Equivalent Orbitals Research Articles

On Averaging Eccentric Orbits: Implications for the Long-term Thermal Evolution of Comets

One of the common approximations in long-term evolution studies of small bodies is the use of circular orbits averaging the actual eccentric ones, facilitating the coupling of processes with very different timescales, such as the orbital changes and the thermal processing. Here we test a number of averaging schemes for elliptic orbits in the context of the long-term evolution of comets, aiming to identify the one that best reproduces the elliptic orbits’ heating patterns and the surface and subsurface temperature distributions. We use a simplified thermal evolution model applied on simulated comets both on elliptic and on their equivalent averaged circular orbits, in a range of orbital parameter space relevant to the inner solar system. We find that time-averaging schemes are more adequate than spatial-averaging ones. Circular orbits created by means of a time average of the equilibrium temperature approximate efficiently the subsurface temperature distributions of elliptic orbits in a large area of the orbital parameter space, rendering them a powerful tool for averaging elliptic orbits.

Effects of electronegativities and charge delocalization on Q2 Raman shifts of alkaline- and alkaline earth-bearing glasses and metasilicate crystals

Abstract Raman shifts of the symmetric stretch of silicate Q2 species vary over a range of ~90 cm−1 in crystals and glasses containing alkali and alkaline earth oxides. The shifts display a striking, sympathetic relationship with the electronegativity of the alkali and alkaline earth metals (M), with the highest frequency observed for Mg-silicate glasses and crystals and the lowest frequency for Cs-bearing glasses. Frequencies are determined primarily by the electron density on constituent Si and O atoms of the Q2 tetrahedra, as measured by Si 2p and O 1s X-ray photoelectron spectra (XPS). The electron density is, in turn, determined by the extent to which electronic charge is transferred from the modifier metal “M” to the NBO of the Q2 tetrahedron. The charge transferred to NBO is redistributed (delocalized) over all atoms of the tetrahedron by the four equivalent Si sp3 orbitals. Although negative charge accumulates on all atoms of the tetrahedron, it accumulates preferentially on Si. Coulombic interactions among Si and all O atoms are thus weakened, resulting in decreased force constants and lowered symmetric stretch frequencies of Q2 species. Density functional theoretical (DFT) calculations on six staggered and eclipsed M6Si2O7 (M = Li, Na, K) molecules corroborate the findings. Charge is transferred from the metal atoms to NBO and delocalized over tetrahedra in accordance with Li, Na, and K electronegativities. Calculated Si-O force constants and Raman shifts decrease with decreasing electronegativity of the cation but surprisingly, calculated Si-NBO bond lengths are largely unaffected, with all being similar at 1.665 ± 0.003 Å.

Boson Subsidiary Solver (BoSS) v1.1

How best to model systems of interacting electrons in an accurate and computationally efficient manner is an outstanding problem in theoretical and computational materials science. For materials where strong electronic interactions are primarily of a localized character and act within a subspace of localized quantum states on separate atomic sites (e.g., in transition metal and rare-earth compounds), their electronic behaviors are typically described by the Hubbard model and its extensions. In this work, we describe BoSS (Boson Subsidiary Solver), a software implementation of the subsidiary-boson (also known as slave-boson or auxiliary-boson) method appropriate for describing a variety of extended Hubbard models, namely p−d models that include both the interacting atomic sites (“d” states) and non-interacting or ligand sites (“p” states). We provide a theoretical background, a description of the equations solved by BoSS, an overview of the algorithms used, the key input/output and control variables of the software program, and tutorial examples of its use featuring band renormalization in SrVO3, Ni 3d multiplet structure in LaNiO3, and the relation between the formation of magnetic moments and insulating behavior in SmNiO3. BoSS interfaces directly with popular electronic structure codes: it can read the output of the Wannier90 software package [1,2] which postprocesses results from workhorse electronic structure software such as Quantum Espresso [3] or VASP [4]. Program summaryProgram title: Boson Subsidiary Solver (BoSS)CPC Library link to program files:https://doi.org/10.17632/3bwx6prn2w.1Developer's repository link:bitbucket.org/yalebosscode/bossCode Ocean capsule:https://codeocean.com/capsule/9605047Licensing provisions: Creative Commons by 4.0Programming language: MATLAB [5]Nature of problem: The BoSS approach, a type of subsidiary-boson method (also called slave-boson or auxiliary-boson method), provides approximate solutions to interacting electron problems described by Hubbard models in a computationally efficient manner. Hubbard models are widely used to describe materials systems with strongly localized electron-electron interactions. The interacting fermion problem is mapped onto two separate, but easier, coupled quantum problems: non-interacting fermions moving on a lattice (spinons) via tunneling between nearby atomic orbitals, and interacting subsidiary bosons that live on individual atomic sites. A self-consistent description of the two degrees of freedom requires matching of mean particle numbers (spinons and bosons) on each site as well as the renormalization of tunneling events for one set of particles due to the fluctuations of the other set of particles. The method can be used to describe the interacting electronic ground state of a particular electronic configuration, or more generally it can find the minimum energy electronic configuration by searching over various symmetry broken phases (e.g., magnetic configurations, configurations with unequal occupation of nominally equivalent atomic orbitals, etc.)Solution method: The spinon and subsidiary-boson problems are each represented as Hermitian eigenvalue problems where the lowest energy (eigenvalue) state is sought. The present implementation uses dense matrix digaonalization for the spinon problem and can use either dense or sparse matrix diagonalization for the boson problem. Particle number matching between the two descriptions is achieved by adjustment of Lagrange multipliers which represent potential energies for the bosons: their appropriate values are found by applying Newton's method to match spinon and boson occupancies. Self-consistency is achieved by simple fixed point iteration (solving spinon, then subsidiary, then spinon, etc.) Minimization of the energy uses gradient descent with adjustable step size.Additional comments including restrictions and unusual features: Most users will prepare the input data for BoSS by running band structure calculations on a material, e.g., density functional theory (DFT) using available software packages such as Quantum Espresso [3] or VASP [4]. Post processing of these calculations to create a spatially localized basis set provides the input to BoSS: most users will create the localized description by using software that transforms the electronic description into a Wannier function basis such as Wannier90 [1] which BoSS interfaces with by default. However, one can bypass this approach and create BoSS input files manually to describe specific localized electron models. Referenceshttp://bitbucket.org/yalebosscode/bosshttp://www.wannier.org/https://www.quantum-espresso.org/https://www.mathworks.com/products/matlab.htmlhttps://www.vasp.at/

Satellite equivalence orbits

Satellite equivalence orbits are orbits coupling two or more relative satellite motions. Equivalence orbits between tropical and meridional motion are direct orbits. They have exactly the period 2 sidereal days. As consequence of Kepler's third law the corresponding Keplerian mean semimajor axis is 66931.447 km and gives an impression of this special class of equivalence orbits. In this case the period is identical for all matching orbits and will be preserved by adjusting the orbital elements. Preset 5 orbital elements the sixth element has to be adjusted, e.g. the semimajor axis. The sum of right ascension and geographic longitude shows no secular variations, but only periodic variations due to periodic perturbations, the equation of the center and the reduction on to the equator. The equivalence between tropical and meridional motion offers an independent check of the consistency of the physical parameters. When computed with the Brouwer analytical orbit model, the groundtrack of such an equivalence orbit shows no or only small variations over long time intervals. Based on the theory developed, the paper extends the term equivalent orbits with respect to Hansen motion, anomalistic motion, draconitic motion, Sun-synodic motion, and Moon-synodic motion.

Resonant three-dimensional nonlinear sloshing in a square base basin. Part 5. Three-dimensional non-parametric tank forcing

Assuming an inviscid incompressible liquid (with irrotational flows) partly filling a square base tank, which performs a small-amplitude sway/surge/pitch/roll periodic motion whose frequency is close to the lowest natural sloshing frequency, a nine-dimensional Narimanov–Moiseev-type (modal) system of ordinary differential equations with respect to the hydrodynamic generalised coordinates was derived in the Part 1 (Faltinsen et al., J. Fluid Mech., vol. 487, 2003, pp. 1–42). Constructing and analysing asymptotic periodic solutions of the system made it possible to classify steady-state resonant sloshing and its stability for the harmonic reciprocating (longitudinal, diagonal and oblique) forcing. The results were supported by experimental observations and measurements. The present paper finalises the case studies by considering the three-dimensional non-parametric (combined sway, pitch, surge, roll and yaw, but no heave) cyclic tank motions. It becomes possible after establishing an asymptotic equivalence of the associated periodic solutions of the modal system to those for a suitable horizontal translatory elliptic forcing so that, as a consequence, resonant steady-state waves and their stability can be considered versus angular position, semi-axis ratio and direction (counter- or clockwise) of the equivalent orbits. The circular orbit causes stable swirling waves (co-directed with the orbit) but may also excite stable nearly standing waves. The orbit direction does not affect the response curves for wall-symmetric (canonic) and diagonal orbit positions. This is not true for the oblique-type elliptic forcing. When the semi-axis ratio changes from 0 to 1, the response curves exhibit astonishing metamorphoses significantly influencing the frequency ranges of stable nearly standing/swirling waves and ‘irregular’ sloshing. For the experimental input data by Ikeda et al. (J. Fluid Mech., vol. 700, 2012, pp. 304–328), the counter-directed swirling disappears as but the frequency range of irregular waves vanishes for .

Dynamics of Waves in the Cubically Nonlinear Model for Mutually Penetrating Continua

In this report we study the mathematical model for mutually penetrating continua. This model consists of the wave equation describing the carrying medium and the equation for oscillators forming the oscillating inclusion. Prescribing the constitutive equation of the carrying medium and kinetics of oscillator’s dynamics for model in question, the cubic nonlinearity is accounted. We are interested in the structure of wave solutions obeying the dynamical system of Hamiltonian type. This allows us to determine the peculiarities of the phase space of dynamical system, namely, the relation describing the homoclinic trajectories, the division of phase plane into the parts with equivalent orbits’ behavior, the conditions of bifurcations. To simulate the wave dynamics, we construct the three level finite-difference numerical scheme and study the evolution of solitary waves, their pair interactions and stability. Propagation of periodic waves is modeled as well.

Au102+ and Au6X42+ clusters: Superatomic molecules bearing an SP3-hybrid Au6core

The octahedral Au6 core is explored for the formation of novel SP3-hybrid superatomic molecules by considering Au102+ and Au6 X42+ clusters (X= F, Cl, Br, I). The bonding between the four capping atoms and the Au6 core requires a combination of 1S and 1P shells of the core leading to a set of four equivalent hybrid orbitals. Thus, combining the superatom concept with both the Lewis structure model and VSEPR theory contributes to the rationalization of structure and bonding in metal clusters. For example, our results consider the Au6 X42+ clusters as analogues of the simplest perhalogenated hydrocarbon, CX4.

Two methods for restricted configuration spaces within the multiconfiguration time-dependent Hartree-Fock method

The multiconfiguration time-dependent Hartree-Fock (MCTDHF) method has shown promise in calculating electronic dynamics in molecules driven by strong and high-energy lasers. It must incorporate restricted configuration spaces (meaning that a particular combination of Slater determinants is used, instead of full configuration interaction) to be applied to big systems. Two different Ans\atze are used to determine the essential term in the equations. The first Ansatz is the Lagrangian variational principle. The explicit, complete MCTDHF equations of motion, satisfying that principle, for arbitrary configuration spaces, are given. The property that a restricted configuration list must satisfy in order for the Lagrangian and McLachlan variational principles to give different results is identified. The second Ansatz keeps the density matrix block diagonal among equivalent orbitals, in a generalization of the method of Worth [J. Chem. Phys. 112, 8322 (2000)]. The methods perform well in calculating the dynamics of Be and ${\mathrm{BC}}^{2+}$ subject to ultrafast, ultrastrong lasers in severely truncated Hilbert spaces, although they exhibit differing degrees of numerical stability as implemented.

Hodographs of the Gravitational Two-Body System and Discrepancies between Newtonian Laws of Equivalent Kepler Orbits and General Relativity

We show first that an orbit, which is naturally characterized by its eccentricity and semi-latus rectum, can equally be characterized by other sets of parameters, and proceed to determine mass-independent characterizations. The latter is employed to obtain the laws of equivalent orbits, which by definition have the same eccentricity and orbit’s parameter [1]. These laws relate the values of the same physical observables on two equivalent orbits to the corresponding total mass; they include the laws of velocity, angular velocity, radial velocity, areal velocity, acceleration, period, energy and angular momentum. Regardless of the share of the two bodies of a fixed total mass, the same relative orbit occurs for the same initial conditions. Moreover, the same orbit can be traced by different total masses but with different relative velocities. The concept of a gravitational field generated by a set of masses is shown to be meaningful only when the center of mass is not changed by the test mass. The associated concept of the “nothing”, which is an infinitesimal mass that allows for the property just mentioned to be fulfilled, is introduced and its orbits are determined. The perturbation of the nothing orbits due to its replacement by a finite mass is determined. It is proved that such a replacement can have a qualitative effect resulting in a “phase transition” of an orbit from unbound to bound, and that the nothing’s circular orbits cannot be occupied by any material body. The Galileo law of free fall, on which the equivalence principle hinges and which is exact only for “nothing-like” falling objects, is revised to determine the duration of free fall of a body of an arbitrary mass. The wholeness of Newton’s laws and the associated concept of force as an interaction are highlighted, and some contradictions between the Newtonian laws of equivalent Kepler’s orbits and the general relativistic predictions are discussed. It is demonstrated that Newton’s law of gravitation is not an approximation of Einstein field Equations even in the case of a static weak field. However, both theories have a common limit corresponding to the case in which the alien concept of a field can be incorporated in the Newtonian theory. We also show that the relative velocity’s hodograph [2-4], the alternative Laplace-Runge-Lenz (LRL) vector derived by Hamilton [4-6], as well as an infinite set of LRL vectors, result all from one vector. The hodograph is a proper circular arc for hyperbolic motion, a circle less a point for parabolic motion, and a full circle for bound motion.

On the Gravitational Two-Body System and an Infinite Set of Laplace-Runge-Lenz Vectors

The current approach of a system of two bodies that interact through a gravitational force goes beyond the familiar expositions [1-3] and derives some interesting features and laws that are overlooked. A new expression for the angular momentum of a system in terms of the angular momenta of its parts is deduced. It is shown that the characteristics of the relative motion depend on the system’s total mass, whereas the characteristics of the individual motions depend on the masses of the two bodies. The reduced energy and angular momentum densities are constants of motion that do not depend on the distribution of the total mass between the two bodies; whereas the energy may vary in absolute value from an infinitesimal to a maximum value which occurs when the two bodies are of equal masses. In correspondence with infinite possible ways to describe the absolute rotational positioning of a two body system, an infinite set of Laplace-Runge-Lenz vectors (LRL) are constructed, all fixing a unique orientation of the orbit relative to the fixed stars. The common expression of LRV vector is an approximation of the actual one. The conditions for nested and intersecting individual orbits of the two bodies are specified. As far as we know, and apart from the law of periods, the laws of equivalent orbits concerning their associated periods, areal velocities, angular velocities, velocities, energies, as well as, the law of total angular momentum, were never considered before.

Embedding and atomic orbitals hybridization

AbstractIn calculation, the electronic structure of crystals, especially those containing point defects, the embedding approach is proved to be useful and convenient. In this approach, a finite part of the crystal, referred to as cluster, is considered instead of infinite crystal and the influence of the rest of the crystal is simulated by the embedding potential. The key problems of this approach are the cluster selection and the embedding potential generation. To select a cluster, the Wigner‐Seitz unit cell is used in the present approach and every border atom, situated at the unit cell face, edge, or vertex is symmetrically “divided” among adjacent unit cells sharing this atom. The atomic hybrid orbitals are used for the border atoms partition between neighboring clusters. It is shown that contrary to the conventional hybridization scheme, the nonorthogonal and even linearly dependent atomic hybrid orbitals can be used to construct the border atom density matrix. This density matrix can be made to satisfy the proper point symmetry and to match the number of equivalent hybrid orbitals and the number of nearest neighbors. Two different types (one‐center and multicenters) of the embedding potential corresponding to the border atom are considered in the article. As a particular example of the border atom the oxygen ion in ZrO2, MgO, and TiO2 rutile crystals is considered. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011

An experimental and computational study of the valence photoelectron spectra of halogenated pyrimidines

The electronic structures of pyrimidine and a selection of its halogen-substituted derivatives have been investigated using ultraviolet photoelectron spectroscopy and ab initio quantum chemical methods. Assignments are proposed for all of the features in the PES spectra by comparison with the vertical ionization energies of the molecular orbitals calculated using the partial third-order quasiparticle approximation as applied to electron propagator theory and a corrected density functional method based on the B3LYP functional. The shifts of the outermost five molecular orbitals of the pyrimidine ring structure in the halogen-substituted derivatives with respect to the binding energies of the equivalent orbitals in the parent pyrimidine molecule are discussed as a function of the identity and ring position of the halogen atom.

Two Equivalent eg Orbitals for the Discussion of Bonding in Octahedral Complexes

Research: Science and Education Transition-metal complexes form a crucial part of lecture courses on coordination, organometallic, and bioinorganic chemistry. The bonding situation in these compounds is often described by either crystal or ligand field theory (1). Since transition metals generally have partly filled or empty d orbit als, these orbitals are usually assumed to be involved in the formation of bonds between the metal atom and the ligands; in almost every textbook, the omnipresent set of the real-valued d orbitals, dxy, dyz, dxz, dx 2 −y 2 , and dz2, is used, which is obtained by one particular linear combination of the complex canonical solutions of the Schrodinger equation for the H atom (2). From this exclusive use, students might think that this is the only existing set. Nevertheless, this is clearly not the case, since every appropriate linear combination of the canonical orbitals (or of the standard dxy, dyz, dxz, dx 2− y 2 , and dz2 orbitals) also represents a valid set and could be used instead (3). For instance, it has been shown by Powell (4) and others (5–9) that a set of five equivalent real-valued d orbitals can be constructed that have the same shape and only differ in their orientation along the slant edges of a pentagonal pyramid. For didactic reasons, the presentation of these equivalent orbitals during a lecture could help students to accept the degeneracy of the standard textbook d orbitals despite their different appearance. In a similar fashion, bonding considerations for octahedral complexes afford two sets of degenerate t2g (dxy, dyz, dxz) and eg orbitals (dx 2 − y 2 , and dz2), whereby the latter often confuse students because of their totally different shape. The reader should be reminded that the interpretation of one-electron wavefunctions (orbitals) in the context of chemical bonding is a frequently discussed topic in this Journal (10–14). It is the aim of this article to present a new set of d orbitals featuring equivalent eg orbitals, which might be intuitively more appropriate for the discussion of the bonding situation in transition-metal complexes, for example, by means of ligand field theory. The Canonical Set

Equivalent orbitals for multiconfigurational spin‐tensor electron propagator method (MCSTEP): The vertical ionization potentials of B, NO, CF, and OF

AbstractThe multiconfigurational spin tensor electron propagator method (MCSTEP) was developed as an implementation of electron propagator/single particle Green's function methods for ionization potentials (IPs) and electron affinities (EAs). MCSTEP was specifically designed for open shell and highly correlated (nondynamically correlated) initial states. For computational efficiency the initial state used in MCSTEP is typically a small complete active space (CAS) multiconfigurational self‐consistent field (MCSCF) state. If in a molecule there are some degenerate orbitals which are not fully or half occupied, usual MCSCF calculations will make these orbitals inequivalent, i.e., the occupied ones will be different from the nonoccupied ones, so that the degeneracy is broken. In this article, we use a state averaged MCSCF method to get equivalent orbitals for the initial state and import the integrals into the subsequent MCSTEP calculations. This gives, in general, more reliable MCSTEP vertical IPs. © 2008 Wiley Periodicals, Inc., 2008

Microscopic origin of diagonal stripe phases in doped nickelates

We investigate the electron density distribution and the stability of stripe phases in a realistic two-band model with hopping elements between ${e}_{g}$ orbitals at Ni sites on the square lattice, and compare these results with those obtained for the doubly degenerate Hubbard model with two equivalent orbitals and diagonal hopping. For both models we determine the stability regions of filled and half-filled stripe phases for increasing hole doping $x=2\ensuremath{-}n$ in the range of $x<0.4$, using the Hartree-Fock approximation for large clusters. In the parameter range relevant to the nickelates, we obtain the most stable diagonal stripe structures with filling of nearly one hole per atom, as observed experimentally. In contrast, for the doubly degenerate Hubbard model the most stable stripes are somewhat reminiscent of the cuprates, with half-filled orbitals at the domain wall sites. This difference elucidates the crucial role of the off-diagonal ${e}_{g}$ hopping terms for the stripe formation in ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}\mathrm{Ni}{\mathrm{O}}_{4}$. The influence of the crystal field is discussed as well.

On the minimum flexing of LISA's arms

The joint ESA–NASA mission LISA relies crucially on the stability of that three spacecraft constellation. All three spacecraft are on heliocentric and weakly eccentric orbits forming a nearly stable triangle. It has been shown that for certain spacecraft orbits, the arms keep constant distances to the first order in eccenticities. However, exact orbitography exhibits the so-called ‘breathing modes’ resulting in slow variations of the armlengths on the timescale of one year. In this paper, we analyse the breathing modes (flexing of the arms) with the help of the geodesic deviation equation up to the octupole order, which is shown to be equivalent to higher order Clohessy–Wiltshire equations. We analytically show that the flexing of the arms can be reduced to a peak-to-peak variation of about 50 000 km, and the corresponding peak-to-peak variation in the Doppler laser frequency shift to about 8 m s−1. This is achieved by slightly changing the well-known tilt of 60°. We further show that it is the minimum within the assumption of equivalent spacecraft orbits, where the orbit of each spacecraft is rotated by 120° from the preceding one.

Mean-field phase diagram of interacting [formula omitted] electrons

We investigate the magnetic phase diagram of the two-dimensional model for e g electrons which describes layered nickelates. One finds a generic tendency towards magnetic order accompanied by orbital polarization. For two equivalent orbitals with diagonal hopping such orbitally polarized phases are induced by finite crystal field.

Molecular orbitals of methane: symmetry or hybridization?

Orbital electron density distributions and momentum distributions of both core and valence space of methane are studied quantum mechanically, using RHF/TZVP and B3LYP/TZVP models, respectively. The three molecular orbitals (MOs) of methane in the ground electronic state (X1A1), namely, the core MO, 1a1 and the valence MOs, i.e. 2a1 and three-fold energy degenerate MOs 1t2, are studied in both coordinate space and momentum space. They are compared with the corresponding atomic orbitals (AOs) of a ‘free’ carbon atom in its ground electronic state (3P) using configuration averaged unrestricted HF (UHF) method. The electronic structure of methane inherits that of a free single carbon atom, indicating that the symmetry of methane contributes to the equivalent orbitals and their behavior. There are no any quantitative evidences of hybridization for the MOs of methane in either coordinate space or momentum space. The core MO (1a1) of methane in momentum space is found to be nearly indistinguishable to the core AO (1s) of a free carbon atom using the same model. The net chemical bonding results as displayed in the valence MO momentum distributions have clearly retained the orbital wave function anisotropy as s-like and p-like in both methane and the free carbon atom.

Molecular orbitals of methane: symmetry or hybridization?

Orbital electron density distributions and momentum distributions of both core and valence space of methane are studied quantum mechanically, using RHF/TZVP and B3LYP/TZVP models, respectively. The three molecular orbitals (MOs) of methane in the ground electronic state (X 1A 1), namely, the core MO, 1 a 1 and the valence MOs, i.e. 2 a 1 and three-fold energy degenerate MOs 1 t 2, are studied in both coordinate space and momentum space. They are compared with the corresponding atomic orbitals (AOs) of a ‘free’ carbon atom in its ground electronic state ( 3P) using configuration averaged unrestricted HF (UHF) method. The electronic structure of methane inherits that of a free single carbon atom, indicating that the symmetry of methane contributes to the equivalent orbitals and their behavior. There are no any quantitative evidences of hybridization for the MOs of methane in either coordinate space or momentum space. The core MO (1 a 1) of methane in momentum space is found to be nearly indistinguishable to the core AO (1s) of a free carbon atom using the same model. The net chemical bonding results as displayed in the valence MO momentum distributions have clearly retained the orbital wave function anisotropy as s-like and p-like in both methane and the free carbon atom.

Dielectric Properties of ZrC by Electron Energy Loss Spectroscopy

Zirconium carbide belongs to the group of refractory compounds having NaCl structure with high chemical inertness and melting point, characteristics that have made these materials to play a prominent role as hard coatings and these properties are closely related to their electronic structure. The electronic configuration of ZrC is: (Xe) 5d2 6s2, one s electron being able to be promoted to a d orbital forming four equivalent sd3 hybrid orbitals, favoring covalent bonds maintaining, however, a percentage in ionic character of about 30%.Some attention has been paid in the last two decades in studying the optical properties of transition metal carbides and nitrides by electron energy loss spectroscopy (EELS), being TiC and TiN the most extensively reported.In this work the optical constants of commercial powder ZrC were obtained using a Gatan Parallel Detection Electron spectrometer (model 766) attached to the CM-200 transmission electron microscope (TEM).