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Constructing a rigorous fluctuating-charge model for molecular mechanics
 

Constructing a rigorous fluctuating-charge model for molecular mechanics

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Slides for my prelim exam in September 2006.

Slides for my prelim exam in September 2006.

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    Constructing a rigorous fluctuating-charge model for molecular mechanics Constructing a rigorous fluctuating-charge model for molecular mechanics Presentation Transcript

    • Constructing a rigorous fluctuating- charge model for molecular mechanics - - + - + + + + + - - -!+ - + + + + + + +!- +!+ Funding Acknowledgments NSF DMR-03 25939 ITR •Todd Martínez DOE DE-FG02-05ER46260 •Martínez Group members, esp. Ben Levine Jiahao Chen September 19, 2006
    • Molecular mechanics is useful water flow in aquaporins1 mechanical deformation in ceramics2 • Since atomic nuclei behave mostly classically, molecular mechanics (MM) is a useful method for doing dynamics • In MM, classical electrostatic effects are important, including polarization 1. E. Tajkhorshid et. al., Science 296 (2002), 525-530. 2. P. S. Branicio, R. K. Kalia, A. Nakano, P. Vashishta, Phys. Rev. Lett. 96 (2006), art. no. 065502.
    • Molecular mechanics • Classical energy function with bonded and nonbonded terms Van der Waals interactions Molecular electrostatics • Nuclear motions propagated using classical equations of motion
    • MM leaves out something time 0 time • Ab initio molecular dynamics (MD) nuclear forces from wavefunction • MM/MD nuclear forces from fixed charge distribution - - + - + + + + + specified • MM/MD cannot describe chemical reactions
    • 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.
    • Physical interpretation of QEq • In equilibrium: – each atom i has the same chemical potential μ – μ uniquely determines the atomic charges qi • Atoms interpreted as subsystems in equilibrium molecule i atom N, V, T Energy derivatives: chemical potential μ, hardness
    • Physical interpretation of QEq • Three-point approximation for derivatives Mulliken1 E Parr-Pearson2 IP EA N N0-1 N0 N0+1 1. R. S. Mulliken, J. Chem. Phys. 2 (1934) 782-793. 2. R. G. Parr, R. G. Pearson, J. Am. Chem. Soc. 105 (1983) 7512-7516.
    • Why QEq is bad • Wrong asymptotic charges predicted 1.2 q/e equilibrium geometry 1.0 0.8 0.6 QEq Mulliken 0.4 ab initio DMA charges 0.2 Ideal dipole 0.0 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 R/Å 8.0 • No penalty for long-range charge transfer • Overestimates molecular electrostatic properties • Especially bad far from equilibrium
    • New charge model: Desiderata • Transferable parameters – Generic, application-independent – No atom typing • Accurate – Able to describe polarization and charge transfer – Correct asymptotic charge distributions – Predicts electrostatic properties accurately • Flexible – Able to handle arbitrary total charge – Able to describe electronic excited states • Rigorous – Well-defined coarse-graining picture from conventional electronic structure methods • Practical to compute – O(N ) or better – Faster than conventional electronic structure methods
    • 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
    • NaCl asymptote correct • QTPIE prediction improved over QEq, even without reoptimized parameters 1.2 q/e 1.0 equilibrium geometry 0.8 0.6 QEq 0.4 QTPIE 0.2 DMA 0.0 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 R / Å8.0 • Slope wrong: cannot capture nonadiabatic effects
    • Water fragments correctly • Asymmetric dissociation: correct asymptotics, charge transfer on OH fragment retained 1.0 q/e equilibrium geometry R 0.5 R/Å 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
    • Water parameters transferable • Parameters transferable across geometries 1.0 q/e 0.8 O H 0.6 H 0.4 DMA 0.2 QEq 0.0 QTPIE R/Å QTPIE -0.20.5 1.5 2.5 3.5 4.5 DMA -0.4 -0.6 QEq -0.8 -1.0
    • Water parameters transferable • Parameters transferable across geometries 1.0 q/e 0.8 O H 0.6 0.4 DMA H 0.2 QEq 0.0 QTPIE R/Å -0.20.5 1.5 2.5 3.5 4.5 QTPIE DMA -0.4 -0.6 QEq -0.8 -1.0
    • Water parameters transferable • Parameters transferable across geometries 1.0 q/e 0.8 O H 0.6 0.4 H DMA 0.2 QEq 0.0 QTPIE R / Å QTPIE -0.20.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 DMA -0.4 -0.6 QEq -0.8 -1.0
    • Water parameters transferable • Parameters transferable across geometries 1.0 q/e 0.8 O H 0.6 H 0.4 DMA 0.2 QEq 0.0 QTPIE R / Å QTPIE -0.20.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 DMA -0.4 -0.6 QEq -0.8 -1.0
    • 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 0.6 H 0.4 0.4 H DMA 0.2 0.2 DMA 0.0 QEq QEq R/Å QTPIE 0.0 R / Å QTPIE -0.20.5 1.5 2.5 3.5 4.5 QTPIE-0.20.5 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 R / Å QTPIE QTPIE -0.20.5 1.5 2.5 3.5 4.5 -0.20.5 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
    • Dipole polarizability of phenol • Response of dipole moment to external electric field • QTPIE: overestimates less than QEq QEq/STO QTPIE/STO MP2/STO- MP2/aug-cc- 3G pVDZ x 24.6244 13.0298 8.4240 13.6758 y 20.3270 10.7566 7.0488 12.3621 z 0.0000 0.0000 0.8595 6.9981 (Å ) • Out-of-plane component missing in QEq, QTPIE • MP2/STO-3G suggests this is largely because of inflexible basis set
    • QTPIE = coarse-grained ab initio? • Reparameterizing with ab initio (MP2/aug-cc- pVDZ) IPs and EAs improves agreement of in- plane polarizabilities at same level of theory (eV) Original ab initio Eigenvalues of dipole IP(H) 11.473 13.588 polarizability tensor/Å IP(C) 10.406 9.607 Old QTPIE New QTPIE ab initio IP(O) 15.423 14.565 13.0298 13.4285 13.6758 EA(H) -2.417 -0.068 10.7566 11.1316 12.3621 EA(C) 0.280 1.000 0.0000 0.0000 6.9981 EA(O) 2.059 3.127 • Similar results for other ab initio methods, e.g. FCI/STO-3G, RHF/aug-cc-pVDZ…
    • Dealing with charged systems I • Constrained minimization with Lagrange multipliers – Problem 1: Cannot be enforced for diatomic molecule and – Problem 2: Generalizing to non-zero diagonal charge transfer variables destroys asymptotic property – Model has insufficient constraints at large bond lengths to guarantee integer charges
    • Dealing with charged systems II • Redefine atoms with formal charges E E IP+1 IP - e- EA+1 EA N N N0-1 N0 N0+1 N0-2 N0-1 N0 • Problem: must account for multiple references IP0, EA0 IP+1, EA+1 IP0, EA0 - e- + + +… IP0, EA0 IP0, EA0 + IP0, EA0 IP0, EA0 IP0, EA0 IP+1, EA+1
    • Test case - water : phenol : sodium -stack • Chemically “obvious” localized charge • Reparameterization appears to work well for QTPIE • Need to figure out extension to general systems qNa/e QEq QTPIE Lagrange 0.6177 0.1876 reparam. 0.4798 0.8648 Mulliken/MP2/cc-pVDZ charge: 0.7394
    • Outlook • QTPIE is a promising new charge model – Implement scalable solution algorithm – Interface with MD code – Chemical applications, e.g. enzyme-substrate docking, electrochemistry • Many open theoretical questions, e.g.: – How to account for out-of-plane polarizabilities? – When does a molecule stop being a molecule? – What is the quantum-mechanical analogue of charge transfer variables? – How to deal with excited states?
    • Conclusions • Focus on charge transfer and including distance penalty improves description of atomic charges Fluctuating-charge model QEq QTPIE (now) Transferable parameters Yes Yes Correct asymptotics No Yes Correct molecular electrostatics No Almost! Established Arbitrary total charge Yes* No New result Coarse-graining picture Yes* Some evidence In progress Practical scaling Yes, O(N2) No, O(N4) Need ideas Excited states No No *with caveats