C8855 Advanced Molecular Modelling Methods -1C8855 Advanced Molecular Modelling Methods Petr KulhΓ‘nek kulhanek@chemi.muni.cz National Centre for Biomolecular Research, Faculty of Science Masaryk University, Kamenice 5, CZ-62500 Brno JS/2022 Present Form of Teaching: Rev1 Lesson 1 Reactive Force Fields C8855 Advanced Molecular Modelling Methods -2- Revisions Classical Force Field Methods C8855 Advanced Molecular Modelling Methods -3𝐸 π‘˜(𝐑) = 𝐸 π‘π‘œπ‘›π‘‘π‘  + 𝐸 π‘Žπ‘›π‘”π‘™π‘’π‘  + πΈπ‘‘π‘œπ‘Ÿπ‘ π‘–π‘œπ‘›π‘  + 𝐸𝑒𝑙𝑒 + 𝐸 𝑣𝑑𝑀+. . . )()()(Λ† ekkek EH rRr RR  = Molecular Mechanics Schrodinger equation - quantum mechanical description bonded contributions non-bonded contributions Classical physics - mechanical description approximation electron motions is omitted (electron motions is implicitly included in empirical parameters) C8855 Advanced Molecular Modelling Methods -4- Nomenclature 𝐸 π‘˜(𝐑) = 𝐸 π‘π‘œπ‘›π‘‘π‘  + 𝐸 π‘Žπ‘›π‘”π‘™π‘’π‘  + πΈπ‘‘π‘œπ‘Ÿπ‘ π‘–π‘œπ‘›π‘  + 𝐸𝑒𝑙𝑒 + 𝐸 𝑣𝑑𝑀+. . . https://en.wikipedia.org/wiki/Force_field_(chemistry) https://en.wikipedia.org/wiki/Coarse-grained_modeling https://en.wikipedia.org/wiki/Molecular_mechanics Molecular mechanics uses classical mechanics to model molecular systems. The Born– Oppenheimer approximation is assumed valid, and the potential energy of all systems is calculated as a function of the atomic coordinates using force fields. In the context of chemistry and molecular modelling, a force field is a computational method that is used to estimate the forces between atoms within molecules and between molecules. More precisely, the force field refers to the functional form and parameter sets used to calculate the potential energy of a system of atoms or coarse-grained particles. + parameters C8855 Advanced Molecular Modelling Methods -5Bonded Contributions Bond stretching Angle bending Bond rotation empirical parameters Main contributions C8855 Advanced Molecular Modelling Methods -6Bond stretching, cont. Morse potential ( ) ( )2 0 1)( rra e eDrV βˆ’βˆ’ βˆ’= Harmonic potential ( )2 0 2 1 )( rrKrV βˆ’= ➒ The harmonic potential does not have dissociation limit. Thus, force fields employing the harmonic approximation cannot describe reactivity. ➒ The reactivity is difficult to describe even with Morse potential properly, a noticeable exceptions are ReaxFF (reactive force field) and EVB (empirical valence bond). Disadvantage of Morse potential β€’ more parameters are needed β€’ more computationally demanding C8855 Advanced Molecular Modelling Methods -7𝐸 𝑣𝑑𝑀 = ෍ 𝑖=1 𝑁 ෍ 𝑗=𝑖+1 𝑁 4πœ€π‘–π‘— πœŽπ‘–π‘— π‘Ÿπ‘–π‘— 12 βˆ’ πœŽπ‘–π‘— π‘Ÿπ‘–π‘— 6 𝐸𝑒𝑙𝑒 = ෍ 𝑖=1 𝑁 ෍ 𝑗=𝑖+1 𝑁 1 4πœ‹πœ€ π‘œ π‘žπ‘– π‘ž 𝑗 π‘Ÿπ‘–π‘— Non-bonded Contributions Electrostatic interactions van der Waals interactions empirical parameters N – number of atoms Main contributions Coulomb Law Lennard-Jones 12-6 potential C8855 Advanced Molecular Modelling Methods -8Reactive Force Field Methods Reactive Molecular Dynamics C8855 Advanced Molecular Modelling Methods -9- Overview Farah, K.; MΓΌller-Plathe, F.; BΓΆhm, M. C. Classical Reactive Molecular Dynamics Implementations: State of the Art. ChemPhysChem 2012, 13 (5), 1127–1151. https://doi.org/10.1002/cphc.201100681. ➒ ReaxFF (Reactive Force Field) ➒ COMB (Charge Optimized Many Body) Potential ➒ EVB (Empirical Valence Bond) C8855 Advanced Molecular Modelling Methods -10- ReaxFF β–ͺ ReaxFF uses a general relationship between bond distance and bond order on one hand and between bond order and bond energy on the other hand that leads to proper dissociation of bonds to separated atoms. β–ͺ Other valence terms present in the force field (angle and torsion) are defined in terms of the same bond orders so that all these terms go to zero smoothly as bonds break. β–ͺ In addition, ReaxFF has Coulomb and Morse (van der Waals) potentials to describe nonbond interactions between all atoms (no exclusions). These nonbond interactions are shielded at short range so that the Coulomb and van der Waals interactions become constant as Rij β†’ 0. β€’ Generally, the results are of an accuracy similar or better than PM3, while ReaxFF is about 100 times faster. ReaxFF (for β€œreactive force field”) is a bond order-based force field developed by Adri van Duin, William A. Goddard, III, and co-workers at the California Institute of Technology. van Duin, A. C. T.; Dasgupta, S.; Lorant, F.; Goddard, W. A. ReaxFF: A Reactive Force Field for Hydrocarbons. J. Phys. Chem. A 2001, 105 (41), 9396–9409. https://doi.org/10.1021/jp004368u. C8855 Advanced Molecular Modelling Methods -11- COMB The COMB (Charge Optimized Many Body) potential developed by Sinnott, Phillpot, and coworkers can describe the different types of bonding in an integrated manner. The first generation was developed to reproduce the phase orders in SiO2 and Cu, respectively. Yu, J.; Sinnott, S. B.; Phillpot, S. R. Charge Optimized Many-Body Potential for the Si/Sio2 System. Phys. Rev. B 2007, 75 (8), 085311. https://doi.org/10.1103/PhysRevB.75.085311. C8855 Advanced Molecular Modelling Methods -12- Questions β€’ Is it possible to use ReaxFF for studying biomolecules? β€’ How are partial atomic charges calculated in ReaxFF? β€’ How many parameters per atom are necessary in ReaxFF? β€’ What is the primary use of COMB potential?