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# COMPUTATIONAL CHEM CHEM 465

UW

GPA 3.92

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This 17 page Class Notes was uploaded by Carmela Kilback on Wednesday September 9, 2015. The Class Notes belongs to CHEM 465 at University of Washington taught by Xiaosong Li in Fall. Since its upload, it has received 38 views. For similar materials see /class/192575/chem-465-university-of-washington in Chemistry at University of Washington.

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Date Created: 09/09/15

2 Geometry Optimization and Molecular Vibration rotentiai energy burraces Geometry Optimization Coordinate Systems Molecular Vibrations lectronic degrees of freedom Basis Atom centered Energy Orbital Electron Density Plane Wave Wave Function Basis Functions Mathematical Methods Hamiltonian Born Single Oppenheimer Configuration Appr Quantum Molecular Analytical Energy Mechanics Mechanics Funcnons EnergyR Dipole Level of Theory Multiple C onfiguration PostSCF Methods Potential Energy Surface EnergyR uclear degrees 0 freedom Classical Equation of Motion Molecular Dynamics Rigid Rotor Geometry amp Harmonic Optimization 9 otational and Minima and Vibrational Levels Transition States Methods Potential Energy Surface 4L 39 Single Point Energies SP F Solutions of the Schrodinger equation at xed nuclear coordinates E Vertical excited states higher than the lowest energy at the same nuclear coordinates szE R gt E0l 1E2R and LPOLP1LP2R L Potential Energy Surfaces PES T A collection of solutions of a same rankroot for the Schrodinger equation in the whole space of nuclear coordinates I Ground state PES vs excited state PES 1E0RE1RE2R ant 11110 1121 1122 R Potential Energy Surfaces quot 39 39 z r39l 39quot w 0 9 I W 049239 w 195 3quot 3quot 39 7 at itquot quot 5W9 9 w PES Minima L K Lowest points in the valleys on a PBS where Oand gt0foralli 6E 62E GR 6122 I Global minimum lowest energy point on the rim only one r Very hard to nd for a complicated system T Local minima lowest energy point in any potential well many T Heats of reaction AE AH and AG energy difference between two minima T Equilibrium constant Potential Energy Surfaces quot 39 39 z r39l 39quot w 0 9 I W 049239 w 195 3quot 3quot 39 7 at itquot quot 5W9 9 w PES Transition States L 1 The highest point on a reaction path where 2 a EO and aEzltO k k 6E 2 U39auu 2gtU1U11 k 612 612 I First order saddle points maximum with respect to one and m1nnna to the rest of coordmates r Many transition states for a reaction but usually only the lowest one is meaningful Reaction barriers AEl AHI and AGl Reaction rates k 7 transition state theory Geometry Optimization General Algorithms F 1 Energy Monte Carlo Simplex 7 Slow convergence 39 Firstderivative Conjugategradient quasiNewtonRaphson 7 Better convergence 7 QNR is the default method in most computational packages first order cost with a secondorder behavior 1 Secondderivative or Hessian NewtonRaphson I Kapld COHV Ig HC 7 Expensive computation of second derivatives Geometry Optimization Finding Minima NewtonRaphson or quasiNewtonRaphson Step 6E 62E g 6R1 6R2 Energy Geometry Optimization Finding Minima E L NewtonRaphson or quasiNewtonRaphson Step aE yE g5 w AR H Geometry ptimization Flowchart Initial guess for geometry amp Hessian lt Calculate single point energy and gradient lt Update Hessian With geometry and gradient lt Take a NR step using Hessian and gradient Q Check for geometry convergence Output Yeg Geometry Optimization Gaussian Keywords Z Opt keyword OptLoose Intended for preliminary work 3 OptTight or OptVeryTight useful when computing Vibrational spectra T Hessian empirical estimates default a Read the initial Hessian from other calculations ReadFC H Calculate the initial Hessian CalcFC i l Calculate the full Hessian at each step in the optimization Cachll Things to try when optimizations fail Tl Number of steps exceeded 7 OptRestart MaxcycleN Tl Change in point group during optimization NOSymm Geometry Optimization Finding Transition States i Linear Synchronous Transit and Quadratic Synchronous Transit w QST2 input a reactantlike structure and a productlike structure QST3 input reactant product and estimate of transition state Geometry Optimization Finding Transition States 1L Sample Input ii Atoms need to be specified in the same order in each structure T Input structures do not correspond to optimized structures OPTQST2 H 5 A 3 C O 1 2 H5 A quot4 H3 C102 Iquot4 Algorithms for Finding Transition States QuasiNewton Raphson OPT TS or OPTSaddlen In ut initial estimate of the transition state 39eornetr Geometry Optimization Testing Stationary Points Compute the full Hessian or vibrational frequencies Freq lquot l Testing Minima lquot 3 Check the number of negative imaginary eigenvalues frequencies of vibrational modes of Hessian 0 required for a minimum 4 If there are any negative eigenvalues frequencies follow the associated eigenvector vibration to a lower energy structure Ile i Testing Transition Structure j Check the number of negative imaginary eigenvalues frequencies of Vibrational modes of Hessian l and only 1 for a transition state 7 If there is no negative eigenvalue frequency follow the associated eigenvector vibration to a higher energy structure Tl Check the nature of the transition vector reaction path following IRC

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