OPTICAL PROPERTIES OF OPTICAL PROPERTIES OF METALLIC NANOPARTICLES, METALLIC NANOPARTICLES, MOLECULES AND POLYMERS MOLECULES AND POLYMERS Dr. Mica Grujicic Dr. Mica Grujicic April, 2004 April, 2004 Department of Mechanical Engineering Department of Mechanical Engineering
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OPTICAL PROPERTIES OF OPTICAL PROPERTIES OF METALLIC NANOPARTICLES, METALLIC NANOPARTICLES,
MOLECULES AND POLYMERSMOLECULES AND POLYMERS
Dr. Mica GrujicicDr. Mica Grujicic
April, 2004April, 2004Department of Mechanical EngineeringDepartment of Mechanical Engineering
Mie Theory Mie Theory --Dilute Colloidal Dilute Colloidal Solution LimitSolution Limit
Spherical ParticlesSpherical Particles
Ref: Ref: C. F.C. F.Bohren Bohren and D. R. Huffman, Absorption and D. R. Huffman, Absorption and Scattering of Light by Small Particles, and Scattering of Light by Small Particles,
Wiley: New York, 1983Wiley: New York, 1983..
Extinction CrossExtinction Cross--section of section of Spherical ParticlesSpherical Particles
( ) 22
2/332
224
pmp
pmpext
RC
εεεε
λεπ
′′++′
′′=
εεmm –– Dielectric Function of the MediumDielectric Function of the Medium
Effective Damping FrequencyEffective Damping Frequency
Effect of the Small Particle SizeEffect of the Small Particle Size
( ) 22
2
eff
Pp Γ+
−=′ ∞ ωω
εωε
( ) ( )22
2
eff
effPp Γ+
Γ=′′
ωω
ωωε
FreeFree--electron Real Part of the electron Real Part of the Dielectric Function of Spherical ParticlesDielectric Function of Spherical Particles
FreeFree--electron Imaginary Part of the electron Imaginary Part of the Dielectric Function of Spherical ParticlesDielectric Function of Spherical Particles
Effect of Effect of Intrabound Intrabound TransitionsTransitions
( ) ( ) ( ) ( )pbulkierbandi
freeii ,int =+= ωεωεωε
Total Complex Dielectric FunctionTotal Complex Dielectric Function
( ) ( ) ( ) ( )ωεωεωεωε freebulkbulk
freepp −+=
Dielectric Constant in Metallic NanoparticlesDielectric Constant in Metallic Nanoparticles
ρρNN –– Number Density of ParticlesNumber Density of Particles
NonNon--spherical Particlesspherical Particles
Ref: R. Ref: R. GansGans, Ann. Phys., 47 (1915) 270, Ann. Phys., 47 (1915) 270
Extinction Cross Section of Extinction Cross Section of NonNon--Spherical ParticlesSpherical Particles
( )cbaj
PP
PRCj
pmj
jp
pjmext ,,
1
13
8
2
2
22332
=
′′+
−+′
′′= ∑
εεε
ελεπ
21
;111ln
211
2
2a
cbaP
PPrr
rrrP
−==
−
−+−
=
( )21 abr −=
Depolarization Vector for Nanorod (a>b=c)Depolarization Vector for Nanorod (a>b=c)
wherewhere
Gold
SilverGold
Silver
Input: Real and Imaginary Parts of the Dielectric Constants For Input: Real and Imaginary Parts of the Dielectric Constants For Gold and Silver as a Function of the Photon WavelengthGold and Silver as a Function of the Photon Wavelength 43704370
Ref: P. B. Johnson and R. W. Christy, Phys. Rev. B, 6 (1972) 4370
Wavelength, nm
Extin
ctio
nC
oeffi
cien
t,M
-1cm
-1
300 400 500 600 7000
1000
2000
3000
4000
5000
Calculated Absorption Spectra of Au Particles in Water
n = 1.334
ResultsResults
Dielectric Constant of
Water
Spherical Spherical ParticlesParticles
Wavelength, nm
Nor
mal
ized
Abso
rban
ce
500 525 550 575 6000
0.5
1
1.5
2
Calculated Absorption Spectra of Au Particles Media with DifferentDielectric Constant
Ref: Ref: J. J. Goodman, B. T.J. J. Goodman, B. T. DraineDraine, and P. J., and P. J.FlateauFlateau, Opt., Opt. LettLett. 16 (1991) 1198.. 16 (1991) 1198.
iii EαP ⋅=
Polarization of Each DipolePolarization of Each Dipole
ααii –– PolarizabilityPolarizability of the Dipole at of the Dipole at rrii
Total Total ElectriclElectricl Field at Position Field at Position rrii
iselfiinci ,, EEE +=
j
N
ijijiself PAE ⋅−= ∑
≠,
Electric Field From Other DipolesElectric Field From Other Dipoles
( )tii iiinc ω−⋅= rkEE exp0,
Electric Field of Incident Plain WaveElectric Field of Incident Plain Wave
k k –– Wave VectorWave Vector
EEoo –– The Amplitude of the Incident Electric Field The Amplitude of the Incident Electric Field
tt –– TimeTime ωω –– FrequencyFrequency
Final Equation for PolarizationFinal Equation for Polarization
( ) iinc
N
ijjijii ,
1 EPAPα =⋅+ ∑≠
−
( ) ( ) ( ) ( )[ ]
⋅−−
+××=⋅ jijijjijij
ijjijij
ij
ijjij r
rikr
krrki
PrrPPrrPA 31exp 2
22
3
Dyadic Green’s Function ApproachDyadic Green’s Function Approach
Although self-consistent field calculations are adequate for the vast majority of ‘normal’ molecules, biradicals and excited states require a more sophisticated treatment.
This is often achieved using configuration interaction methods (CI). In CI calculations, the molecular orbitals for the ground state are calculated and then used unchanged to construct a series of further electronic configurations (microstates) that are mixed to form new electronic states.
CI calculations give not only the ground state, but also the excited states that result from mixing the microstates used. They can therefore be used for the calculation of UV/vis spectra, optimization of excited states, second order hyperpolarizabilities (sum-over-states method) etc.
CI calculations are available only for RHFwavefunctions. Any spin state (single, doublet, etc.) can be requested.
Adsorption Spectrum forAdsorption Spectrum for CinnamateCinnamate
IR Spectra of IR Spectra of PolymersPolymers
Ref: A. Ref: A. Soldera Soldera and J.and J.--P. P. DognonDognon, , ““Optical Coefficients Optical Coefficients of Polymers Versus Wavelength Calculated From of Polymers Versus Wavelength Calculated From Classical Molecular SimulationsClassical Molecular Simulations””, ACS Division of , ACS Division of Polymeric Materials, Science and Engineering, 75 (1996) Polymeric Materials, Science and Engineering, 75 (1996) 227227--228. 228.