Algorithmic Challenges in Photodynamics Simulations

Transcription

1 Algorithmic Challenges in Photodynamics Simulations Felix Plasser González Research Group Institute for Theoretical Chemistry, University of Vienna, Austria Grundlsee, 24 th February 2016

2 Photodynamics What happens to molecules after light irradiation? Photovoltaics Photobiology Phototherapy Photosynthesis Photo... Ultrafast processes (< 1ps) - experiments difficult Computation needed High computational effort for larger systems Parallelization needed

3 Introduction Three primary steps 1. Electronic Schrödinger equation ĤΨ I = E I Ψ I 2. Nonadiabatic Interactions Computed through wave function overlaps S IJ = Ψ I (R) ΨJ (R ) 3. Atomic Forces f α I = R α E I

4 Electronic Schrödinger equation Electronic Schrödinger equation Pauli principle Non-local interactions Standardized task ĤΨ I = E I Ψ I Ψ I (r 1,r 2,...) = Ψ I (r 2,r 1,...)

5 Electronic Schrödinger equation Electronic Schrödinger equation ĤΨ I = E I Ψ I Present context: Columbus program system Various successful applications on the VSC 100 cores Calculations not possible on workstations Routine work VSC-2 > VSC-1 > VSC-3 1 FP, H. Pasalic et al. Angew. Chem.-Int. Ed. 2013, 52, Z. Cui, H. Lischka et al. ChemPhysChem 2014, 15, S. Horn, FP et al. Theor. Chem. Acc. 2014, 133, A. Das, T. Müller, FP, H. Lischka J. Phys. Chem. 2016, in print.

6 Overlaps Wave function overlaps Many-electron wave functions S IJ = Ψ I (R) ΨJ (R ) Expansion into Slater determinants Expansion into MOs Ψ I = n CI d ki Φ k k=1 Φ k = ϕ 1...ϕ nα ϕ nα ϕ n

7 Overlaps Overlap as double sum over Slater determinant overlaps S IJ = Ψ I Ψ J = n CI n CI k=1 l=1 d ki d lj Φk Φ l Computed as determinant over MO overlaps Φk Φ l = ϕ1 ϕ 1. ϕnα ϕ 1... ϕ1 ϕ n α ϕnα ϕ nα ϕ nα +1 ϕ n α ϕ nα +1 ϕ l(n) ϕ n ϕ nα ϕ n ϕ n Formal scaling: O(n CI n CI n3 el ) Simplifications?

8 Overlaps Two independent factors for α and β spin Φk Φ l = ϕ1 ϕ 1. ϕnα ϕ 1... ϕ1 ϕ nα ϕnα ϕ nα ϕ nα +1 ϕ n α +1. ϕ n ϕ nα ϕ nα +1 ϕ l(n) ϕ n ϕ n = S kl S kl Spin-factors reappear Strategy: Precompute and store these factors

9 Overlaps Double molecule AO overlaps χµ χ ν MO coefficients C pµ,c qν Slater Determinants Φ k, Φ l CI-coefficients d ki,d lj Sort MO overlaps ϕp ϕ q Precompute Unique factors S kl, S kl Contract S IJ

10 Overlaps Additional algorithmic improvements Partial Laplace recursion for determinant computations Optimized contraction step using BLAS calls Parallelization (SMP)

11 Verification Verification for selenoacroleine torsion New code 1 against existing state-of-the-art code 2 Implem. Method T 1 (50 ) T 1 (55 ) T 1 (50 ) T 2 (55 ) t CPU (s) current CASSCF(6,5) Ref. 2 CASSCF(6,5) current MR-CIS(4,3) Ref. 2 MR-CIS(4,3) Quantitative agreement 1000 times faster 1 FP, M. Ruckenbauer, S. Mai, M. Oppel, P. Marquetand, L. González JCTC 2016, in print. 2 J. Pittner et al. Chem. Phys. 2009, 356,

12 Performance 100,000 Time(core seconds) 10,000 1, e+05 1e+06 1e+07 1e+08 1e+09 1e+10 1e+11 1e+12 n pair Uniform performance Over 7 orders of magnitude in problem size For various wave function models 2-3 orders of magnitude faster than previous code

13 Parallelization Parallelization in shared memory Excellent scaling behavior Somewhat erratic behavior for contraction step S IJ = n CI n CI d Ik k=1 l=1 d Jl S kl S kl Speedup Time (core hours) Sorting I/O Total Determinants Contraction # Cores

14 Overlaps Integration into the SHARC dynamics code 1 Interface to various other electronic structure codes Multireference methods Columbus, Molcas Time-dependent DFT ADF, Dalton, Gaussian Coupled cluster Turbomole Photoelectron spectra / Dyson orbitals 2 Wave function analysis 1 S. Mai, P. Marquetand, L. González IJQC 2015, 115, 1215, 2 M. Ruckenbauer, S. Mai, P. Marquetand, L. González 2016, arxiv: v1.

15 Conclusions Photodynamics simulations 1 Electronic Schrödinger equation Routine work Interesting applications 2 Wave function overlaps New highly efficient implementation 1 3 Atomic forces Evaluate next 1 FP, M. Ruckenbauer, S. Mai, M. Oppel, P. Marquetand, L. González JCTC 2016, in print.

16 Acknowledgments González group M. Ruckenbauer S. Mai M. Oppel P. Marquetand L. González Collaborators H. Lischka J. Pittner This material is based upon work supported by the VSC Research Center funded by the Austrian Federal Ministry of Science, Research and Economy (bmwfw).