1. Performance of Molecular Polarization Methods Marco Masia

2. Performance of Molecular Polarization Methods - BCN: april 2005 Overview Nonpolarizable Models Algorithms Incorporating Polarizability Fluctuacting Charges (FQ) Point Dipoles (PD) Shell Models (SH) Comparison Among Methods: Case of a Positive Point Charge Case of Cations Damping Methods Conclusions

3. Performance of Molecular Polarization Methods - BCN: april 2005 A: repulsive short range term B: attractive term depending on the (dipole-dipole) London dispersion Nonpolarizable Models qOqO qHqH qHqH

4. Performance of Molecular Polarization Methods - BCN: april 2005 Nonpolarizable Models Drawback: no dynamical response to the fluctuations of the electric fields is considered! We need to implement polarizability in an explicit way!

5. Performance of Molecular Polarization Methods - BCN: april 2005 Algorithms Incorporating Polarizability Several methods have been developed for the last 30 years. Minimization of the energy respect to some parameter

6. Performance of Molecular Polarization Methods - BCN: april 2005 Fluctuacting Charges (FQ) Charges are allowed to fluctuate according to the electronic properties of the molecule as atomic electronegativity and atomic hardness.

7. Performance of Molecular Polarization Methods - BCN: april 2005 Point Dipoles (PD) Atomic polarizabilities  i are assigned to some molecular site The electric field induces the formation of a point dipole  i

8. Performance of Molecular Polarization Methods - BCN: april 2005 Point Dipoles (PD) The calculation is repeated iteratively till convergence. Charge and Dipole Field Tensors

9. Performance of Molecular Polarization Methods - BCN: april 2005 Molecular Polarizability Dependence of the molecular polarizability tensor from the atomic polarizabilities

10. Performance of Molecular Polarization Methods - BCN: april 2005 Shell Model (SH) The point dipole is mapped to a system of two point charges linked by a spring.

11. Performance of Molecular Polarization Methods - BCN: april 2005 Comparison Among Methods Water: Low polarizability (1.47 Å 3 ) Anisotropic Carbon Tetrachloride: High polarizability (10.5 Å 3 ) Isotropic

12. Performance of Molecular Polarization Methods - BCN: april 2005 Case of a Positive Charge Close to Water Five configurations were considered:

13. Performance of Molecular Polarization Methods - BCN: april 2005 Case of a Positive Point Charge Close to Water Similar results were obtained for all the other configurations considered

14. Performance of Molecular Polarization Methods - BCN: april 2005 Case of a Positive Point Charge Close to Water What about the performance with double point charges?

15. Performance of Molecular Polarization Methods - BCN: april 2005 Case of a Positive Point Charge Close to Carbon Tetrachloride Three configurations were considered:

16. Performance of Molecular Polarization Methods - BCN: april 2005 Case of a Positive Point Charge Close to Carbon Tetrachloride

17. Performance of Molecular Polarization Methods - BCN: april 2005 Case of a Positive Point Charge Close to Carbon Tetrachloride

18. Performance of Molecular Polarization Methods - BCN: april 2005 Case of a Positive Point Charge PD and SH models can be reparametrized to reproduce the polarizability tensor of the molecule & the dipole moment induced by a point charge; Also at short distances there is no need to use damping functions; High electric fields cause the linear models to fail due to hyperpolarizability effects;

19. Performance of Molecular Polarization Methods - BCN: april 2005 Case of Cations Potential energy: importance of electron repulsion

20. Performance of Molecular Polarization Methods - BCN: april 2005 Case of Cations

21. Performance of Molecular Polarization Methods - BCN: april 2005 Case of Cations

22. Performance of Molecular Polarization Methods - BCN: april 2005 Damping Functions Thole (1981): for intramolecular interactions the molecular polarizability diverges at short distances Many functional forms for the charge density have been proposed. The most used are the exponential and the linear forms.

23. Performance of Molecular Polarization Methods - BCN: april 2005 Damping Functions

24. Performance of Molecular Polarization Methods - BCN: april 2005 Damping Functions

25. Performance of Molecular Polarization Methods - BCN: april 2005 Damping Functions

26. Performance of Molecular Polarization Methods - BCN: april 2005 Conclusions and Future Work Dimers with cations show a different behaviour from the case of positive point charges; In the case of cations the use of damping functions for the electrostatic interactions is needed; The Thole linear and exponential models have been applied to intermolecular interactions and reparametrized for the interactions cation-water and cation-CCl 4. Study the performance of the same methods with anions (high polarizabilities!)

27. Performance of Molecular Polarization Methods - BCN: april 2005 Bibliography Review Rev. in Comput. Chem. 18, 89 (2002). Methods FQ: J. Chem. Phys. 101, 6141 (1994) PD: J. Am. Chem. Soc. 94, 2952 (1972) SH: The Theory of Optics (Longmans, N. Y., 1902) Damping: Chem. Phys. 59, 341 (1981) Results J. Chem. Phys. 121, 7362 (2004) Comp. Phys. Commun. In press Manuscript in preparation

28. Performance of Molecular Polarization Methods - BCN: april 2005 Aknowledgements Rossend Rey Michael Probst EU Ministerio Español Regione Sardegna Vosotros