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In three out of five cases considered in our work, DFT calculations presented by Xu and Hou in their Comment give the same ground state confirmations. On the other hand, depending on the choice of the exchange-correlation functional, the geometry optimization within DFT results in different ground state confirmations for B@C60 and B60, Table I of the Comment. Therefore, the energy balance between nearest confirmations in these molecular complexes is subtle, and various methods can give different ground state structures. Consequently, the results of our method - the Hartree-Fock (HF) approach with the second order M{\o}ller-Plesset perturbation theory (MP2) - should be compared with the DFT results on equal ground, we cannot agree that the DFT method used in the Comment is superior to HF-MP2. In the Reply, we also present additional HF calculations with the 6-31G* basis set (used in the Comment for the geometry optimization) to show that the polarization functions do not change the ground state confirmations obtained by us earlier at the HF/6-31G level., Comment: Reply to the Comment of J. Xu and G.-L. Hou, Comment on "Multiple locations of boron atoms in the exohedral and endohedral C60 fullerene",to be published in PRA (November, 2022). The Reply has not been allowed to be published by PRA. (Our initial work: A. V. Bibikov, et al. Phys. Rev. A 105, 022813 (2022).)

This work demonstrates the effectiveness of the high-pressure method for the production of graphite and diamond with a high degree of boron doping using adamantanecarborane mixture as a precursor. At 8 GPa and $1700 ^{o}C$, graphite is obtained from adamantane $C_{10}H_{16}$, whereas microcrystals of boron-doped diamond (2{\div}2.5 at.% of boron) are synthesized from a mixture of adamantane and ortho-carborane $C_{2}B_{10}H_{12}$ (atomic ratio B:C = 5:95). This result shows convincingly the catalytical activity of boron in the synthesis of diamond under high pressure. At pressures lower than 7 GPa, only graphite is synthesized from the adamantane and carborane mixture. Graphitization starts at quite low temperatures (below $1400 ^{o}C$) and an increase in temperature simultaneously increases boron content and the quality of the graphite crystal lattice. Thorough study of the material structure allows us to assume that the substitutional boron atoms are distributed periodically and equidistantly from each other in the graphite layers at high boron concentrations (>1 at.%). The theoretical arguments and model ab initio calculations confirm this assumption and explain the experimentally observed boron concentrations.

Studying the tight binding model in an applied rational magnetic field (H) we show that in graphene there are very unusual Landau levels situated in the immediate vicinity of the saddle point (M-point) energy epsilon_M. Landau levels around $\epsilon_M$ are broadened into minibands (even in relatively weak magnetic fields ~40-53 T) with the maximal width reaching 0.4-0.5 of the energy separation between two neighboring Landau levels though at all other energies the width of Landau levels is practically zero. In terms of the semiclassical approach a broad Landau level or magnetic miniband at epsilon_M is a manifestation of the so called self-intersecting orbit signifying an abrupt transition from the semiclassical trajectories enclosing the $\Gamma$ point to the trajectories enclosing the K point in the momentum space. Remarkably, the saddle point virtually does not affect the diamagnetic response of graphene, which is caused mostly by electron states in the vicinity of the Fermi energy \epsilon_F. Experimentally, the effect of the broading of Landau levels can possibly be observed in twisted graphene where two saddle point singularities can be brought close to the Fermi energy.

Combining a precise ab initio electron band structure calculation of the TiO2 rutile structure with the temperature evolution of the Ti mean-square displacements, we reproduce a puzzling temperature increase of the electric field gradient at Ti sites in TiO2, observed experimentally. Our method employs a procedure of averaging two quadrupole electron density components (L = 2) inside a sphere vibrating with the Ti nucleus at its center, where the key factor introducing the temperature dependence is the square root of the Debye-Waller factor. Although the Debye-Waller factor always reduces the corresponding Fourier component, in TiO2 due to the interplay between terms of opposite signs, it results in a net increase of the whole sum with temperature, leading to the growth of the electric field gradient. Quantitatively, we find that the increase of electric field gradient is only half of the experimental value, which we ascribe to anharmonic effects or a strong oxygen position influence. In addition, our method reproduces the unusual temperature dependence of the asymmetry parameter eta, which first decreases with temperature, goes to zero and then increases., Comment: 9 pages, 7 figures, 1 Table

We explore an unusual nature of chemical bonding of the thorium atom with a ring of six carbon atoms (hexagon) in novel carbon materials. Our ab initio calculations of Th-based metallofullerenes (Th@C60, Th@C20) and Th bound to benzene or coronene at the Hartree-Fock level with the second order perturbation (MP2) correction accounting for the van der Waals interactions, demonstrate that the optimal position of the thorium atom is where it faces the center of a hexagon and is located at a distance of 2.01-2.07 A from the center. For Th encapsulated in C60 it is found at 2.01 A, whereas the other local energy minima are shifted to larger energies (0.22 eV and higher). Inside C60 the highest local minimum at 1.17 eV is observed when Th faces the center of the five member carbon ring (pentagon). Based on our calculations for Th with benzene and coronene where the global minimum for Th corresponds to its position at 2.05 A (benzene) or 2.02 A (coronene) from the hexagon center, we conclude that a well pronounced minimum is likely to present in graphene and in a single wall carbon nanotube. The ground state of Th is singlet, other high spin states (triplet and quintet) lie higher in energy (> 1.62 eV). We discuss a potential use of the carbon nanomaterials with the 229Th isotope having the nuclear transition of the optical range, for metrological purposes., Comment: 7 pages, 5 figures, 2 tables

Based on ab initio band structure calculations we formulate a general theoretical method for description of the temperature dependence of electric field gradient in solids. The method employs a procedure of averaging multipole electron density component (l \neq 0) inside a sphere vibrating with the nucleus at its center. As a result of averaging each Fourier component (K \neq 0) on the sphere is effectively reduced by the square root of the Debye-Waller factor [exp(-W)]. The electric field gradient related to a sum of K-components most frequently decreases with temperature (T), but under certain conditions because of the interplay between terms of opposite signs it can also increase with T. The method is applied to calculations of the temperature evolution of the electric field gradients of pristine zinc and cadmium crystallized in the hexagonal lattice. For calculations within our model of crucial importance is the temperature dependence of mean-square displacements which can be taken from experiment or obtained from the phonon modes in the harmonic approximation. For the case of Zn we have used data obtained from single crystal x-ray diffraction. In addition, for Zn and Cd we have calculated mean-square displacements with the density functional perturbation treatment of the Quantum Espresso package. With the experimental data for displacements in Zn our calculations reproduce the temperature dependence of the electric field gradient very accurately. Within the harmonic approximation of the Quantum Espresso package the decrease of electric field gradients in Zn and Cd with temperature is overestimated. Our calculations indicate that the anharmonic effects are of considerable importance in the temperature dependence of electric field gradients., Comment: 13 pages, 11 figures

It is demonstrated that the Landau diamagnetism of the free electron gas and a monovalent metal can be considered as a Fermi surface effect. Only relatively small number of electron states close to the Fermi surface are diamagnetically active whereas the majority of the electron states inside the Fermi surface are diamagnetically inert. This partitioning of the occupied electron states is driven by the structure of Landau levels, around which one can introduce magnetic tubes in the reciprocal space. Completely filled magnetic tubes do not change their energy in an applied magnetic field, and only partially occupied magnetic tubes in the neighborhood of the Fermi surface exhibit a diamagnetic response. Using this partitioning of the occupied electron states we derive a general expression for the steady diamagnetic susceptibility, for calculation of which one needs to know the shape of the Fermi surface and the energy gradient on it. The method is applied to alkali metals, whose Fermi surfaces and energy gradients have been obtained from ab initio band structure calculations. It has been found that the Landau diamagnetic susceptibility is anisotropic depending on the direction of the applied magnetic field in respect to the Fermi surface. This effect is more pronounced for Li and Cs, whose Fermi surfaces show a noticeable deformation from the spherical shape. The method opens a new route for ab initio calculations of the Landau diamagnetism of metals or intermetallic compounds. In the case of free electron gas it is shown that this approach also fully describes the oscillatory de Haas - van Alphen part of the diamagnetic susceptibility. Small oscillations of the Fermi energy found in the model are caused by redistribution (inflow or outflow) of electrons from the equatorial region of the Fermi surface., Comment: 19 pages, 16 figures, 1 Table. arXiv admin note: substantial text overlap with arXiv:1807.08802, version 2: misprints corrected

In order to increase the accuracy of the linearized augmented plane wave method (LAPW) we present a new approach where the plane wave basis function is augmented by two different atomic radial components constructed at two different linearization energies corresponding to two different electron bands (or energy windows). We demonstrate that this case can be reduced to the standard treatment within the LAPW paradigm where the usual basis set is enriched by the basis functions of the tight binding type, which go to zero with zero derivative at the sphere boundary. We show that the task is closely related with the problem of extended core states which is currently solved by applying the LAPW method with local orbitals (LAPW+LO). In comparison with LAPW+LO, the number of supplemented basis functions in our approach is doubled, which opens up a new channel for the extension of the LAPW and LAPW+LO basis sets. The appearance of new supplemented basis functions absent in the LAPW+LO treatment is closely related with the existence of the $\dot{u}_l-$component in the canonical LAPW method. We discuss properties of additional tight binding basis functions and apply the extended basis set for computation of electron energy bands of lanthanum (face and body centered structures) and hexagonal close packed lattice of cadmium. We demonstrate that the new treatment gives lower total energies in comparison with both canonical LAPW and LAPW+LO, with the energy difference more pronounced for intermediate and poor LAPW basis sets., Comment: 11 pages, 3 figues, 9 tables

Time differential perturbed angular gamma-gamma-correlation (TDPAC) method on 111Cd nuclei probes inserted in ZrZn1.9 is used to measure the magnetic hyperfine fields (MHF) at Zr and Zn sites and the electric field gradient (EFG) Vzz at Zn sites as a function of temperature at various pressures and as a function of pressure at the temperature 4 K. Our data indicate that the local magnetic moment of Zr in the magnetically ordered state is substantially larger than its value obtained from the macroscopic measurements and that there is also an induced magnetic moment at the Zn site. We conclude that ZrZn2 is not a simple ferromagnet and discuss a possible type of its magnetic ordering., Comment: 7 pages, 6 figures, submitted for publication

The inclination of the magnetic domain wall plane in electric field is observed. The simple theoretical model of this phenomenon that takes into account the spin flexoelectricity is proposed. The value of electric polarization of the magnetic domain wall is estimated as 0.3{\mu}C/m^2 that agrees well with the results of electric field driven magnetic domain wall motion measurements.

We discuss recent research on the phase transitions in cerium under pressure, including new experiments on the gamma-alpha transition, which indicate that it is a hidden structural phase transition., Comment: A variant based on review in Physics-Uspekhi, v. 55 (7) pp. 657-680

Starting from a model of 4f-electron generated quadrupolar densities on a compressible fcc lattice, the elastic anomalies at the Fm3m -> Pa3 phase transition are studied by means of analytical theory. The model is taken as representative for the gamma-alpha phase transition in Ce. The coupling of the (linear) lattice displacements to the square of the quadrupolar orientational density fluctuations renormalizes the elastic constants. The condensation of the quadrupolar densities into the orientationally ordered Pa3 structure is studied as function of temperature and pressure. Precursor effects of the transition lead to an anomalous softening of the elastic constant c11 while c44 exhibits no such softening. The theoretical results are in excellent qualitative agreement with pressure experiments on the elastic constants (equivalently on sound velocities) at the $gamma-alpha transition in Ce. Lattice dynamical analogies in theory and striking similarities in experimental results with the Fm3m -> Pa3 transition in C60 fullerite are discussed., Comment: 12 pages, 4 figures, 1 table

The electronic structure of Ce2 is studied in a valence bond model with two 4f electrons localized at two cerium sites. It is shown that the low-lying energy spectrum of the simplest cerium chemical bond is determined by peculiarities of the occupied 4f states. The model allows for an analytical solution which is discussed along with the numerical analysis. The energy spectrum is a result of the interplay between the 4f valence bond exchange, the 4f Coulomb repulsion and the spin-orbit coupling. The calculated ground state is the even \Omega=\Lambda=\Sigma=0 level, the lowest excitations situated at 30 K are the odd \Omega=\Lambda=\Sigma=0 state and the $^{3} 6_5$ doublet (\Omega=\pm5,\, \Lambda=\pm6,\, \Sigma=\mp1). The calculated magnetic susceptibility displays different behavior at high and low temperatures. In the absence of the spin-orbit coupling the ground state is the ${}^3 \Sigma_g^-$ triplet. The results are compared with other many-electron calculations and experimental data., Comment: 10 pages, 3 figures, 5 Tables, 18 References

The chirality-dependent magnetoelectric properties of Neel-type domain walls in iron garnet films is observed. The electrically driven magnetic domain wall motion changes the direction to the opposite with the reversal of electric polarity of the probe and with the chirality switching of the domain wall from clockwise to counterclockwise. This proves that the origin of the electric field induced micromagnetic structure transformation is inhomogeneous magnetoelectric interaction., Comment: 6 pages, 4 figures, 1 table

The dynamic observation of domain wall motion induced by electric field in magnetoelectric iron garnet film is reported. Measurements in 800 kV/cm electric field pulses gave the domain wall velocity ~45 m/s. Similar velocity was achieved in magnetic field pulse about 50 Oe. Reversible and irreversible micromagnetic structure transformation is demonstrated. These effects are promising for applications in spintronics and magnetic memory., Comment: 3 pages, 3 figures

The room temperature magnetoelectric effect was observed in epitaxial iron garnet films that appeared as magnetic domain wall motion induced by electric field. The films grown on gadolinium-gallium garnet substrates with various crystallographic orientations were examined. The effect was observed in (210) and (110) films and was not observed in (111) films. Dynamic observation of the domain wall motion in 400 V voltage pulses gave the value of domain wall velocity in the range 30-50 m/s. The same velocity was achieved in magnetic field pulse about 50 Oe., Comment: 12 pages, 2 figures

We report results on ab initio calculations of excited states of the fullerene molecule by using configuration interaction (CI) approach with singly excited determinants (SCI). We have used both the experimental geometry and the one optimized by the density functional method and worked with basis sets at the cc-pVTZ and aug-cc-pVTZ level. Contrary to the early SCI semiempirical calculations, we find that two lowest $^1 T_{1u} \leftarrow {}^1 A_g$ electron optical lines are situated at relatively high energies of ~5.8 eV (214 nm) and ~6.3 eV (197 nm). These two lines originate from two $^1 T_{1u} \leftarrow {}^1 A_g$ transitions: from HOMO to (LUMO+1) ($6h_u \to 3t_{1g}$) and from (HOMO--1) to LUMO ($10h_g \to 7t_{1u}$). The lowest molecular excitation, which is the $1 ^3 T_{2g}$ level, is found at ~2.5 eV. Inclusion of doubly excited determinants (SDCI) leads only to minor corrections to this picture. We discuss possible assignment of absorption bands at energies smaller than 5.8 eV (or $\lambda$ larger than 214 nm)., Comment: 6 pages, 1 figure, 9 Tables

We discuss the triple-$\vec{q}^X$ structures for the ordered cubic phase of NpO$_2$, which are $Pn{\bar 3}m$ and $Pa{\bar 3}$. A special care should be taken to discriminate between these two cases. We analyze the relevant structure-factor amplitudes and the effect of domains on resonant X-ray scattering experiments. We formulate the technique of multipole expansion of the Coulomb interaction and use it to study the crystal electric field and mean field for a number of neptunium many electron configurations ($5f^3$, $7s5f^3$, $7p5f^3$ and $6d5f^3$) on ab initio level. We have found that the crystal field is rather small (50-150 K). The direct quadrupole-quadrupole interaction between neighboring neptunium sites is weak and can not drive the structural phase transition at 25 K. We have introduced an effective (enhanced) quadrupole interaction and considered the interplay between it and the crystal electric field. The influence of both interactions on the transition temperature has been investigated in detail for the $5f^3$ configuration. We discuss the importance of the intrasite multipole interaction between three localized electrons ($5f^3$) and a valence electron on a neptunium site. We show that this interaction combined with the symmetry lowering at 25 K may be responsible for the loss of the magnetic moments in the ordered phase of NpO2., Comment: 20 pages, 5 figures, 20 tables, submitted to PRB

Erratum to Int. J. Quantum Chem. v. 89, pp. 57-85 (2002), Comment: 1 page

Starting from a multipole expansion of intra- molecular Coulomb interactions, we present configuration interaction calculations of the molecular energy terms of the hole configurations hu^m, m=2-5, of C60^{m+} cations, of the electron configurations t1u^n, n=2-4, of the C60^{n-} anions, and of the exciton configurations (hu^+ t1u^-), (hu^+ t1g^-) of the neutral C60 molecule. The ground state of C60^{2-} is either 3 T1g or 1Ag, depending on the energy separation between t1g and t1u levels. There are three close (~0.03 eV) low lying triplets 3T1g, 3Gg, 3T2g for C60^{2+}, and three quartets 4T1u, 4Gu, 4T2u for C60^{3+}, which can be subjected to the Jahn-Teller effect. The number of low lying nearly degenerate states in largest for m=3 holes. We have calculated the magnetic moments of the hole and electron configurations and found that they are independent of molecular orientation in respect to an external magnetic field. The coupling of spin and orbital momenta differs from the atomic case. We analyze the electronic dipolar transitions t1u^2 -> t1u t1g and t1u^3 -> t1u^2 t1g for C60^{2-} and C60^{3-}. Three optical absorption lines (3T1g -> 3Hu, 3T1u, 3Au) are found for the ground level of C60^{2-} and only one line (4Au -> 4T1g) for the ground state of C60^{3-}. We compare our results with the experimental data for C60^{n-} in solutions and with earlier theoretical studies.

The recently discovered structural transition in polymerized KC60 at about 50 K results in a doubling of the unit cell volume and accompanies the metal-insulator transition. Here we show that the (a+c,b,a-c) superstructure results from small orientational charge density waves along the polymer chains and concomitant displacements of the surrounding K+ ions. The effect is specific for the space group Pmnn of KC60 and is absent in Rb- and CsC60 (space group I2/m). The mechanism is relevant for the metal-insulator transition., Comment: 14 pages, 5 figures, and 3 tables

We formulate a Hartree-Fock-LAPW method for electronic band structure calculations. The method is based on the Hartree-Fock-Roothaan approach for solids with extended electron states and closed core shells where the basis functions of itinerant electrons are linear augmented plane waves. All interactions within the restricted Hartree-Fock approach are analyzed and in principle can be taken into account. In particular, we have obtained the matrix elements for the exchange interactions of extended states and the crystal electric field effects. In order to calculate the matrix elements of exchange for extended states we first introduce an auxiliary potential and then integrate it with an effective charge density corresponding to the electron exchange transition under consideration. The problem of finding the auxiliary potential is solved by using the strategy of the full potential LAPW approach, which is based on the general solution of periodic Poisson's equation. Here we use an original technique for the general solution of periodic Poisson's equation and multipole expansions of electron densities. We apply the technique to obtain periodic potentials of the face centered cubic lattice and discuss its accuracy and convergence in comparison with other methods., Comment: 23 pages, 4 figures, 7 tables, Int. J. Quantum Chem., in press

Starting from a model of rigid interacting C60 polymer chains on an orthorhombic lattice, we study the mutual orientation of the chains and the stability of the crystalline structures Pmnn and I2/m. We take into account i) van der Waals interactions and electric quadrupole interactions between C60 monomers on different chains as well as ii) interactions of the monomers with the surrounding alkali atoms. The direct interactions i) always lead to an antiferrorotational structure Pmnn with alternate orientation of the C60 chains in planes (001). The interactions ii) with the alkalis consist of two parts: translation-rotation (TR) coupling where the orientations of the chains interact with displacements of the alkalis, and quadrupolar electronic polarizability (ep) coupling, where the electric quadrupoles on the C60 monomers interact with induced quadrupoles due to excited electronic d states of the alkalis. Both interactions ii) lead to an effective orientation-orientation interaction between the C60 chains and always favor the ferrorotational structure I2/m where C60 chains have a same orientation. The structures Pmnn for KC60 and I2/m for Rb- and CsC60 are the result of a competition between the direct interaction i) and the alkali-mediated interactions ii). In Rb- and CsC60 the latter are found to be dominant, the preponderant role being played by the quadrupolar electronic polarizability of the alkali ions., Comment: J.Chem.Phys., in press, 14 pages, 3 figures, 8 tables

As a possible mechanism of the $\gamma-\alpha$ phase transition in pristine cerium a change of the electronic density from a disordered state with symmetry Fm-3m to an ordered state Pa-3 has been proposed. Here we include on-site and inter- site electron correlations involving one localized 4f-electron and one conduction 5d-electron per atom. The model is used to calculate the crystal field of $\gamma$-Ce and the temperature evolution of the mean-field of $\alpha$-Ce. The formalism can be applied to crystals where quadrupolar ordering involves several electrons on the same site., Comment: 12 pages, 2 figures, 4 tables, submitted to Phys. Rev. B

A numerical method based on the transfer matrix technique is developed to calculate the luminescence spectra of complex layered structures with photon recycling. Using this method we show a strong dependence of the emission spectra on the optical eigenmode structure of the device. The enhancement of the photon recycling and the LED external efficiency can be achieved by placing the active regions inside single or coupled microcavities., Comment: 5 pages, 1 figure

We have calculated the crystal electric field of TmTe (T>T_Q) and have obtained that the ground state of a Tm 4f hole is the $\Gamma_7$ doublet in agreement with Mossbauer experiments. We study the quadrupole interactions arising from quantum transitions of 4f holes of Tm. An effective attraction is found at the L point of the Brillouin zone, $\vec{q}_L$. Assuming that the quadrupolar condensation involves a single arm of $\vec{q}_L$ we show that there are two variants for quadrupole ordering which are described by the space groups C2/c and C2/m. The Landau free energy is derived in mean-field theory. The phase transition is of second order. The corresponding quadrupole order parameters are combinations of $T_{2g}$ and $E_g$ components. The obtained domain structure is in agreement with observations from neutron diffraction studies for TmTe. Calculated lattice distortions are found to be different for the two variants of quadrupole ordering. We suggest to measure lattice displacements in order to discriminate between those two structures., Comment: 10 pages, 2 figures, 5 tables; accepted by PRB

We present a theoretical model of the "isostructural" \gamma-\alpha phase transition in Ce which is based on quadrupolar interactions due to coupled charge density fluctuations of 4f electrons and of conduction electrons. Conduction electrons are treated in tight-binding approximation. The \gamma-\alpha transition is described as an orientational ordering of quadrupolar electronic densities in a Pa3 structure. The quadrupolar order of the conduction electron densities is complementary to the quadrupolar order of 4f electron densities. The inclusion of conduction electrons leads to an increase of the lattice contraction at the \gamma-\alpha transition in comparison to the sole effect of 4f electrons. We calculate the Bragg scattering law and suggest synchrotron radiation experiments in order to check the Pa3 structure. The theory is capable of accounting for transitions to phases of non-cubic symmetry, but it is not sufficient to describe the magnetic phenomena which we ascribe to the Kondo mechanism. We also present a microscopic derivation of multipolar interactions and discuss the crystal field of \gamma-Ce., Comment: 19 pages, 4 figures, full version to be published in Eur. Phys. J. B

The polymer phases of AC60 form distinct crystal structures characterized by the mutual orientations of the (C60-)n chains. We show that the direct electric quadrupole interaction between chains always favors the orthorhombic structure Pmnn with alternating chain orientations. However the specific quadrupolar polarizability of the alkali metal ions leads to an indirect interchain coupling which favors the monoclinic structure I2/m with equal chain orientations. The competition between direct and indirect interactions explains the structural difference between KC60 and RbC60, CsC60., Comment: 4 pages, 2 figures, 1 table