1. National Aeronautics and Space Administration RECENT CHANGES IN THE SPFIT PROGRAM SET H. M. Pickett Jet Propulsion Laboratory, California Institute of Technology

2. National Aeronautics and Space Administration June 21, 2006 Molecular Spectroscopy Symposium 2 Outline Introduction Specifying width of a blend Specifying phase Improved capabilities for -doubling Internal rotation frequencies and intensities

3. National Aeronautics and Space Administration June 21, 2006 Molecular Spectroscopy Symposium 3 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: 359 vibronic states, 9 spins, Euler series, internal rotation, spin interactions with high-order symmetry (e.g. CH 3 O). SPFIT and SPCAT

4. National Aeronautics and Space Administration June 21, 2006 Molecular Spectroscopy Symposium 4 Nature of Spectroscopic Fitting and Prediction Human Spectroscopic Interface: –Line Frequency, Upper-state Quantum Numbers, Lower-state Quantum Numbers –Parameters and matrix operators: H = Σ k Parameter k Operator k Where H is the Hamiltonian matrix and Operator is a matrix operator of type k, and Parameter k 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 = E Q’,q’ – E Q”,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

5. National Aeronautics and Space Administration June 21, 2006 Molecular Spectroscopy Symposium 5 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

6. National Aeronautics and Space Administration June 21, 2006 Molecular Spectroscopy Symposium 6 Diagonalization Option (Assignment Method) If Hamiltonian is separable, program now always assigns eigenvector to the correct subset of basis functions. Example: CH 3 F has A and E symmetry states in the same Hamiltonian block that are not mixed. DIAG=0 now works on A & E sub-block separately.

7. National Aeronautics and Space Administration June 21, 2006 Molecular Spectroscopy Symposium 7 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

8. National Aeronautics and Space Administration June 21, 2006 Molecular Spectroscopy Symposium 8 Phase Choice For Wang Block 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 –Phase convention is ( i ) F(s) where F(0) = 0 and F(s) = 0 or 1 for s = 1,2,3 –Number of non-trivial choices is 8 –The best phase convention is selected behind the scenes, based on the parameter set selected For example, with the standard phase P a P b is real, P a and P b are imaginary, but with a different convention all 3 operators can be real. The phase convention can also be forced using a new option-line parameter

9. National Aeronautics and Space Administration June 21, 2006 Molecular Spectroscopy Symposium 9 Improved Capabilities for -doubling Explicit way to specify z operator Extension of K-origin ‘operator’ to -doubling basis Fix bugs in treatment of K=0 for -doubling basis –Modified Wang: |N, K, > ± |N, -K, - > Can specify z = 3 for three-fold symmetric rotor Provide capability for distinct Δ ≠ 0 operators with ΔK Δ 0 Provide capability for calculation of (ε ab – ε ba ) (S a N b + N b S a – S b N a – N a S b ) –Since the diagonal tensor components of spin-orbit parameters, e.g ε aa, can be quite large, ε ab and ε ba can have a significant effect on the spectrum

10. National Aeronautics and Space Administration June 21, 2006 Molecular Spectroscopy Symposium 10 Two Approaches to Internal Rotation (IAMCALC) 1.Fourier series in cos(2π n ρ K avg / 3) and sin(2π n ρ K avg / 3) –Works well for torsional states below the barrier –Can use an empirical fit of Fourier series or use Mathieu equation (IAMCALC) 2.Use torsional operators sampled at integer K –Best for excited torsional states –Lose capability to extrapolate in K. ρ is not fitted directly in SPFIT, but -2FΔρ (P α – ρK) K can fit differences IAMCALC calculates expectation values of torsional operators of form, ΔK =0,±1,±2 –Can sample ρK from -3/2 to 3/2 to produce Fourier series –Can sample integer K to produce torsional matrix elements –IAMCALC tested operator by operator against I. Kleiner’s program (with no diagonalization) –Have fitted methanol (vt=0,1,2), acetaldehyde (vt=0,1,2), methyl formate (vt=0,1), hydroxyactone (vt=0), and CH 3 NH 2 (vt=0)

11. National Aeronautics and Space Administration June 21, 2006 Molecular Spectroscopy Symposium 11 Methanol Energies, A State Energy is periodic in rho K with period of 3 Energies of E states have phase shift of ±1 in rho K relative to A state v = 3 has an avoided crossing with v=4 near K = 0

12. National Aeronautics and Space Administration June 21, 2006 Molecular Spectroscopy Symposium 12 Interim Conclusions SPFIT/SPCAT program set now has capability for more interactions with selectable or implied phase conventions, with improved -doubling specification. Enhancements for internal rotation and use of blends should also be useful. Several fields have expanded meaning and two have been added –New XOPT field on option line for.par file for new internal rotation features, Lz option, and phase –New definitions on option line for IAX and EWT –New MAXV field on 2 nd line of.INT file to suppress SPCAT output for v > MAXV Source code and windows executables are available for free at http://spec.jpl.nasa.gov/ftp/pub/calpgm/ or anonymous ftp at the same address http://spec.jpl.nasa.gov/ftp/pub/calpgm/

13. National Aeronautics and Space Administration June 21, 2006 Molecular Spectroscopy Symposium 13 Backup

14. National Aeronautics and Space Administration June 21, 2006 Molecular Spectroscopy Symposium 14 Predicting Intensities Absorption cross-section (units = m 2 )  density (m -3 ) = absorption coefficient (m -1 ) Integrated absorption cross-section (units = Hz m 2 ) 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 |  | 2, where  is the transition dipole –  = Σ k  -parameter k Operator k –Relative signs of the dipole parameters can be important

15. National Aeronautics and Space Administration June 21, 2006 Molecular Spectroscopy Symposium 15 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