A Walkthrough For Quantum Chemistry Newbies

Part 1: Basis Sets, Related Functions, and Usage

by Peker Milas

Exact H Wave Functions

Question 1: Why do we need approximated basis sets ???

Fig: http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/hydwf.html#c3

Fig: http://upload.wikimedia.org/wikipedia/en/e/e7/Hydrogen_Density_Plots.png

Answer 1: Even if we use H like wave functions for each atom in a molecule, we will have a big problem in computations….

Question 2: How can we treat electronic structure of a molecule ???

Answer 2a: First we need to simplify our molecule by thinking of electrons can not interact wit each other. We call this Hartree-Fock Method…

Answer 2b: Second, we can write down total electronic part of Hamiltonianas a single Slater determinant or as a product of one-electron wave functions…

But, to proceed we need to make a guess for electron wave functions…

So, We have Basis Sets…

Basis Sets

Minimal Basis Sets

•STO-nG

Pople Basis Sets

•X-YZG •X-YZWG

Correlation-ConsistentBasis Sets

•cc-pVDZ •cc-pVTZ •cc-pVQZ

OtherBasis Sets

•DZV •TZV

Ref: http://en.wikipedia.org/wiki/Basis_set_%28chemistry%29

Split Valence Basis Sets

STO-nG, Minimal Basis Set…

• First developed by J.C. Slater, STO ~ Slater Type Orbitals…• All orbitals are sum of gaussians up to some constants in front of them…• All orbitals are treated as same…• They are simplest basis sets and suitable for large molecules…• They have extended versions as double, triple, quadruple zeta…

reSTO

5.0

3

S. F. Boys came up with2

75.0

2 reGTO

Example STO-3G Basis Set (Extended Triple Zeta)…

3322113 cccGSTO Ref 1: http://www.shodor.org/chemviz/basis/teachers/background.html

Ref 2: http://en.wikipedia.org/wiki/STO-nG_basis_sets

X-YZG, Pople Basis Set…

• First proposed by J. Pople…• Inner orbitals and valence orbitals are treated different…• With X-YZG* and ** p to s and s to p polarizations are included…• With X-YZ+G and ++ p to s and s to p diffusions are included…• With X-YZWG valence orbitals can be extended…• They are relatively easy to calculate…

cc-pVDZ, etc…, Correlation-Consistent Basis Sets…

• Developed by Dunning and coworkers…• A more realistic treatment of molecular orbitals…• cc-p stands for correlation-consistent polarized…• V stands for valence only basis set…• DZ, double zeta…• Widely used for post-Hartree-Fock calculations…

Some ongoing calculations and results…

First step of geometry optimization for Cy3 has finished…• 6-31G Basis Set has been utilized…• Slater Determinant solved numerically without any approximations…

Good news…• Optimization converged smoothly…• Equilibrium geometry can be utilized for next calculation with new Basis Set6-31G(d) or equivalently 6-31G*…

Bad news…• Optimization should be carried at least up to 6-31G*…• Optimization with 6-31G* basis should converge for calculation of RESP charges…• Firefly/PcGamess couldn’t finish optimization because of memory shortages…• A new level of approximation (either ab inito or DFT) should be applied…

Possible calculation ways…• DFT with BLY3P type electron correlation functional…• Ab inito with Moller-Plesset lvl 2 perturbation Theory (MP2)…• As a last resort; cc-pVDZ type post Hartree-Fock method…

Thank you…