Theoretical and Computational Chemistry Group, Scuola Normale Superiore,Istituto di Chimica dei Composti OrganoMetallici (ICCOM-CNR), Pisa, ITALY

Accurate anharmonic IR spectra from integrated CC/DFT approach

Vincenzo Barone, Malgorzata Biczysko, Julien Bloino, Ivan Carnimeo, Cristina Puzzarini

An integrated approach for vibrational spectroscopy

Vibrational spectroscopy

• An easy-to-use and reliable tool – to compute spectroscopic data beyond the

harmonic level, • in particular:

• vibrational averages of a wide range of properties• vibrational energy level (transition energies)• transition integrals (band intensities)

1/11

• Integrated QM approach– Accurate + feasible

• Validation of efficient yet reliable models– DFT/SNSD (B3LYP, CAM-B3LYP)

• Hybrid QM/QM’ approaches– CC/DFT, B2PLYP/B3LYP,…

• Higher level– Properties at ‘bottom of the well’– Harmonic frequencies and intensities

• Lower level– Anharmonic corrections

1. VB, MB, JB PCCP 16, 1759 (2014)2. MB et al. Theor. Chem. Acc. 113, 1201 (2012)

Anharmonic IR intensities from VPT2• Anharmonic IR spectra

– IR: molar extinction coefficient,

• Both and Pe must be treated anharmonically at the VPT2 level

• 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! – Resonance terms removed: DVPT2

s0, s1, s2, P0, Pi, Pij, Pijk and S are property-dependent

J. Bloino, V. Barone J. Chem. Phys. 136, 124108 (2012)

Vibrational spectroscopy

2/11

DFT: basis set benchmark• IR intensities [km mol-1]: benchmark

computations – B3LYP + SNSn and aug-cc-pVnZ basis sets

• Closed- and open- shell systems– VIB67 :15 small molecules, 67 fundamental

vibrations

– VibBio100: medium size

IR intensities

Basis harm anh anh cost

AVTZ 0.2 0.2 0.1 54%

AVDZ 1.1 1.1 0.3 25%

SNST 0.5 0.5 0.2 32%

SNSD 0.8 0.8 0.2 27%

MAE wrt AVQZ [km mol-1]

-1

-1

AVTZ

AVDZ

SNST

SNSD

AVTZ

AVDZ

SNST

SNSD

AVDZ 1.2 2.4 1.6 47%

SNST 0.6 1.5 1.2 65%

SNSD 1.6 1.5 1.1 51%

MAE wrt AVTZ

Test case: furan

3/11 V. Barone, M. Biczysko, J. Bloino PCCP, 2014, 16, 1759-1787

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 4/11

• Best estimated – composite approach– Corrections for basis set incompleteness and core-valence correlation effects

• BestCC = CCSD(T)/CBS(T,Q) + CV(CCSD(T)/CT)• ‘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): cc-pVTZ, cc-pVQZ• 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]MAE MIN MAX MAE MIN MAX

B3LYP 12.4 -38.6 1.0 3.1 -1.9 20.8

B2PLYP 5.3 -8.4 15.1 1.9 -2.7 13.6

MP2 11.0 -3.1 34.0 0.8 -4.4 1.1

CC/VTZ 7.3 -13.4 13.3 3.5 -13.6 20.0

CC/VQZ 5.4 -9.3 8.4 2.5 -9.9 13.9

Best’cheap’ 1.6 -7.2 1.2 0.4 -0.3 1.6

MIN/MAX: largest negative and positive deviations

MAE, MIN and MAX wrt BestCC

O

C

H

5/11 V. Barone, M. Biczysko, J. Bloino, C. Puzzarini , ApJ 785, 107, 2014

R(best) = CCSD(T)+r(CBS) + r(CV)

• IR Vibrational frequencies (cm-1) and IR intensities (km/mol) of oxirane

• Harmonic: CCBest• 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

B3LYP B2PLYP CCSD(T) Exp (HR)mode

anh Ianh anh Ianh anh Ianh I

1 3027 16.4 3024 15.9 3021 15.9 3018

2 1492 0.9 1489 1.1 1490 1.2 1498 0.92

3 1270 14.2 1268 13.8 1266 13.6 1270 13.16

4 1120 0.2 1119 0.3 1115 0.2

5 876 72.0 875 68.7 873 68.9 877 64.76

6 3064 0.0 3062 0.0 3065 0.0

7 1157 0.0 1156 0.0 1160 0.0

8 1027 0.0 1026 0.0 1027 0.0

9 3017 30.2 3015 31.4 3009 31.4 3007 44.31

10 1465 0.1 1463 0.0 1461 0.1 1471 0.25

11 1145 0.2 1144 0.3 1154 0.2

12 818 9.3 817 8.8 816 8.3 822 8.6

13 3077 32.0 3075 35.0 3076 34.2 3066 36.24

14 1146 4.3 1145 4.1 1145 4.1

15 807 0.3 807 0.2 810 0.3 808 0.21

V. Barone, M. Biczysko, J. Bloino, C. Puzzarini , ApJ 785, 107, 20146/11

DFT and hybrid CC/DFT

• 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 – Halo-methanes and halo-ethylenes– 84 vibrations: fundamental, overtones and

combination bands

IR intensities

B3LYP B2PLYP CC/B3LYP CC/B2PLYP

methanes 6.05 6.39 2.11 1.98

ethylenes 7.94 5.37 3.25 3.23

All 6.81 5.98 2.57 2.48

MAE wrt Experiment [km mol-1]

Test case: cis-CHFCHI

7/11 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

Test case: CHBrF2

• Infrared spectrum – Convolution: FWHM 20 cm-1

CC/DFT

• FREQ/INT– DFT: B3LYP/SNSD– HYB: CCSD(T)/B3LYP

I. Carnimeo et al., JCP, 139, 074310 (2013)

Fund

amen

tal b

ands

Overtones and com

bination bands8/11

Test case: CHBrF2

• Integrated cross sections (km/mol)

CC/DFT

I. Carnimeo et al., JCP, 139, 074310 (2013)

Overtones+combination bands

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Unidentified IR bands

• Possible identfication of oxirane and oxiraneH+ in interstellar medium (ISM)• Assignment of unidentfied Infrared bands (UIR)

Theory complement experiment

Simulated:OxiraneOxiraneH+– Observed: ISO-SW

spectrum of planetary nebula NGC 7027

– Identified line fluxes

µ

-1

10/11 V. Barone, M. Biczysko, J. Bloino, C. Puzzarini , ApJ 785, 107, 2014

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

http://compchem.sns.it

References

• 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– Theor. Chem. Acc. 113, 1201 (2012)

• Accurate IR intensities– J. Chem. Phys. 139, 074310 (2013)– ApJ 785, 107 (2014)

http://compchem.sns.it