Dynamical Tensors Research Articles

A database of computed Raman spectra of inorganic compounds with accurate hybrid functionals

Raman spectroscopy is widely applied in identifying local structures in materials, but the interpretation of Raman spectra is non-trivial. An accurate computational database of reference spectra calculated with a consistent level of theory can significantly aid in interpreting measured Raman spectra. Here, we present a database of Raman spectra of inorganic compounds calculated with accurate hybrid functionals in density functional theory. Raman spectra were obtained by calculating dynamical matrices and polarizability tensors for structures from the Inorganic Crystal Structure Database. The calculated Raman spectra and other phonon properties (e.g., infrared spectra) are stored in a MongoDB database publicly shared through a web application. We assess the accuracy of our Raman calculations by statistically comparing ~80 calculated spectra with an existing experimental Raman database. To date, the database contains 161 compounds and is continuously growing as we add more materials computed with our automated workflow.

Bimetric-affine quadratic gravity

Bimetric gravity is a theory of gravity that posits the existence of two interacting and dynamical metric tensors. The spectrum of bimetric gravity consists of a massless and a massive spin-2 particle. The form of the interactions between the two metrics ${g}_{\ensuremath{\mu}\ensuremath{\nu}}$ and ${f}_{\ensuremath{\mu}\ensuremath{\nu}}$ is constrained by requiring absence of the so-called Boulware-Deser ghost. In this work we extend the original bimetric theory to its bimetric-affine counterpart, in which the two connections, associated with the Ricci scalars, are treated as independent variables. We examine in detail the case of an additional quadratic in the Ricci scalar curvature term ${\mathcal{R}}^{2}(g,\mathrm{\ensuremath{\Gamma}})$ and we find that this theory is free of ghosts for a wide range of the interaction parameters, not excluding the possibility of a dark matter interpretation of the massive spin-2 particle.

Constraint algebra of general relativity from a formal continuum limit of canonical tensor model

Canonical tensor model (CTM for short below) is a rank-three tensor model formulated as a totally constrained system in the canonical formalism. In the classical case, the constraints form a first-class constraint Poisson algebra with structures similar to that of the ADM formalism of general relativity, qualifying CTM as a possible discrete formalism for quantum gravity. In this paper, we show that, in a formal continuum limit, the constraint Poisson algebra of CTM with no cosmological constant exactly reproduces that of the ADM formalism. To this end, we obtain the expression of the metric tensor field in general relativity in terms of one of the dynamical rank-three tensors in CTM, and determine the correspondence between the constraints of CTM and those of the ADM formalism. On the other hand, the cosmological constant term of CTM seems to induce non-local dynamics, and is inconsistent with an assumption about locality of the continuum limit.

First principles calculations of magnetism, dielectric properties and spin–phonon coupling in double perovskite Bi2CoMnO6

First principles electronic structure calculations have been performed for the double perovskite Bi2CoMnO6 in its non-centrosymmetric polar state using the generalized gradient approximation plus the Hubbard U approach. We find that the ferromagnetic state is more favored compared to the ferrimagnetic state with both Co and Mn in high spin states. The calculated dynamical charge tensors are anisotropic reflecting a low-symmetry structure of the compound. The magnetic structure dependent phonon frequencies indicate the presence of a weak spin–phonon coupling. Using the Berry phase method, we obtain a spontaneous ferroelectric polarization of 5.88 μC cm−2, which is close to the experimental value observed for a similar compound, Bi2NiMnO6.

Plasmonic Enhancement of Raman Optical Activity in Molecules near Metal Nanoshells

Surface-enhanced Raman optical activity (SEROA) is investigated theoretically for molecules near a metal nanoshell. For this purpose, induced molecular electric dipole, magnetic dipole, and electric quadrupole moments must all be included. The incident field and the induced multipole fields all scatter from the nanoshell, and the scattered waves can be calculated via extended Mie theory. It is straightforward in this framework to calculate the incident frequency dependence of SEROA intensities, i.e., SEROA excitation profiles. The differential Raman scattering is examined in detail for a simple chiroptical model that provides analytical forms for the relevant dynamical molecular response tensors. This allows a detailed investigation into circumstances that simultaneously provide strong enhancement of differential intensities and remain selective for molecules with chirality.

Vibrational spectra of vitreous germania from first-principles

We report on a first-principles investigation of the structural and vibrational properties of vitreous germania $(v\text{\ensuremath{-}}\mathrm{Ge}{\mathrm{O}}_{2})$. Our work focuses on a periodic model structure of 168 atoms, but three smaller models are also studied for comparison. We first carry out a detailed structural analysis both in real and reciprocal spaces. Our study comprises the partial pair correlation functions, the angular distributions, the total neutron correlation function, the neutron and $x$-ray total structure factors, and the Faber-Ziman and Bhatia-Thornthon partial structure factors. We find overall good agreement with available experimental data. We then obtain the vibrational frequencies and eigenmodes. We analyze the vibrational density of states in terms of Ge and O motions, and further in terms of rocking, bending, and stretching contributions. The inelastic neutron spectrum is found to differ only marginally from the vibrational density of states. Using a methodology based on the application of finite electric fields, we derive dynamical Born charge tensors and Raman coupling tensors. For the infrared spectra, we calculate the real and imaginary parts of the dielectric function, including the high-frequency and static dielectric constants. The Raman spectra are shown to be sensitive to the medium-range structure and support an average Ge-O-Ge angle of 135\ifmmode^\circ\else\textdegree\fi{}. We identify the shoulder ${X}_{2}$ as a signature of breathing O vibrations in three-membered rings. Four-membered rings are found to contribute to the main Raman peak. We advance an interpretation for the shoulder ${X}_{1}$ in terms of delocalized bond-bending modes. We derive bond polarizability parameters from the calculated Raman coupling tensors and demonstrate their level of reliability in reproducing the spectra. The calculated vibrational spectra all show good agreement with the respective experimental spectra.

Dynamical charge tensors and infrared spectra of the crystalline α-quaterthiophene polymorph phases from first-principles calculations

Infrared intramolecular vibrations and lattice modes for both the crystalline α-quaterthiophene (4T) polymorph phases are investigated by using the modern theory of polarization combined with density functional theory. For the first time, Born effective charge tensors and far- and mid-infrared responses for both the polymorph phases of 4T have been calculated. We have also proposed an assignment of the main spectral infrared signatures of the 4T polymorph phases. These assignments could be of particular interest in the far-infrared domain for the understanding of the electronic transport of these materials.

Surface charges and dynamical Killing tensors for higher spin gauge fields in constant curvature spaces

In the context of massless higher spin gauge fields in constant curvature spaces, we compute the surface charges which generalize the electric charge for spin one, the color charges in Yang-Mills theories and the energy-momentum and angular momentum for asymptotically flat gravitational fields. We show that there is a one-to-one map from surface charges onto divergence free Killing tensors. These Killing tensors are computed by relating them to a cohomology group of the first quantized BRST model underlying the Fronsdal action.

Born charge differences ofTiO2polytypes: Multipole expansion of Wannier charge densities

The bonding Wannier functions (WF's) associated with the O 2s/2p valence states of TiO 2 have been calculated for both the futile and the anatase forms. They are similar in the two polymorphs, and correspond to three distorted O sp 2 -like hybrids in the plane of the Ti 3 coordination triangle, and one p-like orbital perpendicular to this plane. For both structures, the WF's show that the OTi 3 triangular complex is the relevant structural unit for understanding TiO 2 electronic properties. WF's differences between the two phases are quantitatively measured with a multipole expansion of the static charge density of the fourfold WF complex. These differences reflect the opposite distortion from equilateral shape that the isosceles Ti 3 triangle has in the two structures, and correlate quantitatively with the opposite anisotropy of the dynamical Bom charge tensors calculated for the two polytypes.

Raman scattering intensities in α-quartz: A first-principles investigation

Using a first-principles density functional approach, we calculate the first-order Raman intensities of alpha -quartz. The dynamical charge tensors, vibrational frequencies and eigenmodes, and polarizability tensors are obtained within a perturbational approach. We calculate Raman intensities by evaluating the variation of the polarizability tensors for finite displacements of the atoms. Calculated intensities agree well with experimental data, showing an average error of 13% for relative intensities. Using our first-principles results as reference, we critically examine simple models for the Raman activity. We first consider a bond polarizability model, for which the parameters are derived from our first-principles results for alpha -quartz. This model reproduces the first-principles intensities with an average error of 15%. In the attempt of reducing this error, we then introduce a model in which the symmetry of the first neighbor shell is accounted for in the most general way. For alpha -quartz, this model extends the bond polarizability model, which is recovered as a special case. The model, which fully accounts for the local symmetry, describes the first-principles results within an average error of 12%, marginally improving upon the bond polarizability model (15%). However, when these models with parameters derived for alpha -quartz are applied to a cristobalite polymorph, only the bond polarizability model shows good transferability properties. These results support the use of the bond polarizability model as a simple scheme for calculating Raman intensities in tetrahedrally bonded SiO2 systems.

Dynamical-charge neutrality at a crystal surface

For both molecules and periodic solids, ionic dynamical charge tensors---measuring the coupling of electric fields to ionic displacements---are known to obey a dynamical neutrality condition. This condition forces their sum to vanish over the whole finite system, or over the crystal cell, respectively. We extend this sum rule to the nontrivial case of the surface of a semi-infinite solid and show that, in the case of a polar surface of an insulator, the surface ions cannot have the same dynamical charges as in the bulk. The sum rule is demonstrated through calculations for a couple of SiC surfaces.

Dynamical Charge Tensors and Infrared Spectrum of AmorphousSiO2

Using a model structure consisting of a network of corner sharing tetrahedra, we calculate the infrared spectrum of amorphous SiO2 within a first-principles approach and find good agreement with experiment both for the positions and the intensities of the main peaks. In addition to the vibrational properties, this required the dynamical charge tensors, which were obtained applying the recent quantum polarization theory. The relative intensities in the spectrum depend sensitively on the charge tensors and their anisotropic components are crucial to obtain good agreement with experiment. We find that the Born charges can be correlated to the local structural properties.

Diffraction models, dynamical structure tensors and electron-phonon interaction

A coherent exposition of the theory of scattering from a dynamic lattice, which applies to the scattering of Bloch-wave electrons as well as to the scattering of plane waves, is presented. This is achieved by developing a generalised diffraction model, along the lines conceived by Van Hove, appropriate for the scattering of Bloch waves. The resulting diffraction model provides a basis for treating processes controlled by electron-phonon interaction in general and subsumes the standard diffraction model results. The diffraction model origins of the standard approximate expressions used to describe electron-phonon interaction-controlled processes are also revealed.

The quantum theory of lattice dynamics. III

The electronic contribution to the dynamical tensors is examined in more detail and the following results are obtained. First the electronic contribution is shown to be translationally invariant, secondly the assumption that this term can be approximately represented by a two-body interaction is shown to be equivalent to a rigid ion model, and finally this approximation is shown to become exact in the limit q = 0.

The quantum theory of lattice dynamics. I

The dynamics of a crystal is examined on the basis of the adiabatic approximation. In part I we examine the form of the dynamical and anharmonic tensors on the assumption that the effective nuclear potential energy can be represented as a simple two-body interaction. In part II we derive expressions for the electronic contributions on the basis of the Hartree-Fock approximation and show that these electron-nuclear interactions are more complex than a simple two-body interaction. In part III we examine these interactions in more detail and find that the two-body approximation is equivalent to a rigid-ion model and that this approximation becomes exact in the limit q = 0.

The quantum theory of lattice dynamics. Il

Expressions are derived for the expansion of the total energy of the electrons in their ground state in a crystal in powers of displacements of the nuclei from their equilibrium configuration. The expansion is taken up to third order on the basis of the coupled Hartree-Fock equations and thus one obtains expressions for the electronic contributions to the dynamical and anharmonic tensors.