Transcription of Introduction to Geometry Optimization
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Introduction to Geometry Optimization
Introduction to Geometry Optimization Dr. Zaheer Ul-HaqAssociate Professor Dr. PanjwaniCenter for Molecular Medicine and Drug Research ICCBS, University of Karachi, PakistanDFT 2016, Isfahan, Iran. 6-5-2016 IntroductionInthelasttwodecadesanewfield inchemistr yhasopenedup;experim (SPM),atomicforcemicroscopy(AFM) :elasticpropertiesofpolymersconfor molecular :the equilibrium Geometry Reqand the transition state Geometry Rtsbothcorrespondtothestationarypointson thepotentialenergysurface(PES)(molecular energyE(R)asafunctionofnuclearpositionsR =(R1,R2,..))Theequilibriumgeometry localminimumThetransitionstate saddlepoint(I-storder)Thesepointsaredete rminedbytheconditionthatthefirstderivati vesoftheenergywithrespecttothenucleiposi tionsvanish(thetotalforceactingoneachnuc leusvanishes) molecular structuresItisproposetousethegeometryopt imizationprocedurealsotodetermineenforce dstructuralchangesinamolecule.
Molecular geometry and mathematical interpretation • The geometry of a set of atoms or molecules can be described by Cartesian coordinates of the atoms or, internal coordinates formed from a set of bond lengths, bond angles and dihedral angles. • Given a set of atoms and a vector, r, describing the atoms' positions, one can introduce the concept of the energy as a functionof …
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