Algorithmic Challenges in Photodynamics Simulations on HPC systems

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1 Algorithmic Challenges in Photodynamics Simulations on HPC systems Felix Plasser González Research Group Institute for Theoretical Chemistry, University of Vienna, Austria Bratislava, 21 st March 2016

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

3 Introduction Computation steps 1. Electronic Schrödinger equation 2. Nonadiabatic couplings ĤΨ I = E I Ψ I h IJ (R) = Ψ I (R) Ψ J (R)

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: Multireference CI Columbus program system Static calculations 100 cores Calculations not possible on workstations Fairly routine

6 Applications Unpaired electrons in graphene nanoflakes Multireference approach needed to treat open-shell character 1 FP, H. Pasalic et al. Angew. Chem.-Int. Ed. 2013, 52, S. Horn, FP et al. Theor. Chem. Acc. 2014, 133, A. Das, T. Müller, FP, H. Lischka J. Phys. Chem. 2016, 120, 1625.

7 Dynamics For dynamics: more than just energies Gradients Coupling terms Nonadiabatic coupling vectors h IJ (R) = Ψ I (R) Ψ J (R) approximated through Wave function overlaps h IJ (R) Ψ I (R) Ψ J (R + R)

8 Overlaps Wave function overlaps S IJ = Ψ I (R) Ψ J (R ) Simpler formalism than coupling vectors Transferable between methods More stable in the case of highly peaked couplings 1 Access to phase information 1 FP, G. Granucci et al. JCP 2012, 137, 22A514.

9 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

10 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?

11 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

12 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

13 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 et al. JCTC 2016, 12, J. Pittner et al. Chem. Phys. 2009, 356,

14 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

15 Parallelization Parallelization in shared memory Excellent scaling behavior Speedup Time (core hours) Sorting I/O Total Determinants Contraction # Cores

16 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 RI-CC2, RI-ADC(2) 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.

17 Wave Function Analysis Electronic Schrödinger equation ĤΨ I = E I Ψ I How to compare different levels of theory? (Excitation) energies E I Selected physical observables Oscillator strength Dipole moment Reduced density matrices 1,2 Natural orbitals Natural transition orbitals Attachment/detachment densities 1 FP, S. A. Bäppler, M. Wormit, A. Dreuw JCP 2014, 141, S. A. Bäppler, FP, M. Wormit, A. Dreuw Phys. Rev. B 2014, 90,

18 Wave Function Analysis Electronic Schrödinger equation ĤΨ I = E I Ψ I What about the Ψ I as a whole? Compare through wave function overlaps S IJ = Ψ I Ψ J Ψ I,Ψ J - computed by different methods

19 Wave Function Analysis Selenoacrolein: avoided crossing geometry T 1 and T 2 computed with different methods Compare by energies By state characters Method T 1 T 2 CASSCF(6,5)/VDZP 2.40 (ππ ) 2.49 (nπ ) MR-CIS(6,5)/VDZP 2.67 (nπ ) 2.76 (ππ ) MR-CISD(6,5)/VDZP 2.51 (ππ /nπ ) 2.56 (nπ /ππ ) MR-CISD(8,7)/VDZP 2.55 (ππ /nπ ) 2.61 (nπ /ππ ) MR-CISD(6,5)/VTZP 2.48 (ππ /nπ ) 2.53 (nπ /ππ ) What do we learn from this?

20 Wave Function Analysis Ψ meth. 2 I Ψ MR-CISD(6,5)/D J T 1, T 2, orth. complement Comparison to lower level methods CASSCF - correct state ordering MR-CIS - state mixing always - large weight of orth. complement T 1 T 2 CASSCF(6,5)/VDZP MR-CIS(6,5)/VDZP 1 FP, L. González 2016, in preparation.

21 Wave Function Analysis Ψ meth. 2 I Ψ MR-CISD(6,5)/D J T 1, T 2, orth. complement Comparison to higher level methods General agreement Basis set slightly more important than active space T 1 T 2 MR-CISD(8,7)/VDZP MR-CISD(6,5)/VTZP

22 Conclusions Photodynamics simulations 1 Electronic Schrödinger equation Routine work, even on HPC systems Interesting applications 2 Wave function overlaps New highly efficient implementation 1 Transferable to various wave function models and quantum chemistry codes Application to wave function analysis 3 Combine and run dynamics FP, M. Ruckenbauer, S. Mai, M. Oppel, P. Marquetand, L. González JCTC 2016, 12,

23 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).