1. SILYL FLUORIDE: LAMB-DIP SPECTRA and EQUILIBRIUM STRUCTURE Cristina PUZZARINI and Gabriele CAZZOLI Dipartimento di Chimica “G. Ciamician”, Università di Bologna Jürgen GAUSS Institut für Physikalische Chemie, University of Mainz Columbus — June 26, 2009

2. 1) Hyperfine Structure: - Instrument & Technique - Instrument & Technique - Theory & Computations - Theory & Computations

3. 1) Hyperfine Structure: - Instrument & Technique - Instrument & Technique - Theory & Computations - Theory & Computations

4. MILLIMETER-WAVE EXPERIMENTAL SET-UP BLOCK DIAGRAM OF THE 50-800 GHz SPECTROMETER BLOCK DIAGRAM OF THE 50-800 GHz SPECTROMETER SYNTH 10 kHz-1 GHz MULT fSfS nfSnfS MIX MULT SYNCR ref: 20 MHz RF OSCILL 3.7- 7.6 GHz f RF 20 MHz 90 MHz |f G - mf RF | GUNN P. SUPPLY and SYNCR ref: 73 MHz |f RF - nf S | HP8642A SYNTH MIX corr fGfG fGfG MULTIPLIER InSb DETECTOR PREAMPL LOCK - IN 10 MHz freq. standard 1.666 kHz ref GUNN DIODES THERMOSTAT or liquid N 2 system

5. Measurements: Lamb-dip technique Corner cube mirror Cell InSb detector Polarizer Frequency modulated source Scheme of the radiation path Using free-space cell G. Cazzoli & L. Dore, J. Mol. Spectrosc. 143, 231 (1990).

6. 1) Partial saturation 2) Only Doppler profile 3) Rad: back and forward Measurements: Lamb-dip technique + v za - v za vz= 0vz= 0vz= 0vz= 0

7. Measurements: Lamb-dip technique CH 2 BrF Doppler Lamb-dip

8. 1) Hyperfine Structure: - Instrument & Technique - Instrument & Technique - Theory & Computations - Theory & Computations

9. Parameters of Rotational Spectroscopy Rotational Hamiltonian Rotational constants Effective Hamiltonian: determination of H Rot via quantum chemistry

10. Parameters of Rotational Spectroscopy Rotational Hamiltonian Rotational constants Nuclear quadrupole coupling constants Effective Hamiltonian: determination of H Rot via quantum chemistry

11. Parameters of Rotational Spectroscopy Rotational Hamiltonian Rotational constants Nuclear quadrupole coupling constants Spin-rotation interactions Effective Hamiltonian: determination of H Rot via quantum chemistry

12. Parameters of Rotational Spectroscopy Rotational Hamiltonian Rotational constants Nuclear quadrupole coupling constants Spin-rotation interactions Spin-spin (direct) interactions interactions Effective Hamiltonian: determination of H Rot via quantum chemistry

13. Quantum-Chemical Calculation of Spectroscopic Parameters Spin-rotation interaction Spin-rotation interaction second-order property: requires second derivatives of energy

14. requires equilibrium geometry: no „electronic property“ addditional contribution due to:  indirect spin-spin coupling (usually negligible) Quantum-Chemical Calculation of Spectroscopic Parameters Spin-spin coupling Spin-spin coupling DIPOLAR SPIN-SPIN COUPLING TENSOR  vibrational corrections (anharmonic force field)

15. Beyond the Rigid-Rotator Approximation COUPLING of ROTATIONAL and VIBRATIONAL MOTION  Vibrational corrections to properties: PERTURBATION THEORY starting from the rigid-rotator harmonic oscillator approximation the rigid-rotator harmonic oscillator approximation Vibrational corrections require: anharmonic force field calculations anharmonic force field calculations

16. Accurate hyperfine parameters >>>> Main requirements : - accurate method - cc basis set - CV corrections - vibrational corrections

17. Accurate hyperfine parameters >>>> Main requirements : - accurate method [CCSD(T)] - cc basis set - CV corrections - vibrational corrections

18. Accurate hyperfine parameters >>>> Main requirements : - accurate method [CCSD(T)] - cc basis set [n  Q] - CV corrections - vibrational corrections

19. Accurate hyperfine parameters >>>> Main requirements : - accurate method [CCSD(T)] - cc basis set [n  Q] - CV corrections [additivity/CV bases] - vibrational corrections

20. Accurate hyperfine parameters >>>> Main requirements : - accurate method [CCSD(T)] - cc basis set [n  Q] - CV corrections [additivity/CV bases] - vibrational corrections [ff: -correlated method method -basis: n  T]

21. 1) Hyperfine Structure: - Instrument & Technique - Instrument & Technique - Theory & Computations - Theory & Computations RESULTS RESULTS

22. (values in kHz) Theory F C N (C xx =C yy ) 2.71 C K (C zz ) 44.94 H C xx 0.64 C yy -1.19 C zz -6.64 C xz 0.60 C zx 3.03 H-F -3D 1 (1.5 D zz ) -11.36 -0.5D 2 ( (D xx -D yy )/4 ) -1.75 H-H 1.5D 3 (1.5 D zz ) 12.46 28 SiH 3 F 28 SiH 3 F C FOUR : http://www.cfour.de THEORY: Equilibrium: (ae)CCSD(T)/aug-cc-pCVQZ Vib. Corrections: (ae)CCSD(T)/cc-pCVTZ

23. 28 SiH 3 F 28 SiH 3 F

25. (values in kHz) TheoryExperiment F C N (C xx =C yy ) 2.71 2.71 fixed C K (C zz ) 44.94 45.74(35) H C xx 0.64 C yy -1.19 C zz -6.64 C xz 0.60 C zx 3.03 H-F -3D 1 (1.5 D zz ) -11.36 -0.5D 2 ( (D xx -D yy )/4 ) -1.75 H-H 1.5D 3 (1.5 D zz ) 12.46 28 SiH 3 F 28 SiH 3 F

26. (Values in kHz) Theory F C N (C xx =C yy ) 2.69 C K (C zz ) 44.93 Si C N (C xx =C yy ) -8.89 C K (C zz ) -41.89 H C xx 0.63 C yy -1.18 C zz -6.64 C xz 0.59 C zx 3.03 F-Si 1.5D 3 (1.5 D zz ) 16.45 F-H -3D 1 (1.5 D zz ) -7.46 -0.5D 2 ((D xx -D yy )/4) 4.84 Si-H -3D 1 (1.5 D zz ) -11.30 -0.5D 2 ((D xx -D yy )/4) -1.73 H-H 1.5D 3 (1.5 D zz ) 12.42 29 SiH 3 F 29 SiH 3 F C FOUR : http://www.cfour.de THEORY: Equilibrium: (ae)CCSD(T)/aug-cc-pCVQZ Vib. Corrections: (ae)CCSD(T)/cc-pCVTZ

27. 29 SiH 3 F 29 SiH 3 F

28. recorded in natural abundance

29. (values in kHz) Theory F C N (C xx =C yy ) 2.23 C K (C zz ) 45.46 30 SiH 3 F 30 SiH 3 F C FOUR : http://www.cfour.de THEORY: Equilibrium: (ae)CCSD(T)/aug-cc-pCVQZ Vib. Corrections: (ae)CCSD(T)/cc-pCVTZ

30. 30 SiH 3 F 30 SiH 3 F

31. recorded in natural abundance

32. 2) Equilibrium Structure: - semi-exp structure - semi-exp structure - pure ab initio structure - pure ab initio structure

33. 2) Equilibrium Structure: - semi-exp structure - semi-exp structure - pure ab initio structure - pure ab initio structure

34. Empirical equilibrium structure from EXPERIMENT (various isotopic species) From THEORY (cubic force field)

35. 1) 28 SiH 3 F: A 0 & B 0 1) 28 SiH 3 F: A 0 & B 0 2) 28 SiD 3 F: A 0 & B 0 2) 28 SiD 3 F: A 0 & B 0 3) 29 SiH 3 F: B 0 3) 29 SiH 3 F: B 0 4) 29 SiD 3 F: B 0 4) 29 SiD 3 F: B 0 5) 30 SiH 3 F: B 0 5) 30 SiH 3 F: B 0 6) 30 SiD 3 F: B 0 6) 30 SiD 3 F: B 0 7) 28 SiHD 2 F: A 0, B 0 & C 0 7) 28 SiHD 2 F: A 0, B 0 & C 0 8) 28 SiH 2 DF: A 0, B 0 & C 0 8) 28 SiH 2 DF: A 0, B 0 & C 0 B 0 from EXPERIMENT (various isotopic species) (various isotopic species) - harmonic ff: analytic 2nd deriv. of E - anharmonic part: numerical differ. Vibrational Corrections from THEORY (cubic force field: (all)CCSD(T)/CVTZ ) Actual FIT: Actual FIT: moments of inertia

36. Computation of Cubic and Quartic Force Fields cubic force fields: cubic force fields: single numerical differentiation along q r quartic force fields: quartic force fields: double numerical differentiation along q r Schneider & Thiel, Chem. Phys. Lett. 157, 367 (1989) Stanton et al., J. Chem. Phys. 108, 7190 (1998) C FOUR : http://www.cfour.de THEORY: Cubic Force Field: (ae)CCSD(T)/cc-pCVTZ (ae)CCSD(T)/cc-pCVTZ

37. 2) Equilibrium Structure: - semi-exp structure - semi-exp structure - pure ab initio structure - pure ab initio structure

38. Best estimated equilibrium structure - geometry optimization : (bases: cc-pVn Z, n =Q,5,6; cc-pCV5Z) - full-T corrections : (basis: cc-pVTZ) - pert-Q corrections : (basis: cc-pVDZ) - on the whole :

39. 2) Equilibrium Structure: - semi-exp structure - semi-exp structure - pure ab initio structure - pure ab initio structure RESULTS RESULTS

40. (dist: Å / ang: º) F-SiSi-H  HSiF CCSD(T)/VQZ1.60071.4755108.34 CCSD(T)/V5Z1.59701.4745108.34 CCSD(T)/V6Z1.59631.4744108.33 CBS1.59611.4744108.31 CBS+CV1.59091.4699108.31 CBS+CV+full-T1.59111.4701108.31 CBS+CV+full-T+(Q)1.59151.4702108.32 Pure ab initio equilibrium structure: basis set convergence and higher excitations

41. EQUILIBRIUM STRUCTURE: pure ab initio structure vs semi-experimental geometry (dist: Å / ang: º) F-SiSi-H  HSiF CBS+CV+full-T+(Q)1.59151.4702108.32 Semi-experimental [uncertainties: 3  ] 1.5906(1)1.4698(2)108.29(2)

42. THANK YOU for your attention!! THANK YOU for your attention!!