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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.

• where I is the identity matrixand τ i is a unit vector representing the reaction path tangent at r i. By projecting out components of the energygradient or the optimization step that are parallel to the reaction path, an optimization algorithm significantly reduces the tendency of each of the beads to be optimized directly to a minimum.

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