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**Daniel Sánchez-Portal**

Calculation of optical properties and macroscopic polarization with SIESTA Daniel Sánchez-Portal Centro de Física de Materiales, Centro Mixto CSIC-UPV/EHU,San Sebastián, Spain Efficient density-functional calculations with atomic orbtitals: a hands-on tutorial on the SIESTA code CECAM Tutorial Lyon, June 18-22

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**Polarizability Molecule Exact many body wavefunctions and eigenvalues**

Approximation with Kohn-Sham orbitals and eigenvalues

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**Dielectric function in solids**

Without local field corrections Unfortunately there is no way to apply this formula to a solid Position operator is ill-defined for extended wavefunctions

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Momentum formulation

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**A word of caution for non-local potentials**

No problem: localized objects

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**Thomas-Reiche-Kuhn or f-sum rule**

Drude term for metals (ω0)

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Parameters and input OpticalCalculation : default .false., set to .true. Optical.NumberOfBands : all of them used if not specified %block Optical.Mesh n n n3 %endblock Optical.Mesh Optical.Broaden: small “artificial” broadening, 0.X eV Optical.PolarizationType: polarized, unpolarized, polycrystal %block Optical.Vector Ex Ey Ez %endblock Optical.Vector Either E, electric field or k, propagation vector

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**Optical.Vector Polarized: Unpolarized:**

Polycrystal: Average over three spatial directions

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**What is left out in this approach**

*Classical collective modes (plasmons). They can be included at the RPA level. Important at low energies for small systems, not that much for bulk. *Excitonic effects (electron-hole interaccion). Quite hard to include *Spectrum beyon Kohn-Sham approx. At the moment just the “scissor operator” to correct excitation energies.

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**SIESTA Diamond and Silicon Silicon Diamond PW, CASTEP**

G.F. Bertsch et al.Phys.Rev. B 62, 7998 (2000). SIESTA Silicon Diamond PW, CASTEP DZP basis set (26 bands)

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**Optical response of 4-Å diameter SWCNT with SIESTA**

Testing the accuaracy of SIESTA band structures on graphene: Including a diffuse 3s orbital we have perfect with PW up to 6 eV Adding an additional 3p shell the agreement is extended to eV In fact, ... Our band structures for the 4-Å are in very nice agreement with the PW calculations of Li et al.

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**Optical response of 4-Å diameter SWCNT with SIESTA (cont.)**

(5,0) (4,2) (3,3) (3,3) (4,2) (5,0) All channels occupied 1:0.7:0.2 (5,0):(3,3):(4,2) f=2x10-4

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Optimization of Numerical Atomic Orbitals

Optimization of Numerical Atomic Orbitals

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