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

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

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

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

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

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

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

1.The solvent is an infinite, structureless medium characterised by macroscopic properties (dielectric constants, density, etc.) 1. Solvent effect Bulk Solvent effect: PCM model 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 (  ) appearing on the cavity surface 3.The solute with its own electron density is inserted within the cavity

Gas Gas Phase+ Gas Phase+ PCM+ Phase 4 H 2 O PCM 4 H 2 O 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 Experiment gas phase water The intensity of S2 and S3 increases with the polarity of the solvent In many cases only the inclusion of both explicit and bulk solvent effects can provide reliable estimates of the solvent shift. 1b. Solvent effect: hydrogen bonding effect J. Am. Chem. Soc. 2004, 126, J. Am. Chem. Soc. 2006, 128, J. Am. Chem. Soc. 2006, 128, solute Solute+ 1st solvation shell Solute+ 1st solvation shel + PCMl

1.c Solvent: Examples Discrepancy between the computed Vertical Excitation Energies and the Experimental band maxima in solution ≤ 0.25 eV TPP4S 2- water Exp.Band Max.* Q 1.94(0.25) 1.96(  0.1) B 2.95(1) 2.86(1) TPP4H 2+ CH 2 Cl 2 Q 1.94(0.27) 1.91(  0.18) B 2.96(1) 2.86(1) TPP2H benzene Qx 2.20(0.011) 1.91(  0.005) Qy 2.35(0.018) 2.25(  0.01) B 2.95(1) 2.96(1) Computed VEE*transition *relative intensity in parentheses

Absorption spectra including vibrational effect Franck-Condon integrals spectrum |e  |e′  Condon approximation · · Different methods for computing FC integrals are available….BUT 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 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 typical width of an absorption spectrum states; computationally unfeasible Coumarin C153 vibrational states the fortran code FCclasses is freely distributed upon request, see also the Village web-site 2. Vibrations

2b. Optical spectra in solution Coumarin C153 TD-DFT PCM/PBE0/6-31G(d) S1S1 S0S0 ΔE exp.-theor.  400 cm -1 Angew. Chemie (2007) 46, 405 Convolution with a gaussian for inhomogeneous broadening FWHM larger in the case of polar DMSO DMSOcyclohexane J. Chem. Phys. (2007) 126, Solvent effect on the energy and the shape of absorption spectra is computed with accuracy

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

exp. frequency (cm -1 ) C 60 Phosphorescence Spectrum 174 normal modes T 1 ( 3 T 2g )S0S0 Cautions: the optical transition is forbidden by symmetry and the spectrum should be computed in the Herzberg-Teller formalism Possibility for nonadiabatic couplings (Jahn-Teller distortions) theor. frequency (cm -1 ) ΔE exp.-theor.  400 cm -1 2b.Spectra in solution: larger molecules PBE0/6-31G(d)

2c. Spectra including the temperature effect 295 K 77 K ΔE exp.-theor.  2800 cm -1 Stilbene in cyclohexane PCM/PBE0/6-31+G(d,p) S1S1 S0S0 phenyl torsion 9 cm -1 S 0 45 cm -1 S 1 J. Chem. Phys. (2007) 126,

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

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

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 3. Interacting excited states

Calculations on a stacked dimer of 9-methyladenine 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 Mutual arrangement frozen as in B-DNA 3. Interacting excited states Proc. Nat. Acad. Sci. U.S.A. (2007) in press

Conclusion Theor.Chem. Acc. (2007) 117, 1073 Reliable description of the excited state properties (transition moments, excite state dipole moments) in the gas phase and in solution Accurate computation of the energy, the geometry, and the vibrations of excited states 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

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

Perspectives

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