Jiahao Chen and Todd J. Martínez Center for Advanced Theory and Molecular Simulation, Center for Biophysics and Computatio...
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QTPIE: A fluctuating-charge model for molecular systems with correct asymptotics

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QTPIE: A fluctuating-charge model for molecular systems with correct asymptotics

  1. 1. Jiahao Chen and Todd J. Martínez Center for Advanced Theory and Molecular Simulation, Center for Biophysics and Computational Biology, Frederick T. Seitz Materials Research Laboratory, Beckman Institute for Advanced Science and Technology Department of Chemistry, School of Chemical Sciences, University of Illinois at Urbana-Champaign (UIUC), 600 South Mathews Avenue, Urbana, Illinois 61801, USA QTPIE: A fluctuating-charge model involving charge-transfer variables with correct asymptotics <ul><li>Our New Model, QTPIE </li></ul><ul><li>Energy expression contains explicit geometry-dependent electronegativities </li></ul><ul><li>Antisymmetric charge-transfer (bond) variables p ij instead of charge (site) variables q i </li></ul><ul><li>Unconstrained minimization solves the model </li></ul><ul><li>New picture of polarization as induced quasistatic currents rather than charge separation </li></ul><ul><li>Known limitations of existing models </li></ul><ul><li>No HOMO-LUMO band gap: high-temperature limit, all bonds are metallic </li></ul><ul><li>For chemical purposes, want low temperature limit: </li></ul><ul><li>Below Fermi temperature, where T F ~ 10 5 K for electron gases </li></ul><ul><li>No difference between  ,  , metallic or ionic bonds </li></ul><ul><li>Unable to describe out-of-plane polarizabilities </li></ul><ul><li>Difficulty in interpreting parameters, e.g. negative electron affinity of H in QEq </li></ul>Acknowledgements We thank the other members of the Martínez group, esp. B. Levine, and D. Miller (Lisy group), for insightful discussions. This work was supported by the National Science Foundation under Award No. DMR-03 25939 ITR, via the Materials Computation Center at UIUC. J. C. thanks the Graduate College of UIUC for a travel award. <ul><li>Conclusions </li></ul><ul><li>Geometry-dependent electronegativity gives correct asymptotic behavior </li></ul><ul><li>Charge transfer variables offer network interpretation analogous to electric circuits </li></ul><ul><li>Simplified description in models requires nonlocal corrections to local quantities </li></ul><ul><li>Multiconfiguration effects important but unclear how to treat them in charge models </li></ul><ul><li>Connections with density functional theory (DFT) </li></ul><ul><li>Grand-canonical DFT can be used to construct fluctuating-charge models </li></ul><ul><li>Free energy corresponding to ensemble of states of different particle numbers </li></ul><ul><li>For a minimal-basis diatomic, a restricted model gives electronegativity and hardness </li></ul><ul><li>Recovers derivative discontinuity in zero temperature limit, i.e. non-interacting limit </li></ul><ul><li>Gives interpretation of temperature as tuning coupling strength, e.g. Hubbard models </li></ul><ul><li>Dissociation of NaCl molecule </li></ul><ul><li>QEq: fractional charges at infinite separation limit </li></ul><ul><li>QTPIE (this work): correct asymptotic limit, wrong decay behavior </li></ul><ul><li>ab initio : decay behavior arises from nonadiabatic curve-crossing effects </li></ul><ul><li>Experimental dipole moment used to fit QEq parameters, which were later used in QTPIE </li></ul><ul><li>Amino acids: QEq v. ab initio </li></ul><ul><li>Charge analyses of MP2/6-31G* and MP2/cc-pVDZ optimized geometries: distributed multipole analysis restricted to multipoles only (DMA0) and Mulliken populations </li></ul><ul><li>Best agreement for singly bonded species; increasingly poor descriptions of multiply-bonded, aromatic and highly polarized (charged) species </li></ul><ul><li>Reparameterization did not improve fit </li></ul><ul><li>Results suggest need for geometry-dependent parameterization of charge models </li></ul>equilibrium geometry <ul><li>Charged systems: sodium ion : phenol  -complexes </li></ul><ul><li>The hydrogen bonding behavior of water to phenol changes in the presence of Na + </li></ul><ul><li>(3) and (5) preferred over (2) and (6) respectively (D. Miller, personal communication) </li></ul><ul><li>Excellent test structures for investigating status of charged reference parameters </li></ul><ul><li>Charges with Na + reference superior to Na 0 reference with constraint on total charge </li></ul><ul><li>Analogy with electrical circuits </li></ul><ul><li>Charge transfer variables and classical currents have same pseudoscalar symmetry </li></ul><ul><li>QTPIE leads to electrical interpretation of atomic capacitors storing partial charges </li></ul><ul><li>Charging asymmetry due to band gap : potential difference between conductor ‘plates’ </li></ul><ul><li>Circuit sum rules for equivalent circuits give coarse-grained effective circuit branches </li></ul>H q 3 p 21 p 31 H q 2 O q 1 H H O S C CH x NH 2 N, NH OH O q( ab initio ) q(QEq ) -1.0 -0.5 0.0 0.5 1.0 1.5 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 <ul><li>Sudden dissociation of NaCl . 6H 2 O cluster </li></ul><ul><li>Hexamer is smallest cluster needed to fully solvate NaCl </li></ul><ul><li>Sudden limit of dissociation dynamics: no solvent reorganization </li></ul><ul><li>Charge on chlorine atom goes to zero as it moves away </li></ul><ul><li>Charge on sodium changes only slightly: polarization effects charge transfer in water </li></ul>equilibrium geometry <ul><li>Asymmetric dissociation of water molecule </li></ul><ul><li>Pull one hydrogen (H1) off into infinity suddenly </li></ul><ul><li>QTPIE-calculated charge on H1 converges exponentially to zero far away </li></ul><ul><li>Remaining hydroxyl radical retains polarization </li></ul>TIP3P equilibrium geometry R <ul><li>Fluctuating-charge models </li></ul><ul><li>Need electrostatics for molecular modeling </li></ul><ul><li>Fluctuating-charge models offer coarse-grained description of electronic structure </li></ul><ul><li>QEq: A. K. Rappé, W. A. Goddard III, J. Phys. Chem. 95 , 1991 , 3358-3363 </li></ul><ul><li>fluc-q : S. W. Rick, S. Stuart, B.J. Berne, J. Chem. Phys. 101 , 1994 , 6141-6156 </li></ul><ul><li>Chemically important local quantities parameterize these models </li></ul><ul><li>Electronegativities  i and hardnesses  i = J ii </li></ul><ul><li>Common features </li></ul><ul><li>Quadratic, classical energy </li></ul><ul><li>Constrained minimization </li></ul><ul><li>Minimal basis representation </li></ul>LUMO HOMO + V E V C + C - C + C - V -1.0 -0.8 -0.6 -0.4 -0.2 S C CH x NH x OH O DMA, MP2/cc-pVDZ QEq -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 S C CH x NH x OH O -1.0 -0.5 0.0 0.5 1.0 1.5 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 DMA, MP2/6-31G* QEq
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