1. Antal Zoltan-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 2

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 3

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 – 0 th order perturbation value Direct evaluation of the full derivative expression (dE/dλ) λ=0 for CI-type wavefunctions Nuclear/electronic contribution - geometry 4

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 COPH 3 H2SH2SNH 3 H20H20H 2 COLiHNaHNaCl 0.1220.580.971.471.852.345.836.969.00 5

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 6

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

8. MAD=0.48D 3-21G with Experimental Geometries HFCOPH 3 H2SH2SNH 3 H20H20H 2 COLiHNaHNaCl 3-21G-0.39351.17541.81032.17352.43552.63895.89536.91929.9467 Exp.0.1220.580.971.471.852.345.836.969 8

9. MAD=0.32D 9

10. MAD=0.1D 10

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 11

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13. HFCOPH 3 H2SH2SNH 3 H20H20H 2 COLiHNaHNaCl 3-21G-0.39691.24231.82971.75252.38742.65815.9897.006910.1653 Exp.0.1220.580.971.471.852.345.836.969 3-21G – Optimized Geometries 13

14. MAD=0.30D 14

15. MAD=0.1D MAD=0.2D 15

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 16

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 17

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 18

19. Thank You ! 19