Ab-initio modeling of opto-electronic properties of molecules in solvents and in proximity to a semiconductor nanoparticle
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1 Ab-initio modeling of opto-electronic properties of molecules in solvents and in proximity to a semiconductor nanoparticle Alain Delgado (a,b), Stefano Corni (b), Carlo Andrea Rozzi (b) Stefano Pittalis (b), Guido Goldoni (b) (a)quantum Theory Group, University of Ottawa, ON, Canada. (b)nrc-institute of Nanoscience, S3 Center, Modena, Italy.
2 Outline 1) Brief Introduction. 2) Modeling solvation effects in real-space and real-time within DFT. 2.1) The basics of the Polarizable Continuum Model (PCM). 2.2) Regularization of the solvent potential in a real-space representation. 2.3) Ground and excited states: DFT & TDDFT + PCM. 2.4) Benchmark: Solvation energies and optical response of simple molecules in water. 3) Extended PCM to model a dye molecule in proximity to a semiconductor NP. 3.1) The generalized PCM response matrix. 3.2) Excited state oxidation potential (ESOP) of the dye L0 in proximity to a TiO2 NP. 4) Conclusions and Perspectives.
3 Dye-sensitized solar cells (DSSCs) Typical architecture Multi-scale system composed by: mesoporous semiconductor film. Sensitizer adsorbed onto the surface. Electrolyte solution with a redox couple. Counter electrode like platinum. Nazeeruddin et al. Sol. Energy 85, 1172 (2011) Working principle 1. Photon absorption in the dye Electron injection into the NP. 3. Dye regeneration M. Gratzel, Inor. Chem., 44, 6841 (2005) 4. Reduction of redox mediator. Solvent polarization may influence all these processes
4 Ultrafast charge separation dynamics Solvent effects unexplored in the dynamics - Science 344, 1001 (2014) - Adv. Funct. Mater. 25, 2047 (2015) Absorption spectrum of the carotene-porphyrin-fullerene triad Nat. Commun. 4:1602 (2013) Experimental (in toluene) RT-TDDFT + Ehrenfest nuclear dynamics Theory (TDDFT) in vacuo
5 The basics of PCM model J. Tomasi et al. Chem. Rev. 105, 2999 (2005) The solvent is a continuous dielectric medium polarized by the solute molecule. Solute molecule is hosted by the cavity within the surface. for r out of the cavity (C) The shape of should reproduced the molecular shape. The molecule is treated quantum mechanically. Poisson equation + boundary conditions at within C outside C :solvent reaction potential in and outside C in Γ at infinity
6 Apparent surface charge method (ASC) can be expressed in terms of an apparent surface charges: is the unique solution of the equation: Cances et al. J. Math. Chem. 23, 309 (1998) Γ
7 Apparent surface charge method (ASC): in practice 1- The cavity is defined by the union of interlocking van der Waals spheres. 2- Cavity surface tessellation: projecting the faces of polyhedra inscribed in each sphere. Pascual et al. J. Comp. Chem. 11, 1047 (1990) There are many other algorithms. discretized equations
8 Apparent surface charge method (ASC): in practice 1- The cavity is defined by the union of interlocking van der Waals spheres. 2- Cavity surface tessellation: projecting the faces of polyhedra inscribed in each sphere. Pascual et al. J. Comp. Chem. 11, 1047 (1990) There are many other algorithms. discretized equations PCM response matrix.
9 IEF-PCM equations: Molecule + solvent Green functions S and D matrix elements
10 IEF-PCM equations: Molecule + solvent Green functions PCM response matrix
11 PCM + DFT The starting point is the free energy functional: By taking the functional derivative : Kohn-Sham Eqs.
12 PCM + DFT: real-space (RS) representation Finite-differences methods are robust and accurate. Potentials and orbitals are directly evaluated in RS. Well suited for massive parallel computing. Center for Theor. and Comput. Chemistry, Norway. Real-space numerical grid methods in quantum chemistry Phys. Chem. Chem. Phys. 17, (2015). Coulomb singularity: We used Gaussians to regularize the reaction field A. Delgado et al. J. Chem. Phys. 143, (2015)
13 Results: set of molecules for testing PCM implementation Real-space calculations performed with Octopus ( Solvent = water Benchmark with similar calculations obtained with GAMESS
14 Solvation free energies in water Density functional GGA - PBE RS grid: R= 5 Å Δ = 0.15 Å Octopus GTO: G(d,p) GAMESS 1 kcal/mol = ev A. Delgado et al. J. Chem. Phys. 143, (2015)
15 Showing the singularity effects: calculations in Density functional GGA - PBE RS grid: R= 5 Å Δ = 0.15 Å Octopus A. Delgado et al. J. Chem. Phys. 143, (2015)
16 Dependence on the parameter α Density functional GGA - PBE RS grid: R= 5 Å Δ = 0.15 Å Octopus biphenyl GTO: G(d,p) GAMESS nitrobenzene A. Delgado et al. J. Chem. Phys. 143, (2015)
17 Optical properties: TDDFT + PCM Real-time propagation of KS orbitals (time domain) Perturbation at t = 0: propagate in time
18 Optical properties: TDDFT + PCM Real-time propagation of KS orbitals (time domain) Perturbation at t = 0: propagate in time Solvent response in real-time S. Corni et al. J. Phys. Chem. A, 119, 5405 (2015) (Debye solvent) is frequency independent. Singling out the frequency in IEF-PCM is possible but not trivial. Take a look at the reference above.
19 Optical properties: TDDFT + PCM Real-time propagation of KS orbitals (time domain) Perturbation at t = 0: propagate in time Solvent response in real-time S. Corni et al. J. Phys. Chem. A, 119, 5405 (2015) (Debye solvent) By considering - solvent polarization equilibrates - Good approximation for weakly polar solvents
20 Optical properties: TDDFT + PCM RT propagation of KS orbitals (time domain) Perturbation at t = 0: propagate in time Solvent response in real-time
21 Optical properties: TDDFT + PCM RT propagation of KS orbitals (time domain) Perturbation at t = 0: propagate in time Solvent response in real-time nitrobenzene
22 Optical properties: TDDFT + PCM RT propagation of KS orbitals (time domain) Linear response approx. (frequency domain) Perturbation at t = 0:. propagate in time Solvent response in real-time (unoccupied) (occupied) KS orbitals
23 Optical properties: TDDFT + PCM RT propagation of KS orbitals (time domain) Linear response approx. (frequency domain) Perturbation at t = 0: propagate in time Solvent response in real-time
24 Absorption spectra XC = PBE piperazine RS-DFT: R= 5 Å Δ = 0.19 Å RT-TDDFT: Tmax=30 fs Δt=1.7 as a b s o r p t i o n ( a r b. u n i t s ) a b s o r p t i o n ( a r b. u n i t s ) LR-TDDFT: G(d,p) nitrobenzene
25 Solvatochromic shifts: RT-TDDFT.vs. LR-TDDFT
26 Back to dye-sensitized solar cells (DSSCs) Typical architecture Multi-scale system composed by: mesoporous semiconductor film. Sensitizer adsorbed onto the surface. Electrolyte solution with a redox couple. Counter electrode like platinum. Nazeeruddin et al. Sol. Energy 85, 1172 (2011) Working principle 1. Photon absorption in the dye Electron injection into the NP. 3. Dye regeneration M. Gratzel, Inor. Chem., 44, 6841 (2005) 4. Reduction of redox mediator. Solvent and NP polarizations may influence all these processes
27 ESOP as a key parameter in DSSCs 1. Photon absorption in the dye. 2. Electron injection into the NP. 2 1 Energy levels picture ESOP Our goal: NP M To compute the ESOP of a dye molecule accounting for the polarization effects of both, the solvent and the nanoparticle.
28 IEF-PCM equations: Molecule + solvent + NP A. Delgado et al. J. Chem. Phys. 139, (2013) Legendre polynomials
29 IEF-PCM equations: J. Chem. Phys. 139, (2013)
30 IEF-PCM equations: Molecule + solvent + NP J. Chem. Phys. 139, (2013)
31 Lowest excitations of the L0 prot / deprot dyes LR-TDDFT calculations: XC = CAM-B3LYP / 6-31G(d,p)
32 ESOP of the L0 prot/deprot dyes ESOP referenced to its value in solvent: ESOP(prot) = 2.95 ev ESOP(deprot) = 2.33 ev Pastore et al. J. Phys. Chem. C 114, (2010) ESOP(exp) = 2.91 ev ESOP(theo) = 2.86 ev The larger d, the smaller the ESOP renormalization (expected). For NP : solvation condition. d acetonitrile Protonated dye renormalizes stronger. prot-deprot ESOP gap reduces with d.
33 ESOP of the L0 prot/deprot dyes ESOP referenced to its value in solvent: ESOP(prot) = 2.95 ev ESOP(deprot) = 2.33 ev Pastore et al. J. Phys. Chem. C 114, (2010) ESOP(exp) = 2.91 ev ESOP(theo) = 2.86 ev ESOP renormalization increases by rotating the dye. Maximum renormalization about ev. prot-deprot ESOP gap reduces by rotating the dye. NP d φ acetonitrile
34 Independent contributions to the ESOP Values in solvent ( 6.23; 5.92 ) ev ( 3.28; 3.59 ) ev Optical excitation gap renormalizes weakly due to the NP polarization. Main contribution difference between energies. comes from the the ground state
35 prot/deprot effect on the calculated ESOP electron injection
36 Conclusions 1) A novel methodology was implemented to account for solvation effects in real-space ab-initio electronic structure calculations. - We used the IEF-PCM model to calculate the solvent polarization response. - The numerical singularity in the solvent reaction field was regularized by using Gaussian functions to distribute the apparent charges in the van der Waals surface of the solute system. 2) The PCM was extended to the real-time domain to address solvent effects in the electron dynamics under the influence of time-dependent fields. - The real-time solvent polarization was assumed to equilibrate instantaneously the molecular electronic density. - PCM in the time domain provides a suitable approach to model the optical response, non-linear and ultrafast quantum phenomena in large molecules in a polarizable environment. - The new methodology is available in the code Octopus ( 3) The PCM equations were generalized to calculate ground and excited states properties of a molecule close to a semiconductor NP (SNP). - This methodology was applied to calculate the ESOP of the molecular dye L0 adsorbed to a TiO2 SNP. - Weak effects due to the NP polarization on the optical absorption excitation. ESOP renormalization dominated by the electrostatic interaction between the oxidized dye and the SNP. - Implemented in the program GAMESS (
37 Further extensions pcm module octopus code cavity surface Γ system geometry DFT ground state solvent data (,, ) PCM response matrices Applications - solvation free energies - electrochemical properties at equilibrium e.g. ground-state oxidation potentials RT-TDDFT electron dynamics (fixed nuclei) - solvatochromic shifts of the absorption bands - non-equilibrium solvation effects - optical spectroscopy out of the equilibrium e.g. pump-probe experiments - non-linear optical processes RT-TDDFT Ehrenfest nuclear dynamics - coupled electrons-nuclei dynamics - pump-probe of non-adiabatic processes - ultrafast charge transfer from photoexcited states Dynamic solvent response RT charge propagation PCM contribution to the forces
38 Acknowledgements HPC-ISCRA project DEMOOPT. FP7 HY-SUNLIGHT grant FP7 CRONOS grant FP7 MODENADYNA grant
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