The split-charge method:

Transcription

1 Split charge equilibration: A charge transfer method for electrolytes and other non-metallic materials The split-charge method: Martin H. Müser Materialwissenschaften und Werkstoffwissenschaften

2 Motivation A great deal about materials in general can be learned from force-field based molecular dynamics. Force fields for many materials require partial charges. Partial charge of atoms usually environment dependent - interfaces, e.g., Si-SiO 2, molten salts, electrolytes, fixed charge potential unsuitable Existing approaches, such as regular charge equilibration, have unsatisfactory properties (tend to be metallic) need for a new approach

3 Outline Brief review of existing ways of how to handle charges in MD - atom and bond based descriptions Basic ideas of split charge model including - parameterization - dielectric properties of split charge methods Comparison of split-charge to other approaches - first results by us and others Things left to be done Should I stay or should I go

4 Background In this talk: Only partial charges, no atomic polarizability V = V short range ({ R} ) + 1 4"# $ Q i Q j + charge - dipole i, j<i R ij - fixed-charge potentials: Q i = f (i) configuration independent no transferability, no heterogeneous systems - flexible-charge potentials: Q i =f ({R}) potentially transferable and suitable for heterogeneity

5 Charge equilibration (QE) Basic idea: Determine charges with the help of a minimization principle. V = V non -Q + V Q V Q = " 1 2 # Q 2 + $ Q + 1 i i i i 4%& 0 i " i, j<i Q i Q j R ij 'V Q = 0 under constraint that " Q i = 0 'Q i i Mortier, Genehten, Gasteiger, JACS 107, 829 (1985) show that functional form can be motivated from DFT arguments Rappé, Goddard, JPC 95, 3358 (1991) introduce screening for Coulomb to avoid charge blow up implemented in reaxff

6 QE: Points of criticism improper dissociation limit DFT has similar trouble non-integer charge transfer occurs over R Chen, Martinez, CPL 438, 315 (2007) shows scaling of α with N 3 instead of linear Warren, Davis, Patel, JCP 128, (2008) corresponds to ε r = (metal) with δ 0.3µm Nistor, Müser, PRB 79, (2009) Smallest ioniziation energy of stable isotopes: Cs 375 kcal/mol, typical alkali 500 kcal/mol Highest electron affinities: Cl 352 kcal/mol and F 331 kcal/mol

7 Previous fixes to QE fluc-q 2 Berne et al., JCP 115, 2237 (2001) local charge neutrality constraints (fluc-q): Rick, Stuart, Berne, JCP 101, 6141 (1994) used for H 2 O cannot describe bond breaking, wrong α(n) for polymers distance-dependent Δχ: Chen, Martinez, CPL 438, 315 (2007) produces correct dissociation limit of dimers but metallicity problem remains and no physical motivation

8 Bond-based descriptions static bond charges, e.g., C sp3 -H: q H = 0.1e Allinger et al., JACS 99, 8127 (1977) used in MM2 force field does not describe bond breaking polarizable bonds Chelli, Procacci, Righini, et al, JCP 111, 8569 (1999) used in MM3 force field can describe bond breaking in principle (bond-length dependent polarizability / bond hardness) and solves the metallicity problem but: - loses motivation of atomic hardness from DFT - wrong scaling of α(n) for oligomers in limit N 1 Warren, Davis, Patel, JCP 128, (2008) - zero skin depth for electrostatic field Nistor, Müser, PRB 79, (2009)

9 Bond versus atom based QE bond based atom-based α(n)/n ~ N (small N) no yes finite skin depth δ no yes retains atomic hardness κ no yes α(n)/n ~ const (large N) yes no finite dielectric constant ε yes no correct dissociation limit yes no

10 Outline Brief review of existing ways of how to handle charges in MD - atom and bond based descriptions Basic ideas of split charge model including - parameterization - dielectric properties of split charge methods Comparison of split-charge to other approaches - first results by us and others Things left to be done

11 Split charge approach (SQE) allow for charge transfer only between (chemical) bonds and parameterize bonds in addition to atoms q H"O = #q O"H q ij = "q ji Q i = " q ij with q ij = #q ji V Q = &V Q &q ij j " i, j,k 1 2 $ 1 iq ij q ik + " ( 2 % i # % j )q ij + V ext i, j " = 0 ' &V Q = const 0 while Q i = 0 &Q i i can be made distance dependent s + Σ ij κ ij q ij q ij κ i = 0 bond approach s κ ij = 0 atom approach Nistor, Polirhonov, Mosey, Müser, JCP 125, (2006)

12 Determination of model parameters for a given molecule 1. relax structure 2. calculate ESP surface (ÞESP charges), Mulliken charges 3. fit model parameters for learning set to match target 4. determine error on test set If you fit to ESP, you ll get good polarizabilities; charges themselves will be less good. personal communication by Toon Verstraele (2010) Nistor, Polirhonov, Mosey, Müser, JCP 125, (2006)

13 Dielectric properties of SQE crystals split-q energy is quadratic in charges analytical solution possible for periodic systems dielectric constant and skin depth can be solved analytically Simplest symmetry: simple cubic / rock salt Exploit isomorphism to regular lattice problem: q(r lmn R l+1mn ) q 1 (R lmn ) displacement in x direction q(r lmn R lm+1n ) q 2 (R lmn ) q(r lmn R lmn +1 ) q 3 (R lmn ) κ = spring between neighbors κ s = on-site spring Q(R) a α q α (R) = Tr{strain tensor} Nistor, Müser, PRB 79, (2009)

14 Dielectric properties of SQE crystals I d like to show some of the maths but will simply state results for simple cubic dielectric constant analogous to truncated Clausius Mossotti relation penetration depth setting κ s to zero implies: Diverging dielectric constant similarly, exaggerated polarizability for polymers setting κ to zero implies: δ 0.3µm similarly, wrong polarizability for small molecules split-charge representation should allow one to calculate general / continuum dielectric problems Nistor, Müser, PRB 79, (2009)

15 Test of results in capacitor geometry keep penetration depth constant keep dielectric permittivity constant Please ask about: Discretization corrections, how split-q can be used to speed up fast multipole and Ewald summations Nistor, Müser, PRB 79, (2009)

16 Bond breaking in SQE Make κ ij diverge as R ij increases: Matthieu, JCP 127, (2007): κ ij = neuroleptics Razvan Nistor (unpublished) κ ij ~ exp(r ij /σ ij ) HF 3 unpublished work by others B3LYP charges

17 Outline Brief review of existing ways of how to handle charges in MD - atom and bond based descriptions Basic ideas of split charge model including - parameterization - dielectric properties of split charge methods Comparison of split-charge to other approaches - first results by us and others Things left to be done

18 Charge equilibration energies default split-charge model Q ij := Q i " Q j ; Q ij := Q i + Q j V Q = 1 2 MM3 Rappé Goddard %{# s q q + # q Q + # q Q + $ q + 2V ( ij q )} ij ij ij ij ik ij ij ij ij ij ext ij i, j 2 fit parameters per atom (κ i ; χ i ) (κ ij ; κ ij ; χ i ) 1 fit parameter per bond κ ij s + arsenal of possible generalizations such as chemical induction,

19 First split charge results elements: Si, C, O, H 1,1,1-(trihydroxyl) disilane (molecule 13) Nistor, Polirhonov, Mosey, Müser, JCP 125, (2006)

20 Polarizability of chain molecules Warren, Davis, Patel, JCP 128, (2008):

21 Comparison of SQE to QE Verstraelen, Speybroek, Waroquier JCP 128, (2009): test polarizabilities and partial charges of small moleculues different cost and target functions (ESP, Mulliken/ Hirschfeld-I charges,...) 20 benchmark tests The training data on 500 organic molecules containing H, C, N, O, F, S, Cl, and Br selected from almost small organic molecules. It is clear that SQE outperforms EEM in all benchmark assessments.

22 Electrostatics of protease Electrostatic fields of real molecules as predicted by different models vary hugely Unpublished work by others courtesy of Toon Verstraelen

23 Dynamics in QE versus BQE/SQE (I) Cheesy model for aging in a battery / dynamics of molten salt completely symmetric Lennard Jones interaction species only differ by electronegativity χ implicit solvent with very large screening length SQE anode small χ catode large χ both materials are neutral in bond & split QE as long as no wire connects them slow mixing dynamics

24 Dynamics in QE versus BQE/SQE (II) Cheesy model for aging in a battery / dynamics of molten salt completely symmetric Lennard Jones interaction species only differ by electronegativity χ implicit solvent with very large screening length QE anode small χ catode large χ both materials have charged surface layer in regular QE even if not connected by wire fast mixing dynamics

25 Dynamics in QE versus BQE/SQE (III)

26 Other dynamics AQE no volatage at t=0 V suffers from slow dynamics in extended Lagrangian just like CPMD of metals SQE V correct voltage but only polarization current through resistor slower than regular FFs

27 Summary Split-charge equilibration (SQE): - solves metallicity problem of regular QE approaches while maintaining correct polarizabilities for small molecules - new bond hardness term ~ inverse dielectric constant - atomic hardness controls skin depth - continuous bond breaking w.o. connectivity matrix Our papers: Nistor, Müser, PRB 79, (2009) Nistor, Polirhonov, Mosey, Müser, JCP 125, (2006) Further reading: extensive parameterization, testing, Verstraelen, Speybroek, Waroquier JCP 128, (2009)

28 Things to be done: Outlook add atomic polarizability improve bond breaking descriptions include ideas of reactive force fields such as sp2/sp3 can distance dependence of κ s explain violation of Cauchy relations (C 12 C 66 ) in ionic systems and 3-body effects? speed up fast-multipole and fast Ewald summation Real challenges: describe true charge transfer non-adiabatic homo/lumo transitions, tribo charging, batteries, proton transfer, Peierls distortion / Jahn Teller effect

29 Thanks for your attention and thanks Razvan Nistor formerly UWO now IBM Nick Mosey formerly UWO now Queen s, Kingston, ON