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National Aeronautics and Space Administration Theory of Molecular Frequencies H. M. Pickett Jet Propulsion Laboratory, California Institute of Technology National Aeronautics and Space Administration SPFIT and SPCAT • Fitting and prediction programs for JPL Molecular Spectroscopy Catalog – Core software developed to replace special purpose spectroscopy programs • Introduced well thought-out organization of the program with modular function calls and data structures. Uses spherical tensor formulation of rotation and spin operators, so diagonal and off-diagonal matrix operators are calculated consistently. • Originally written in FORTRAN-77, but recoded to ‘c’ for dynamic memory allocation and portability. Currently tested with Microsoft Visual C++ and gnu gcc. • Many features have been added, but I have tried to keep input formats backward compatible. • Current capabilities: 280 vibronic states, 9 spins, Euler series, internal rotation, spin interactions with high-order symmetry (e.g. CH3O). Oct. 19-20, 2006 Caltech Spectroscopy Workshop 2 National Aeronautics and Space Administration Nature of Spectroscopic Fitting and Prediction • Human Spectroscopic Interface: – Line Frequency, Upper-state Quantum Numbers, Lower-state Quantum Numbers – Parameters and matrix operators: H = Σk Parameterk Operatork • Where H is the Hamiltonian matrix and Operator is a matrix operator of type k, and Parameterk is a numerical value • Usually H is factorable into finite dimension Hermitian sub-blocks • Each block of H must be diagonalized to give energy • Computer View: – Line Frequency = EQ’,q’ – EQ”,q” where Q labels a block of the Hamiltonian and q labels the index for a particular eigenvector within block Q – Line Frequency can be an energy or can represent lines that do not have any absorption strength. – SPFIT is restricted to cases where H is a purely real matrix Oct. 19-20, 2006 Caltech Spectroscopy Workshop 3 National Aeronautics and Space Administration Automated Spectroscopic Fitting and Prediction • There is no automated algorithm for assigning quantum numbers to an observed line frequency – SPFIT/SPCAT defines a mapping of quantum numbers to Q and q, although the determination of q is much more arbitrary. – The quantum number assignment is the most important task where the skill of a well-trained spectroscopist is needed • Several Graphical User Interfaces have been developed to aid assignment that use SPFIT/SPCAT as computational core • Options for Gaussian quantum program have been developed to ouput calculations in SPCAT format • Fitting line frequencies involves least square fitting of line frequencies to the Parameters and can be very non-linear – Need a good starting point Oct. 19-20, 2006 Caltech Spectroscopy Workshop 4 National Aeronautics and Space Administration Predicting Intensities • Absorption cross-section (units = m2) × density (m-3) = absorption coefficient (m-1) • Integrated absorption cross-section (units = Hz m2) is directly related to spontaneous emission rate through the Einstein detailed balancing – Units of JPL catalog are MHz (nm)2 • Cross-section is proportional to |μ|2, where μ is the transition dipole – μ = Σk μ-parameterk Operatork – Relative signs of the dipole parameters can be important Oct. 19-20, 2006 Caltech Spectroscopy Workshop 5 National Aeronautics and Space Administration Predicting Intensities (con.) • The dipole parameters are scalar constants obtained usually from Stark effect (shifts of line frequencies in an electric field) or from Zeeman effect (shifts of line frequencies in a magnetic field) – Dipole parameters can include first and second order Hermann-Wallis corrections (centrifugal distortion effects on the dipole) – SPCAT can output contributions to the transition dipole as well as intensities, allowing fitting of Stark effect in the presence of centrifugal distortion – SPCAT computations of Dipole operators use the same routines as computation of Energy operators (an anti-bugging advantage). – User can specify both electric and magnetic dipoles Oct. 19-20, 2006 Caltech Spectroscopy Workshop 6 National Aeronautics and Space Administration Recent Extensions to SPFIT/SPCAT (1 / 3) • New option for blends – Old option: successive lines in .lin file with the same frequency are considered weighted blend if uncertainty is the same – New: if last line in the .lin file with the same frequency has uncertainty xerr that is at lest 2 times larger, then the rms width of the blend is included in the fit with uncertainty of xerr. The quantum numbers for this last line are ignored 9 9 0 8 8 0 234123.44 0.4 1.0 9 9 1 8 8 1 234123.44 0.4 1.0 9 9 1 8 8 1 234123.44 2.0 1.0 • New spin coupling scheme for 3-fold through 6-fold symmetric tops with hyperfine, e.g. CH3O. Allows full symmetry to be applied with no states that are not allowed by spin statistics. – Augments earlier capability to couple 2 equivalent spins together so that proper ortho- para symmetry is retained, e.g. ClOCl Oct. 19-20, 2006 Caltech Spectroscopy Workshop 7 National Aeronautics and Space Administration Recent Extensions to SPFIT/SPCAT (2 / 3) • New option for increased phase flexibility – Standard phase convention for Wang block is (i)s, where s = 0,1,2,3 for ee, oe, oo,eo, respectively • This makes all even-order operators real and all odd-order operators imaginary – Earlier versions were very permissive, allowing user to specify imaginary operators that are actually anti-symmetric because i was ignored – We then required that all operators diagonal in v be real and several applications to fail that had ‘worked before.’ – We were able to identify 8 different Wang block phase conventions – The best phase convention is selected behind the scenes, based on the parameter set selected • For example, with the standard phase PaPb, Pa and Pb only PaPb is real, but with a different convention all 3 operators can be real. • The phase convention can also be forced using a new option-line parameter Oct. 19-20, 2006 Caltech Spectroscopy Workshop 8 National Aeronautics and Space Administration Recent Extensions to SPFIT/SPCAT (3 / 3) • Inclusion of Euler series – Provides better convergence than standard power series, particularly for light molecules like water • Improved capabilities for l-doubling basis – Explicit way to specify lz operator – Extension of K-origin ‘operator’ to l-doubling basis – Fix bugs in treatment of K=0 for l-doubling basis – Provide capability for distinct Δl ≠ 0 operators with ΔK Δl < 0 and ΔK Δl > 0 • Provide capability for calculation of (εab – εba) (SaNb + NbSa – SbNa – NaSb) – Since the diagonal tensor components of spin-orbit parameters, e.g εaa, can be quite large, εab and εba can have a significant effect on the spectrum Oct. 19-20, 2006 Caltech Spectroscopy Workshop 9 National Aeronautics and Space Administration Methanol Energies, A State 3000 • Energy is periodic in rho K with period of 3 2500 • Energies of E states have phase shift of ±1 in rho K relative to A state 2000 V_3 • v = 3 has an avoided crossing with v=4 v=0 near K = 0 v=1 Energy v=2 1500 v=3 v=4 v=5 1000 v=6 500 0 -1.5 -1 -0.5 0 0.5 1 1.5 rho * K Oct. 19-20, 2006 Caltech Spectroscopy Workshop 10 National Aeronautics and Space Administration Future Extensions to SPFIT/SPCAT • Current program is mature, and don’t I expect to make sweeping changes – Current capabilities of SPFIT appear adequate for astrophysics needs – Limiting resource is spectroscopic expertise • We need to explore if there are better ways of handling torsional states above the barrier along with states below the barrier – Perturbations not enfolded into the pure torsional problem are mixing across vibrations that are not well characterized • We would like to cross-compare different programs that calculate internal rotation (program A generates noise-free energies and/or lines, program B fits these lines) – JPL has started these tests and it looks feasible and useful Oct. 19-20, 2006 Caltech Spectroscopy Workshop 11

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posted: | 10/30/2008 |

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