Calculation of Highly Accurate Rovibrational Spectra for Molecules Containing a Large-Amplitude Motion: Ammonia

Xinchuan Huang, David W. Schwenke, Timothy J. LeeSpace Science and Astrobiology Division

NASA Ames Research Center, Moffett Field, CA

Joel M. BowmanDepartment of Chemistry, Emory University

The Astrochemistry Lab

Thanks for a great start Russ!

Other Spectroscopy Studies

• Development of an approach for QFF calculations wherein small corrections are included in the QFF.

• Application of this procedure to H2O, HO2+, NH2

-, CCH-, etc…• Calculation of a global PES and DMS for CO2; empirical

improvement, and generation of an accurate line list with intensities; accurate to high temperatures.

• Similar studies for CH3OH and CH3CN, but lower temperature.• Studies of the electronic spectroscopy of PAHs, PAH derivative

compounds, and PAH clusters (e.g., Extended Red Emission).• Comparison of different approaches for computing rovibrational

energy levels.• Calculation of fundamental vibrational frequencies for

cyclopropenylidene using CCSD(T) with approximate integrals.

NASA IR Astronomy Missions

• NASA has several missions aimed at infrared astronomy: SOFIA, Spitzer, Herschel, JWST.

• Spitzer Space Telescope is in operation, but the IR spectra are relatively low-resolution.

• SOFIA (Stratospheric Observatory for Infrared Astronomy) is an airplane-based observatory, which should allow for updates to instruments periodically.

• The Herschel Space Observatory is mainly an ESA endeavor with some NASA involvement; Launch scheduled for 2008.

• James Webb Space Telescope (JWST) is scheduled for launch in 2011.

• Beginning of a Golden Age for IR and Far IR Astronomy!

Ammonia in the Universe

• First polyatomic molecule observed in the interstellar medium (ISM); 1968, Townes and coworkers.

• Found in a wide range of celestial environments and objects:1. Cold ISM (ices and mixed ices); 0-100 K2. Uranus, Neptune, Saturn, and Titan; 50-100 K3. External galaxies (NGC 253, etc.); 140-400 K4. Atmosphere of Jupiter; ≈500 K5. Sgr B2 molecular cloud complex; ≈700 K6. T dwarfs: e.g., Gl 570D (≈800 K), and Gl 229B (≈1000 K)7. L dwarfs; ≈1500K

• Ammonia’s rovibrational spectrum is highly temperature sensitive due to the presence of the umbrella or inversion mode -- its spectrum can be used to characterize the temperature of its environment.

• Present day knowledge of its rovibrational spectrum is not adequate, especially for high temperature environments (i.e., anything over 300 K).

Comparison of a synthetic spectrum (solid line) based on the HITRAN database with an observed spectrum (histogram) of Gl 570D from the IRS instrument on the Spitzer Space Telescope.

IR fundamental band of the NH3 Inversion mode

RMS for line positions: 5.5 cm-1 over 1800 – 18000 cm-1

Limited to 296 K.

Not suitable for astronomical analysis!

500 cm-1

Fundamental band of NH3 Inversion mode

calc

obs

Present HITRAN NH3 IR Spectral Database

What Can Theory Do?

• Over the last 18 years, CCSD(T) studies on small molecules have shown that purely theoretical predictions can be very accurate, predicting fundamentals to within a few cm-1.

• Theoretical rovibrational spectroscopy, if including small effects, is approaching an uncertainty <1.0 cm-1, for absolute transition energies, with rotational patterns even more reliable.

• Small effects: core-correlation; basis set extrapolation; higher-order correlation; scaler relativistic; diagonal B-O correction.

• Empirical improvement of a highly accurate ab initio PES using high-resolution experimental data can lead to uncertainties of <0.07 cm-1 for absolute transition energies, even for high temperature spectra -- e.g., H2O

• Must start with a highly accurate ab initio PES for extrapolation! And the PES must be global!

Comparison of an observed spectrum (Bernath and coworkers) from a sunspot (red line) with a synthetic spectrum (black line) including H2O, OH, and CO.

H2O IR simulation at 3400 K

Excellent agreement|∆| < 0.05 cm-1 for freq|∆| < 5 – 10 % for Icalc

4 cm-1 width

Based on refined ab initio PES (Schwenke andPartridge, 1996)

D.F. Carbon, Unpublished.

Accurate Line List with Intensities for Ammonia

• Our goal is to produce an accurate line list, with intensities, for NH3 and all isotopologues that is high-resolution and reliable for high temperatures -- up to 20,000 cm-1 above ZPE.

• This data is needed now to interpret observations coming from NASA observatories, such as the Spitzer Space Telescope.

• Accurate line list will be even more important in the coming decade as much higher-resolution space telescopes (Herschel and JWST) and airborne observatories (SOFIA) come on line.

• An accurate NH3 line list will allow for the reliable physical characterization of many celestial environments and objects, e.g. understand what conditions allow ND3 to accumulate.

• For the very high-resolution instruments, this will also allow NH3 spectra to be subtracted out, thus revealing new species to be observed that otherwise would be impossible.

Previous Theoretical Work

• 1992: Martin et al. produce first CCSD(T)/QZ quartic force field for NH3 with 5-10 cm-1 errors for fundamentals -- error for inversion mode much larger. QFF expanded about the C3v minimum, no splittings, not adequate for high energies (i.e., 20,000 cm-1).

• 2004: Rajamaki et al. generate a CCSD(T) based PES that includes so-called small corrections (core correlation, DBOC, scalar relativity, higher-order correlation, 2-pt basis set extrapolation) for some degrees of freedom, but not all. Quartic expansion about a 2D cut of the sym + inv modes; D3h reference structure. Agreement for rovibrational levels below 5000 cm-1 is good, <2 cm-1 error. Not empirically improved. Long range part of PES not adequate for high energies.

• 2005: Yurchenko et al. compute PES/DMS that is CCSD(T) based (core correlation, 2-pt basis set extrapolation, scalar relativity, expanded about C3v minimum). Agreement for rovibrational levels below 6100 cm-1 is ok (<10 cm-1 errors), but deteriorates rapidly up to 10,300 cm-1. Empirically improved PES gives much better agreement below 5000 cm-1 (<0.4 cm-1 errors). Long range part of PES not adequate for high energies.

General Procedure

• Compute the best possible ab initio data at a series of points, including, 3-point basis set extrapolation, core correlation, scalar relativity, DBOC, and higher-order correlation correction at every point.

• Fit points to produce analytical, realistic global PES and DMS.

• Refine the PES using reliable high-resolution laboratory data.

• Use final PES and DMS to compute accurate rovibrational energies and wavefunctions (differences between rovibrational energies line positions; compute transition dipole matrix elements line strengths).

• Release to public the sorted millions of spectral lines and line positions for use in interpreting/analyzing astronomical data.

Form of the PES

• The PES was written as a sum of short and long range parts: V = VShort + VLong

Where• P full permutation of the 3 H atoms (units of Bohr, radian, and cm-1).

• 12th order fit (for VShort) leading to 3393 coefficients.

• De was raised by 10,000 cm-1 above the experimentally derived value in order to yield smooth 1D dissociation curves.

Mixed Ab Initio PES

• Several PESs were fit and tested, e.g., with the ACPF/TZ or ACPF/QZ correction, or without it; 2pt extrapolation vs. 3pt extrapolation; for 2pt extrapolation, TQ vs. Q5; with and without the DBOC.

• Rovibrational energies calculated with all these PESs were compared with experiment for reliable lines below 6000 cm-1.

• Findings: 3pt extrapolation is more accurate and preferred; include DBOC; difference between ACPF/TZ and ACPF/QZ is small, but…

• Our “Best” ab initio PES results from a mixture of surfaces where the ACPF/TZ correction is included or neglected.

• That is, if sum(indices for N-H str) > sum(indices for bond angles), use ACPF/TZ coefficients, otherwise use no-ACPF coefficients. This is the PES we refer to as “Best.”

Comparison to Previous Work: < 5000 cm-1

• Mixed potential performs best of our new potentials.

• Transition energies are better than Yurchenko et al., but not splits below 5000 cm-1.

• Rajamaki et al. better for transitions below 5000 cm-1.

• Higher transition energies?

Comparison to Previous Work: Up To 10,300 cm-1

• Quality of Mixed potential retained above 5000 cm-1.

• RMS error for transition energies up to 10,300 cm-1, similar to that for up to 5000 cm-1.

• Significant improvement over Yurchenko et al.

Spectrum From Ab Initio PES

• Ab initio (red; J ≤ 4) room temperature spectrum compared with HITRAN (green; includes higher J).

Agreement for J ≤ 4 energy levels is very good.

Agreement for IR intensities is also very good.

Empirical Refinement

• The first step in the refinement procedure is to identify which high resolution experimental data is reliable enough to use in the refinement -- Schwenke found that 2-3% of the HITRAN data for H2O was unreliable.

• Our initial analysis is complete, and for NH3 we have rejected conflicting assignments, low-resolution observations, and/or those observations associated with large uncertainties. We expect to re-assign 5-10% of the spectroscopic data in the current HITRAN database.

• During the refinement procedure, it is useful to have higher energy spectra, even if unassigned, with which to compare as a check. We are in contact with spectroscopists at JPL who have many unassigned spectra.

• An initial rovibrational basis has been obtained for the refinement procedure and utilized to compute new eigenvalues and new eigenvectors on empirically adjusted potentials.

• Optimization thus far includes J=0-2 states; up to quartic constants varied; max variation is < 8.5%.

• We expect to complete the refinement step by the end of 2008.

Comparison to Previous Work: < 5000 cm-1

• Empirically adjusted surface significantly better than earlier work.

• Errors now small enough that we are identifying even small errors/inconsistencies in HITRAN.

• Ultimately, we plan to include states up to J=5 or 6 in optimization scheme.

Comparison to HITRAN

• Actual errors relative to HITRAN are small.

• When one state appears to have a larger error, it is a “red flag”.

• We will be working with laboratory experimentalists to identify HITRAN errors and assign higher energy spectra.

Conclusions

• We are entering a golden age of sorts for high-resolution rovibrational astronomy -- but there are many data needs in order to utilize fully the enormous amount of data that will result!

• Ammonia is one molecule for which an accurate line list + intensities for transitions up to 20,000 cm-1 above ZPE is needed.

• Due to its inversion mode, ammonia’s rovibrational spectrum is very temperature sensitive, and thus it can be used to physically characterize its environment, if such data were available.

• Ammonia is found in a wide variety of celestial environments and objects -- from a few K to 1500 K, and possibly hotter.

• While very good, none of the previous NH3 PESs are reliable for energy levels up to 20,000 cm-1, nor the accuracy needed.

• We have completed a new ab initio PES that is reliable to high energies, and we are in the process of empirically improving it; -- initial refinement is very promising.

Acknowledgements

Funding from the Following NASA Programs is gratefully acknowledged:

• The GO-4 Cycle from the Spitzer Science Center• NASA’s contribution to the ESA Mission Venus Express• NASA’s Astronomy and Physics Research and Analysis Program• The GO-0 Cycle from the Herschel Science Center• The NASA Postdoctoral Program

Ab Initio Calculations

• CCSD(T) calculations with TZ, QZ, 5Z correlation consistent basis sets (diffuse and core functions included); core correlation and scalar relativity (Douglas-Kroll) included directly.

• 3-point extrapolation of CCSD(T) energies to the one-particle basis set limit: E(l) = E() + B•(l+1/2)-4 + C•(l+1/2)-6

• Higher-order correlation correction included to approximate FCI: TZ = E(icACPF/TZ) – E(CCSD(T)/TZ), or QZ = E(icACPF/QZ) – E(CCSD(T)/QZ)

• Diagonal Born-Oppenheimer correction computed at the icMRCI level of theory.

• Very tight convergence thresholds used in all phases of calculations (tight enough for QFF calculations).

• Distribution of points governed by energy at 1500 cm-1 increments.

Higher-Order Correlation Correction

• Internally contracted Averaged coupled pair functional (icACPF) used to approximate FCI.

• The CAS reference space was augmented with one additional orbital.

• icACPF, like most multireference methods, is prone to incorrect solutions.

• Plot at left was used to identify and eliminate or re-run outliers.

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

Energy Distribution of Points for PES & DMS

• At left is shown the distribution of points by energy.

• Also shown is the total number of accumulated points for a given energy.

• Less than 6000 points are needed for NH3.

Typical RMS Fitting Error

• Plot of a typical distribution of fitting errors.

• Points below 40,000 cm-1 are weighted more heavily.

• The overall fitting error is well below 0.20 cm-1 for up to 40,000 cm-1.

DMS Fitting Error• Plot of a fitting

errors (in a.u.) for different order polynomial fits for the ACPF/QZ (core correlation included) Dipole Moment Surface (DMS).

• For current needs, a 7th order fit was deemed the best compromise between accuracy and number of coefficients.

• This is a preliminary DMS, but results so far suggest that it is reliable.