Introduction to Geometry Optimization

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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. 6-5-2016IntroductionInthelasttwodecadesa newfieldinchemistr 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.

• An optimization algorithm can use some or all of E(r) , ∂E/∂r and ∂∂E/∂r i ∂r j to try to minimizethe forces and thiscould in theory be any methodsuch as gradient descent, conjugate gradient or Newton'smethod. • For most systems of practical interest, however, it may be prohibitively expensive to compute the second derivative ...