Performance of Molecular Polarization Methods

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Performance of Molecular Polarization Methods

• Marco Masia

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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

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Nonpolarizable Models
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Nonpolarizable Models

• Drawback no dynamical response to the
  fluctuations of the electric fields is considered!

We need to implement polarizability in an
explicit way!
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Algorithms Incorporating Polarizability

• Several methods have been developed for the last
  30 years.

Minimization of the energy respect to some
parameter
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Fluctuacting Charges (FQ)

• Charges are allowed to fluctuate according to
  the electronic properties of the molecule as
  atomic electronegativity and atomic hardness.

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Point Dipoles (PD)
Atomic polarizabilities ai are assigned to some
molecular site The electric field induces the
formation of a point dipole mi
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Point Dipoles (PD)
The calculation is repeated iteratively till
convergence.
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Molecular Polarizability
Dependence of the molecular polarizability tensor
from the atomic polarizabilities
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Shell Model (SH)

• The point dipole is mapped to a system of two
  point charges linked by a spring.

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Comparison Among Methods

• Water
• Low polarizability (1.47 Å3)
• Anisotropic
• Carbon Tetrachloride
• High polarizability (10.5 Å3)
• Isotropic

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Case of a Positive Charge Close to Water

• Five configurations were considered

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Case of a Positive Point Charge Close to Water
Similar results were obtained for all the other
configurations considered
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Case of a Positive Point Charge Close to Water

• What about the performance with double point
  charges?

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Case of a Positive Point ChargeClose to Carbon
Tetrachloride
Three configurations were considered
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Case of a Positive Point ChargeClose to Carbon
Tetrachloride
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Case of a Positive Point ChargeClose to Carbon
Tetrachloride
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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

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Case of Cations
Potential energy importance of electron repulsion
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Case of Cations
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Case of Cations
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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.
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Damping Functions
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Damping Functions
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Damping Functions
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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-CCl4.
• Study the performance of the same methods with
  anions (high polarizabilities!)

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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

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Aknowledgements

• Rossend Rey
• Michael Probst

• EU
• Ministerio Español
• Regione Sardegna

• Vosotros