Molecular Mechanics Molecular Dynamics A Classical Mechanics A

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• • Molecular Mechanics Molecular Dynamics

• • Molecular Mechanics Molecular Dynamics

• A Classical Mechanics • A I. Classical mechanics and molecules • A

• A Classical Mechanics • A I. Classical mechanics and molecules • A II. Molecular mechanics (MM) and molecular dynamics (MD) A III. Alternative formulations of Newton’s laws, Lagrange equations, Hamiltonan •

Isaaca Newton (1642 -1727) F V Molecules: Central Importance of Energy

Isaaca Newton (1642 -1727) F V Molecules: Central Importance of Energy

Boltzmann distribution Partition function

Boltzmann distribution Partition function

Energy derivatives … molecular properties

Energy derivatives … molecular properties

Energy in MD Lennard Jones Potential

Energy in MD Lennard Jones Potential

QB Charles-Augustin de Coulomb RAB 1785 Coulomb (electrostatic) forces QA

QB Charles-Augustin de Coulomb RAB 1785 Coulomb (electrostatic) forces QA

(Covalent) bond

(Covalent) bond

Bond Angle

Bond Angle

Torsion (dihedral) angle

Torsion (dihedral) angle

Out of plane wagging

Out of plane wagging

MD Molecular Energy

MD Molecular Energy

“Anharmonic terms” “cross/mixed terms”

“Anharmonic terms” “cross/mixed terms”

(MM) Minimization

(MM) Minimization

(MM) Minimization -Closest minimum to initial geometry - cannot overcome barriers

(MM) Minimization -Closest minimum to initial geometry - cannot overcome barriers

MD • Motion: whole energy landscape (potential energy surface)

MD • Motion: whole energy landscape (potential energy surface)

MD

MD

• Uveřejněné materiály jsou určeny studentům Vysoké školy chemickotechnologické v Praze jako studijní

• Uveřejněné materiály jsou určeny studentům Vysoké školy chemickotechnologické v Praze jako studijní materiál. Některá textová i obrazová data v nich obsažená jsou převzataz veřejných zdrojů. V případě nedostatečných citací nebylo cílem autora/ů záměrně poškodit event. autora/y původního díla. • S eventuálními výhradami se prosím obracejte na autora/y konkrétního výukového materiálu, aby bylo možné zjednat nápravu. • The published materials are intended for students of the University of Chemistry and Technology, Prague as a study material. Some text and image data contained therein are taken from public sources. In the case of insufficient quotations, the author's intention was not to intentionally infringe the possible author(s) rights to the original work. • If you have any reservations, please contact the author(s) of the specific teaching material in order to remedy the situation.

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