Excited state dynamics with the Effective Fragment Potential

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Excited state dynamics with the Effective Fragment Potential method? Lyudmila V. Slipchenko Department of

Excited state dynamics with the Effective Fragment Potential method? Lyudmila V. Slipchenko Department of Chemistry, Purdue University • Effective Fragment Potential method (EFP) • Beyond polarizable embedding • Prospects for excited state dynamics

Methodology: Effective Fragment Potential method (EFP) Perturbation theory applied to non-interacting fragments Einteraction =

Methodology: Effective Fragment Potential method (EFP) Perturbation theory applied to non-interacting fragments Einteraction = + + Eint EFP Ecoulomb Epolarization Edispersion Eexchange-repulsion Echarge-transfer Eint EFP Lyudmila V. Slipchenko short-range perturbation theory distributed approach used for all terms QM Eint EFP long-range perturbation theory EFP Day et al, J. Chem. Phys. 1996, 105, 1968 -1986; Gordon et al, . Phys. Chem. A 2001, 105, 293 -307; Gordon et al, Ann. Rep. Comp. Chem. , 2007, 3, 177 -193; Ghosh et al, J. Phys. Chem. A 2010, 114, 12739 -12754 EFP: full embedding Excited state dynamics, Buffalo 2018

EFP set-up 1. Preparation of EFP fragment parameters general fragment: MAKEFP run (GAMESS) a

EFP set-up 1. Preparation of EFP fragment parameters general fragment: MAKEFP run (GAMESS) a set of ab initio calculations on each unique fragment § Coulomb: set of point multipoles (DMA) § Polarization: static polarizability tensors at LMO (coupled HF) § Dispersion: dynamic polarizability tensors at LMO (TDHF) § Exchange-repulsion: wave function & Fock matrix (HF) 2. EFP calculation (energy, optimization, MD, MC, …) § § EFP-EFP interactions by (semi)-classical formulas QM-EFP interactions via 1 -electron terms in QM Hamiltonian Lyudmila V. Slipchenko EFP: full embedding Excited state dynamics, Buffalo 2018

S 22: performance of popular methods MAD, kcal/mol HF B 3 LYP PBE M

S 22: performance of popular methods MAD, kcal/mol HF B 3 LYP PBE M 06 -2 X B 97 X-D MP 2 SCS-CCSD Amber OPLSAA MMFF 94 EFP 10% error Lyudmila V. Slipchenko HB 3. 29 1. 77 1. 13 0. 89 0. 73 0. 27 0. 24 1. 54 0. 40 4. 64 4. 45 3. 61 1. 82 1. 38 disp 7. 24 6. 22 4. 53 0. 99 0. 36 0. 30 1. 69 0. 55 0. 23 0. 98 1. 07 0. 73 0. 57 0. 48 mixed 3. 15 2. 64 1. 66 0. 67 0. 32 0. 42 0. 61 0. 37 0. 08 0. 89 0. 56 0. 60 0. 35 0. 39 overall 4. 56 3. 54 2. 44 0. 85 0. 47 0. 33 0. 88 0. 80 0. 24 2. 12 1. 98 1. 61 0. 89 0. 74 J. Chem Theory Comp. , 8 (8), dynamics, 2835– 2843 (2012) EFP: full embedding Excited state Buffalo 2018

EFP in a nutshell • rigid-geometry fragment-based polarizable force field • all EFP force

EFP in a nutshell • rigid-geometry fragment-based polarizable force field • all EFP force field parameters are obtained from a separate ab initio calculation: no fitted parameters • provides physical insight into intermolecular interaction • accuracy: 10 -15% relative error in interaction energies (similar to MP 2, better than many DFT functionals, superior to classical force fields) • accuracy can be further improved Lyudmila V. Slipchenko EFP: full embedding Excited state dynamics, Buffalo 2018

Lib. EFP: stand-alone EFP implementation • written in standard C 99 • uses native

Lib. EFP: stand-alone EFP implementation • written in standard C 99 • uses native EFP data format • • generated by GAMESS 2 -clause BSD license uses BLAS wherever possible for better performance available as a shared or static library parallelization across multiple nodes using hybrid MPI/Open. MP Dr. Ilya Kaliman http: //www. libefp. org/ Kaliman and Slipchenko, JCC 34, 2284 (2013) Kaliman and Slipchenko, JCC 36, 129 (2015) Lyudmila V. Slipchenko EFP: full embedding Excited state dynamics, Buffalo 2018

Lib. EFP LIBEFP Q-Chem PSI 4 various QM/EFP methods EFPMD • distributed with LIBEFP

Lib. EFP LIBEFP Q-Chem PSI 4 various QM/EFP methods EFPMD • distributed with LIBEFP code • molecular dynamics in NVE, NVT, and NPT ensembles NWChem Gamess Tinker Molcas Gromacs Lyudmila V. Slipchenko EFP-only system EFP: full embedding • MM/EFP schemes • free energy calculations with EFP Excited state dynamics, Buffalo 2018

QM-Lib. EFP interface Lyudmila V. Slipchenko EFP: full embedding Excited state dynamics, Buffalo 2018

QM-Lib. EFP interface Lyudmila V. Slipchenko EFP: full embedding Excited state dynamics, Buffalo 2018

i. Spi. EFP: GUI and job manager molecular structure computational resource xyz, pdb, cif

i. Spi. EFP: GUI and job manager molecular structure computational resource xyz, pdb, cif data formats high-performance server cloud computing i. Spi. EFP local machine Lyudmila V. Slipchenko § molecular visualization /animation / editor tool § job workflow editor / manager / scheduler § Java applet with integrated Jmol molecular viewer / editor EFP: full embedding EFPdb My. SQL database with fragment parameters Excited state dynamics, Buffalo 2018

i. Spi. EFP: EFP workflow molecular structure visualization fragmentation visualization of fragmented system automatic

i. Spi. EFP: EFP workflow molecular structure visualization fragmentation visualization of fragmented system automatic proteins, DNA, fatty acids manual user-defined fragmentation smart substructure search locally preparing fragment parameters search EFPdb database compute parameters prepare EFP input submit job to computational resource prepare MAKEFP GAMESS input submit GAMESS job ( remove capping points ) visualization, animation, analysis Lyudmila V. Slipchenko EFP: full embedding Excited state dynamics, Buffalo 2018

Solute-solvent tete-a-tete Solvatochromism = differential solvation of the ground and excited states of a

Solute-solvent tete-a-tete Solvatochromism = differential solvation of the ground and excited states of a chromophore Influence of solvent on properties of solute Lyudmila V. Slipchenko EFP: full embedding Excited state dynamics, Buffalo 2018

QM / EFP EFP solute QM Eint EFP electrostatic embedding Lyudmila V. Slipchenko solvent

QM / EFP EFP solute QM Eint EFP electrostatic embedding Lyudmila V. Slipchenko solvent coupling term EFP polarizable embedding EFP: full embedding Excited state dynamics, Buffalo 2018

Polarization within HF cycle HF self-consistent cycle polarization self-consistent cycle Lyudmila V. Slipchenko EFP:

Polarization within HF cycle HF self-consistent cycle polarization self-consistent cycle Lyudmila V. Slipchenko EFP: full embedding Excited state dynamics, Buffalo 2018

QM/EFP for the electronic excited states Generally, each excited state has different electron density

QM/EFP for the electronic excited states Generally, each excited state has different electron density & charge distribution different response from environment statespecific perturbative treatment Polarization correction to the excitation energy due to polarizable environment (using one-electron excited state density): DEpol = Epol, ai(mex) – Epol, gr(mgr) - S (mex – mgr)Fai, ex Thompson & Schenter, JPC 99, 6374 (1995) Lyudmila V. Slipchenko leading correction to the interaction between mex and Y ex EFP: full embedding Excited state dynamics, Buffalo 2018

Solvatochromism in para-nitroaniline Para-nitroaniline (p. NA) – a chromophore with bright lowlying charge-transfer state

Solvatochromism in para-nitroaniline Para-nitroaniline (p. NA) – a chromophore with bright lowlying charge-transfer state - absorption spectrum charge-transfer p->p* transition + mex = 15. 3 D mgr = 6. 2 D Kovalenko, Schanz, Farztdinov, Hennig, Ernsting, CPL 323, 312 (2000) Lyudmila V. Slipchenko EFP: full embedding Excited state dynamics, Buffalo 2018

Solvatochromic shifts in p. NA gas phase water 1. 02 e. V expt: 1.

Solvatochromic shifts in p. NA gas phase water 1. 02 e. V expt: 1. 0 e. V Dr. Dmytro Kosenkov dioxane 0. 44 e. V expt: 0. 72 e. V c-hexane 0. 20 e. V expt: 0. 41 e. V Kosenkov & Slipchenko, JPCA, 115, 392 (2011); Kovalenko et al, CPL 323 (2000) 312; Morgan et al, JCP 115 (2001) 912 Lyudmila V. Slipchenko EFP: full embedding Excited state dynamics, Buffalo 2018

A closer look at solvatochromism Electrostatic terms (dominant in Short-range “cavity terms” polar or

A closer look at solvatochromism Electrostatic terms (dominant in Short-range “cavity terms” polar or polarizable solvents) (dominant in non-polar solvents) stabilize the electronic state with stabilize the electronic state of larger partial charges, with “smaller” size QM/EFP larger dipole moment dispersion, electrostatic, exchange+ - + polarization + repulsion + + - + - + + Lyudmila V. Slipchenko - + EFP: full embedding Excited state dynamics, Buffalo 2018

QM / EFP: toward full embedding EFP solvent solute QM Eint EFP coupling term

QM / EFP: toward full embedding EFP solvent solute QM Eint EFP coupling term EFP Smith, Ruedenberg, Gordon, Slipchenko, JCP 136, 244107 (2012); Slipchenko, Ruedenberg, Gordon, JPCA 2017, 121, 9495− 9507 Lyudmila V. Slipchenko EFP: full embedding Excited state dynamics, Buffalo 2018

Long-range perturbation theory r. A electrostatic energy r. B polarization (induction) energy dispersion energy

Long-range perturbation theory r. A electrostatic energy r. B polarization (induction) energy dispersion energy Lyudmila V. Slipchenko EFP: full embedding Excited state dynamics, Buffalo 2018 29

Dispersion energy between EFP fragments Applying multipole expansion to classical fragments A and B,

Dispersion energy between EFP fragments Applying multipole expansion to classical fragments A and B, the perturbation H’ becomes: T, T and T are the electrostatic tensors of zero, first, and second rank The leading term (C 6): Introducing Casimir-Polder identity: and notations for dynamic polarizability tensor: Principal fragment-fragment energy Lyudmila V. Slipchenko EFP: full embedding Excited state dynamics, Buffalo 2018

QM-EFP dispersion Applying multipole expansion to classical fragment B, while A remains quantum, the

QM-EFP dispersion Applying multipole expansion to classical fragment B, while A remains quantum, the perturbation H’ is: Again, using Casimir-Polder identity and gathering terms for dynamic polarizability tensor on fragment B: Approximating the sum-over-state expression by the orbital-based summation, obtain the principal expression: Lyudmila V. Slipchenko EFP: full embedding Excited state dynamics, Buffalo 2018

QM-EFP dispersion electric field integrals in occupied-virtual block (“transition” electric field) computed using 12

QM-EFP dispersion electric field integrals in occupied-virtual block (“transition” electric field) computed using 12 -point quadrature • Distributed polarizability tensors (on fragments) are used • Information from the QM subsystem: electric field integrals, orbital energies • Additive correction to SCF energy of the QM-EFP system Slipchenko, Ruedenberg, Gordon, JPCA 2017, 121, 9495− 9507 Lyudmila V. Slipchenko EFP: full embedding Excited state dynamics, Buffalo 2018

Dispersion energy, kcal/mol Simple tests Lyudmila V. Slipchenko R-R Angstrom EFP: full 0, embedding

Dispersion energy, kcal/mol Simple tests Lyudmila V. Slipchenko R-R Angstrom EFP: full 0, embedding Excited state dynamics, Buffalo 2018

Dispersion for the ground electronic state occ vir Lyudmila V. Slipchenko EFP: full embedding

Dispersion for the ground electronic state occ vir Lyudmila V. Slipchenko EFP: full embedding Excited state dynamics, Buffalo 2018

Dispersion for the excited electronic state Suppose CIS formalism: occ i a vir Lyudmila

Dispersion for the excited electronic state Suppose CIS formalism: occ i a vir Lyudmila V. Slipchenko EFP: full embedding Excited state dynamics, Buffalo 2018

Dispersion for the excited electronic state Suppose CIS formalism: occ i a vir occ

Dispersion for the excited electronic state Suppose CIS formalism: occ i a vir occ vir Lyudmila V. Slipchenko EFP: full embedding Excited state dynamics, Buffalo 2018

Dispersion for the excited electronic state Suppose CIS formalism: occ i a vir Lyudmila

Dispersion for the excited electronic state Suppose CIS formalism: occ i a vir Lyudmila V. Slipchenko EFP: full embedding Excited state dynamics, Buffalo 2018

Dispersion for the excited electronic state Lyudmila V. Slipchenko EFP: full embedding Excited state

Dispersion for the excited electronic state Lyudmila V. Slipchenko EFP: full embedding Excited state dynamics, Buffalo 2018

Solvatochromism in p. NA: revisited QM/EFP: polarizable embedding + dispersion QM/EFP dispersion in the

Solvatochromism in p. NA: revisited QM/EFP: polarizable embedding + dispersion QM/EFP dispersion in the ground state: -1. 26 e. V Excitation Dispersion energy correction S 2 5. 26 -0. 29 4. 97 S 5 6. 16 -1. 65 4. 51 π π* p. NA in small benzene cluster CIS/6 -31+G* //EFP Lyudmila V. Slipchenko Total energy π Ryd Repulsion between QM and EFP regions is a MUST! EFP: full embedding Excited state dynamics, Buffalo 2018

QM / EFP: toward full embedding EFP solute solvent QM Eint EFP coupling term

QM / EFP: toward full embedding EFP solute solvent QM Eint EFP coupling term EFP Annu. Rev. Phys. Chem. , 64, 553 -78 (2013); Viquez-Rojas and Slipchenko, in prep Lyudmila V. Slipchenko EFP: full embedding Excited state dynamics, Buffalo 2018

QM-EFP exchange-repulsion • 3 -center-1 -electron integrals are computed • Need a pair of

QM-EFP exchange-repulsion • 3 -center-1 -electron integrals are computed • Need a pair of parameters for each unique LMO • Parameterization is done based on comparison to SAPT 0 ex-rep and total energies and EFP ex-rep energies for molecular clusters extracted from hightemperature MD trajectories • Exchange-repulsion in QM/EFP 1 (EFP 1: water potential) is done similarly Viquez-Rojas, Fine, Slipchenko, submitted to JCP Lyudmila V. Slipchenko EFP: full embedding Claudia Viquez-Rojas Excited state dynamics, Buffalo 2018

Solvatochromism in p. NA: revisited 2 Full-embedded QM/EFP dispersion in the ground state: -1.

Solvatochromism in p. NA: revisited 2 Full-embedded QM/EFP dispersion in the ground state: -1. 22 e. V Excitation Dispersion energy correction S 2 5. 35 -0. 21 5. 14 S 8 7. 97 -0. 51 7. 46 π π* p. NA in small benzene cluster CIS/6 -31+G* //EFP Lyudmila V. Slipchenko Total energy π Ryd Full-embedded QM/EFP provides qualitatively correct description of Rydberg states EFP: full embedding Excited state dynamics, Buffalo 2018

Full QM/EFP energies for S 22 dataset QM/EFP performs better than EFP! Viquez-Rojas, Fine,

Full QM/EFP energies for S 22 dataset QM/EFP performs better than EFP! Viquez-Rojas, Fine, Slipchenko, submitted to JCP Lyudmila V. Slipchenko EFP: full embedding Excited state dynamics, Buffalo 2018

Conclusions • EFP is first-principles based polarizable force field • LIBEFP is a stand-alone

Conclusions • EFP is first-principles based polarizable force field • LIBEFP is a stand-alone EFP implementation designed for interfacing with ab initio and dynamics software • QM/EFP: full embedding scheme for describing electronic structure in heterogeneous environments • Excited state dynamics? § Missing analytic gradients: state-specific polarization and excited state dispersion contribution. Can they be ignored? § Need QM dynamics driver. Limited possibilities exist in GAMESS, Q-Chem, … We are interested in collaborations! Lyudmila V. Slipchenko EFP: full embedding Excited state dynamics, Buffalo 2018

Acknowledgements Group members: Dr. Danil Kaliakin Pradeep Gurunathan Yen Bui Yongbin Kim Claudia Viquez

Acknowledgements Group members: Dr. Danil Kaliakin Pradeep Gurunathan Yen Bui Yongbin Kim Claudia Viquez Rojas Nikita Dubinets Hanjjing Xu Jia Lin Cheoh Ryan De. Rue Lyudmila V. Slipchenko Group alumni: Dr. Carlos Borca $$$: Dr. Ilya Kaliman NSF CTMC Dr. Dmytro Kosenkov NSF SI 2 -SSI Dr. Ben Nebgen NSF AIR: TT Dr. Mandy Green Dr. Mike Hands Dr. Frank Emmert … EFP: full embedding Excited state dynamics, Buffalo 2018