth order MˋLLER-PLESSET (MP4) perturbation theory with contributions due to single, double, triple and quadruple excitations to the electron correlation energy(MP4(SDTQ)). The dipole moment surface is calculated at the MP2 level of theory. Multimode code is used to calculate the vibrational energies up to 4000 cm-1 . Zero point vibrational energy is further compared with Diffusion Monte Carlo (DMC) calculations. The other most interesting and extensively studied molecule is methane. Adiabatic rotation approximation is used to obtain Hamiltonian for rotating molecule. Ro-vibrational energies, transition matrix elements and Einstein coefficients are calculated for J = 0, 1, 3, 5, 10, 15, 20, 25, 30. The present calculations are in good agreement with the well established HITRAN database for methane.