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Introduction to Computational Chemistry



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Introduction to Computational Chemistry NSF Computational Nanotechnology and Molecular Engineering Pan American Advanced Studies Institutes PASI Workshop January 5 16 2004 California Institute of Technology Pasadena CA Andrew S Ichimura For the Beginner There are three main problems 1 Deciphering the language 2 Technical implementation 3 Quality assessment Focus on Calculating molecular structures and relative energies 1 Hartree Fock Self Consistent Field 2 Electron Correlation 3 Basis sets and performance Molecular properties Transition States Reaction coords Ab initio electronic structure theory Hartree Fock HF Electron Correlation MP2 CI CC etc Geometry prediction Benchmarks for parameterization Spectroscopic observables Prodding Experimentalists Goal Insight into chemical phenomena Setting up the problem What is a molecule A molecule is composed of atoms or more generally as a collection of charged particles positive nuclei and negative electrons The interaction between charged particles is described by qi q j q iq j Vij V rij 4 0 rij rij Coulomb Potential rij qj qi Coulomb interaction between these charged particles is the only important physical force necessary to describe chemical phenomena But electrons and nuclei are in constant motion In Classical Mechanics the dynamics of a system i e how the system evolves in time is described by Newton s 2nd Law F force F ma a acceleration 2 dV d r r position vector m 2 m particle mass dr dt In Quantum Mechanics particle behavior is described in terms of a wavefunction H ih t Time dependent Schr dinger Equation i 1 h h 2 H Hamiltonian Operator Time Independent Schr dinger Equation H r t H r r t r e iEt h If H is time independent the timedependence of may be separated out as a simple phase factor H r r E r Time Independent Schr dinger Equation Describes the particle wave duality of electrons Hamiltonian for a system with N particles H T V Sum of kinetic T and potential V energy N 2 2 2 2 2 h h 2 T T i i 2 2 2 2m 2m y i



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