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Interface MD
Theory
July 15, 2017
Hendrik HeinzDepartment of Chemical and Biological
EngineeringMaterials Science and Engineering Program
University of Colorado-Boulder, CO, USA
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Motivation for Models and Simulations
Overcome difficulties to monitor nanostructures at the 1 to 1000 nm scale in experiment
Use as a “computational microscope” to analyze the complexity of multi-phase systems
Length and time scales
Computing resources
Accuracy (FF)
Properties of interest
IFF
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The INTERFACE Force Field (IFF)
• Broad utility for biomaterials, polymer, energy, and construction materials
(bone, teeth, biomarkers, polymer composites, nanometal catalysts, solar cells)
• First uniform classical simulation platform (force field parameters) for inorganic
compounds and biomolecules at the 1-100 nm scale
• Based on thermodynamic consistency of classical Hamiltonian for organic and
inorganic components (extended PCFF, CVFF, CHARMM, AMBER, OPLS-AA, …)
Heinz, Emami et al. Langmuir Feature 2013, 29, 1754. http://bionanostructures.com (freely available).
MetalsSilicates Apatites
(γAB)Sim=(γAB)Expt
Aluminates
and Sulfates
Epot(r1, r2, ..., rN) = Ebonds + Eangles + Etorsions (+ Eout-of-plane) + ECoulomb + EvdW
(a,b,c,α,β,γ)Sim=(a,b,c,α,β,γ)ExptBonding (qi)
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Potential Energy Function
• Bonded terms describe the energy contained in the internal degrees of freedom, and non-bonded terms the interactions between molecules
Epot(r1, r2, ..., rN) = Ebonds + Eangles + Etorsions (+ Eout-of-plane) + ECoulomb + EvdW
bond non-bond
ijkl
ijkl
φ
ijkltorsions φk
φE )3cos1(2
)(
Bonded Interactions:
ij ijij
ijvdWr
r
r
rE
6
0
12
0 2
Non-bonded Interactions:
ij ij
ji
Coulombr
qqE
04
20 )(
2)( rr
krE ij
ij
ij
ijbonds ijk
ijk
ijk
ijkangles θθk
θE 20 )(
2)(
ImproperProper dihedralBond potential Angle potential
LJ 12-6 (or 9-6) potential for
van-der-Waals interactionsElectrostatic interactions (polarity)
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Interpretation of Parameters
Heinz, Emami, et al. Langmuir Feature 2013, 29, 1754.
Parameter Impact in simulation
Compatibility of parameters with existing
force fields for (bio)organic compounds Scope of application
Atomic charges
Chemical bonding, surface and interface
properties, adsorption, conformation of
molecules
Lennard-Jones well depth
Surface and interface properties,
adsorption, cohesion, conformation of
molecules
Surface chemistry
(hydration, protonation, charge defects) Interfacial properties and dynamics
Torsion potential Molecular conformation, chain folding
Lennard-Jones diameter (knowledge-based) Density (atom size)
Vibration constants IR/Raman spectra, elastic properties
Bond and angle constants (X-ray) Geometry of covalent bonds and angles
The physical-chemical interpretation of all parameters distinguishes IFF from other
force fields and enables order-of-magnitude higher accuracy
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Key Elements of Parameterization
• Parameters in agreement with measured properties at the atomic and
macroscopic scale:
Heinz, Emami, et al. Langmuir Feature 2013, 29, 1754.
Contact angles, surface energies
(001)
5 Å
H2PO4- /apatite
pH (surface protonation)
Atomic charges in silica
(3) Surface energy (γ, θ, ΔHimm)(1) Polarity of chemical bonds (q, μ)
(2) Structure (XRD)
Lattice parameters
in Ca-aluminate
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Seq
uen
ce o
f P
ara
mete
rizati
on
Heinz, Emami, et al. Langmuir Feature 2013, 29, 1754.
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Analysis of Chemical Bonding & Atomic Charges
Heinz, Emami, et al. Langmuir Feature 2013, 29, 1754.
• A fundamental difference in atomic charges qi in quantum mechanics
versus those in force fields is recognized by IFF
qi are poorly defined in quantum mechanics (±100%)
qi are well defined in force fields (approx. ±5%)
Heinz, Suter J. Phys. Chem. B 2004, 108, 17281.
• Example 1: A diatomic molecule with a given dipole moment μ from expt (±2%)
has exactly defined atomic charges (±2%)
• Example 2: Atomic charges from X-Ray deformation densities (expt) and
near-spherical partition are suitable for force fields, consistent with μ from expt
• The force field must exactly reproduce internal multiple moments for every
compound included, else other properties and transferability are compromised
• The extended Born model enables accurate relative estimates of atomic charges
among different compounds using atomization energies, ionization energies,
coordination numbers, and other physical/chemical properties (acidity, melting T)
Heinz, Suter J. Phys. Chem. B 2004, 108, 17281.
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Determination of Atomic Charges and Bonding
Heinz, Emami, et al. Langmuir Feature 2013, 29, 1754.
• Use five independent sources of atomic charges for each new compound to
achieve <10% uncertainty (multiple related μ, def. e density, Born model)
• Always include analogies, e.g., silicate-carbonate-aluminate, NiO-CaO-MgO-FeO
• Include bonded terms between pairs of atoms in IFF when average atomic
charges are less than half the formal charges, else use nonbonded terms only
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Structure and Validation of Interfacial Properties
Heinz, Emami, et al. Langmuir Feature 2013, 29, 1754; Chem. Soc. Rev. 2016, 45, 412.
• Assign initial bond lengths (r0) and angles (θ) from X-ray structure
• Assign initial vibration constants (kij, kijk) from IR spectrum, or by analogy
• Assign initial LJ parameters (σ, ε) according to crystallographic radii and
polarizability
• Test and refine XRD cell parameters using LJ parameters σ and ε (0.0-0.5% dev)
• Test and reproduce a surface property from expt by adjusting ε (and σ) (<5% dev)
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Secondary Validation and Transferability
Heinz, Emami, et al. Langmuir Feature 2013, 29, 1754; Chem. Soc. Rev. 2016, 45, 412.
• One surface property is enough to reproduce other energies and derivatives (heat
capacity, modulus, thermal expansion)
• Carefully evaluate experimental reference data and their uncertainty
• Corroborate consistency by testing several surface/interfacial properties
• Perform final fit of vibration constants to experimental IR & Raman spectra using
computed power spectra of the velocity autocorrelation function
• Review final parameters for internal consistency (especially σii and εii)
• Review final number of atom types
• Review differentiation of surface chemistry (e.g. protonation/deprotonation) and
develop/extend surface models
• Perform adjustments in LJ parameters to adapt from 12-6 to 9-6 potentials
• Perform adjustments in LJ parameters (and bonded parameters) to adapt among
CHARMM, AMBER, OPLS-AA due to different scaling of 1,4 nonbond interactions
and combination rules
• Verify that all major features (bonding, structure, energy) and the respective
parameters (σii and εii for various atom types) are in proportion to each other
Aim at an accurate chemical code for each compound = highest transferability
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Additional Details
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Useful Data on Atomic Charges from X-Ray
Deformation Densities
Heinz, Emami, et al. Langmuir Feature 2013, 29, 1754.
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Example: Electron Densities and Atom-Based Charges
from Experimental Data
Cu +1.23(6)
Si +1.17(15)
O(1) -1.04(6)
O(2) -0.92(6)
O(3) -0.98(6)
Water
O(4) -0.74(6)
Dioptase Cu6[Si6O18]·6H2O
Belokoneva et al. Phys. Chem. Miner. 2002, 29, 430-438.
O: -0.82e in
SPC water
Si: +1.1e in
IFF
Charges in atomistic simulations must match internal dipoles and multipoles
Ab-initio charges (Mulliken, Bader, Lowdin, Hirshfeld) are not useful
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Atomic Charges from the Extended Born Model
H. Heinz and U. W. Suter J Phys Chem B 2004, 108, 18341.
• Atomization energies ΔUat reflect the
ability for covalent bonding
(purely covalent bonding is possible
only in the elements)
• Ionization energies ΔUi/electron affinities
ΔUea reflect the ability for ionic bonding
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Atomic Charges from the Extended Born Model
H. Heinz and U. W. Suter J Phys Chem B 2004, 108, 18341.
• Electron affinities ΔUea • Electronegativity helps summarize effect
of ionization energies ΔUi/electron
affinities ΔUea
• Consider non-linear progression of ΔUea
for partial charges, e.g., in O and N
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Contribution of Components in the Extended Born
Model
H. Heinz and U. W. Suter J Phys Chem B 2004, 108, 18341.
Compound
SiO2 (s)
Electrostatic
Lattice, SiO2
4
Uel
Charged Atoms
Six+ (g) + 2 Ox/2- (g)
3
Ui –Uea
Atomic Elements
Si (g) + 2 O (g)
2 Uat
Elements
Si (s) + O2 (g)
1
– Uf
5Ucov
• The Extended Born Model
describes the relationship
between these properties of
the elements and resulting
properties in a compound,
including atomic charges
4 Electrostatic attraction
3 Partial charge transfer 0.0 to 0.7 MJ/mol atom
2 Atomization 0.0 to 0.85 MJ/mol atom
5 Nonionic cohesion
1 Reverse formation -0.3 to 0.3 MJ/mol atom
0.0 to 1.1 MJ/mol atom
Range of
contribution
(any
compound)