Representing molecules as atomic-scale electrical circuits with fluctuating-charge models

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Slides for my talk at the APS (March 2007) national meeting.

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Representing molecules as atomic-scale electrical circuits with fluctuating-charge models

  1. 1. Representing molecules as atomic‐scale electrical  circuits with fluctuating‐charge models + + ‐ ‐ q1 q2 Jiahao Chen Department of Chemistry and Beckman Institute University of Illinois at Urbana‐Champaign APS Meeting P19.5, 2007‐03‐07 Acknowledgments Funding •Todd Martínez •NSF DMR‐03 25939 ITR •Martínez Group members •DOE DE‐FG02‐05ER46260
  2. 2. Polarization and charge transfer in  molecular mechanics (MM) • Want to describe both polarization and charge  transfer with reasonable computational cost • Common models to describe polarization: – Charge‐on‐spring/Drude oscillator, e.g. Drude (1902) – Point‐polarizable dipole, e.g. Vesely (1977) – Chemical potential equilibration (CPE), a.k.a.  fluctuating‐charge: Rappé and Goddard (1991); Rick,  Stuart and Berne (1994) • Only CPE models can account for both effects P. Drude, The Theory of Optics, Longmans, Green and Co., New York (1902); F.J. Vesely,  J. Comp. Phys. 24 (1977), 361‐371;  A. K. Rappé, W. A. Goddard, III, J. Phys. Chem. 95 (1991), 3358‐3363; S. W. Rick, S. J. Stuart, B. J. Berne, J. Chem. Phys. 101 (1994), 6141‐6156.
  3. 3. A simple DC circuit DC source + capacitor V C ‐ ground 0 V
  4. 4. A simple DC circuit What is the charge q on C? energy depleted energy gain from DC source of capacitor DC source + capacitor charge V ‐ C q E = −qV + 1 C −1 q 2 2 ∂E −1 = −V + C q = 0 ground ∂q 0 V ∴q =VC This Hamiltonian approach works for molecules too: fluctuating‐charge/electronegativity equilibration models
  5. 5. CPE models: The QEq model QEq model for a diatomic molecule source capacitance term term electronegativity X 1 2 + + χ1 χ2 E = qi χi + ηi qi i 2 ‐ ‐ Coulomb 1X Coulomb interaction + qi qj Jij term chemical 2 hardness η q J12 ∂E i6=j 1 1 η2 q2 =μ ∂qi chemical μ potential A. K. Rappé, W. A. Goddard III, J. Phys. Chem. 95 (1991), 3358‐3363.
  6. 6. QEq: wrong NaCl dissociation 1.0 q/e equilibrium geometry 0.9 0.8 + + 0.7 ‐ ‐ 0.6 0.5 QEq 0.4 QEq, R → ∞ 0.3 + + ‐ J12 → 0 ‐ 0.2 0.1 ab initio DMA0 CASSCF(8/5)/6‐31G* 0.0 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 R/Å 8.0 DMA0 = distributed multipole analysis restricted to point charges only CASSCF = complete active space self‐consistent field method
  7. 7. The QTPIE model: Motivation X 1. Introduce charge transfer variables qi = pji X 1 2 X j EQEq = qi χi + ηi qi + qi qj Jij i 2 i6=j X X1 1X = pji χi + ηi pji pki + pki plj Jij ij 2 2 ijk ijkl 2. Introduce overlap integral: explicit notion of distance X X1 1X EQTPIE = pji χi Sij + ηi pji pki + pki plj Jij ij 2 2 ijk ijkl ∂EQTPIE =0 ∂pji J. Chen, T. J. Martínez, Chem. Phys. Lett., in press.
  8. 8. QTPIE: Correct NaCl asymptote 1.0 0.9 q/e equilibrium geometry 0.8 0.7 0.6 0.5 QEq 0.4 0.3 QTPIE 0.2 0.1 ab initio 0.0 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 R/Å 8.0 QTPIE prediction improved over QEq without reoptimizing parameters, but variation is still slower than ab initio
  9. 9. Water fragments correctly • Asymmetric dissociation: correct asymptotics, charge  transfer on OH fragment retained 1.0 q/e equilibrium geometry ab initio R 0.5 QEq R/Å QTPIE 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 ‐0.5 ‐1.0
  10. 10. Water parameters transferable 1.0 • Parameters transferable across geometries q/e 1.0 q/e 0.8 O H 0.8 0.6 O H H 0.6 0.4 0.4 H DMA 0.2 0.2 DMA 0.0 QEq 0.0 QEq R/Å QTPIE R/Å QTPIE ‐0.2 0.5 1.5 2.5 3.5 4.5 QTPIE‐0.2 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 QTPIE ‐0.4 DMA ‐0.4 DMA ‐0.6 ‐0.6 ‐0.8 QEq ‐0.8 QEq ‐1.0 ‐1.0 1.0 1.0 q/e q/e 0.8 0.8 O H O H 0.6 0.6 H 0.4 H 0.4 0.2 DMA 0.2 DMA 0.0 QEq 0.0 QEq R/Å QTPIE R/Å QTPIE ‐0.2 0.5 1.5 2.5 3.5 4.5 ‐0.2 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 QTPIE QTPIE ‐0.4 DMA ‐0.4 DMA ‐0.6 ‐0.6 ‐0.8 QEq ‐0.8 QEq ‐1.0 ‐1.0
  11. 11. Dipole polarizability of phenol • Response of dipole moment to external electric  field • QTPIE: overestimates less than QEq QEq QTPIE ab initio* x 24.6244 13.0298 13.6758 y 20.3270 10.7566 12.3621 z 0.0000 0.0000 6.9981 (ų) *ab initio method: MP2/aug‐cc‐pVDZ
  12. 12. Conclusions • Fluctuating‐charge models are analogous to DC  electrical circuits • QTPIE (our new charge model) predicts correct  dissociation behavior of atomic charges • Explicit distance cutoff for electronegativities improves qualitative behavior Thank You
  13. 13. QEq v. ab initio charges 1.2 q/e equilibrium geometry 1.0 0.8 QEq 0.6 Mulliken ab initio 0.4 DMA charges Ideal dipole 0.2 0.0 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 R/Å 8.0
  14. 14. QEq1, a fluctuating charge model • Given geometry, find charge distribution energy to charge atom Coulomb interaction q1 q2 q3 • Minimization with fixed total charge  q4 q5 defines Lagrange multiplier μ 1. A. K. Rappe, W. A. Goddard III, J. Phys. Chem. 95 (1991) 3358‐3363.
  15. 15. QTPIE: charge transfer with  polarization current equilibration • Shift focus to charge transfer variables pji: – Charge accounting: where it came from, where it’s  going p 12 p23 p34 p45 – Explicitly penalize long‐distance charge transfer

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