C7790 Introduction to Molecular Modelling -1C7790 Introduction to Molecular Modelling TSM Modelling Molecular Structures Petr Kulhánek kulhanek@chemi.muni.cz National Centre for Biomolecular Research, Faculty of Science Masaryk University, Kamenice 5, CZ-62500 Brno PS/2021 Present Form of Teaching: Rev2 Lesson 23 Classification of Interactions C7790 Introduction to Molecular Modelling -2- Context microworldmacroworld equilibrium (equilibrium constant) kinetics (rate constant) free energy (Gibbs/Helmholtz) partition function phenomenological thermodynamics statistical thermodynamics microstates (mechanical properties, E) states (thermodynamic properties, G, T,…) microstate ≠ microworld Description levels (model chemistry): • quantum mechanics • semiempirical methods • ab initio methods • post-HF methods • DFT methods • molecular mechanics • coarse-grained mechanics Structure EnergyFunction Simulations: • molecular dynamics • Monte Carlo simulations • docking • … C7790 Introduction to Molecular Modelling -3Revision: Schrödinger Equation ෡𝐻𝜓 𝑘(𝐫, 𝐑) = 𝐸 𝑘(𝐑)𝜓 𝑘(𝐫, 𝐑) Schrödinger equation by its essence provide ultimate description of (bio)chemical systems: ➢ Solution of SR is the potential energy 𝐸 𝑘 and wavefunction 𝜓 𝑘. ➢ the potential energy quantify strength of inter-atomic interactions ➢ the wavefunction provides further information Remember: use of SE has some dark sides: ➢ one-electron approximation (correlation energy) ➢ basis set effects ➢ long-tails of some interactions (dispersion energy in HF and DFT calculations) ➢ size consistency By analyzing 𝐸 𝑘 and 𝜓 𝑘 one can classify interactions between atoms to better understand origin of forces that keep them together. Two major categories of interactions between atoms are: ➢ covalent bonding ➢ non-covalent interactions C7790 Introduction to Molecular Modelling -4𝐸 𝑘(𝐑) = 𝐸 𝑏𝑜𝑛𝑑𝑠 + 𝐸 𝑎𝑛𝑔𝑙𝑒𝑠 + 𝐸𝑡𝑜𝑟𝑠𝑖𝑜𝑛𝑠 + 𝐸𝑒𝑙𝑒 + 𝐸 𝑣𝑑𝑤+. . . )()()(ˆ 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) Molecular Mechanics C7790 Introduction to Molecular Modelling -5Covalent Bonding C7790 Introduction to Molecular Modelling -6Covalent Bonding A covalent bond is a chemical bond that involves the sharing of electron pairs between atoms. Notable types of covalent bonds: ➢ s-bonds (each atom formally contributes by one electron) ➢ p-bonds (each atom formally contributes by one electron) ➢ coordinate covalent bonds (one atom contributes two electrons (a lone pair) and the second atom provides a vacant (empty) orbital) ➢ aromatic bonding ➢ metallic bonding ➢ three-center two-electron bond (see boron chemistry) ➢ …. https://en.wikipedia.org/wiki/Covalent_bond Covalent bonding represents strong interatomic interactions. C7790 Introduction to Molecular Modelling -7Covalent Bonding, cont. single C-C bond (1 s-bond) double C-C bond (1 s-bond + 1 p-bond) triple C-C bond (1 s-bond + 2 p-bonds) s and p covalent bonds: Bond dissociation energies: ~85 kcal/mol ~145 kcal/mol ~200 kcal/mol https://en.wikipedia.org Conjugated p-bonds (aromaticity): Coordinate covalent bonds: C7790 Introduction to Molecular Modelling -8Molecular Deformations ➢ Some molecular deformations can be described by vibrational motions. ➢ There is 3N-6(5) unique molecular vibrations, which are called normal modes. ➢ A normal vibrational mode is a molecular motion, in which ALL atoms oscillate at the same frequency and phase. ➢ However, some vibrations are more "localized". Meaning that such vibrations exhibit larger amplitudes only on a few atoms, while the rest of the molecule is almost restful. ➢ The other vibrations represent skeletal molecular deformations. Bond stretching 𝐸 𝑉 = 𝑣 + 1 2 ℎ𝜐 Model of harmonic oscillator: 𝜐 = 1 2𝜋 𝐾 𝜇 v = 0, 1, 2, … characteristic frequency force constantreduced mass 𝐾 = 𝜕2 𝑉(𝑟) 𝜕𝑟2 curvature of PES at stationary point C7790 Introduction to Molecular Modelling -9Molecular Deformations, cont. Valence bond stretching symmetric asymmetric Valence angle deformations inplaneout-of-plane scissoring rocking wagging twisting + + + - 0 + up down "no" motion - 0 Some types of molecular vibrations Usually, stronger bonds exhibits higher vibrational frequencies and vice versa. C7790 Introduction to Molecular Modelling -10Molecular Deformations, cont. In chemistry, conformational isomerism is a form of stereoisomerism in which the isomers can be interconverted just by rotations about formally single bonds (refer to figure on single bond rotation). C7790 Introduction to Molecular Modelling -11- Non-covalent Interactions C7790 Introduction to Molecular Modelling -12Non-covalent Interactions Contribution Additive? Sign Comment Long-range (𝑬(𝑹)~𝑹−𝒏) Electrostatic Yes +/- Strong orientation dependence Induction No Dispersion Approx. - Always present Resonance No +/- Degenerate states only Magnetic Yes +/- Very small Short-range (𝑬(𝑹)~𝒆−𝜶𝑹 ) Exchange-repulsion Approx. + Dominates at very short range Exchange-induction Approx. + Exchange-dispersion Approx. + Charge transfer No - Donor-acceptor interactions Stone, A. J.; Oxford University Press. The Theory of Intermolecular Forces; Oxford University Press: Oxford, 2016. C7790 Introduction to Molecular Modelling -13HW: Recommended Readings Rackers, J. A.; Wang, Q.; Liu, C.; Piquemal, J.-P.; Ren, P.; Ponder, J. W. An Optimized Charge Penetration Model for Use with the AMOEBA Force Field. Phys. Chem. Chem. Phys. 2016, 19 (1), 276–291. https://doi.org/10.1039/C6CP06017J. Rackers, J. A.; Liu, C.; Ren, P.; Ponder, J. W. A Physically Grounded Damped Dispersion Model with Particle Mesh Ewald Summation. J Chem Phys 2018, 149 (8), 084115. https://doi.org/10.1063/1.5030434. Rackers, J. A.; Ponder, J. W. Classical Pauli Repulsion: An Anisotropic, Atomic Multipole Model. J Chem Phys 2019, 150 (8), 084104. https://doi.org/10.1063/1.5081060. Read Introduction and Overview of given interaction type: