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, Teresa Fornaro

Spectroscopic studies: challenges – small prebiotic molecules – nucleobases, aminoacids – systems of increasing complexity complexes, oligomers – heterogeneous environments – microsolvation – dynamic effects Computation of vibrational spectra for large/complex systems – General/flexible theoretical models – Integrated QM schemes – Weak intermolecular interactions – Simplified/reduced dimensionality models – Accuracy Validation and applications – From uracil to its oligomers Computational spectroscopy Spectroscopy: biomolecules “building blocks”

PES PES – polynomial of 4 th order containing at most three independent normal coordinates Vibrational elergy levels Vibrational elergy levels  ij set of anharmonic constants simple function of 3rd (K ijk ) and semidiagonal 4th (K iijj ) energy derivatives with respect to normal modes Energy third and semi-diagonal fourth derivatives are computed numerically 1 Energy third and semi-diagonal fourth derivatives are computed numerically 1 – Computational cost grows quickly with the system size ! Solutions to limit computation cost: Solutions to limit computation cost: – Hybrid models – Reduced-dimensionality 2 VPT2 for medium-to-large systems Vibrational spectroscopy: PES and FF if 1.V. Barone, J. Chem. Phys. 122, (2005), V.B et al Chem. Phys. Lett., 496, (2010) 2.V. B., M. B., J. B., M. Borkowska-Panek, I. Carnimeo, P. Panek, Int. J. Quantum. Chem. 112, 2185 (2012)

Reduced dimensionality models Vibrational spectroscopy V. B., M. B., J. Bloino, M. Borkowska-Panek, I. Carnimeo, P. Panek, Int. J. Quantum. Chem (2012) Displacement along selected vibrations Displacement along selected vibrations – set of M normal modes for which anharmonic frequencies will be evaluated – spectra range of interest, most intense (observed) vibrations, molecular probe etc.. Anharmonic constants  ij Anharmonic constants  ij – index i corresponds to an active mode cubic force constants K ijk where index i is present at least once (i.e. K ijk, K ijj, K iik, K iii ) evaluated along with all semi-diagonal quartic force constants K iijj Difference wrt full treatment Difference wrt full treatment – some limited number cubic force constants (terms including only j and k indices) not evaluated – non-resonant terms (treatment of Fermi resonances not affected) – important ONLY if vibrations j,k and i are coupled vibrations mainly localized on the same region of a molecular system (e.g. functional group) and with similar frequencies Practical recipe to define sets normal modes to be considered simultaneously based on nature of the vibrations and energy range Practical recipe to define sets normal modes to be considered simultaneously based on nature of the vibrations and energy range

Vibrational frequencies [cm -1 ] CC/DFT and DFT: validation Medium-size systems (over 250 vibrations) Medium-size systems (over 250 vibrations) – DFT vs Experiment – Hybrid CC/DFT models vs Experiment – B3LYP/SNSD, B2PLYP/AVTZ, CCSD(T)/AVTZ(CBS) Dispersion-corrected DFT Dispersion-corrected DFT – adenine, cytosine, uracil, hypoxanthine and thymine – B3LYP-D3/SNSD vs Exp and B3LYP mean absolute error (MAE) in cm -1 DFT vs Exp Overall good acuracy + applicability to larger systems V. Barone, M. Biczysko, J. Bloino PCCP, 2014, 16, MAE wrt ExpMAE wrt B3LYP   anh T. Fornaro, M. Biczysko, S. Monti, V. Barone PCCP, 2014, 16, 10112

MAX and MAE calculated for ALL normal modes MAX and MAE calculated for ALL normal modes – Mean absolute error (MAE) and largest absolute error (|MAX|) with respect to experiment – Experimental data for 28 over total of 30 normal modes – anharmonic contributions computed by means of the GVPT2 model. IR anharmonic spectra of uracil: Accuracy B3LYP-D3M06-2X  B97XD CC/B3LYPExp.Assign. mode sc*anhsc*anhsc*anh Ar Matr Assign N1H str N3H str C5H str C6H str C2=O str C4=O str. | MAX| MUE Experimental and computed spectra * Harmonic frequencies were scaled by for NH stretch, and for other vibrations (eg. Zwier et al. JACS 134, 17186−17201 (2012)) C. Puzzarini, M. Biczysko, V. Barone, J. Chem. Theory. Comp. 2011, 7, 3702–3710 T. Fornaro, M. Biczysko, S. Monti, V. Barone PCCP, 2014, 16, 16, 10112

DFT-D: validation B3LYP-D3: dimers Nucleobases dimers Nucleobases dimers – B3LYP fails in the case of the stacked dimers. – B3LYP-D3 predict reliable binding energies and structural parameters (wrt Hobza database) Model H-Bonded systems: vibrational frequencies Model H-Bonded systems: vibrational frequencies – O-H..O (pyruvic acid Tc conformer) – O-H..N (glycine II n /ccc conformer) Glycine II n Further benchmark: weakly bound complexes Further benchmark: weakly bound complexes – Accurate experimental data: structures + frequencies !!!! B3LYP/SNSDB3LYP-D3B2PLYP/AVTZCC/B2Exp  anh  anh  anh OH..O OH..N Pyruvic Tc

IR spectra: uracil and its dimers Experimental and computed spectra B3LYP-D3/SNSD GVPT2/DVPT2

Reduced GVPT2 scheme: validation uracil dimer uracil dimer – GVPT2, B3LYP-D3/SNSD – Full: 66 normal modes = 133 Hessian computations Full, Reduced (N Modes) and diagonal (ND) approach Full, Reduced (N Modes) and diagonal (ND) approach – coupled modes, eg. N-H..O stretchings – graphical representation of couplings absolute value of the cubic force constants K iij Vibrational spectroscopy mode1D1M2D6 M12 MFull M K iii, K iiii K iab, K iiab K iii, K ijj, K iijj, K ijjj K iab, K iiab all K abc, all K aabc (N-H…O) asym. str (N-H…O) sym. str log 10 (|K iij |) M: other strongly coupled vibrations (i.e. N-H..O bendings) 6M: other strongly coupled vibrations (i.e. N-H..O bendings) 12M: cm -1 range  uracil monolayer 12M: cm -1 range  uracil monolayer (N-H…O) sym. str. (N-H…O) sym. str.

From single molecule to oligomers: uracil Spectroscopic signatures of intermolecular interactions Spectroscopic signatures of intermolecular interactions – B3LYP-D3/SNSD – uracil monomer, dimers: full-GVPT2 – heptamer RD-GVPT2: 12 modes Toward larger systems assign  (HB-mono) monodim1dim2hept N1H N3H C2=O C4=O N1 N3 O2 O4

V. Barone, A. Baiardi, C. Cappelli, I. Carnimeo, F. Egidi, T. Fornaro, D. Licari (SNS) J. Bloino, S. Monti (CNR) C. Puzzarini (UniBo) R. Fausto, I. Reva (University of Coimbra) Acknowledgements Goska

References Anharmonic vibrational spectroscopy Anharmonic vibrational spectroscopy – J. Chem. Theory Comput. 8, 1015 (2012) – J. Chem. Phys. 136, (2012) – Phys. Chem. Chem. Phys. 16, 1759 (2014) Integrated QM/QM’ models Integrated QM/QM’ models – Theor. Chem. Acc. 113, 1201 (2012) DFT+dispersion for anharmonicity DFT+dispersion for anharmonicity – Phys. Chem. Chem. Phys. 16, (2014)