From anisotropy of dielectric tensors to birefringence: a quantum mechanics approach

Rérat, Michel; D’Arco, Philippe; Lacivita, Valentina; Pascale, Fabien; Dovesi, Roberto

doi:10.1007/s12210-020-00931-9

Cited by 4 publications

(7 citation statements)

References 53 publications

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“…α-Quartz is a uniaxial positive mineral belonging to the P 2 1 21 space group with a mean refractive index equal to n = 1.458, a birefringence (δ = n e – n o ) value smaller than 0.01 (see refs , and ), and an experimental optical rotatory power of 21.7 deg.·mm –1 along the optic (and extraordinary) Z -axis at λ = 589 nm . It is worth noting that the rotation angle of the polarized light due to the birefringence (δ ∼ 10 –2 ) is still two orders of magnitude larger than that due to chirality (λ/πΦ Z ∼ 10 –4 ) at λ ∼ 1 μm.…”

Section: Resultsmentioning

confidence: 99%

“…We can see that the principal γ -axis is not exactly an optic axis since n β – n α is not equal to zero. Thus, the optical indicatrix was rotated by an angle around the β-axis (see ref ) given by to obtain the optic Z -axis from the diagonal components of the refractive index matrix (not reported in the table). In every instance (V0 or LC and SOS or SC-CP), was found to be equal to 70 ± 10°, which agrees with the value (77.4°) assumed by Mucha et al.…”

Section: Resultsmentioning

confidence: 99%

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First-Principles Calculation of the Optical Rotatory Power of Periodic Systems: Application on α-Quartz, Tartaric Acid Crystal, and Chiral (n,m)-Carbon Nanotubes

Rérat

2021

J. Chem. Theory Comput.

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The self-consistent coupled-perturbed (SC-CP) method in the CRYSTAL program has been adapted to obtain electromagnetic optical rotation properties of chiral periodic systems based on the calculation of the magnetic moment induced by the electric field. Toward that end, an expression for the magnetic transition moment is developed, which involves an appropriate electronic angular momentum operator. This operator is forced to be hermitian so that the chiroptical properties are real. In our formulation, the trace of the optical rotatory power matrix is gauge-origin-invariant as long as the electric dipole transition matrix elements are obtained using the velocity (rather than position) operator. On the other hand, the component along the optic axis is invariant in general for uniaxial and biaxial crystals. Under the same conditions, these properties also do not depend on the so-called missing integers that occur in the treatment of the electric dipole moment of quasi-one-dimensional periodic systems or the analogue of missing integers for the case of higher dimensionality. Tests on a model H2O2 polymer confirm the formalism and, as desired, show that the calculated properties are independent of the size and definition of the unit cell. In addition, an empirical relation to a finite oligomer gauge-including atomic orbital (GIAO) calculation is found. Applications, with comparison to experiment, are carried for α-quartz, tartaric acid crystal, and carbon nanotubes. Future developments of this initial approach to chiroptical properties in the solid state are noted.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

First-Principles Calculation of the Optical Rotatory Power of Periodic Systems: Application on α-Quartz, Tartaric Acid Crystal, and Chiral (n,m)-Carbon Nanotubes

Rérat

2021

J. Chem. Theory Comput.

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“…Far off the resonance frequency of the oscillator, where no absorption is observed, the refractive index is dominated by the electronic polarizability α of molecules in the VIS/NIR-region of the spectrum. [71] Thus the birefringence Δn defined as…”

Section: Optical Anisotropy -Ellipsometrymentioning

confidence: 99%

“…In the typically applied Born-Oppenheimer approximation, the polarizability can be split into the electronic contribution, that governs the UV-vis region and nuclear relaxation for the IR or Raman part of the spectrum. [31,71] Both contributions can be calculated separately. Also, the polarizability is closely related to the structure of the molecule.…”

Section: Single Molecule Calculationsmentioning

confidence: 99%

The Many Facets of Molecular Orientation in Organic Optoelectronics

Hofmann

Schmid

Brütting

2021

Advanced Optical Materials

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exploitation in devices has only recently become a major topic in organic optoelectronics. [10][11][12] Moreover, as different (and sometimes competing) effects can even occur in one and the same type of device application, their underlying principles and design rules need to be well understood.In this article, we review the current understanding of this emerging field of organic optoelectronics and discuss recent developments as well as some open issues.

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“…For low-polar media, the dielectric tensor is related to the electric dipole-electric dipole polarizability tensor α (all in a.u.) as 25,60…”

Section: B Periodic Electric Quadrupolementioning

confidence: 99%

Derivation and Implementation of the Optical Rotation Tensor for Chiral Crystals

Balduf

Caricato

2022

Preprint

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This work reports the derivation and implementation of the electric dipole-magnetic dipole and electric dipole- electric quadrupole polarizability tensors at density functional theory level with periodic boundary conditions (DFT-PBC). These tensors are combined to evaluate the Buckingham/Dunn tensor that describes the optical rotation (OR) in oriented chiral systems. We detail several aspects of the derivation of the equations, and present test calculations that verify the correctness of the tensors formulation and of their implementation. The results show that the full OR tensor is completely origin invariant as for molecules and that PBC calculations match molecular cluster calculations on 1D chains. A preliminary investigation on the choice of density functional, basis set, and gauge indicates a similar dependence as for molecules: the functional is the primary factor that determines the OR magnitude, followed by the basis set and to a much smaller extent the choice of gauge. However, diffuse functions may be problematic for PBC calculations even if they are necessary for the molecular case. A comparison with experimental data of OR for the tartaric acid crystal shows reasonable agreement given the level of theory employed. The development presented in this work offers the opportunity to simulate the OR of chiral crystalline materials with general purpose DFT-PBC methods, which in turn may help to understand the role of intermolecular interactions on this sensitive electronic property.

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From anisotropy of dielectric tensors to birefringence: a quantum mechanics approach

Cited by 4 publications

References 53 publications

First-Principles Calculation of the Optical Rotatory Power of Periodic Systems: Application on α-Quartz, Tartaric Acid Crystal, and Chiral (n,m)-Carbon Nanotubes

First-Principles Calculation of the Optical Rotatory Power of Periodic Systems: Application on α-Quartz, Tartaric Acid Crystal, and Chiral (n,m)-Carbon Nanotubes

The Many Facets of Molecular Orientation in Organic Optoelectronics

Derivation and Implementation of the Optical Rotation Tensor for Chiral Crystals

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