1. Model Chemistries Lecture CompChem 4 Chemistry 347 Hope College

2. Terminology Model chemistry –Should be unbiased, well-defined, uniformly applicable –Theoretical method and basis set (ex: HF/3-21G) Basis set –Functions that approximate atomic orbitals Theoretical method –Method for computing molecular energy

3. Model Chemistries HF B3LYP MP2MP4…Full CI STO-3G 3-21G 6-31G(d) 6-311+G(d,p) …  Schrödin- ger Eqn  Electron correlation   Basis Set Size 

4. Basis Sets Miminal –One function per core and valence atomic orbital –STO-3G: 5 functions (1s,2s,2p x,y, z ) for C Split Valence –Additional functions allow orbitals to change size –3-21G: 9 functions (1s,2s,3s,2p,3p) for C Polarized –Additional functions allow orbitals to change shape –6-31G(d) : 15 functions (1s,2s,3s,2p,3p,3d) for C

5. Basis Sets (con’t) Diffuse –Additional “diffuse” functions allow orbitals to occupy large regions of space –6-31+G(d) : 19 functions for C High Angular Momentum –Additional p,d,f functions allow orbitals to change shape even more –6-311+G(d,p): 22 functions for C

6. Basis Set Effects Larger basis set results in more accurate calculations (variational theorem) Larger basis sets require more time, memory, disk (calculations scale as N 4 ) Additional functions do not have physical meaning, but allow better mathematical description of molecular orbitals

7. Theoretical Methods Semi-Empirical Methods (AM1, PM3) –Parameterized from experimental data on simple organic molecules –Very fast –Semi-quantitaive –Good for very large systems or to get initial geometries for subsequent calculations –Reported energies are heats of formation, rather than energy from isolated nuclei and electrons

8. Theoretical Methods (con’t) Hartree-Fock (HF) –Solves Schrödiner Equation from first principles (ab initio) –Uses Self-Consistent Field (SCF) approximation for electron positions, thereby neglecting electron correlation –Good base-level theory for geometries and frequencies –Relatively robust

9. Theoretical Methods (con’t) Post-SCF Methods (MP2, MP4, QCISD, CCSD) –Include some electron correlation –Analytical gradients for MP2 and MP4SDQ; analytical frequencies for MP2 (in general, don’t optimize or calculate frequencies at MP4) –Small but necessary improvement in accuracy (0.1 H = 63 kcal/mol  0.01H = 6.3 kcal/mol) –Very costly in time

10. Theoretical Methods (con’t) Density Functional Theory (B3LYP) –Electron correlation is built-in –Faster than MP2 –Only electron density is available, not orbitals (but one can project density onto a set of orbitals) –“MP2 quality results with HF speed”

11. Compound Methods Do it yourself –Pre-optimize at Hartree-Fock; calculate frequencies for thermal corrections ( OPT FREQ ) –Re-optimize geometry at MP2 ( OPT ) –Calculate energy at MP4 ( SP ) –Assemble results Terminology –En Method/En Basis//Geom Method/Geom Basis –Ex: MP4/6-311+G(2d,p)//MP2/6-31G(d)

12. Compound Methods (con’t) G1, G2(MP2), and G2 –Procedure for computing and calculating energies using HF, MP2, and MP4 and large basis sets –Mean Absolute Deviation = 1.6 - 1.2 kcal/mol CBS-4M, CBS-40, and CBS-Q –Reduce basis set size as method improves –Mean Absolute Deviation = 2.0 - 1.0 kcal/mol CBS-4M has most accuracy for calculation time