Dipole Moments of Selected Small Molecules- A Computational Study

1. Dipole Moments of Selected Small Molecules- A Computational Study AntalZoltan-PhD candidate 6304-Computational Chemistry March 2010

2. Outline • Introduction • How do we calculate dipoles? • Theories and basis sets • Experimental geometries • Optimized geometries • HF vs. Electron Correlation • The curious case of Carbon Monoxide • Conclusions

3. Introduction • Dipole moments: magnetic, bond, nuclear, electric, etc. • Vector quantity - Polarity – Debye(not SI) • Convention: chemist’s vs. physicist's • Why are they important? • Charge distribution affects exterior potential – determines the Hamiltonian – determines the wave function • Dipole moments directly result from charge distributions • Good and simple way to test theories and basis sets

4. How do we calculate dipoles? • Experimentally – microwave spectroscopy (provides some info on sign and direction) • Theoretically: • Direct calculation of expectation value of dipole moment operator – 0th order perturbation value • Direct evaluation of the full derivative expression (dE/dλ)λ=0 for CI-type wavefunctions • Nuclear/electronic contribution - geometry

5. Theories and basis sets • HF, B3LYP, MP2, CCSD(T)-Golden Method • STO-3G, 3-21G, 6-31G(d), cc-PVTZ • Ascending experimental dipole moment values (D) and known experimental geometries • Calculations in increasing theory/basis set direction using Gaussian 03

6. Experimental geometries • Results in agreement with other sources • Basis set performance almost independent of theory • Small basis sets perform bad – same tendencies with all theories • Larger basis sets perform well

7. MAD=0.53 D Exp. CO = 0.122 D Exp=5.83 D HF = 4.85 D

8. 3-21G with Experimental Geometries MAD=0.48D

9. MAD=0.32D

10. MAD=0.1D

11. Optimized geometries • Geometries are extremely important –NH3 • Small basis sets fail • STO-3G – too pyramidal • 3-21G – too planar • HF - as the basis set gets larger – better results • Electron correlation important

13. 3-21G – Optimized Geometries

14. MAD=0.30D

15. MAD=0.1D MAD=0.2D

16. HF vs. Electron Correlation • HF performs good with large basis sets, but has difficulties with low range dipoles (0-5D) • Electron correlation: theories perform good only if the right amount of correlation is included in the wave function • CO –favorite candidate for evaluating the performance of various theoretical models

17. The curious case of Carbon Monoxide • HF/large basis set good, but predicts the wrong sign - vector • Electron correlation – better if right amount of corr. is included Experimental Most of theory/basis B3LYP/cc-PVTZ (0.122 D) set comb. (0.125 D) • CCSD(T) – usually small errors, but needs the right basis set

18. Conclusions • Small basis sets fail • Larger basis set perform better • Amount of correlation is important • For the system to be studied – homework must be done first • Basis set optimization for specific system

19. Thank You !