Uncedu 10 what is computational chemistry what is

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its.unc.edu 10 What is Computational Chemistry? What is Computational Chemistry? Application of computational methods and algorithms in chemistry Quantum Mechanical i.e., via Schrödinger Equation also called Quantum Chemistry Molecular Mechanical i.e., via Newton ’s law F=ma also Molecular Dynamics Empirical/Statistical e.g., QSAR , etc., widely used in clinical and medicinal chemistry Focus Today Focus Today H t i ˆ
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its.unc.edu 11 How Big Systems Can We Deal with? How Big Systems Can We Deal with? Assuming typical computing setup (number of CPUs, memory, disk space, etc.) Ab initio method: ~100 atoms DFT method: ~1000 atoms Semi-empirical method: ~10,000 atoms MM/MD: ~100,000 atoms
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its.unc.edu 12  i j n 1 i ij n 1 i N 1 i 2 i 2 r 1 r Z - 2m h - H    n i j n 1 i ij n 1 i r 1 i h H Starting Point: Time- Independent Schrodinger Equation Independent Schrodinger Equation E H H t i ˆ
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its.unc.edu 13 Equation to Solve in ab initio Theory Equation to Solve in ab initio Theory E H Known exactly: 3N spatial variables (N # of electrons) To be approximated: 1. variationally 2. perturbationally
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its.unc.edu 14 Hamiltonian for a Molecule Hamiltonian for a Molecule kinetic energy of the electrons kinetic energy of the nuclei electrostatic interaction between the electrons and the nuclei electrostatic interaction between the electrons electrostatic interaction between the nuclei nuclei B A AB B A electrons j i ij nuclei A iA A electrons i A nuclei A A i electrons i e R Z Z e r e r Z e m m 2 2 2 2 2 2 2 2 2 ˆ H
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its.unc.edu 15 Ab Initio Methods Ab Initio Methods Accurate treatment of the electronic distribution using the full Schrödinger equation Can be systematically improved to obtain chemical accuracy Does not need to be parameterized or calibrated with respect to experiment Can describe structure, properties, energetics and reactivity What does “ ab intio ” mean? Start from beginning, with first principle Who invented the word of the “ ab initio ” method? Bob Parr of UNC-CH in 1950s; See Int. J. Quantum Chem. 37 (4), 327(1990) for details.
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its.unc.edu 16 Three Approximations Three Approximations Born-Oppenheimer approximation Electrons act separately of nuclei, electron and nuclear coordinates are independent of each other, and thus simplifying the Schrödinger equation Independent particle approximation Electrons experience the ‘field’ of all other electrons as a group, not individually Give birth to the concept of “orbital”, e.g ., AO, MO, etc. LCAO-MO approximation Molecular orbitals (MO) can be constructed as linear combinations of atom orbitals, to form Slater determinants
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its.unc.edu 17 Born-Oppenheimer Approximation Born-Oppenheimer Approximation the nuclei are much heavier than the electrons and move more slowly than the electrons freeze the nuclear positions (nuclear kinetic energy is zero in the electronic Hamiltonian) calculate the electronic wave function and energy
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