interface md theory - wordpress.com · theory july 15, 2017 hendrik heinz ... non-bonded...

1

Interface MD

Theory

July 15, 2017

Hendrik HeinzDepartment of Chemical and Biological

EngineeringMaterials Science and Engineering Program

University of Colorado-Boulder, CO, USA

2

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

3

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)

http://bionanostructures.com/

4

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)

5

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

6

Key Elements of Parameterization

• Parameters in agreement with measured properties at the atomic and

macroscopic scale:


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

7

Seq

uen

ce o

f P

ara

mete

rizati

on


8

Analysis of Chemical Bonding & Atomic Charges


• 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.

9

Determination of Atomic Charges and Bonding


• 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

10

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)

11

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

12

Additional Details

13

Useful Data on Atomic Charges from X-Ray

Deformation Densities


14

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

15

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

16

Atomic Charges from the Extended Born Model


• 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

17

Contribution of Components in the Extended Born

Model


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)

interface md theory - wordpress.com · theory july 15, 2017 hendrik heinz ... non-bonded...

Documents