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1 Lec20 Fri 3mar17 [PDF]GAUSSIAN 09W TUTORIAL by A Tomberg - Cited by 8 - Related articles GAUSSIAN 09W TUTORIAL. AN INTRODUCTION TO COMPUTATIONAL CHEMISTRY USING G09W AND. AVOGADRO SOFTWARE. Anna Tomberg.
2 More TERMS Polarization Basis sets The previous page was about changing the size of orbitals without change in shape. But when in a molecule, the electron density on an atom is not the same as an isolated atom. This is accomplished by adding orbitals that have d character in the first row, and p character for H. Examples: 6-31g* = 6-31g(d) adds 6 d-type GTFs for the atoms Li-Ca, and 10 f- type GTFs for Sc-Zn. Diffuse Basis Sets 6-31g** = 6-31g(d,p) adds p character to H, in addition. Anions particularly benefit from include large basis functions. e.g, 6-31+g includes extra large s and p functions on heavy atoms, and g in addition at a diffuse s orbital to H
3 Some General Terms Names key words Route card: # method/basis for example: hf/6-31g* single point geometry optimization opt vibrational frequency (must be opt first) freq transition state search reaction path following potential energy surface solvation Open Shell Calculations ( some MOs have only 1 electron) ROHF (restricted open shell) means electrons with opposite spin in same MO have the same spatial orbital. UHF (unrestricted HF) means alpha and beta spins may have different spatial functions, thereby giving a slightly lower energy. (but, will not usually be eigenfunctions of the S 2 operator (i.e., neither singlet or triplet, for example)
4 Even Larger Basis sets For example G(3df,3pd) is triple zeta set defined for H-Ar, that provides diffuse functions on all atoms, 3 sets of d and 1 set of f functions to non-h atoms, and 3 sets of p functions, 1 set of d functions for H. This also called a VTZ3PD, meaning valence triple zeta with triple polarization and diffuse on all atoms. The above were developed by Pople. Dunning and co-workers developed as series of basis functions denoted cc-pvnz: i.e., cc-pvdz, cc-pvtz...,cc-pv6z, which stand for correlation-consistent, polarized valence double-zeta, etc. These basis sets were specifically designed to be used with methods that introduce electron correlation. Each set increases the orbital types as follows: cc-pvdz, cc-pvtz cc-pvqz, cc-pv5z cc-pv6z [3s2p1d] [4s3p2d1f] ] [5s4p3d2f1g] [6s5p4d3f2g1h] [7s6p5d4f3g2h1i] The number and degree of polarization (angular momentum) function increases rapidly from left to right, meaning more nodes, which is what is needed to introduce fine-grained correlation (better dodging). Doing a series of calculations with these basis sets on a molecule allow smooth extrapolation to what may be considered a near exact value. If diffuse functions are added to the cc-pvnz sets, they are called aug- cc-pvnz.
5 If electron-correlation is added to the wavefunction, all properties converge to experimentally observed values. B3LYP is the most popular DFT method; B3LYP/cc-pVTZ 99.87% of experiment; Takes 5 sec on a PC
6 Electron Correlation Electrons are particles and dodge each other= electron correlation (London dispersion force and energy = electron correlation between electrons on different molecules) Two basic types: 1)dynamic correlation = dodging because of Coulombic repulsion 2)static (non-dynamic, strong) correlation = the ground state not well described by a single Slater determinant. Multi Configurational SCF (MCSCF) needed. The wavefunction statically keeps the electrons apart. Methods for electron correlation 1. Configuration interaction (CI): mixing ground state configuration with excited state configurations (or configuration state functions (CSFs ) in variational formalism. 2. Moeller-Plesett (MP) perturbation theory = CI in the perturbation formalism MP2, MP3, MP4 = 2 nd, 3 rd, 4 th, order theory 3. Coupled cluster (CC): CI by Taylor expansion in a size-consistent way 4. DFT No CI at all; static correlation built into the electron density functional that minimizes the energy.
7 How can CI (mixing higher energy state with ground state cause correlation??? Higher states have more nodes. Squaring the linear combination gives cross terms (interference terms), which are negative when 2 electrons are on different sides of a nodal surface. Ψ*Ψ is thereby reduced. Example: The H 2 molecule ( ionic and covalent terms, difference between the MO and Valence Bond (VB) methods x x σ u * σ u *(1) σ u *(2) σ g σ g (1) σ g (2) σ u * x x σ g
8 H 2 Molecule Configuration State Functions (CSFs) A(1) = 1s(1) on Nucleus A B(1) = 1s(1) on Nucleus B Doubly excited CSF σ u 2 Ground CSF σ g 2 Energy ionic covalent σ u2 = [A(1) - B(1)] [A(2) - B(2)] = AA + BB - AB BA (not normalized) σ g2 = [A(1) + B(1)] [A(2) + B(2)] = AA + BB + AB + BA covalent* = AB + BA = valence bond method ionic + covalent = molecular orbital method (not normalized) *Heitler-London (1927) the first wavefunction proposed for H 2 at the dawn of quantum mechanics.
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