Polarization and charge
  transfer in classical
 molecular dynamics
               Jiahao Chen
            Martínez Group
...
Methods of computational chemistry
ˆ
HΨ = EΨ                          What is the charge distribution?

   direct         ...
Molecular models/force fields
Typical energy function


E = covalent bond effects
                          +


           ...
Molecular models/force fields
Typical energy function


E=     b∈bonds
                 kb (rb − req,b )2+
                ...
Why care about polarization
  and charge transfer?

   Unique to condensed
    phases, where most
   chemistry and biology...
Polarization in chemistry
• Effect of local environment in liquid phases
• Ex. 1: Stabilizes carbonium in lysozyme
• Ex. 2...
3 models for
    polarization


Review: H Yu and WF van Gunsteren Comput. Phys. Commun. 172 (2005), 69-85.
Drude oscillators
or charge-on-spring
  or shell models
                          Q
                      R k Ideal spring...
Inducible dipoles

   α1                                                       α2



µinduced,1                           ...
Fluctuating charges
                                    χ1 , η1

                                     -0.3
charge transfer...
Better Electrostatics
                                         Polari- Charge
                        Model               ...
QEq, a fluctuating-
  charge model
E=        qi χi +                         qi qj Jij
     i     atomic      i<j          ...
QEq has wrong asymptotics
1.0
        q/e

                                      Na               Cl
                     ...
QTPIE: our new model

         E=                           qi χi +                           qi qj Jij
                  ...
QTPIE has correct limit
1.0
        q/e

                                      Na                Cl
                      ...
Execution times
                                   TImes to solve the QTPIE model
                       4
               ...
Cooperative
     polarization in water
        +                 −→
• Dipole moment of water increases from 1.854
  Debye1...
Polarization in water chains
  • Use parameters from single water molecule
    to model chains of waters


  • Compare QEq...
Dipole moment per water
 2.6
           ( /N)/Debye

 2.5
                                                                ...
Charge transfer in 15 waters
                                       Charges per molecule in chain of 15 water molecules
  ...
Summary

• Polarization and charge transfer are important
  effects usually neglected in classical MD
• Our new charge mod...
Acknowledgments



   Prof. Todd J. Martínez
 Martínez Group and friends

          $: DOE
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Polarization and charge transfer in classical molecular dynamics

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Polarization and charge transfer in classical molecular dynamics

  1. 1. Polarization and charge transfer in classical molecular dynamics Jiahao Chen Martínez Group Chemistry, MRL and Beckman, UIUC
  2. 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. 3. Molecular models/force fields Typical energy function E = covalent bond effects + noncovalent interactions
  4. 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. 5. Why care about polarization and charge transfer? Unique to condensed phases, where most chemistry and biology happens
  6. 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. 7. 3 models for polarization Review: H Yu and WF van Gunsteren Comput. Phys. Commun. 172 (2005), 69-85.
  8. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 22. Acknowledgments Prof. Todd J. Martínez Martínez Group and friends $: DOE
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