Polarizable Continuum Model Implementation in the Octopus code
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1 Polarizable Continuum Model Implementation in the Octopus code Alain Delgado, Carlo Andrea Rozzi, Stefano Corni S3 Center, CNR Institute of Nanoscience, Modena, Italy.
2 Outline 1- The basics of the Polarizable Continuum Model (PCM). 2- PCM terms entering the Kohn-Sham Hamiltonian. 2.1 Atomic basis and real-space representations. 2.2 Regularization of the Coulomb singularity in real-space. 3- Numerical results. 3.1 Solvation free energies of neutral solutes. 3.2 Optical absorption spectra of selected molecules. 4- What has been coded about PCM in Octopus? 4.1 PCM module: main types and subroutines. 5- Conclusions.
3 The basics of PCM model S. Miertuš et al. Chem. Phys. 55, 117 (1981). The solvent is a continuous dielectric medium polarized by the solute molecule. Solute molecule is hosted by the cavity within the surface. The shape of molecular shape. The molecule is treated quantum mechanically. Γ should reproduced the Effective Hamiltonian Poisson equation + boundary conditions at Solvent Reaction potentials.
4 Apparent surface charges (ASC) The latter Poisson Eq. can be rewritten as: with being a apparent charge density distributed on the cavity surface. The PCM potential is expressed in terms of is the unique solution of the equation: : Cances et al. J. Math. Chem. 23, 309 (1998) Integral operators Γ PCM-IEF
5 Apparent surface charge method (ASC): in practice Definition of the cavity and its subdivision in tesserae (GEPOL procedure) Pascual et al. J. Comp. Chem. 11, 1047 (1990) 1- The cavity is defined by the union of interlocking spheres. 2- Cavity surface tessellation: projecting the 60 faces of a pentakis dodecahedron inscribed in each sphere. Polarization charges are computed by using the PCM matrix (JCP 139, (2013) ) response matrix. Molecule electrostatic potential.
6 IEF-PCM equations: Molecule + solvent Green function in vacuo. Typical solvation condition.
7 IEF-PCM equations: Molecule + solvent + NP Delgado et al. J. Chem. Phys. 139, (2013)
8 PCM terms in the Kohn-Sham Eqs. The starting point is the free energy functional: By taking the functional derivative :
9 atomic basis set representation: Gaussian, Gamess, NWChem.... self-consistent term
10 real-space representation: Octopus,? The solvent reaction potential becomes singular in the limit How does the PCM field is regularized? is the area of the i-th tessera and is a parameter to fit the gaussian width.
11 Regularized PCM potential with: exact integral fit (Padé approximant)
12 PCM terms in the ground state energy simulation domain - Finding the closest grid point for each tessera. - Building the eight cube's vertices. - Trilinear interpolation to get
13 Numerical results: set of molecules to test PCM Neutral organic molecules (Andreussi et al. JCP 136, (2012)). Geometries optimized with GAMESS at the level of PBE / 6-31(d).
14 solute - solvent electrostatic interaction energy in water XC = PBE Octopus: R= 5 Å Δ = 0.15 Å GAMESS: TZ 6311+G(d,p) piperazine default 013
15 solute - solvent electrostatic interaction energy in water XC = PBE Octopus: R= 5 Å Δ = 0.15 Å GAMESS: TZ 6311+G(d,p) piperazine 013
16 solute - solvent electrostatic interaction energy in water XC = PBE Octopus: R= 5 Å Δ = 0.15 Å GAMESS: TZ 6311+G(d,p) trimethylamine piperazine 013 biphenyl nitrobenzene 206
17 Solvation free energies in water XC = PBE Octopus: R= 5 Å Δ = 0.15 Å GAMESS: TZ 6311+G(d,p) m-016 m-140 m-142 m-163 m-160 m-079 m-206 m-036 m-090 m-200 m-013 m-069 m-117
18 Solvation free energies in water XC = PBE Octopus: R= 5 Å Δ = 0.15 Å GAMESS: TZ 6311+G(d,p)
19 Looking for the singularity: calculations in XC = PBE Octopus: R= 5 Å Δ = 0.15 Å
20 Looking for the singularity: calculations in iteration
21 Absorption spectra: selected cases XC = PBE Octopus: R= 5 Å Δ = 0.19 Å GAMESS: TZ 6311+G(d,p) m-016 m-079 m-206 m-013
22 Absorption spectra solvatochromic shifts (ev) Oct: R= 5 Å Δ = 0.19 Å real-time propagation d b mol-013 a Octopus Gamess c GAMESS: 6311+G(d,p) LR-TDDFT d b a peak a b c d c
23 Absorption spectra solvatochromic shifts (ev) peak a b c d Octopus b mol-016 d Octopus Gamess c a Gamess LR-TDDFT b c d a
24 Absorption spectra solvatochromic shifts (ev) mol-079 Octopus c peak a b c Octopus Gamess a b Gamess LR-TDDFT c a b
25 Absorption spectra solvatochromic shifts (ev) mol-206 Octopus d a a1 peak a a1 b c Octopus Gamess d b c Gamess LR-TDDFT a d b c
26 Structure of the PCM type pcm variable is of type pcm_t and can be accessed through any variable of type hamiltonian_t run_pcm tess(1:t) input_cavity gaussian_width n_tesserae(1:t) pcm_t v_e(n)(1:t) matrix(1:t,1:t) epsilon_0 epsilon_infty q_e(n)(1:t) info_unit v_e(n)_rs(1:np)
27 main pcm subroutines main program call hamiltonian_init(..) call pcm_init(..) end program
28 main pcm subroutines main program call hamiltonian_init(..) call pcm_init(..) - read the cavity geometry from a external file call nearest_cube_vertices(..) end program
29 main pcm subroutines main program call hamiltonian_init(..) call pcm_init(..) - read the cavity geometry from a external file call nearest_cube_vertices(..) call pcm_matrix(.., pcm%matrix ) end program
30 main pcm subroutines main program call hamiltonian_init(..) call pcm_init(..) - read the cavity geometry from a external file call nearest_cube_vertices(..) call pcm_matrix(.., pcm%matrix ) call hamiltonian_epot_generate(..) call v_nuclei_cav(hm%pcm%v_n,..) call pcm_charges (hm%pcm%q_n,..) call pcm_pot_rs (hm%pcm%v_n_rs,..) end program
31 main pcm subroutines main program call hamiltonian_init(..) call pcm_init(..) - read the cavity geometry from a external file call nearest_cube_vertices(..) call pcm_matrix(.., pcm%matrix ) call hamiltonian_epot_generate(..) call v_nuclei_cav(hm%pcm%v_n,..) call pcm_charges (hm%pcm%q_n,..) call pcm_pot_rs (hm%pcm%v_n_rs,..) call v_ks_hartree(..) call v_electrons_cav_li(vhartree,..) call pcm_charges (hm%pcm%q_e,..) call pcm_pot_rs (hm%pcm%v_e_rs,..) end program
32 main pcm subroutines main program call hamiltonian_init(..) call pcm_init(..) - read the cavity geometry from a external file call nearest_cube_vertices(..) call pcm_matrix(.., pcm%matrix ) call hamiltonian_epot_generate(..) call v_nuclei_cav(hm%pcm%v_n,..) call pcm_charges (hm%pcm%q_n,..) call pcm_pot_rs (hm%pcm%v_n_rs,..) call v_ks_hartree(..) call v_electrons_cav_li(vhartree,..) call pcm_charges (hm%pcm%q_e,..) call pcm_pot_rs (hm%pcm%v_e_rs,..) hamiltonian_update end program
33 main pcm subroutines main program call hamiltonian_init(..) call pcm_init(..) - read the cavity geometry from a external file call nearest_cube_vertices(..) call pcm_matrix(.., pcm%matrix ) call hamiltonian_epot_generate(..) call v_nuclei_cav(hm%pcm%v_n,..) call pcm_charges (hm%pcm%q_n,..) call pcm_pot_rs (hm%pcm%v_n_rs,..) call v_ks_hartree(..) call v_electrons_cav_li(vhartree,..) call pcm_charges (hm%pcm%q_e,..) call pcm_pot_rs (hm%pcm%v_e_rs,..) hamiltonian_update call energy_calc_total(..) call pcm_elect_energy(..) end program
34 main pcm subroutines main program call hamiltonian_init(..) call pcm_init(..) - read the cavity geometry from a external file call nearest_cube_vertices(..) call pcm_matrix(.., pcm%matrix ) call hamiltonian_epot_generate(..) call v_nuclei_cav(hm%pcm%v_n,..) call pcm_charges (hm%pcm%q_n,..) call pcm_pot_rs (hm%pcm%v_n_rs,..) call v_ks_hartree(..) call v_electrons_cav_li(vhartree,..) call pcm_charges (hm%pcm%q_e,..) call pcm_pot_rs (hm%pcm%v_e_rs,..) hamiltonian_update call energy_calc_total(..) call pcm_elect_energy(..) call pcm_end end program
35 Conclusions 1. About PCM. The PCM model was implemented within Octopus to solve the KS equations in real-space. The Integral Equation Formalism (IEF) has been used to solve the electrostatic problem molecule + solvent. The proposed PCM potential in real-space regularizes the Coulomb singularity for grid points infinitesimally close the solute cavity surface. 2. About the results. The solvation free energies were calculated for 13 organic molecules in water and shown to be in excellent agreement with similar results obtained with GAMESS. In all cases, the solute-solvent interaction energy shows a smooth behavior as the regularization parameter α is varied around its default value (1.0). The optical absorption spectra for selected systems (piperazine, trimethylamine, biphenyl, nitrobenzene) were calculated in vacuo and in water. The solvatochromic shifts found with Octopus (TD-DFT) compare qualitatively well with those obtained with GAMESS (LR-TDDFT). 3. About future implementations. Coding a subroutine in Octopus to generate the solute cavity surface. Inclusion of the non-equilibrium effects within the PCM to model consistently the real-time polarization response. Extending the PCM implementation to perform the real-time electron-nuclei dynamics. Extending the PCM implementation to perform linear-response TDDFT calculations. Generalization of the PCM Eqs. to address more complex dielectric environments.
36 Acknowledgements HPC-ISCRA projects OCT_PCM & DEMOOPT. FP7 CRONOS grant FP7 HY-SUNLIGHT grant
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