Contribution Of Core Electrons Research Articles

N-representable one-electron reduced density matrix reconstruction with frozen core electrons.

Recent advances in quantum crystallography have shown that, beyond conventional charge density refinement, a one-electron reduced density matrix (1-RDM) satisfying N-representability conditions can be reconstructed using jointly experimental X-ray structure factors and directional Compton profiles (DCP) through semidefinite programming. So far, such reconstruction methods for 1-RDM, not constrained to idempotency, have been tested only on a toy model system (CO2). In this work, a new method is assessed on crystalline urea [CO(NH2)2] using static (0 K) and dynamic (50 K) artificial experimental data. An improved model, including symmetry constraints and frozen core-electron contribution, is introduced to better handle the increasing system complexity. Reconstructed 1-RDMs, deformation densities and DCP anisotropy are analysed, and it is demonstrated that the changes in the model significantly improve the reconstruction quality, even when there is insufficient information and data corruption. The robustness of the model and the strategy are thus shown to be well adapted to address the reconstruction problem from actual experimental scattering data.

Core-electron contributions to the magnetic response of molecules with heavy elements and their significance in aromaticity assessments.

This study delves into the magnetic response of core electrons and their influence on the global magnetic response of planar and three-dimensional systems containing heavy elements, employing the removing valence electron (RVE) approximation. We also explore electronic aromaticity indices to understand the potential role of core electrons on electron delocalization in the absence of an external perturbation. The study reveals that core electrons significantly contribute to the overall magnetic response, especially to the magnetic shielding, affecting the interpretation of aromaticity. In contrast, the calculation of the electronic aromaticity indices suggests a negligible participation of the core electrons on electron delocalization. Despite their widespread use, the study emphasizes caution in labeling systems as strongly aromatic based solely on shielding function computations. It is noteworthy to emphasize the limitations associated with each aromaticity criterion; particularly in the context of magnetic shielding function calculations, the core-electron effect contamination is undeniable. Hence, the integration of various criteria becomes imperative for attaining a comprehensive understanding of magnetic responses within complex systems.

Trajectory sampling and finite-size effects in first-principles stopping power calculations

Real-time time-dependent density functional theory (TDDFT) is presently the most accurate available method for computing electronic stopping powers from first principles. However, obtaining application-relevant results often involves either costly averages over multiple calculations or ad hoc selection of a representative ion trajectory. We consider a broadly applicable, quantitative metric for evaluating and optimizing trajectories in this context. This methodology enables rigorous analysis of the failure modes of various common trajectory choices in crystalline materials. Although randomly selecting trajectories is common practice in stopping power calculations in solids, we show that nearly 30% of random trajectories in an FCC aluminum crystal will not representatively sample the material over the time and length scales feasibly simulated with TDDFT, and unrepresentative choices incur errors of up to 60%. We also show that finite-size effects depend on ion trajectory via “ouroboros” effects beyond the prevailing plasmon-based interpretation, and we propose a cost-reducing scheme to obtain converged results even when expensive core-electron contributions preclude large supercells. This work helps to mitigate poorly controlled approximations in first-principles stopping power calculations, allowing 1–2 order of magnitude cost reductions for obtaining representatively averaged and converged results.

Topological contribution to magnetism in the Kane-Mele model: An explicit wave-function approach

In our previous publication [Ozaki and Ogata, Phys. Rev. Res. 3, 013058 (2021)], the quantization of the orbital-Zeeman (OZ) cross term in the magnetic susceptibility, or the cross term of spin Zeeman and orbital effect, was shown for the Kane-Mele model using the expansion around the Dirac points. In the present study, we accurately evaluate the orbital, spin-Zeeman, and OZ cross term of the Kane-Mele model using a recently developed formulation. This method uses the explicit real-space Bloch wave functions and enables us to accurately evaluate each contribution taking into account an infinite number of high-energy bands and core electron contribution at arbitrary chemical potential. We find that the effect beyond the previous formulations does not change the quantization of the OZ cross term. We also study the OZ cross term in the metalic case, and the sum rule of the OZ cross term with respect to the chemical potential is found. The possibility of experimental detection of the quantization is also discussed.

Core-electron contributions to the molecular magnetic response.

Orbital contributions to the magnetic response depend on the method used to compute them. Here, we show that dissecting nuclear magnetic shielding tensors using natural localized molecular orbitals (NLMOs) leads to anomalous core contributions. The arbitrariness of the assignment might significantly affect the interpretation of the magnetic response of nonplanar molecules such as C60 or [14]helicene and the assessment of their aromatic character. We solve this problem by computing the core- and σ-components of the induced magnetic field (and NICS) and the magnetically induced current density by removing the valence electrons (RVE). We estimate the core contributions to the magnetic response by performing calculations on the corresponding highly charged molecules, such as C6H630+ for benzene, using gauge-including atomic orbitals and canonical molecular orbitals (CMOs). The orbital contributions to nuclear magnetic shielding tensors are usually estimated by employing a natural chemical shielding (NCS) analysis in NLMO or CMO bases. The RVE approach shows that the core contribution to the magnetic response is small and localized at the nuclei, contrary to what NCS calculations suggest. This may lead to a completely incorrect interpretation of the magnetic σ-orbital response of nonplanar structures, which may play a major role in the overall magnetic shielding of the system. The RVE approach is thus a simple and inexpensive way to determine the magnetic response of the core- and σ-electrons.

Surface for methane combustion: O(3P) +CH4 → OH+CH3**Project supported by the National Natural Science Foundation of China (Grant No. 51574016) and completed while the author was in residence at UNSW, Australia supported by the International Cooperation Training Program for Innovative Talents of USTB.

Kinetic investigations including quasi-classical trajectory and canonical unified statistical theory method calculations are carried out on a potential energy surface for the hydrogen-abstraction reaction from methane by atom O(3P). The surface is constructed using a modified Shepard interpolation method. The ab initio calculations are performed at the CCSD(T) level. Taking account of the contribution of inner core electrons to electronic correlation interaction in ab initio electronic structure calculations, modified optimized aug-cc-pCVQZ basis sets are applied to the all-electrons calculations. On this potential energy surface, the triplet oxygen atom attacks methane in a near-collinear H–CH3 direction to form a saddle point with barrier height of 13.55 kcal/mol, which plays a key role in the kinetics of the title reaction. For the temperature range of 298–2500 K, our calculated thermal rate constants for the O(3P) + CH4 → OH + CH3 reaction show good agreement with relevant experimental data. This work provides detailed mechanism of this gas-phase reaction and a theoretical guidance for methane combustion.

K-Shell Core-Electron Excitations in Electronic Stopping of Protons in Water from First Principles.

Understanding the role of core-electron excitation in liquid water under proton irradiation has become important due to the growing use of proton beams in radiation oncology. Using a first-principles, nonequilibrium simulation approach based on real-time, time-dependent density functional theory, we determine the electronic stopping power, the velocity-dependent energy transfer rate from irradiating ions to electrons. The electronic stopping power curve agrees quantitatively with experimental data over the velocity range available. At the same time, significant differences are observed between our first-principles result and commonly used perturbation theoretic models. Excitations of the water molecules' oxygen core electrons are a crucial factor in determining the electronic stopping power curve beyond its maximum. The core-electron contribution is responsible for as much as one third of the stopping power at the high proton velocity of 8.0a.u. (1.6MeV). K-shell core-electron excitations not only provide an additional channel for the energy transfer-they also significantly influence the valence electron excitations. In the excitation process, generated holes remain highly localized within a few angstroms around the irradiating proton path, whereas electrons are excited away from the path. In spite of their great contribution to the stopping power, K-shell electrons play a rather minor role in terms of the excitation density; only 1% of the hole population composes K-shell holes, even at the high proton velocity of 8.0a.u. The excitation behavior revealed is distinctly different from that of photon-based ionizing radiation such as x or γ rays.

Benchmark Theoretical Study on the Dissociation Energy of Chlorine

The currently accepted D(0)((35)Cl(2)) is 239.221 ± 0.001 kJ/mol, whereas popular theoretical model chemistries provide values in the range of 233-247 kJ/mol, and even the so-called high-accuracy protocols can yield values as low as 237.9 kJ/mol and as high as 240.1 kJ/mol for D(0)((35)Cl(2)). The aim of this study was to uncover the sources of error inherent in the theoretical approaches. Therefore, a coupled-cluster-based composite model chemistry was utilized that included contributions of up to pentuple excitations, as well as corrections beyond the nonrelativistic and Born-Oppenheimer approximations. In our calculations, correlation consistent basis set families were used up to octuple-ζ basis sets. It was found that the following factors, in order of significance, can be identified as the most important error sources: (i) the considerably large relativistic contributions carrying large uncertainties, (ii) the very slow convergence of the Møller-Plesset (MP2) correlation energy (with the octuple-ζ basis set, it still contains an error of a few tenth of a kJ/mol), (iii) the slow convergence of the coupled-cluster singles and doubles (CCSD) contribution (it needs a octuple-ζ basis set to converge within 0.1 kJ/mol), and (iv) the relatively large basis set (quadruple-ζ) needed in the calculation of an accurate perturbative quadruples contribution. It is also notable that, for chlorine, the use of a quintuple-ζ basis set for the Hartree-Fock energy, the MP2 correlation energy, and for the CCSD and perturbative triples contributions, which is the usual treatment in almost every high-accuracy model chemistry, resulted in the overestimation of all of these contributions (altogether about by 1.8 kJ/mol). However, this overestimation is accidentally compensated by (i) using an inappropriate, small basis set for the valence electron contribution due to quadruple excitations (∼1.2 kJ/mol), (ii) neglecting the effects of core electron contributions due to quadruple excitations (∼0.2 kJ/mol), and (iii) neglecting relativistic effects beyond the scalar relativistic treatment (∼0.3 kJ/mol). The most reliable theoretical estimate for D(0)((35)Cl(2)) obtained in this study, 239.27 ± 1.30 kJ/mol, differs by only 0.05 kJ/mol from the most accurate experimental result. This study also underpins the effect of relativistic contributions, which precludes current model chemistries to enter the range of sub-kJ/mol accuracy for second-row systems.

Applying an information transmission approach to extract valence electron information from reconstructed exit waves

The knowledge of the valence electron distribution is essential for understanding the properties of materials. However this information is difficult to obtain from HREM images because it is easily obscured by the large scattering contribution of core electrons and by the strong dynamical scattering process. In order to develop a sensitive method to extract the information of valence electrons, we have used an information transmission approach to describe the electron interaction with the object. The scattered electron wave is decomposed in a set of basic functions, which are the eigen functions of the Hamiltonian of the projected electrostatic object potential. Each basic function behaves as a communication channel that transfers the information of the object with its own transmission characteristic. By properly combining the components of the different channels, it is possible to design a scheme to extract the information of valence electron distribution from a series of exit waves. The method is described theoretically and demonstrated by means of computer simulations.

Second- and third-harmonic generation in metal-based structures

We present a new theoretical approach to the study of second and third harmonic generation from metallic nanostructures and nanocavities filled with a nonlinear material, in the ultrashort pulse regime. We model the metal as a two-component medium, using the hydrodynamic model to describe free electrons, and Lorentz oscillators to account for core electron contributions to both the linear dielectric constant and to harmonic generation. The active nonlinear medium that may fill a metallic nanocavity, or be positioned between metallic layers in a stack, is also modeled using Lorentz oscillators and surface phenomena due to symmetry breaking are taken into account. We study the effects of incident TE- and TM-polarized fields and show that a simple re-examination of the basic equations reveals additional exploitable dynamical features of nonlinear frequency conversion in plasmonic nanostructures.

Optical absorption and electronic band structure first-principles calculations ofα-glycine crystals

Light absorption of $\ensuremath{\alpha}$-glycine crystals grown by slow evaporation at room temperature was measured, indicating a $5.11\ifmmode\pm\else\textpm\fi{}0.02\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ energy band gap. Structural, electronic, and optical absorption properties of $\ensuremath{\alpha}$-glycine crystals were obtained by first-principles quantum mechanical calculations using density functional theory within the generalized gradient approximation in order to understand this result. To take into account the contribution of core electrons, ultrasoft and norm-conserving pseudopotentials, as well as an all electron approach were considered to compute the electronic density of states and band structure of $\ensuremath{\alpha}$-glycine crystals. They exhibit three indirect energy band gaps and one direct $\ensuremath{\Gamma}\text{\ensuremath{-}}\ensuremath{\Gamma}$ energy gap around $4.95\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$. The optical absorption related to transitions between the top of the valence band and the bottom of the conduction band involves $\mathrm{O}\phantom{\rule{0.2em}{0ex}}2p$ valence states and $\mathrm{C},\mathrm{O}\phantom{\rule{0.2em}{0ex}}2p$ conduction states, with the carboxyl group contributing significantly to the origin of the energy band gap. The calculated optical absorption is highly dependent on the polarization of the incident radiation due to the spatial arrangement of the dipolar glycine molecules; in the case of a polycrystalline sample, the first-principles calculated optical absorption is in good agreement with the measurement when a rigid energy shift is applied.

The convergence of complete active space self-consistent-field configuration interaction including all single and double excitation energies to the complete basis set limit

Examination of the convergence of full valence complete active space self-consistent-field configuration interaction including all single and double excitation (CASSCF-CISD) energies with expansion of the one-electron basis set reveals a pattern very similar to the convergence of single determinant energies. Calculations on the lowest four singlet states and the lowest four triplet states of N(2) with the sequence of n-tuple-zeta augmented polarized (nZaP) basis sets (n=2, 3, 4, 5, and 6) are used to establish the complete basis set limits. Full configuration-interaction (CI) and core electron contributions must be included for very accurate potential energy surfaces. However, a simple extrapolation scheme that has no adjustable parameters and requires nothing more demanding than CAS(10e(-),8orb)-CISD/3ZaP calculations gives the R(e), omega(e), omega(e)X(e), T(e), and D(e) for these eight states with rms errors of 0.0006 Angstrom, 4.43 cm(-1), 0.35 cm(-1), 0.063 eV, and 0.018 eV, respectively.

Quasiquenching size effects in gold nanoclusters embedded in silica matrix

The surface plasmon energy of gold clusters formed by Ar + ion beam mixing of Au/silica is investigated for the size effect. The redshift with decreasing cluster size is assigned to the ‘spillout’ effect in small clusters (<5 nm). Core-electron contribution to the metal dielectric function is mainly responsible for the blueshift with decreasing cluster size (quenching of the size effect) in case of bigger cluster size (>5 nm), assisted with annealing treatment. The competition between ‘spillout’ effect and the frequency dependence of interband dielectric function leads to a quasiquenching of the size effects in the optical response.

Dynamics of solid inner-shell electrons in collisions with bare and dressed swift ions

We analyze the dynamical interactions of swift heavy projectiles and solid inner-shell electrons. The dielectric formalism employed to deal with the free-electron gas is extended to account for the core electrons, by using the local plasma approximation. Results for stopping power, energy straggling, and inner-shell ionization in collisions of bare ions with metals are displayed, showing very good accord with the experimental data. Simultaneous excitations of projectile and target electrons are also analyzed. In the high-energy range we find a similar contribution of target core and valence electrons to the probability of projectile-electron loss. The problem of no excitation threshold within the local plasma approximation and the possibility of collective excitations of the shells are discussed.

Positron characteristics of various SiO 2 polymorphs

Theoretical calculations of positron lifetimes, affinities and core electron contributions to Doppler broadening spectra are carried out for several phases (polymorphs) of SiO 2. An interesting feature of SiO 2 is that not all polymorphs have the same coordination of Si and O atoms, which also affects positron properties. The calculated quantities are compared with available experimental data and discussed with reference to SiO 2/Si interfaces.

Molecular Design for Organic Nonlinear Optics: Polarizability and Hyperpolarizabilities of Furan Homologues Investigated by Ab Initio Molecular Orbital Method

Static polarizabilities and hyperpolarizabilities have been calculated for the furan homologues including furan (C4H4O), thiophene (C4H4S), selenophene (C4H4Se), and tellurophene (C4H4Te), at the Hartree−Fock and various correlation levels by ab initio molecular orbital methods. The influence of substitution with heavy atoms on the molecular properties of the homologues was examined theoretically. In the calculations for molecules with Se and Te atoms, the contribution of core electrons in the atoms was estimated using effective core potential (ECP) methods. With the calculation for the thiophene molecule, effectiveness of the use of the ECP method was examined, and the ECP method was found to give the (hyper)polarizability values similar to those obtained considering all electrons for the molecule. The calculated results show that substitution of the heteroatom with heavy atoms systematically increases the individual components of the polarizability, α, and second hyperpolarizability, γ. On the other hand, this does not give systematic variations on the first hyperpolarizability, β. The variation of these values depending on the homologues was examined in terms of the perturbation expansion formula and was explained by the energy levels of the electronic excited states in the valence states. The second hyperpolarizability values calculated, including electron correlation effect, are well correlated with the observed electronic components of nonlinear optical susceptibilities, χ(3), obtained using optical Kerr effect experiments, which have been done in our laboratory. However, some discrepancy is observed between the theoretical and the experimental values for the homologues with heavier heteroatoms. Possible causes for the discrepancy are discussed in detail.

Bonding in hypohalous acids HOX (X=F, Cl, Br, and I) from the topological analysis of the electron localization function

The bonding in hypohalous acids has been investigated from the topological analysis of the electron localization function (ELF) at the Becke3LYP and Hartree–Fock levels. The interaction between halogen and oxygen atoms has been characterized by the presence of bonding, disynaptic attractors V(O,X) X=F, Cl, Br, and I with the mean electron population N̄ of 0.32, 0.61, 0.45, and 0.35e, respectively. In the case of HOBr, the possibility of a strong contribution of 3d bromine core electrons to the valence shell has been observed. On the base of the bonding evolution theory (BET), the O–F bond has been recognized as a covalent, polarized one whereas, the bonding between O and Cl, Br, and I atoms is of the electron donor–acceptor-type with halogen donating the electron density to valence shell of oxygen. The observed difference between HO+F− and HO−X+ (X=Cl, Br, and I) polarizations is reflected in topology of ELF maps with a large localization domain surrounding the V(F) and V(F,O) attractors in HOF and a common superbasin encompassing the V(O,H), V(O), and V(X,O) attractors in HOCl, HOBr, and HOI. The very large values of the relative quantum fluctuation (λ), above 0.8, found for V(O,X) suggest that the covalent electron density is almost entirely delocalized over other basins. The comparison of the mean electron population (N̄) of the V(H,X) and V(H,O) basins computed for hydrohalic (HX) and hypohalous acids (HOX) has revealed that the population alters in line with values of ΔEacid, therefore can be used as a approximate measure of acidic properties of molecules. The topological analysis of the ELF function supports the concept of probonded electronegativity and its usefulness as a tool for prediction of the nature of the oxygen–halogen linkage.

Quenching of the Size Effects in Free and Matrix-Embedded Silver Clusters

The surface plasmon energy of silver clusters is investigated in the framework of the time-dependent local density approximation. The results are in good agreement with experimental data on free ${\mathrm{Ag}}_{N}^{+}$ clusters and on ${\mathrm{Ag}}_{N}$ clusters embedded in solid argon and alumina. The size effects are weak and very sensitive to the matrix, the porosity at the interface, and the cluster charge. It is shown that the core-electron contribution to the metal dielectric function is mainly responsible for the quenching of the size effects in the optical response.

Magnetic moment and hyperfine field on Fe sites in RFe6Sn6 compounds

Electronic structure and hyperfine fields are calculated for antiferromagnetic YFe6Sn6 using the linear muffin-tin orbital method. The results show that Fe atoms have a strong ferromagnetic character with a full majority-spin band. The Fe moment is 2.2 μB while the Fermi contact term contributes a hyperfine field of 20 T at the natural lattice parameters. The hyperfine field is close to the experimental value of 22 T measured at low temperature. The calculation shows that the core s electrons contribute 24 T to the hyperfine field, but the 4s electron contributes 4 T in the opposite direction. Calculations using different unit cell volumes reveal that only the core electron contributions to the hyperfine field are proportional to the Fe magnetic moment with a conversion factor of 11.8 T/μB; the 4s contribution is not. The large local Fe moment and small hyperfine field are similar to those found in Fe2P and FeO.

Magnetic susceptibility of semiconductors by an all-electron first-principles approach

The magnetic susceptibility $(\ensuremath{\chi})$ of the semiconductors (diamond, Si, GaAs, and GaP) and of the inert-gas solids (Ne, Ar, and Kr) are evaluated within density-functional theory in the local-density approximation, using a mixed-basis all-electron approach. In Si, GaAs, GaP, Ar, and Kr, the contribution of core electrons to $\ensuremath{\chi}$ is comparable to that of valence electrons. However, our results show that the contribution associated with the core states is independent of the chemical environment and can be computed from the isolated atoms. Moreover, our results indicate that the use of a ``scissor operator'' does not improve the agreement of the theoretical $\ensuremath{\chi}$ with experiments.