1. Some Problems (Precautions) of ab initio Quantum Chemistry Jim Jr-Min Lin Most papers only show the “good” sides of the calculation and hide the problematic sides. Such that, experimentalists tend to think that theory is nearly perfect. An actual situation:

2. ab initio calculations Correlation Energy e-e- e-e- Wave Function Orbitals 1s, 2s, 2p,... Configurations (1s) 2 (2s) 2 (2p) 1... (1s) 2 (2s) 1 (2p) 2

3. Methods: (Approximation, Algorithm) HF-SCF CAS-SCF CAS-PT2 (Rayleigh-Schrodiger) MP2 (Moller-Plesset) CCSD(T)/QCISD(T) Density Functional B3-LYP B3-Half and Half

4. Basis Set (BS): numerical functions to fit orbitals Gaussian BS 6-31G(d,p) 6-311++G(3df,3p) Dunning’s correlation consistent BS cc-pVTZ, cc-pVQZ, cc-pV5Z: cc-pVNZ, N=3,4,5 aug-cc-pVNZ, N=3,4,5 Number of Zeta, 

5. One electron Wave Function => Approximate Orbital (s, p, d, f,... ) l=(1,2, 3, 4,...) Polarization Functions more number of , more diffuse

6. JPC, A 101, 7923 (1997)

7. R(F-F) Energy Hartree F2F2 Even methods that are widely used and known of high accuracy may have Significant Errors.

8. JCP 127, 164317 (2007)

9. F2F2 Usually big basis set can’t solve the Defect of a method

10. F2F2 Basis set size has significant effect on accuracy of relative energy and less effect on the geometry.

11. ClF Another Example of Basis Set size

12. ClF Another Example of Methods

13. F2F2 The ‘Shape’ of Potential Energy Curve depends on the Methods

14. Complete Basis Set Extrapolation cc-pVNZ, N=3,4,5 => N=infinity De(Cl-F) Hartree ClF (N+0.5) -4 v3z v4z v5z v∞zv∞z 0.01H=6.3 kcal/mol

15. Take Home Messages Error of ab initio calculation depends on geometry {R i } and bonding character. Err = f ({R i }) Form of f ({Ri}) : very sensitive to Methods, not so sensitive to Basis Set Especially for Transition State, different methods often predict quite different geometry. Most methods behave well at equilibrium geometries (Here the bonding is well described by most MO methods) Testing and Calibration are necessary. Most papers only show the good sides.

16. Check your results with other methods. Check if a Multi-Reference (MR) calculation is necessary.