Coupled-cluster theory and the discovery of astronomical molecules: A pragmatic perspective

1. Coupled-cluster theory and the discovery of astronomical molecules: A pragmatic perspective

2. Identification of molecules in space Radio astronomical detection Very sensitive technique that can allow for unambiguous detection of molecular species Searches are usually based on rotational Hamiltonians based on laboratory data Sensitivity goes with square of the molecular dipole moment First radio detection: OH in 1963; NH3, H2O, H2CO before end of decade (first polyatomics); HCO+ in 1970 (first positive ion); C6H- in 2006 (first negative ion) Strength: Observation of several lines at expected frequencies provides excellent evidence for the existence of particular species inspace Weakness: Inherent bias towards polar molecules. Questions regarding the existence of fundamental molecules like benzene, C60, etc. will never be answered by radio astronomy.

3. Infrared detection ISO satellite (European Space Agency) Operating range: 2.5 - 240 µm (42-4000 cm-1) Allows for the observation of non-polar polyatomic molecules and condensed phases (ice, for example) Can (in principle) detect near-IR electronic spectra of radicals and metastables with low-lying excited states Some molecules have extremely intense vibrational transitions A few molecules detected this way: H2CO, HF (recent), ice, OH, benzene (?), C3, C5 First detection: CO (1979, Kuiper Airborne Observatory - Lockheed C141 flying at ca. 12 km); first new molecule: C2H4 (1983), then SiH4 (1984), C2H2 and CO2(1989), CH4 (1991), others. Strength: Observation of several lines at expected frequencies provides excellent evidence for the existence of particular species inspace Weakness: Atmosphere largely opaque to long-wavelength radiation, satellites required for good data. Ultimately a less precise (more uncertain) means of molecular identification than radio astronomy. Identification often based on one (1) line!

4. The evidence for benzene in the interstellar medium

5. Optical detection ISO satellite (European Space Agency) Operating range: 2.5 - 240 µm (42-4000 cm-1) Historically the first technique used: CH discovered in space in 1937. CN and CH+ discovered during WWII. CO and H2 seen optically in 1970, N2 in 2004. Can (in principle) detect any molecule; selection rules are not as restrictive; e.g. H2 and N2 are IR and MW-inactive species. Some molecules have extremely intense electronic transitions Strength: Less difficult to obtain data than for IR. Ground-based measurements with CCD cameras now yield now yield high quality spectra. Weakness: Laboratory data for complex molecules not easy to acquire, some molecules do not have intense electronic transitions; dissociative excited states lead to broad features

7. The general process of identifying new molecules Obtain precise line positions and molecular constants in the laboratory. Determine or predict potential candidate line positions Quality (robustness) of identification depends on: PRECISION of observed line positions AGREEMENT with laboratory lines NUMBER of lines used in identification Conduct astronomical search for lines, usually choosing the strongest lines, or those that are in an accessible region of the spectrum. What can a quantum chemist do to help?

8. A different sort of synthetic chemistry Obtain precise line positions and molecular constants in the laboratory. Determine or predict potential candidate line positions C2H2, C4H2 Benzene,Toluene SiH4, H2S, S vapor N2 Conduct astronomical search for lines, usually choosing the strongest lines, or those that are in an accessible region of the spectrum.

9. C6H6 + 2000 volts and (unquestionably) many, many, many more: both known and unknown species…. The challenge to quantum chemists: Guide the laboratory searches for particular compounds The laboratory data is then used in turn to guide the astronomical search.

10. Theoretical predictions Laboratory identification Astronomical search Astronomy and astrochemistry: Models of interstellar chemistry Abundance, isotopic studies Chemical physics: Molecular properties (geometries) Studies of dynamics (S4), etc.

11. What ab initio theory can provide to laboratory searches:: Rotational Spectroscopy: Molecular geometries (re) and associated moments of inertia. Centrifugal distortion constants, dipole moments. In principle: Observable rotational constants, but not really important in general for laboratory astrophysics. ``Adequate’’ levels of theory (i.e. CCSD(T)/cc-pVTZ basis set)) Geometry optimization, harmonic force field calculation, perhaps larger basis set energy calculations. Ae, Be, Ce, CD constants Dipole moment (e)  Evaluation of anharmonic (cubic or quartic) molecular force field, followed by application of vibrational perturbation theory.    Ao, Bo, Co, CD constants Dipole moment (o)

12. Increases bond lengths Ie Be Increased treatment of correlation Basis set improvement Decreases bond lengths Ie Be

13. Be =Beexact FCI CCSD(T) MP2 CCSD SCF Be < Beexact Level of calculation Be Beexact Be > Beexact STO-3G 6-31G* cc-pVDZ cc-pVTZ cc-pVQZ Exact Basis set

14. In general, CCSD(T)/cc-pVTZ overestimates bond lengths a bit: Becalc < Beexpt However, experiments do not measure Be, but rather Bv Usually positive Molecular vibration effects tend to extend the structure (rg > re) B0 < Be Exact

15. In general, CCSD(T)/cc-pVTZ overestimates bond lengths a bit: Becalc < Beexpt However, experiments do not measure Be, but rather Bv Usually positive Molecular vibration effects tend to extend the structure (rg > re) B0 < Be Exact CCSD(T)/cc-pVTZ

16. In general, CCSD(T)/cc-pVTZ overestimates bond lengths a bit: Becalc < Beexpt However, experiments do not measure Be, but rather Bv Usually positive Molecular vibration effects tend to extend the structure (rg > re) B0 < Be Exact CCSD(T)/cc-pVTZ

17. An empirical observation: CCSD(T)/cc-pVTZ Be constants usually within 1% of experimental B0 constants, and are in better agreement than the theoretical B0 values Serve as a general-purpose guide To laboratory searches for new molecules A more or less trivial application of quantum chemistry

18. An example: Isomers of C5H2 Theory:

19. An example: Isomers of C5H2 Theory: ``eiffelene’’

20. However … heroic calculations can act to support important new claims… McCarthy, Gottlieb, Gupta and Thaddeus Ap. J. 652, L141 (2006). Laboratory spectra of C4H- and C8H- recently recorded (Gupta et al., preprint) First molecular anion found in space (carrier of U1377 in IRC+10216)

21. Vibrational Spectroscopy: With high quality atomic natural orbital basis sets, CCSD(T) and a good treatment of anharmonicity, it is now possible to predict fundamental and two-quantum level positions and intensities relatively accurately for rigid molecules (frequencies within 10 cm-1, intensities to a few percent). Laboratory spectra can be assigned by this means, a field that is well-ploughed and certainly not limited to laboratory astrophysics. An example: Overtone spectrum of nitric acid from 4000-6000 cm-1

22. These calculations require evaluation of: the harmonic, cubic and quartic force fields the first three derivatives of the dipole moment components vibrational second-order perturbation theory for levels and intensities A practical point and an advertisement: Combined with CCSD(T) and VPT2, the ANO basis sets ofTaylor and Almlöf work extremely well for vibrational level positions. But, alas… While nice, it remains a fact that infrared spectroscopy is not used as often as microwave spectroscopy as an analytical technique to detect new molecules in the astrochemistry community. Exceptions, however, exist: Maier, McMahon, others. Lack of precision in laboratory data (relative to MW) makes it less attractive.

23. Electronic Spectroscopy: Precise prediction of band positions is extraordinarily difficult (impossible) here. Accuracy of 0.1 eV (800 cm-1) is in fact rare. Using calculated band positions to guide laboratory searches is a dubious proposition. Moreover, the number of observable vibronic features much less than that typical of a microwave spectrum. And with regard to the relationship between astrophysics and quantum chemistry, things are largely inverted: Laboratory lines Molecular identity Astronomical lines MW Elec

24. Electronic Spectroscopy: Precise prediction of band positions is extraordinarily difficult (impossible) here. Accuracy of 0.1 eV (800 cm-1) is in fact rare. Using calculated band positions to guide laboratory searches is a dubious proposition. Moreover, the number of observable vibronic features much less than that typical of a microwave spectrum. And with regard to the relationship between astrophysics and quantum chemistry, things are largely inverted: Laboratory lines Molecular identity Astronomical lines MW Elec

25. The diffuse interstellar bands (DIBS) First published report of (two) DIBs in 1921 Found along lines of sight associated with reddened stars Catalog of Herbig (1975): 39 bands Catalog of Jenniskens and Desert (1994): >200 bands Source(s) of DIBS remain(s) unknown in late 2006!

26. Some ideas from the past: Molecular carriers first suspected (Struve, Russell, Saha,Swings) ca. 1937-1944 … but population of polyatomics in typical interstellar clouds thought to be too small. Led to movement towards… Solid-state carriers lots of ideas: impurities in dust grains, solid oxygen, etc. … but lack of characteristic solid-state absorption features (notably inhomogeneous broadening) led to movement towards Molecules again! An excellent review: G.H. Herbig Ann. Rev. Astrophys. 33, 19 (1995)

27. Bis-pyridyl magnesium tetrabenzoporphyrin (in part) Postulated to account for ALL diffuse interstellar bands when just 39 were known (1972) Crashed and burned in the 1970’s: Occam’s razor, spectra not reproducible.

28. Some molecular ideas: Molecular hydrogen, albeit not simply Gaps between intermediate state and higher levels fit many DIBs positions BUT } } } Model required photon fluxes of ca. 1010 s-1 Flux in typical ISM cloud: ca. 1 year-1 … insufficient by 17 orders of magnitude!

29. Polycyclic Aromatic Hydrocarbons (PAHs)

30. Polycyclic Aromatic Hydrocarbons (PAHs)

31. The Unidentified Infrared Bands (UIRs) C-H out-of-plane bend C-H in-plane bend C-C stretch C-H stretch Flux Density (10-13 W/m2/µ) NGC 7027 Orion Bar Wavelength (µ) ISO spectra of the Planet. Neb. NGC 7027 and the PDR region at the Orion Bar Peeters et al., 2003

32. The unidentified infrared (UIR) features

34. Carrier of 4429? 4435 4395

35. Corannulene, C20H10 exp= 2.07(2)D B = 509.8MHz Lovas et al., 2005

36. However, there has not been a single unambiguous detection of any PAH in space to date, despite considerable publicity. Nonpolarity is a problem, although two smallest polar PAH species have not been found Apart from benzene, there is no evidence of anything other than three-membered ring compounds in the ISM No hard evidence supports PAH carriers of DIBs

37. Something quite remarkable transpired in 1998… Tulej, Kirkwood, Pachkov and Maier ,Ap.J.Lett. 506, 69 (1998)

38. Something quite remarkable transpired in 1998… C7- !? Tulej, Kirkwood, Pachkov and Maier ,Ap.J.Lett. 506, 69 (1998)

40. Since this time, sobered experimentalists have not yet advanced another candidate An interesting puzzle, though…

41. Molecule produced in a benzene discharge, also with toluene No REMPI signal (suggests high IP - cation?) Evidence from isotopic substitution studies: Similar geometry in lower and upper states Five hydrogen atoms, two pairs of symmetry equivalent hydrogens What molecule is this? An interesting twist: No longer are we trying to identify the carrier of a line in the ISM, but the carrier of a line measured in a basement laboratory in Massachusetts Has not proven to be easy - Quantum chemistry not the best approach (we’ll discuss this shortly), only suggestion for carrier thus far seems a rather unlikely molecule. Still not solved definitively - moreover, carrier of 4429 in the laboratory probably is not carrier of astronomical line

42. Is my favorite molecule (NO3) a DIBs carrier? 6616 6235 6278 X B Absorption spectrum of NO3 (a very strong transition) From DIBS catalog: Lines at 6234.3, 6278.3 and 6613.8 v. 6235 6278 6616

43. What can quantum chemistry do to help? Calculate line positions? Most techniques have accuracies ca. 0.1-0.5 eV TDDFT CASPT, EOM-CCSD MR-CISD, EOM-CCSDT MR-AQCC Applicability Accuracy To be useful as a “screener’’ for DIBS candidates requires accuracy of ca. 100 cm-1

44. What can quantum chemistry do to help? Calculate line positions? Most techniques have accuracies ca. 0.1-0.5 eV TDDFT CASPT, EOM-CCSD MR-CISD, EOM-CCSDT MR-AQCC Applicability Accuracy To be useful as a “screener’’ for DIBS candidates requires accuracy of ca. 100 cm-1

45. Calculate absorption profiles? Experimental spectrum  Calculated spectrum for candidate molecule 

46. Calculate absorption profiles? Experimental spectrum  Calculated spectrum for candidate molecule Assignment 

47. Calculate absorption profiles? Experimental spectrum  Calculated spectrum for candidate molecule Assignment  This sort of assignment can often provide clear picture of the nature of vibronic states

48. What is required in the simulation of electronic spectra? The simplest case: The Franck-Condon approximation Applicable to most transitions from one “isolated” electronic state to another, particularly in low-energy part of the spectrum. Assumptions: (r,R) = (r;R) (R) Vibrational Wavefunction [calculated from Veff(R)] Vibronic Electronic Wavefunction Wavefunction < ’’(r,R) |  | ’(r,R) > = < ’’(r,R0) |  | ’(r,R0) > “Mij”’ Dipole operator Reference geometry

49. Vibronic level positions Electronic energy difference (adiabatic)

50. Vibronic level positions Electronic energy difference - ZPE of ground state