1. Theoretical and Computational Chemistry Group, Scuola Normale Superiore, Istituto di Chimica dei Composti OrganoMetallici (ICCOM-CNR), Pisa, ITALY Vincenzo Barone, Malgorzata Biczysko, Julien Bloino, Ivan Carnimeo, Cristina Puzzarini

2. An integrated approach for vibrational spectroscopy Vibrational spectroscopy if An easy-to-use and reliable tool An easy-to-use and reliable tool – to compute spectroscopic data beyond the harmonic level, in particular: in particular: vibrational averages of a wide range of properties vibrational energy level (transition energies) transition integrals (band intensities) Integrated QM approach Integrated QM approach – Accurate + feasible Validation of efficient yet reliable models Validation of efficient yet reliable models – DFT/SNSD (B3LYP, CAM-B3LYP) Hybrid QM/QM’ approaches Hybrid QM/QM’ approaches – CC/DFT, B2PLYP/B3LYP,… Higher level Higher level – Properties at ‘bottom of the well’ – Harmonic frequencies and intensities Lower level Lower level – Anharmonic corrections 1. VB, MB, JB PCCP 16, 1759 (2014) 2. MB et al. Theor. Chem. Acc. 113, 1201 (2012)

3. Anharmonic IR intensities from VPT2 Anharmonic IR spectra Anharmonic IR spectra – IR: molar extinction coefficient, Both  and P e must be treated anharmonically at the VPT2 level Both  and P e must be treated anharmonically at the VPT2 level Generalized formulation for the transition dipole moment Generalized formulation for the transition dipole moment – Integrals for fundamentals, overtones and combinations bands – Extensible to other properties (Raman, VCD implemented) Fermi resonances can be present, as well as 1-1 resonances! Fermi resonances can be present, as well as 1-1 resonances! – Resonance terms removed: DVPT2 s 0, s 1, s 2, P 0, P i, P ij, P ijk and S are property-dependent J. Bloino, V. Barone J. Chem. Phys. 136, 124108 (2012) Vibrational spectroscopy

4. DFT: basis set benchmark IR intensities [km mol -1 ]: benchmark computations IR intensities [km mol -1 ]: benchmark computations – B3LYP + SNSn and aug-cc-pVnZ basis sets Closed- and open- shell systems Closed- and open- shell systems – VIB67 :15 small molecules, 67 fundamental vibrations – VibBio100: medium size IR intensities Basisharmanh  anh cost AVTZ0.2 0.154% AVDZ1.1 0.325% SNST0.5 0.232% SNSD0.8 0.227% MAE wrt AVQZ [km mol -1 ] AVTZ AVDZ SNST SNSD AVTZ AVDZ SNST SNSD AVDZ1.22.41.647% SNST0.61.51.265% SNSD1.61.51.151% MAE wrt AVTZ Testcase: furan Test case: furan V. Barone, M. Biczysko, J. Bloino PCCP, 2014, 16, 1759-1787

5. Mixture: anharmonic IR spectra of butane Butane anti- and gauche- conformer abundances at 298 K B3LYP/SNSD; Spectra GVPT2/DVPT2;  G=SPT/HDCPT2, 64% anti-, 36 % gauche- Vibrational spectra: GVPT2/DVPT2 1.Generalized VPT2/Deperturbed VPT2: JB,VB JCP 136, 124108 (2012) 2.Simple Perturbation Theory, D. Truhlar JCP 94, 357 (1991), JCTC 8, 1015 (2012) 3.Hybrid Degeneracy Corrected PT2: JB, MB, VB JCTC 8, 1015 (2012) V. Barone, M. Biczysko, J. Bloino PCCP, 2014, 16, 1759-1787 Exp: http://webbook.nist.gov

6. Best estimated – composite approach Best estimated – composite approach – Corrections for basis set incompleteness and core-valence correlation effects BestCC = CCSD(T)/CBS(T,Q) + CV(CCSD(T)/CT) BestCC = CCSD(T)/CBS(T,Q) + CV(CCSD(T)/CT) ‘cheap’=CCSD(T)/cc-pVTZ+CBS(MP2)+CV(MP2) ‘cheap’=CCSD(T)/cc-pVTZ+CBS(MP2)+CV(MP2) – Avoid unfeasible ‘full’ computations -Some corrections computed at lower level (MP2) MP2: aug-cc-pVTZ; CCSD(T): MP2: aug-cc-pVTZ; CCSD(T): cc-pVTZ, cc-pVQZ DFT: DFT: B3LYP/SNSD, B2PLYP/aug-cc-pVTZ Harmonic frequencies and IR intensities: Accuracy CC/DFT for spectroscopy Frequencies [cm -1 ]IR intensities [km mol -1 ] MAEMINMAXMAEMINMAX B3LYP12.4-38.61.03.1-1.920.8 B2PLYP5.3-8.415.11.9-2.713.6 MP211.0-3.134.00.8-4.41.1 CC/VTZ7.3-13.413.33.5-13.620.0 CC/VQZ5.4-9.38.42.5-9.913.9 Best’cheap’1.6-7.21.20.4-0.31.6 MIN/MAX: largest negative and positive deviations MAE, MIN and MAX wrt BestCC O C H V. Barone, M. Biczysko, J. Bloino, C. Puzzarini, ApJ 785, 107, 2014 R(best) = CCSD(T)+  r(CBS) +  r(CV)

7. IR Vibrational frequencies (cm -1 ) and IR intensities (km/mol) of oxirane IR Vibrational frequencies (cm -1 ) and IR intensities (km/mol) of oxirane Harmonic: CCBest Harmonic: CCBest Anharmonic Anharmonic – CCSD(T)/VQZ |MAX|: 10.5 cm -1, MAE: 5.5 cm -1 – B2PLYP/aug-cc-pVTZ 8.8 cm -1, MAE: 5.7 cm -1 – B3LYP/SNSD 11 cm -1, MAE: 5.5 cm -1 – Mean absolute error (MAE) and largest absolute error (|MAX|) with respect to experiment IR anharmonic spectra of oxirane: Accuracy CC/DFT for spectroscopy B3LYPB2PLYPCCSD(T)Exp (HR) mo de anh I anh anh I anh anh I anh I 1 302716.4302415.9302115.93018 2 14920.914891.114901.214980.92 3 127014.2126813.8126613.6127013.16 4 11200.211190.311150.2 5 87672.087568.787368.987764.76 6 30640.030620.030650.0 7 11570.011560.011600.0 8 10270.010260.010270.0 9 301730.2301531.4300931.4300744.31 10 14650.114630.014610.114710.25 11 11450.211440.311540.2 12 8189.38178.88168.38228.6 13 307732.0307535.0307634.2306636.24 14 11464.311454.111454.1 15 8070.38070.28100.38080.21 V. Barone, M. Biczysko, J. Bloino, C. Puzzarini, ApJ 785, 107, 2014

8. DFT and hybrid CC/DFT IR intensities [km mol -1 ]: benchmark computations IR intensities [km mol -1 ]: benchmark computations – B3LYP/SNSD and B2PLYP/cc-pVTZ – CC: CCSD(T) + at least cc-pVTZ Set of 8 halo-hydrocarbons Set of 8 halo-hydrocarbons – Halo-methanes and halo-ethylenes – 84 vibrations: fundamental, overtones and combination bands IR intensities B3LYPB2PLYPCC/B3LYPCC/B2PLYP methanes6.056.392.111.98 ethylenes7.945.373.253.23 All6.815.982.572.48 MAE wrt Experiment [km mol -1 ] Testcase: cis-CHFCHI Test case: cis-CHFCHI I. Carnimeo et al., JCP, 139, 074310 (2013) (A)CCF and CHI out of plane bending. (B)CF stretching (C)CHI/CHF symmetric in plane bending (D)CHI/CHF asymmetric in plane bending. (E)Overtones and combination bands of CCF bending. (F)CC stretching (G)Overtones and combination bands of CHI out of plane bendings

9. Test case: CHBrF 2 Infrared spectrum Infrared spectrum – Convolution: FWHM 20 cm -1 CC/DFT FREQ/INT FREQ/INT – DFT: B3LYP/SNSD – HYB: CCSD(T)/B3LYP I. Carnimeo et al., JCP, 139, 074310 (2013) Fundamental bands Overtones and combination bands

10. Test case: CHBrF 2 Integrated cross sections (km/mol) Integrated cross sections (km/mol) CC/DFT I. Carnimeo et al., JCP, 139, 074310 (2013) Overtones+combination bands

11. Unidentified IR bands Possible identfication of oxirane and oxiraneH + in interstellar medium (ISM) Possible identfication of oxirane and oxiraneH + in interstellar medium (ISM) Assignment of unidentfied Infrared bands (UIR) Assignment of unidentfied Infrared bands (UIR) Theory complement experiment Simulated: Oxirane OxiraneH+ – Observed: ISO-SW spectrum of planetary nebula NGC 7027 – Identified line fluxes µ V. Barone, M. Biczysko, J. Bloino, C. Puzzarini, ApJ 785, 107, 2014

12. V. Barone, C. Cappelli, I. Carnimeo, F. Egidi, T. Fornaro, D. Licari (SNS) J. Bloino (CNR) C. Puzzarini (University of Bologna) N. Tasinato, P. Stoppa, A. Pietropolli Charmet (Università Cà Foscari Venezia) Acknowledgements Goska

13. References Anharmonic vibrational spectroscopy Anharmonic vibrational spectroscopy – J. Chem. Theory Comput. 8, 1015 (2012) – J. Chem. Phys. 136, 124108 (2012) – Phys. Chem. Chem. Phys. 16, 1759 (2014) Integrated QM/QM’ models Integrated QM/QM’ models – Theor. Chem. Acc. 113, 1201 (2012) Accurate IR intensities Accurate IR intensities – J. Chem. Phys. 139, 074310 (2013) – ApJ 785, 107 (2014)