External Force Explicitly Included DFT Simulations: Modeling Responses of Mechanophores

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Xiao Huang, MIT Chemistry and Chemical Engineering

05/20/2024

Context Statement

Goal: For computationally modeling the reactivity and response of mechanophores

MONET relevance

For a (potential) mechanophore, we would want to:

• Quantitatively determine its reactivity--activation force or force-rate relationship
• Understand its mechanochemical response—bond breaking/rearrangement, molecular elongation, or small molecule release

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Those properties fundamentally affect the mechanical properties and functionalities of polymer networks

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Reactivity and response—can be modeled with EFEI

• Reactivity: computing force-modified TS barriers
• Response: optimizing structures under applied forces

Y. Sun, I. Kevlishvili et al., Chem, 2024 (just accepted)

Y. Sun et al., J. Am. Chem. Soc. 2024, 146, 10943–10952

EFEI: A Simple, Versatile Modification of Conventional DFT

E^EFEI (R₁, …,R_n) = E^DFT (R₁, …,R_n) + E^Force

External Force Explicitly Included

(EFEI, Marx @ RUB)

R_i

R_j

E^Force = F × |R_i − R_j|

Model energy and structure of molecules under applied force

SO₂-TBO Under 1.44 nN

SO₂-TBO Under 0 nN

We can do EVERYTHING we can do with force-free DFT with EFEI

• Force-Modified Geometry Optimization: YES
• Force-Modified Spin State Ordering: YES
• Force-Modified Reaction Energetics and/or Transition State Calculation: YES

Ribas-Arino, et al. Angew. Chem. Int. Ed. 2009, 48, 4190-4193

Y. Sun et al., J. Am. Chem. Soc. 2024, 146, 10943–10952

Data: Energy and Molecular Structure

Reaction/Activation Barrier under Force

Molecular Structures under Force

Original/Unfluorinated

Phenyl

Phenoxy

QAXQAJ (Fe²⁺): 0nN, LS

QAXQAJ (Fe²⁺): 3nN, HS

Limitations and caveats

Limitation 1: Ignoring Kinetic Effects

EFEI is an ‘static’ technique: can not account for dynamic effects caused by pulling

Limitation 2: Force Directionality

Solution: use AISMD to generate statistics

Pulling direction cannot be explicitly set in EFEI: we may want to test influences of force directions

Solution: use FMPES to test pulling variations

Y. Sun et al., J. Am. Chem. Soc. 2024, 146, 10943–10952

Martinez, et al. J. Am. Chem. Soc. 2009, 131, 6377–6379

E^FMPES (R₁, …,R_n) = E^PES (R₁, …,R_n) + E^Force

R_i

R_j

EFEI:

E^Force = F × |R_i − R_j|

FMPES (Martinez @ Stanford)

E^Force = F × (|R_i − R_m| + |R_k − R_n| )

R_m

R_k

R_n

Practical considerations

Computing Resource/Orca Installation

• Hardware: any CPU-based university/external supercomputers
• Software: Orca (free for academics)
• Very well-documented, easy to install following the online instructions

Common computational setups

• Functional: B3LYP-D3BJ
• Basis: def2-SVP
• No solvent in most cases, use implicit solvent models if necessary

Reach out to us for help on Orca setup/input examples/data analysis!

Input Files/Execution Process

• A bash script: containing basic execution information and the line for running Orca
• An Orca input file: specifying molecular structure + computational setups, see Orca manual
• A xyz file of molecule