An effective method to study the excited state behaviour and to compute vibrationally resolved

1. An effective method to study the excited state behaviour and to compute vibrationally resolved optical spectra of large molecules in solution Roberto Improta1,2, Fabrizio Santoro3, Alessandro Lami3, Vincenzo Barone2,4 1 IBB/Consiglio Nazionale Ricerche 2 CR-INSTM Village 3 IPCF/Consiglio Nazionale Ricerche 4 Università Federico II Napoli

2. Excited electronic states are involved in many phenomena/properties of potential technological interest Non linear optics Electron transfer Molecular electronics/Optoelectronics Conductivity Photophysics and photochemistry The study of the processes of charge, energy and excitatation transfer require the detailed knowledge of the static and dynamical behavior of the excited states

3. The understanding and the tailoring of the properties of a material often requires Definition of suitable subsystems: building blocks A possible (handle with care) approach: Bottom-up Knowledge of the Excited States of the building blocks Quantum mecanical calculations have always been very useful but….

4. Materials of technological interest Standard QM calculations size Medium/large size molecule Small/medium size molecule environment Condensed phase Gas phase temperature vibrating molecule at finite temperature vibrations Rigid molecule at 0 K What is the interaction between the excited states of the building blocks?

5. DNA Bases as building blocks for photoactive materials isolated molecule In solution Base pairing Base stacking macromolecule in solution

6. Final goal describing the static and the dynamical behavior of the excited states of macromolecular systems in solution 1)Solvent 2)Vibrations 3)Interactions between the building blocks Where did we arrive, until now?

7. Our reference method for electronic calculations: Density Functional Theory (DFT) Time Dependent DFT (TD-DFT) hybrid functionals: PBE0 Analytic gradients in solution are available: equilibrium geometry of the excited state in solution Properties: dipole, polarizability…. Best compromise between accuracy and computational cost

8. 1.The solvent is an infinite, structureless medium characterised by macroscopic properties (dielectric constants, density, etc.) 2.A cavity is defined, such that the solvent distribution function is 0 inside the cavity and 1 outside. 4.The whole reaction field can be described in terms of an apparent charge density ( s) appearing on the cavity surface 3.The solute with its own electron density is inserted within the cavity 1. Solvent effect Bulk Solvent effect: PCM model

9. 1b. Solvent effect: hydrogen bonding effect Solute+ 1st solvation shell solute Solute+ 1st solvation shel + PCMl Experiment gas phase water 5.08 4.79 6.05 6.14 The intensity of S2 and S3 increases with the polarity of the solvent Gas Gas Phase+ Gas Phase+ PCM+ Phase 4 H2O PCM 4 H2O S1 4.77(0.00) 4.98(0.00) 5.14(0.00) 5.23(0.00) S2 5.24(0.14) 5.25(0.14) 5.19(0.19) 5.08(0.20) S3 6.06(0.03) 6.32(0.05) 6.29(0.12) 6.23(0.17) in eV, intensities in parentheses TD-PBE0/PCM calculations In many cases only the inclusion of both explicit and bulk solvent effects can provide reliable estimates of the solvent shift. J. Am. Chem. Soc. 2004, 126, 14320 - J. Am. Chem. Soc. 2006, 128, 607 - J. Am. Chem. Soc. 2006, 128, 16312

10. 1.c Solvent: Examples Exp.Band Max.* transition Computed VEE* Qx 2.20(0.011) 1.91( 0.005) Qy 2.35(0.018) 2.25(0.01) TPP2H benzene B 2.95(1) 2.96(1) Q 1.94(0.27) 1.91(0.18) B 2.96(1) 2.86(1) TPP4H2+ CH2Cl2 Q 1.94(0.25) 1.96(0.1) B 2.95(1) 2.86(1) TPP4S2- water *relative intensity in parentheses Discrepancy between the computed Vertical Excitation Energies and the Experimental band maxima in solution ≤ 0.25 eV

11. spectrum · · · · |e · · · · Condon approximation Franck-Condon integrals |e′ 2. Vibrations Absorption spectra including vibrational effect Different methods for computing FC integrals are available….BUT

12. 2. Vibrations the number of vibrational states (and of the FC integrals to be computed) increases steeply with the dimension of the molecule and with the energy most of them do not contribute to the spectrum typical width of an absorption spectrum 1017 states; computationally unfeasible Coumarin C153 vibrational states we devised a method to select the relevant contributions, building up a computational tool that is able to automatically compute converged spectra in large molecules without requiring manual and ad hoc choices of the user the fortran code FCclasses is freely distributed upon request, see also the Villageweb-site

13. 2b.Optical spectra in solution S0 S1 DMSO cyclohexane Convolution with a gaussian for inhomogeneous broadening FWHM larger in the case of polar DMSO Coumarin C153 ΔE exp.-theor.400 cm-1 TD-DFT PCM/PBE0/6-31G(d) Solvent effect on the energy and the shape of absorption spectra is computed with accuracy Angew. Chemie (2007) 46, 405 J. Chem. Phys. (2007) 126, 84509

14. 2b.Spectra in solution: larger molecules ΔE exp.-theor.1500 cm-1 cpu time=20 s Vibrationally Resolved Phophorescence Spectra Porphyrin (96 normal modes)

15. 2b.Spectra in solution: larger molecules theor. frequency (cm-1) 13000 12000 ΔE exp.-theor.  400 cm-1 exp. frequency (cm-1) 12600 12000 11000 174 normal modes Cautions: • Possibility for nonadiabatic couplings (Jahn-Teller distortions) S0 T1(3T2g) • the optical transition is forbidden by symmetry and the spectrum should be computed in the Herzberg-Teller formalism C60 Phosphorescence Spectrum PBE0/6-31G(d)

16. S0 S1 phenyl torsion 9 cm-1 S0 45 cm-1 S1 295 K 77 K 2c. Spectra including the temperature effect Stilbene in cyclohexane PCM/PBE0/6-31+G(d,p) ΔE exp.-theor. 2800 cm-1 J. Chem. Phys. (2007) 126, 184102

17. shift~1700cm-1 2d. Spectra including Herzberg-Teller effect Fluorescence Spectra of porphyrin

18. 3. Interacting excited states Adenine stacked oligomers Interaction between UV radiation and nucleic acids Potential nanotecnological interest

19. 3. Interacting excited states Computed absorption spectra in aqueous solution of different oligomers of 9-methyl-adenine Computations on systems (with size and in condition) comparable to those studied in the experiments

20. 3. Interacting excited states Calculations on a stacked dimer of 9-methyladenine Mutual arrangement frozen as in B-DNA When going from the monomer to the oligomer 1)Small blue shift of the band maximum 2)Small red shift of the low energy side 3)Decrease of the inteensity Calculations are able to reproduce the effect of stacking on the spectra Proc. Nat. Acad. Sci. U.S.A. (2007) in press

21. Conclusion Accurate computation of the energy, the geometry, and the vibrations of excited states in solution Reliable description of the excited state properties (transition moments, excite state dipole moments) in the gas phase and in solution Computation of optical spectra of molecules of potential nanotechonological interest in realistic conditions (environment,temperature) First encouraging steps towards the study of the excited states of macromolecular systems Theor.Chem. Acc. (2007) 117, 1073

22. Perspectives DFT and TD-DFT calculations as basis for Quantum Mechanical dynamical studies Integration with the results of other computational methods (CASSCF-CASPT2) Providing the parameters for excitonic models NOW Increasing the complexity of the system under study Dynamical Simulations on macromolecules

23. Perspectives

24. V. Barone F. Santoro J. Bloino S. Lami Federico II Napoli IPCF-CNR Pisa LSDM- Napoli N. Rega G. Morelli O. Crescenzi M. Pavone Acknowledgements Gaussian M. Frisch G. Scalmani