Ab initio calculation of nonlinear optical properties of infinite polymers Alberto Martinez Limia In

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Ab initio calculation of nonlinear optical
properties of infinite polymersAlberto
Martinez LimiaInstitute for Theoretical
ChemistryUniversity of Erlangen-Nuremberg
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Ab initio calculation of nonlinear optical
properties of infinite polymersA. Martinez

Introduction

Calculation of (hyper-)polarizabilities
Molecules
Oligomers
Polymers

Vibrational contribution to the static
polarizabilities of polymers

Correlation contribution to the static
polarizabilities of polymers

Conclusion
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Ab initio calculation of nonlinear optical
properties of infinite polymers A. Martinez

(Hyper-)polarizabilities

Susceptibilities
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Ab initio calculation of nonlinear optical
properties of infinite polymers A. Martinez

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Ab initio calculation of nonlinear optical
properties of infinite polymers A. Martinez

From the hyperpolarizabilities to the
susceptibilities

Gas state

Liquid state



Spherical cavity
Polarizable continuum
Polarizable dipole grid

Solid state

There was not available a method to find ?crys
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Ab initio calculation of nonlinear optical
properties of infinite polymers A. Martinez

Contributions to the polarizabilities
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Ab initio calculation of nonlinear optical
properties of infinite polymers A. Martinez

Hartree-Fock-Roothaan equation
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Ab initio calculation of nonlinear optical
properties of infinite polymers A. Martinez

Finite field method for the calculation of the
static electronic (hyper-)polarizabilities
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Ab initio calculation of nonlinear optical
properties of infinite polymers A. Martinez

Coupled Perturbed Hartree-Fock (CPHF) equations
I
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Ab initio calculation of nonlinear optical
properties of infinite polymers A. Martinez

Coupled Perturbed Hartree-Fock (CPHF) equations
II
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Ab initio calculation of nonlinear optical
properties of infinite polymers A. Martinez

Coupled Perturbed Hartree-Fock (CPHF) equations
III
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Ab initio calculation of nonlinear optical
properties of infinite polymers A. Martinez

Coupled Perturbed Hartree-Fock (CPHF) equations
IV
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Ab initio calculation of nonlinear optical
properties of infinite polymers A. Martinez

Coupled Perturbed Hartree-Fock (CPHF) equations
V
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Ab initio calculation of nonlinear optical
properties of infinite polymers A. Martinez

Calculations
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Ab initio calculation of nonlinear optical
properties of infinite polymers A. Martinez

Oligomer method for the calculation of polymer
properties
? approximation /N approximation
mean value of the property for the ground cell


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Ab initio calculation of nonlinear optical
properties of infinite polymers A. Martinez

Oligomer method meaning of calculated properties
The problem The definition of the cell is not
unique
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Ab initio calculation of nonlinear optical
properties of infinite polymers A. Martinez

Oligomer method meaning of calculated properties
Die geometrische Zelle (G-Zelle) Sie ist durch
starre Ebenen begrenzt, die durch die
Mittelpunkte der Bindungen zwischen benachbarter
Zellen verlaufen.
Die Ladungszelle (L-Zelle) Sie ist durch zwei
Ebenen begrenzt, die senkrecht zur Oligomerachse
stehen, und die so gewählt werden, daß die
gesamte Ladung (Summe der elektronischen Ladung
und der Kernladung) jeder Zelle Null ist.
Die Kristallzelle (K-Zelle) Diese Zelle hat
eine über mehrere Zellen des Oligomers
verbreitete elektronische Ladung. Für die
Berechnung ihrer Eigenschaften wird über alle
Beiträge summiert, an welchen Basisfunktionen
teilhaben, die zu den Atomen der Zelle gehören.
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Ab initio calculation of nonlinear optical
properties of infinite polymers A. Martinez

Oligomer method meaning of calculated properties
Polyethin oligomer
Polyethen oligomer
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Ab initio calculation of nonlinear optical
properties of infinite polymers A. Martinez

Operator of the electric fiel for polymers I
Molecular potential
energy
energy
Polymer potential
a) without field
b) with field
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Ab initio calculation of nonlinear optical
properties of infinite polymers A. Martinez

Operator of the electric fiel for polymers II
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Ab initio calculation of nonlinear optical
properties of infinite polymers A. Martinez

Operator of the electric fiel for polymers III
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Ab initio calculation of nonlinear optical
properties of infinite polymers A. Martinez

Objective solution of the time dependent
Schrödingers equation in the presence of a
dynamic electric field
Methods
Hartree-Fock-Roothaan method for molecules
Born-von-Kármán boundary conditions
Time dependent perturbation theory
Hartree-Fock Crystal Orbital method
Coupled Perturbed Hartree-Fock (CPHF) equations
for periodic quasi-one-dimensional systems
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Ab initio calculation of nonlinear optical
properties of infinite polymers A. Martinez

Hartree-Fock Crystal Orbital method
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Ab initio calculation of nonlinear optical
properties of infinite polymers A. Martinez

Coupled Perturbed Hartree-Fock equations for
polymers I
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Ab initio calculation of nonlinear optical
properties of infinite polymers A. Martinez

Coupled Perturbed Hartree-Fock equations for
polymers II
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Ab initio calculation of nonlinear optical
properties of infinite polymers A. Martinez

Coupled Perturbed Hartree-Fock equations for
polymers III
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Ab initio calculation of nonlinear optical
properties of infinite polymers A. Martinez

Coupled Perturbed Hartree-Fock equations for
polymers IV
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Ab initio calculation of nonlinear optical
properties of infinite polymers A. Martinez

Coupled Perturbed Hartree-Fock equations for
polymers IV
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Ab initio calculation of nonlinear optical
properties of infinite polymers A. Martinez

Dielectric properties from the solution of the
CPHF equations for polymers
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Ab initio calculation of nonlinear optical
properties of infinite polymers A. Martinez

Calculations Poly(H2O) , minimal basis
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Ab initio calculation of nonlinear optical
properties of infinite polymers A. Martinez

Calculations polycarbonitrile , minimal basis
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Ab initio calculation of nonlinear optical
properties of infinite polymers A. Martinez

Calculations polycarbonitrile , minimal basis
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Ab initio calculation of nonlinear optical
properties of infinite polymers A. Martinez

Calculations polycarbonitrile , double-zeta
basis
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Ab initio calculation of nonlinear optical
properties of infinite polymers A. Martinez

Calculations polyfurane, polypyrrole,
polythiophene und polyparaphenylene
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Ab initio calculation of nonlinear optical
properties of infinite polymers A. Martinez

Schwingungsbeiträge zu statischen
Polarisierbarkeiten I
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Ab initio calculation of nonlinear optical
properties of infinite polymers A. Martinez

Schwingungsbeiträge zu statischen
Polarisierbarkeiten II
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Ab initio calculation of nonlinear optical
properties of infinite polymers A. Martinez

Numerische Anwendungen Poly-HF, doppelt-zeta
Basissatz
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Ab initio calculation of nonlinear optical
properties of infinite polymers A. Martinez

Korrelationsbeiträge zu statischen
Polarisierbarkeiten I
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Ab initio calculation of nonlinear optical
properties of infinite polymers A. Martinez

Korrelationsbeiträge zu statischen
Polarisierbarkeiten II
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Ab initio calculation of nonlinear optical
properties of infinite polymers A. Martinez

Numerische Anwendungen
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Ab initio calculation of nonlinear optical
properties of infinite polymers A. Martinez

What is to be made...
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Ab initio calculation of nonlinear optical
properties of infinite polymers A. Martinez

Conclusions
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Ab initio calculation of nonlinear optical
properties of infinite polymers A. Martinez

Ich danke