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Polarisability (Read 5180 times)
Gerrit-Jan Linker
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Polarisability
04.06.08 at 17:16:54
 
Polarizability
 
(Hyper)polarizabilities are defined as the coefficients in the Taylor series expansion of the dipole moment or the energy in the presence of static and/or oscillating electric fields.
 
E(F) = E(0) - μ0F -αF2 + ...
where:
E = Energy
F = Electric field
μ = dipole
α = dipole polarisability
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« Last Edit: 04.07.15 at 14:49:12 by Gerrit-Jan Linker »  

Gerrit-Jan Linker
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Polarisability / Polarizability
Reply #1 - 21.07.08 at 22:25:04
 
Polarisability
 
Molecules have their electric moment perturbed under the influence of an electrical field such as that deriving from the electrical moments of another molecule. To say it differently: molecules are polarisable.
 
To extend a force field to include polarizability each attom is assigned a polarizability tensor.
In the presence of the permanent electric field of the molecule (the field derived from the atomic charges or the bond-dipole moments), a dipole moment will be induced on each atom.
 
The total electric field is the sum of the permanent electric field and that created by the induced dipoles.
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« Last Edit: 07.08.08 at 10:23:26 by Gerrit-Jan Linker »  

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Re: Polarizability
Reply #2 - 07.08.08 at 10:25:36
 
Quote:
The (dipole) polarisability:
The extent to which the charge density distorts to form an additional dipole as the results of an applied permanent electric field.

Ref: thesis Alex de Vries
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Gerrit-Jan Linker
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Polarizabilities are not additive
Reply #3 - 30.04.10 at 09:02:00
 
Polarizabilities are not additive
 
Polarisabilities are not additive. When there is a polarisability A and another polarisability B1 acts on it there is a net induction energy due to the induction force. Polarisability B1 polarises A and A polarises B1.  
 
When we introduce a third polarisability B2 there is an extra polarisation on A but we cannot just add this to the induction energy as B2 also polarises B1 and vise versa. In other words the polarisabilities act on all other polarisabilities, causing a polarisation at that point which affects in turn the polarisability at that point.
 
To illustrate this consider the following example.
(EDOTTF)2PF6 is a molecular crystal with 4xEDOTTF and 2xPF6 in one tetramer building block. Each molecule in the system is allowed to interact with all other molecules in the system. The induction energy is calculated of these interactions.
 
System: central tetramer (4x EDOTTF + 2x PF6)
Within the central tetramer the induction energy is -19 kcal/mol with an induced dipole of 15 Debije.
 
We now add a shell of surrounding tetramers (44 tetramers). We look at the induction energy of molecules:
molecules within the central tetramer: -22 kcal/mol
molecules in shell 1 with molecules in the central tetramer: -35 kcal/mol
molecules within shell 1: -1354 kcal/mol
 
Please note the large induction energy of the induction interactions between molecules within shell 1.  
 
We now add another shell of surrounding tetramers (another 180 tetramers). We look again at the induction energy of molecules:
molecules within the central tetramer: -23 kcal/mol
molecules in shell 1 with molecules in the central tetramer: -34 kcal/mol
molecules in shell 2 with molecules in the central tetramer: -8 kcal/mol
molecules in shell 1 with molecules in shell 2: -557 kcal/mol
molecules within shell 1: -1360 kcal/mol
molecules within shell 2: -5956 kcal/mol
 
Adding another shell of tetramers (367 tetramers). The induction energy of molecules:
molecules within the central tetramer: -23 kcal/mol
molecules in shell 1 with molecules in the central tetramer: -34 kcal/mol
molecules in shell 2 with molecules in the central tetramer: -6 kcal/mol  
   (note that this is reduced by 2 kcal/mol due to the extra shell)
molecules in shell 3 with molecules in the central tetramer: -5 kcal/mol
molecules in shell 1 with molecules in shell 2: -481 kcal/mol
  (note that this is reduced by 76 kcal/mol due to the extra shell)
molecules in shell 2 with molecules in shell 3: -1552 kcal/mol
molecules in shell 1 with molecules in shell 3: -208 kcal/mol
molecules within shell 1: -1351 kcal/mol
molecules within shell 2: -5892 kcal/mol
molecules within shell 3: > -9999 kcal/mol
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« Last Edit: 30.04.10 at 10:46:04 by Gerrit-Jan Linker »  

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Calculating the Polarisability
Reply #4 - 28.06.12 at 15:44:20
 
Calculating the Polarisability
 
Polarisability can be obtained from the second derivative of E w.r.t. the electric field F.
 
Polarisabilities can be calculated using:
  • PT: Perturbation Theory
    Not the suggested method. Although a scheme exists with which a complete basis can be simulated. In that case it offers an efficient procedure.
  • CHF: Coupled Hartree-Fock theory
    Converges slowly with increasing basis set. Should be able to get at maximum approx 70% of the experimental polarisability.
  • CKS: Coupled Kohn-Sham theory
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    « Last Edit: 29.06.12 at 07:32:43 by Gerrit-Jan Linker »  

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