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Feb 20, 2024 544 likes •1.16k views

A Winter Short Course on Statistical Mechanics for Molecular Simulations Lecture 2: Molecular Mechanics & Classical Force Fields Yuan-Chung Cheng yuanchung@ntu.edu.tw 2/2/2015 Many materials taken from Prof. A. D. MacKerells

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A Winter Short Course on Statistical Mechanics for Molecular Simulations

Lecture 2: Molecular Mechanics & Classical Force Fields

Yuan-Chung Cheng yuanchung@ntu.edu.tw 2/2/2015

Many materials taken from Prof. A. D. MacKerell’s presentation, which is gratefully acknowledged.

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The Molecular Hamiltonian

In atomic units: 1 Hartree = 27.2114 eV = 627.509 kcal/mol

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Solving this is a huge part of molecular simulation in chemistry (i.e. quantum chemistry), but this is not the topic that I will pursue.

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Potential Energy Surface

n QM calculations yield potential energy

surface that governs nuclear motions

E(R) = Ψ Helec Ψ

Determines reactions/thermodynamics/… Multidimensional Complex

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Potential Energy Surface

n Large systems –

complex energy landscape, many degrees of freedom, à full quantum all-electron calculations become infeasible!!

n We need simple classical

models

n No need for all the details,

anyway…

Protein folding funnel The curse of dimensionality!!

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2013 !年諾貝爾化學獎 ! !

n 2013 Nobel Chemistry Prize jointly to Martin Karplus,

Michael Levitt and Arieh Warshel "for the development

  • f multiscale models for complex chemical systems".

n 複雜系統多層級計算方法的建立 n 將化學實驗帶入電腦時空

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Martin Karplus Michael Levitt Arieh Warshel

Pictures from nobelprize.org

Slide from Prof. Jhih-Wei Chu

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Michael Levitt’s Nobel Lecture

Very informative read!

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General Considerations

n Description of molecules? n Optimization of force field parameters? n Training set of compounds/data? n Test set of compounds/data? n Limitations – questions you should not ask

  • f your force field
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Common All-Atom Force Fields

n Class I: Standard structural terms

CHARMM, CHARMm (Accelyrs), AMBER, OPLS, ECEPP, GROMOS, SYBYL (Tripos)

n Class II: Standard + cross terms

CFF95 (Accelrys), MM3, MMFF94, UFF

n Class III: Non-additive, polarizable terms

QM/MM, Polarizable FF - Freisner/ Berne(Schroedinger), AMOEBA (Tinker)

They are different!!! So parameters from one cannot be used in another force field.

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The Urey-Bradley term captures the influence of the stretch-stretch and stretch-bend coupling terms on vibrational frequencies. It is not included in class II force fields (Amber/GROMOS, do you know why?).

See Norman Allinger, Molecular Structure: Understanding Steric and Electronic Effects from Molecular Mechanics.

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LJ-9-6 Buckingham

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Taken care of via nonbond list

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Construct New Force Fields

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Needs new parameters

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Molecular Mechanics

n Simplest type of calculation

¨ Used when systems are very large and approaches that are more

accurate become too costly (in time and memory)

n Does not use any quantum mechanics instead uses

parameters derived from experimental or ab initio data

¨ Uses information like bond stretching, bond bending, torsions,

electrostatic interactions, van der Waals forces and hydrogen bonding to predict the energetics of a system

¨ The energy associated with a certain type of bond is applied

throughout the molecule. This leads to a great simplification of the equation

n It should be clarified that the energies obtained from molecular

mechanics do not have any physical meaning, but instead describe the difference between varying conformations (type of isomer). Molecular mechanics can supply results in heat of formation if the zero of energy is taken into account.

Courtesy of Shalayna Lair, University of Texas at El Paso

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OTHER ISSUES

Solvation, electrostatics…

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Solvation Models

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Born Model

n Solvent modeled as

continuum dielectric medium

n Solvation free energy of

a charge easily calculated

n No molecular details,

assumes instantaneous solvant relaxation…

n Can be generalized…

q

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Born Model

n Solvent modeled as

continuum dielectric medium

n Solvation free energy of

a charge easily calculated

n No molecular details,

assumes instantaneous solvant relaxation…

n Can be generalized…

https://chemistry.osu.edu/~herbert/projects/PCM.html

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Explicit Solvent Model

Long range electrostatic interactions can be troublesome!

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Ewald Sum

Particle-mesh Ewald: combine short-range cut-off and FFT for long-range part on a mesh.