1. Cristina PUZZARINI Dip. di Chimica “G. Ciamician”, Università di Bologna QUANTUM-CHEMICAL CALCULATIONS of SPECTROSCOPIC PARAMETERS for ROTATIONAL SPECTROSCOPY: the NEED of the INTERPLAY between EXPERIMENT and THEORY Int. Symposium on Molecular Spectroscopy 66th Meeting – Columbus, OH – June 20-24, 2011

2. Laboratory of Millimetre-wave Spectroscopy of Bologna OUTLINE 1) QUANTUM-CHEMICAL CALCULATIONS: CALCULATIONS: Some details Some details 2) INTERPLAY between EXPERIMENT and THEORY: EXPERIMENT and THEORY: The need: why The need: why

3. Laboratory of Millimetre-wave Spectroscopy of Bologna OUTLINE 1) QUANTUM-CHEMICAL CALCULATIONS: CALCULATIONS: Some details Some details 2) INTERPLAY between EXPERIMENT and THEORY: EXPERIMENT and THEORY: The need: why The need: why

4. QUANTUM-CHEMICAL CALCULATIONS of SPECTROSCOPIC PARAMETERS For ROTATIONAL SPECTROSCOPY: the NEED of the INTERPLAY between EXPERIMENT and THEORY Int. Symposium on Molecular Spectroscopy 66th Meeting – Columbus, OH – June 20-24, 2011

5. Laboratory of Millimetre-wave Spectroscopy of Bologna Rotational Hamiltonian Rotational constants

6. Laboratory of Millimetre-wave Spectroscopy of Bologna Rotational Hamiltonian Rotational constants RIGID ROTOR + CENTRIFUGAL DISTORTION

7. Laboratory of Millimetre-wave Spectroscopy of Bologna Rotational Hamiltonian Nuclear quadrupole coupling            K KK K JK JJII qeQ 22 2 2 3 3 )12()12(22 1 JIJIJI Rotational constants + Centrif.distort. constants

8. Laboratory of Millimetre-wave Spectroscopy of Bologna Rotational Hamiltonian Rotational constants + Centrif.distort. constants Nuclear quadrupole coupling            K KK K JK JJII qeQ 22 2 2 3 3 )12()12(22 1 JIJIJI Spin-rotation interactions  K KK JCI

9. Laboratory of Millimetre-wave Spectroscopy of Bologna Rotational Hamiltonian Spin-spin (direct) interactions interactions Nuclear quadrupole coupling            K KK K JK JJII qeQ 22 2 2 3 3 )12()12(22 1 JIJIJI Spin-rotation interactions  K KK JCI Rotational constants + Centrif.distort. constants

10. Laboratory of Millimetre-wave Spectroscopy of Bologna Rotational Hamiltonian Spin-spin (direct) interactions interactions Nuclear quadrupole coupling            K KK K JK JJII qeQ 22 2 2 3 3 )12()12(22 1 JIJIJI Spin-rotation interactions  K KK JCI Rotational constants + Centrif.distort. constants

11. Accuracy of Theoretical Rotational Constants STATISTICAL ANALYSIS for 16 molecules (97 isotopologues) 16 molecules (97 isotopologues) 180 rotational constants 180 rotational constants Reference values: B 0 from experiment HF, N 2, C  O, F 2, HC  N, HN  C, O=C=O, H 2 O, NH 3, CH 4, HC  CH, HOF, HNO, NH=NH, CH 2 =CH 2, H 2 C=O C. Puzzarini, M. Heckert, J. Gauss JCP 128, 194108 (2008)

12. Laboratory of Millimetre-wave Spectroscopy of Bologna CCSD(T)/VTZ CCSD(T)/VQZCCSD(T)/V5ZCCSD(T)/V6Z CCSD(T)/V6Z + CV CCSD(T)/V6Z + CV + fT + fQ + fQ CCSD(T)/V  Z + CV + fT + fQ + fQ CCSD(T)/V  Z + CV + fT + fQ + vib + fQ + vib CCSD(T)/V  Z + CV + fT + fQ + vib + ele + fQ + vib + ele B 0 calc vs B 0 exp normal distributions of relative errors C. Puzzarini, M. Heckert, J. Gauss JCP 128, 194108 (2008)

13. Laboratory of Millimetre-wave Spectroscopy of Bologna B 0 calc vs B 0 exp normal distributions of relative errors CCSD(T)/V  Z + CV + CV + fT + fT + fQ + fQ + vib + vib + ele + ele mean error -0.001% standard deviation 0.09% CCSD(T)/V6Z + CV + CV + fT + fT + fQ + fQ mean error 0.70% standard deviation 0.75% C. Puzzarini, M. Heckert, J. Gauss JCP 128, 194108 (2008)

14. C2C2 C4C4 C5C5 C6C6 N1N1 N3N3 O7O7 O8O8 H11 H12 H9H9 b a H10 COMPOSITE APPROACH extended to large molecule URACIL

15.  Equilibrium Rotational Constants MP2/cc-pV(T,Q)Z MP2/cc-pCVTZ MP2/aug-cc-pVTZ CCSD(T)/cc-pVTZ  Vibrational Corrections to Rotational Constants B3LYP/N07DMP2/cc-pVTZ

16. CalculatedExperiment A0A0A0A0MHz3885.4753883.873021(60) B0B0B0B0MHz2027.7632023.732581(45) C0C0C0C0MHz1332.7611330.928108(33) DJDJDJDJkHz0.0610.06336(44) D JK kHz0.1070.1055(23) DKDKDKDKkHz0.4470.4530(32) d1d1d1d1kHz-0.026-0.02623(18) d2d2d2d2kHz-0.006-0.00680(13)  aa MHz1.739 1.7600 (25)  bb MHz1.9521.9811(29)  aa MHz1.8711.9255(24)  bb MHz1.4911.5273(32) Puzzarini & Barone, PCCP 13, 7158 (2011) URACIL <0.2%

17. COMPOSITE APPROACH extended to large molecule  Equilibrium Rotational Constants MP2/cc-pV(T,Q)Z MP2/cc-pCVTZ MP2/aug-cc-pVTZ CCSD(T)/cc-pVTZ  Vibrational Corrections to Rotational Constants B3LYP/N07DMP2/cc-pVTZ  Centrifugal-Distortion Constants CVdiffuse Puzzarini & Barone, PCCP 13, 7158 (2011)

18. CalculatedExperiment A0A0A0A0MHz3885.4753883.873021(60) B0B0B0B0MHz2027.7632023.732581(45) C0C0C0C0MHz1332.7611330.928108(33) DJDJDJDJkHz0.0610.06336(44) D JK kHz0.1070.1055(23) DKDKDKDKkHz0.4470.4530(32) d1d1d1d1kHz-0.026-0.02623(18) d2d2d2d2kHz-0.006-0.00680(13)  aa MHz1.739 1.7600 (25)  bb MHz1.9521.9811(29)  aa MHz1.8711.9255(24)  bb MHz1.4911.5273(32) ~1% URACIL Puzzarini & Barone, PCCP 13, 7158 (2011)

19. Laboratory of Millimetre-wave Spectroscopy of Bologna OUTLINE 1) QUANTUM-CHEMICAL CALCULATIONS: CALCULATIONS: Some details Some details 2) INTERPLAY between EXPERIMENT and THEORY: EXPERIMENT and THEORY: The need: why The need: why

20. Laboratory of Millimetre-wave Spectroscopy of Bologna INTERPLAY INTERPLAYof Theory and Experiment in Rotational Spectroscopy INTERPLAY INTERPLAYof Theory and Experiment in Rotational Spectroscopy Assignment of “unknown” spectra Assignment of “unknown” spectra

21.  Analyze the spectra: ITERATIVE PROCEDURE Calculated spectrum  Preliminary assignments  Improved calculated spectrum  Further assignments …… Complete assignment AABS package Kisiel, Pszczolkowski, Medvedev, Winnewisser, De Lucia, Herbst, J. Mol. Spectrosc. 233, 231 (2005) GRAPHYCAL SUPPORT

22. trans-CH 35 Cl=CHF Unknown spectrosocpic parameters … Need: accurate estimate of rotational parameters parameters, dipole moment & quadrupole coupling constants from ab initio computations - Accurate equilibrium structure (B e ) - Accurate centrifugal-distortion constants - Accurate vibrational corrections (B e  B 0 )

23. trans-CH 35 Cl=CHF Unknown spectrosocpic parameters … Need: accurate estimate of rotational parameters parameters, dipole moment & quadrupole coupling constants from ab initio computations Need: accurate estimate of rotational parameters & dipole moment

24. Laboratory of Millimetre-wave Spectroscopy of Bologna For a detailed example: LISTEN to next TALK “Rotational Spectrum of CH 2 FI” C. Puzzarini et al., JCP 134, 174312 (2011)

25. Laboratory of Millimetre-wave Spectroscopy of Bologna INTERPLAY INTERPLAYof Theory and Experiment in Rotational Spectroscopy INTERPLAY INTERPLAYof Theory and Experiment in Rotational Spectroscopy Hyperfine structure of rotational spectra Hyperfine structure of rotational spectra

26. Laboratory of Millimetre-wave Spectroscopy of Bologna 2 non-equivalent hydrogens (I 1 = I 2 = 1/2) HFS of trans-HCOOH Cazzoli, Puzzarini, Stopkowicz & Gauss, A & A 520, A64 (2010)

27. Laboratory of Millimetre-wave Spectroscopy of Bologna J.-C. Chardon, C. Genty, D. Guichon, & J.-G. Theobald, J. Chem. Phys. 64, 1434 (1976) “rf spectrum and hyperfine structure of formic acid”

28. Laboratory of Millimetre-wave Spectroscopy of Bologna J.-C. Chardon, C. Genty, D. Guichon, & J.-G. Theobald, J. Chem. Phys. 64, 1434 (1976) ????

29. Laboratory of Millimetre-wave Spectroscopy of Bologna J.-C. Chardon, C. Genty, D. Guichon, & J.-G. Theobald, J. Chem. Phys. 64, 1434 (1976) What does Quantum Chemistry say?

30. Laboratory of Millimetre-wave Spectroscopy of Bologna Accurate hyperfine parameters >>>> Main requirements : - accurate method [CCSD(T)] - cc basis set [n  Q] - CV correction [additivity] - vibrational correction [ff: correlated method] method]

31. Laboratory of Millimetre-wave Spectroscopy of Bologna

32. Laboratory of Millimetre-wave Spectroscopy of Bologna

33. Laboratory of Millimetre-wave Spectroscopy of Bologna

34. Laboratory of Millimetre-wave Spectroscopy of Bologna ExperimentTheory RF results C aa [H(C)] -6.835(46)-7.02 C bb [H(C)] 1.0371.04 C cc [H(C)] -0.8014(96)-0.82 C aa [H(O)] -6.868(45)-6.94 C bb [H(O)] 0.781(20)0.77 C cc [H(O)] -1.290(15)-1.32 1.5  D aa 4.49(12)4.62-- (D bb – D cc )/4 -3.53(35)-3.47-- Equil: CCSD(T)/CV5Z + Equil: CCSD(T)/CV5Z + Vib. Corr: CCSD(T)/CVTZ Hyperfine parameters of trans-HCOOH

35. Laboratory of Millimetre-wave Spectroscopy of Bologna ExperimentTheory RF results C aa [H(C)] -6.835(46)-7.02-7.50(20) C bb [H(C)] 1.0371.04 C cc [H(C)] -0.8014(96)-0.82 C aa [H(O)] -6.868(45)-6.94-6.55(20) C bb [H(O)] 0.781(20)0.77 C cc [H(O)] -1.290(15)-1.32 1.5  D aa 4.49(12)4.62-- (D bb – D cc )/4 -3.53(35)-3.47-- Equil: CCSD(T)/CV5Z + Equil: CCSD(T)/CV5Z + Vib. Corr: CCSD(T)/CVTZ Hyperfine parameters of trans-HCOOH

36. Laboratory of Millimetre-wave Spectroscopy of Bologna ExperimentTheory RF results C aa [H(C)] -6.835(46)-7.02-7.50(20) C bb [H(C)] 1.0371.04-7.2(40) C cc [H(C)] -0.8014(96)-0.827.5(40) C aa [H(O)] -6.868(45)-6.94-6.55(20) C bb [H(O)] 0.781(20)0.778.2(40) C cc [H(O)] -1.290(15)-1.32-8.6(40) 1.5  D aa 4.49(12)4.62-- (D bb – D cc )/4 -3.53(35)-3.47-- Hyperfine parameters of trans-HCOOH Cazzoli, Puzzarini, Stopkowicz, Gauss, A & A 520, A64 (2010)

37. Puzzarini, Cazzoli, Harding, Vázquez & Gauss, JCP 131, 234304 (2009) H 2 17 O:

38. Laboratory of Millimetre-wave Spectroscopy of Bologna Results Results Lamb-dip spectra recorded Hyperfine parameters computed Spectra analysis Spectra analysis & assignment ITERATIVELY + GRAPHYCAL SUPPORT

39. Laboratory of Millimetre-wave Spectroscopy of Bologna INTERPLAY INTERPLAYof Theory and Experiment in Rotational Spectroscopy INTERPLAY INTERPLAYof Theory and Experiment in Rotational Spectroscopy Determination of equilibrium structure Determination of equilibrium structure

40. “Empirical” equilibrium structure from EXPERIMENT (various isotopic species) from THEORY (cubic force field) Accuracy: experimental quality Pawłowski, Jørgensen, Olsen, Hegelund, Helgaker, Gauss, Bak, Stanton JCP 116 6482 (2002) FIT

41. C2C2 C4C4 C5C5 C6C6 N1N1 N3N3 O7O7 O8O8 H11 H12 H9H9 b a H10 Semi-exp equilibrium structure of large molecule URACIL: 21 independent geometrical parameters Isotopic substitution: - 16 O  18 O - 14 N  15 N - 12 C  13 C 10 isotopic species 20 rotational constants Puzzarini & Barone, PCCP 13, 7158 (2011) Vaquero, Sanz, López, Alonso, J. Phys. Chem. Lett. 111A, 3443 (2007).

42. Best est. r e a Semi-exp. r e b Exp. r s c Fit 1Fit 2Fit 3 Distances N1-C21.37851.38175(53)1.38163(65)1.38161(51)1.386(5) C2-N31.37561.3763 1.3762 N3-C41.39741.39793(40)1.39823(47)1.39835(45)1.38(2) C4-C51.45391.45500(57)1.45485(99)1.45481(57)1.451(4) C5-C61.34331.34496(59)1.34576(107)1.34473(58)1.379(4) C6-N11.37231.37196(55)1.37160(100)1.37258(66)1.352(14) C2-O71.21121.21025(21)1.21015(26)1.21015(21)1.219(4) C4-O81.21381.21278(24)1.21268(34)1.21269(24)1.22(2) N1-H91.0046  1.0004(70)  N3-H101.0090  1.0110(96)  C5-H111.0766  1.0695(52) C6-H121.0793  1.0856(32) Angles C2-N1-C6123.38123.374(19)123.394(35)123.370(21)123.0(11) N1-C6-C5121.91121.924(10)121.920(10)121.9237(97)122.3(6) C6-C5-C4119.49119.516(16)119.501(20)119.523(16)118.8(12) C5-C4-N3113.97113.860(22)113.859(33)113.858(22)115.4(16) C4-N3-C2127.75127.942127.947127.945 N3-C2-N1113.51113.383113.379113.380 N1-C2-O7123.62123.883(44)123.878(54)123.874(42)122.3(8) C5-C4-O8125.83125.768(48)125.765(75)125.767(45)118.8(7) C2-N1-H9115.22  C2-N3-H10115.70  115.52(40)  C6-C5-H11122.11  N1-C6-H12115.34  Non-determinable Parameters: fixed at the corresponding theo values

43. Laboratory of Millimetre-wave Spectroscopy of Bologna THANK YOU for your attention!! THANK YOU for your attention!!

45. Electronic contribution to B g  = rotational g tensor m e = mass of the electron m p = mass of the proton  =x,y,z princ. inertia system CCSD(T) calc: Gauss, Ruud, Kallay, JCP 127, 074101 (2007)