Polarization and charge transfer in classical molecular dynamics
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Slides for the UIUC biophysics symposium (Fall 2007).
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Polarization and charge transfer in classical molecular dynamics
- 1. Polarization and charge transfer in classical molecular dynamics Jiahao Chen Martínez Group Chemistry, MRL and Beckman, UIUC
- 2. Methods of computational chemistry ˆ HΨ = EΨ What is the charge distribution? direct density coarse- ab initio semiempirical molecular continuum numerical functional grained theories methods models (MM) electrostatics quadrature theory models more variables less variables numerical quadrature, classical coarse- finite element e.g. real-time path ab initio molecular dynamics molecular grained methods integral propagators dynamics dynamics ˆ ˙ HΨ = iΨ What does the system do?
- 3. Molecular models/force fields Typical energy function E = covalent bond effects + noncovalent interactions
- 4. Molecular models/force fields Typical energy function E= b∈bonds kb (rb − req,b )2+ a∈angles κa (θa − θeq,a )2 + d∈dihedrals n lnd cos (nπ) bond stretch angle torsion dihedrals + - 12 6 qi qj σij σij + r + ij rij − rij i<j∈atoms ij i<j∈atoms electrostatics dispersion
- 5. Why care about polarization and charge transfer? Unique to condensed phases, where most chemistry and biology happens
- 6. Polarization in chemistry • Effect of local environment in liquid phases • Ex. 1: Stabilizes carbonium in lysozyme • Ex. 2: Hydrates chloride in water clusters TIP4P/FQ OPLS/AA polarizable non-polarizable force field force field 1. A Warshel and M Levitt J. Mol. Biol. 103 (1976), 227-249. 2. SJ Stuart and BJ Berne J. Phys. Chem. 100 (1996), 11934 -11943.
- 7. 3 models for polarization Review: H Yu and WF van Gunsteren Comput. Phys. Commun. 172 (2005), 69-85.
- 8. Drude oscillators or charge-on-spring or shell models Q R k Ideal spring q−Q Response = change in R Review: H Yu and WF van Gunsteren Comput. Phys. Commun. 172 (2005), 69-85.
- 9. Inducible dipoles α1 α2 µinduced,1 µinduced,2 Response = change in induced dipoles Review: H Yu and WF van Gunsteren Comput. Phys. Commun. 172 (2005), 69-85.
- 10. Fluctuating charges χ1 , η1 -0.3 charge transfer = 0.5 charge transfer = 0.2 e -1.1 χ2 , η2 +1.4 charge transfer = 0.9 e χ3 , η3 Response = change in atomic charges Review: H Yu and WF van Gunsteren Comput. Phys. Commun. 172 (2005), 69-85.
- 11. Better Electrostatics Polari- Charge Model Cost zation transfer qi qj r i<j∈atoms ij Pairwise fixed charges ❙ Drude oscillator ✓ ❙❙ Inducible dipoles ✓ ❙❙❙❙❙❙ Fluctuating charges ✓ ✓ ❙❙❙
- 12. QEq, a fluctuating- charge model E= qi χi + qi qj Jij i atomic i<j screened electronegativities Coulomb “voltages” interactions φ2 (r1 )φ2 (r2 ) i j Jij = dr1 dr2 R3×2 |r1 − r2 | φi (r) = Ni |r − Ri |ni −1 e−ζi |r−Ri | AK Rappé and WA Goddard III J. Phys. Chem. 95 (1991), 3358-3363.
- 13. QEq has wrong asymptotics 1.0 q/e Na Cl R 0.8 χ1 − χ2 q= J11 + J22 − J12 0.6 QEq 0.4 asymptote ~ 0.43 ≠ 0 0.2 ab initio 0.0 R/Å 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0
- 14. QTPIE: our new model E= qi χi + qi qj Jij i i<j replace atomic pji χi kij S ij electronegativities with distance-dependent pairwise i<j electronegativities or “potential differences” Sij = φi (r)φj (r)dr overlap integral R3 φi (r) = Ni |r − Ri |ni −1 e−ζi |r−Ri | J Chen and T J Martínez, Chem. Phys. Lett. 438 (2007), 315-320.
- 15. QTPIE has correct limit 1.0 q/e Na Cl R 0.8 χ1 − χ2 q= J11 + J22 − J12 0.6 QEq 0.4 (χ1 − χ2 )S12 q= J11 + J22 − J12 QTPIE 0.2 ab initio 0.0 R/Å 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0
- 16. Execution times TImes to solve the QTPIE model 4 10 N6.20 1000 N1.81 100 Solution time (s) 10 1 0.1 Bond-space SVD Bond-space COF Atom-space iterative solver Atom-space direct solver 0.01 4 5 10 100 1000 10 10 N Number of atoms J Chen and T J Martínez, in preparation.
- 17. Cooperative polarization in water + −→ • Dipole moment of water increases from 1.854 Debye1 in gas phase to 2.95±0.20 Debye2 at r.t.p. (liquid phase) • Polarization enhances dipole moments • Missing in models with implicit or no polarization 1. D R Lide, CRC Handbook of Chemistry and Physics, 73rd ed., 1992. 2. AV Gubskaya and PG Kusalik J. Chem. Phys. 117 (2002) 5290-5302.
- 18. Polarization in water chains • Use parameters from single water molecule to model chains of waters • Compare QEq and QTPIE with: ๏ Gas phase experimental data1 ๏ Ab initio DF-LMP2/aug-cc-pVDZ ˆ HΨ = EΨ ๏ AMOEBA2, an inducible dipole model ๏ TIP3P, a common implicit polarization model 1. WF Murphy J. Chem. Phys. 67 (1977), 5877-5882. 2. P Ren and JW Ponder J. Phys. Chem. B 107 (2003), 5933-5947.
- 19. Dipole moment per water 2.6 ( /N)/Debye 2.5 AMOEBA DF-LMP2/aug-cc-pVDZ 2.4 TIP3P/QTPIE TIP3P 2.3 TIP3P/QEq 2.2 2.1 2.0 1.9 gas phase (experimental) Number of water molecules, N 1.8 0 5 10 15 20 25 30 35 40
- 20. Charge transfer in 15 waters Charges per molecule in chain of 15 water molecules 0.03 Charge on N molecule QTPIE QEq 0.02 Mulliken/DF-LMP2/aug-cc-pVDZ th 0.01 0 -0.01 -0.02 Molecule No. N -0.03 1 3 5 7 9 11 13 15
- 21. Summary • Polarization and charge transfer are important effects usually neglected in classical MD • Our new charge model corrects deficiencies in existing fluctuating-charge model at similar computational cost • We obtain quantitative polarization and qualitative charge transfer trends in linear water chains
- 22. Acknowledgments Prof. Todd J. Martínez Martínez Group and friends $: DOE