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All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Density-matrix based determination of low-energy model Hamiltonians from ab initio wavefunctions

We propose a way of obtaining effective low energy Hubbard-like model Hamiltonians from ab initio quantum Monte Carlo calculations for molecular and extended systems. The Hamiltonian parameters are fit to best match the ab initio two-body density matrices and energies of the ground and excited states, and thus we refer to the method as ab initio density matrix based downfolding. For benzene (a finite system), we find good agreement with experimentally available energy gaps without using any experimental inputs. For graphene, a two dimensional solid (extended system) with periodic boundary conditions, we find the effective on-site Hubbard U{sup ∗}/t to be 1.3 ± 0.2, comparable to a recent estimate based on the constrained random phase approximation. For molecules, such parameterizations enable calculation of excited states that are usually not accessible within ground state approaches. For solids, the effective Hamiltonian enables large-scale calculations using techniques designed for lattice models.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Communication: Towards ab initio self-energy embedding theory in quantum chemistry

The self-energy embedding theory (SEET), in which the active space self-energy is embedded in the self-energy obtained from a perturbative method treating the non-local correlation effects, was recently developed in our group. In SEET, the double counting problem does not appear and the accuracy can be improved either by increasing the perturbation order or by enlarging the active space. This method was first calibrated for the 2D Hubbard lattice showing promising results. In this paper, we report an extension of SEET to quantum chemical ab initio Hamiltonians for applications to molecular systems. The self-consistent second-order Green’s function method is used to describe the non-local correlations, while the full configuration interaction method is carried out to capture strong correlation within the active space. Using few proof-of-concept examples, we show that SEET yields results of comparable quality to n-electron valence state second-order perturbation theory with the same active space, and furthermore, the full active space can be split into smaller active spaces without further implementation. Moreover, SEET avoids intruder states and does not require any high-order reduced density matrices. These advantages show that SEET is a promising method to describe physical and chemical properties of challenging molecules requiring large active spaces.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Ab initio pressure-dependent reaction kinetics of methyl propanoate radicals

The unimolecular dissociation and isomerization kinetics of the three methyl propanoate (MP) radicals, CH 3 CH 2 C(=O)O$\dot{C}$H 2 (MP-m), CH 3 $\dot{C}$HC(=O)OCH 3 (MP-α), and $\dot{C}$H 2 CH 2 C(=O)OCH 3 (MP-β), are theoretically investigated using high-level ab initio methods and the Rice–Ramsperger–Kassel–Marcus (RRKM)/master equation (ME) theory. Stationary-point energies are obtained using the coupled cluster singles and doubles with perturbative triples correction (CCSD(T)), multi-reference singles and doubles configuration interaction (MRSDCI) with the Davidson-Silver (DS) correction, and multi-reference averaged coupled pair functional (MRACPF2) theories. The isomerization barriers between the three radicals are predicted to be generally lower than the corresponding bond dissociation channels, leading to a strongly coupled reaction system in subsequent kinetics studies. The phenomenological temperature- and pressure-dependent rate coefficients are computed using the RRKM/ME theory over a temperature range of 500 to 2000 K and at a pressure range of 0.01 atm to the high-pressure limit, which are then fitted to modified Arrhenius expressions. The β-scission rate coefficients of MP-α to CH 3 CHC(=O) and CH 3 $\dot{O}$ are predicted to be the smallest because of its highest activation energy among all studied unimolecular reactions channels. Analysis of branching fractions shows that both MP-m and MP-α radicals mainly decompose to the bimolecular products CH 3 CH 2 $\dot{C}$(=O) and H 2 CO, whereas the MP-β radical primarily decomposes via cleavage of a C–C bond to form C 2 H 4 and CH 3 O$\dot{C}$(=O). The isomerization channels dominate at low temperatures, the branching fractions of which decrease with increasing temperature and become very minor at about 2000 K. Our accurate rate coefficients and branching fractions help to illuminate the unique combustion properties of MP.

09 BIOMASS FUELS↗
DOE OSTI2020

Ab initio molecular dynamics simulation of Nd3+ incorporation in calcite

Trivalent rare-earth elements (REEs) readily incorporate in Ca-bearing minerals such as calcite (CaCO3), a phenomenon with important implications for the use of REEs as biogeochemical tracers as well as for environmental remediation. Despite substantial efforts, determining the incorporation modes of trivalent REEs in calcite has remained challenging due to their presence in multiple coordination environments. This is particularly problematic for the interpretation of extended X-ray absorption fine structure (EXAFS) spectroscopy. In this work, ab initio molecular dynamics (AIMD) simulations of Nd3+ incorporated in calcite were performed to resolve its incorporation modes. Nd3+ and Ca2+ have very similar ionic radii but the additional positive charge requires a charge compensation scheme (CCS). Five CCSs were considered in AIMD simulations, and the resulting atomic trajectories were then used to compute EXAFS spectra for direct fitting to a published experimental spectrum. The results of the fits indicated that Nd3+ incorporates at the Ca2+ site in calcite in a mixture of six- and seven-fold coordination environments and through three main incorporation modes: associated with a protonated nearest-neighbor Ca2+ vacancy, incorporated as NdOH2+, and charge compensated by a remote species (on the spatial scale probed by EXAFS). The incorporation of Nd3+ in calcite via multiple modes was consistent with previous work, but the AIMD-EXAFS approach allowed for resolving the nature, proportion, and structure of the different coordination environments.

Kerisit, Sebastien N.↗
DOE OSTI2016

The interaction of reactants, intermediates and products with Cu ions in Cu-SSZ-13 NH3 SCR catalysts: An energetic and ab initio X-ray absorption modeling study

Copper-exchanged SSZ-13 (Cu-SSZ-13) provides excellent catalytic activity and hydrothermal stability in the selective catalytic reduction (SCR) of NOx by using NH3 as a reductant. In this contribution, we compare the most likely positions for Cu with a single charge compensating Al atom (ZCu), including the effect of the adsorption of reactants, intermediates and products of a NH3 SCR reaction by using first-principles calculations based on density functional theory. We find that the 6-membered ring (6MR) site is the most energetically favorable while the 8-membered ring (8MR) sites are less favorable with energy differences about 0.5 eV with respect to the 6MR site. Upon molecular adsorption, the energy differences between Cu in the 8MR and 6MR sites decreases and almost disappears, which means that the thermodynamic stability of ZCu with molecularly adsorbed species is nearly identical for Cu in different sites. Considering more complicated scenarios of NO (or CO) adsorption, we find that the co-adsorption of 2 NO (or 2 CO) molecules weakens their interaction with Cu, as well as their co-adsorption with OH and H2O. The X-ray absorption near edge structure (XANES) of Cu in Cu-SSZ-13 under different conditions was also modeled from first principles. We find that the pre-edge feature in the K-edge XANES of Cu in clean Cu-SSZ-13 with Cu in a 8MR site is induced by a 1s to 4s transition while there is no pre-edge peak when Cu is in a 6MR site. Molecular adsorption onto Cu in a 6MR or a 8MR site results in the same K-edge XANES. When NO is adsorbed onto Cu in SSZ-13, we find that the origin of the small pre-edge peak in the K-edge XANES lies in a 1s to 3d electron transition. On the other hand, when CO or N2 is adsorbed onto an isolated Cu atom in SSZ-13, a transition from the 1s state to the hybridized state of 3d and 4p results in a pre-edge peak in the K-edge of the XANES spectrum. It is also found that the edge position and intensity of the maximum peak of Cu K-edge XANES depend on the Cu locations and the adsorbed molecules. By studying the Cu K-edge XANES of ZCu with adsorption of species of different oxidizing power, we conclude that a higher oxidation state of Cu will result in a higher energy edge position in the Cu K-edge XANES. These results are expected to greatly aid our understanding of Cu-SSZ-13 SCR catalysts. This work was supported by institutional funds provided to JSM from the Voiland School of Chemical Engineering and Bioengineering. Financial support was also provided by the National Science Foundation GOALI program under contract Nos. CBET-1258717, CBET-1258715 and CBET-1258690. We thank Prof. Fabio Ribeiro, Mr. Atish Parekh, Prof. W. F. Schneider, Mr. Christopher Paolucci, Mr. Trunjoyo Anggara and Prof. Jeff Miller for stimulating discussions on the modeling of the XANES spectrum and Ms. Alyssa Hensley for her comments on the manuscript. J.Sz. acknowledges the financial support of this work by the U.S. Department of Energy (DOE), Office of Energy Efficiency and Renewable Energy, Vehicle Technologies Program. A portion of the computer time for the computational work was performed using EMSL, a national scientific user facility sponsored by the Department of Energy’s Office of Biological and Environmental Research and located at PNNL. PNNL is a multi-program national laboratory operated for the US DOE by Battelle.

Zhang, Renqin↗
DOE OSTI2016

Ab Initio Reaction Kinetics of CH 3 O$\dot{C}$(=O) and $\dot{C}$H 2 OC(=O)H Radicals

The dissociation and isomerization kinetics of the methyl ester combustion intermediates methoxycarbonyl radical (CH3O$\dot{C}$(=O)) and (formyloxy)methyl radical ($\dot{C}$H2OC(=O)H) are investigated theoretically using high-level ab initio methods and Rice–Ramsperger–Kassel–Marcus (RRKM)/master equation (ME) theory. Geometries obtained at the hybrid density functional theory (DFT) and coupled cluster singles and doubles with perturbative triples correction (CCSD(T)) levels of theory are found to be similar. We employ high-level ab initio wave function methods to refine the potential energy surface: CCSD(T), multireference singles and doubles configuration interaction (MRSDCI) with the Davidson–Silver (DS) correction, and multireference averaged coupled-pair functional (MRACPF2) theory. MRSDCI+DS and MRACPF2 capture the multiconfigurational character of transition states (TSs) and predict lower barrier heights than CCSD(T). The temperature- and pressure-dependent rate coefficients are computed using RRKM/ME theory in the temperature range 300–2500 K and a pressure range of 0.01 atm to the high-pressure limit, which are then fitted to modified Arrhenius expressions. Dissociation of CH3O$\dot{C}$(=O) to $\dot{C}$H3 and CO2 is predicted to be much faster than dissociating to CH3$\dot{O}$ and CO, consistent with its greater exothermicity. Isomerization between CH3O$\dot{C}$(=O) and $\dot{C}$H2OC(=O)H is predicted to be the slowest among the studied reactions and rarely happens even at high temperature and high pressure, suggesting the decomposition pathways of the two radicals are not strongly coupled. The predicted rate coefficients and branching fractions at finite pressures differ significantly from the corresponding high-pressure-limit results, especially at relatively high temperatures. Finally, because it is one of the most important CH3$\dot{O}$ removal mechanisms under atmospheric conditions, the reaction kinetics of CH3$\dot{O}$ + CO was also studied along the PES of CH3O$\dot{C}$(=O); the resulting kinetics predictions are in remarkable agreement with experiments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Communication: GAIMS—Generalized Ab Initio Multiple Spawning for both internal conversion and intersystem crossing processes

Full multiple spawning is a formally exact method to describe the excited-state dynamics of molecular systems beyond the Born-Oppenheimer approximation. However, it has been limited until now to the description of radiationless transitions taking place between electronic states with the same spin multiplicity. This Communication presents a generalization of the full and ab initio multiple spawning methods to both internal conversion (mediated by nonadiabatic coupling terms) and intersystem crossing events (triggered by spin-orbit coupling matrix elements) based on a spin-diabatic representation. The results of two numerical applications, a model system and the deactivation of thioformaldehyde, validate the presented formalism and its implementation.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2015

Bridging a gap between continuum-QCD and ab initio predictions of hadron observables

Within contemporary hadron physics there are two common methods for determining the momentum-dependence of the interaction between quarks: the top-down approach, which works toward an ab initio computation of the interaction via direct analysis of the gauge-sector gap equations; and the bottom-up scheme, which aims to infer the interaction by fitting data within a well-defined truncation of those equations in the matter sector that are relevant to bound-state properties. We unite these two approaches by demonstrating that the renormalisation-group-invariant running-interaction predicted by contemporary analyses of QCD's gauge sector coincides with that required in order to describe ground-state hadron observables using a nonperturbative truncation of QCD's Dyson–Schwinger equations in the matter sector. This bridges a gap that had lain between nonperturbative continuum-QCD and the ab initio prediction of bound-state properties.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2014

Toward spectroscopically accurate global ab initio potential energy surface for the acetylene-vinylidene isomerization

A new full-dimensional global potential energy surface (PES) for the acetylene-vinylidene isomerization on the ground (S{sub 0}) electronic state has been constructed by fitting ∼37 000 high-level ab initio points using the permutation invariant polynomial-neural network method with a root mean square error of 9.54 cm{sup −1}. The geometries and harmonic vibrational frequencies of acetylene, vinylidene, and all other stationary points (two distinct transition states and one secondary minimum in between) have been determined on this PES. Furthermore, acetylene vibrational energy levels have been calculated using the Lanczos algorithm with an exact (J = 0) Hamiltonian. The vibrational energies up to 12 700 cm{sup −1} above the zero-point energy are in excellent agreement with the experimentally derived effective Hamiltonians, suggesting that the PES is approaching spectroscopic accuracy. In addition, analyses of the wavefunctions confirm the experimentally observed emergence of the local bending and counter-rotational modes in the highly excited bending vibrational states. The reproduction of the experimentally derived effective Hamiltonians for highly excited bending states signals the coming of age for the ab initio based PES, which can now be trusted for studying the isomerization reaction.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Coherent band excitations in CePd 3 : A comparison of neutron scattering and ab initio theory

In common with many strongly correlated electron systems, intermediate valence compounds are believed to display a crossover from a high-temperature regime of incoherently fluctuating local moments to a low-temperature regime of coherent hybridized bands. In this work, we show that inelastic neutron scattering measurements of the dynamic magnetic susceptibility of CePd 3 provides a benchmark for ab initio calculations based on dynamical mean field theory. The magnetic response is strongly momentum dependent thanks to the formation of coherent f-electron bands at low temperature, with an amplitude that is strongly enhanced by local particle-hole interactions. Finally, the agreement between experiment and theory shows that we have a robust first-principles understanding of the temperature dependence of f-electron coherence.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Bergman-type medium range order in amorphous Zr77Rh23 alloy studied by ab initio molecular dynamics simulations

In recent years, some arguments about the existence of medium-range order (MRO) in the Zr-Rh system have been put forward. However, research on the structural features of the Zr-Rh binary alloy at the atomic level is still lacking. This study uses ab initio molecular dynamics simulations to systematically study the local structures of Zr77Rh23 from the liquid to the glassy states. Pair correlation function (PCF), coordination number (CN), Honeycutt–Anderson(HA) index, bond-angle distribution functions, and the Voronoi tessellation method are used to reveal a clear icosahedral-like configuration in the amorphous Zr77Rh23 alloy. It is noteworthy that the splitting in the second peak of the partial PDF implies the existence of a medium range order (MRO) in the Zr77Rh23 system. We obtain the local order in three-dimensional atomic density distributions by using a new atomistic cluster alignment (ACA) method. Interestingly, a Bergman-type MRO is observed in the glassy Zr77Rh23. Furthermore, the spatial distribution and connections of icosahedral-like clusters are shown to further demonstrate the MRO network. Our findings shed light on the nature of atomic local structures of amorphous Zr77Rh23 alloy and have important implications to understanding the formation of various MROs in metallic glasses.

Guo, Y. R.↗
DOE OSTI2021

Insights into Spontaneous Solid Electrolyte Interphase Formation at Magnesium Metal Anode Surface from Ab Initio Molecular Dynamics Simulations

Spontaneous chemical reactivity at multivalent (Mg, Ca, Zn, Al) electrode surfaces is critical to solid electrolyte interphase (SEI) formation, and hence, directly affects the longevity of batteries. Here, we report an investigation of the reactivity of 0.5 M Mg(TFSI)2 in 1,2-dimethoxyethane (DME) solvent at a Mg(0001) surface using ab initio molecular dynamics (AIMD) simulations and detailed Bader charge analysis. Based on the simulations, the initial degradation reactions of the electrolyte strongly depend on the structure of the Mg(TFSI)2 species near the anode surface. At the surface, the dissociation of Mg(TFSI)2 species occurs via cleavage of the N-S bond for the solvent separated ion pair (SSIP) and via cleavage of the C-S bond for the contact ion pair (CIP) configuration. In the case of the CIP, both TFSI anions undergo spontaneous bond dissociation reactions to form atomic O, C, S, F, and N species adsorbed on the surface of the Mg anode. These products indicate that the initial SEI layer formed on the surface of the pristine Mg anode consists of a complex mixture of multiple components such as oxides, carbides, sulfides, fluorides, and nitrides. We believe that the atomic level insights gained from these simulations will lay the groundwork for the rational design of tailored and functional interphases that are critical for the success of multivalent battery technology.

Agarwal, Garvit↗
DOE OSTI2016

The development of explosions in axisymmetric ab initio core-collapse supernova simulations of 12–25 M{sub ⊙} STARS

We present four ab initio axisymmetric core-collapse supernova simulations initiated from 12, 15, 20, and 25 M{sub ⊙} zero-age main sequence progenitors. All of the simulations yield explosions and have been evolved for at least 1.2 s after core bounce and 1 s after material first becomes unbound. These simulations were computed with our Chimera code employing RbR spectral neutrino transport, special and general relativistic transport effects, and state-of-the-art neutrino interactions. Continuing the evolution beyond 1 s after core bounce allows the explosions to develop more fully and the processes involved in powering the explosions to become more clearly evident. We compute explosion energy estimates, including the negative gravitational binding energy of the stellar envelope outside the expanding shock, of 0.34, 0.88, 0.38, and 0.70 Bethe (B ≡ 10{sup 51} erg) and increasing at 0.03, 0.15, 0.19, and 0.52 B s{sup −1}, respectively, for the 12, 15, 20, and 25 M{sub ⊙} models at the endpoint of this report. We examine the growth of the explosion energy in our models through detailed analyses of the energy sources and flows. We discuss how the explosion energies may be subject to stochastic variations as exemplfied by the effect of the explosion geometry of the 20 M{sub ⊙} model in reducing its explosion energy. We compute the proto-neutron star masses and kick velocities. We compare our results for the explosion energies and ejected {sup 56}Ni masses against some observational standards despite the large error bars in both models and observations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Skutterudites under pressure: An ab initio study

Ab initio results on the band structure, density of states, and Fermi surface (FS) properties of LaRu{sub 4}X{sub 12} (X = P, As, Sb) are presented at ambient pressure as well as under compression. The analysis of density of states reveals the major contribution at the Fermi level to be mainly from the Ru-d and X-p states. We have a complicated Fermi surface with both electron and hole characters for all the three compounds which is derived mainly from the Ru-d and X-p states. There is also a simpler FS with hole character derived from the P-p{sub z} orbital for LaRu{sub 4}P{sub 12} and Ru-d{sub z{sup 2}} orbital in the case of As and Sb containing compounds. More interestingly, Fermi surface nesting feature is observed only in the case of the LaRu{sub 4}P{sub 12}. Under compression, we observe the topology of the complicated FS sheet of LaRu{sub 4}As{sub 12} to change around V/V{sub 0} = 0.85, leading to a behaviour similar to that of a multiband superconductor, and in addition, we have two more hole pockets centered around Γ at V/V{sub 0} = 0.8 for the same compound. Apart from this, we find the hole pocket to vanish at V/V{sub 0} = 0.8 in the case of LaRu{sub 4}Sb{sub 12} and the opening of the complicated FS sheet gets reduced. The de Haas van Alphen calculation shows the number of extremal orbits in the complicated sheet to change in As and Sb containing compounds under compression, where we also observe the FS topology to change.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2014

Ab-initio calculations of electronic, transport, and structural properties of boron phosphide

We present results from ab-initio, self-consistent density functional theory calculations of electronic and related properties of zinc blende boron phosphide (zb-BP). We employed a local density approximation potential and implemented the linear combination of atomic orbitals formalism. This technique follows the Bagayoko, Zhao, and Williams method, as enhanced by the work of Ekuma and Franklin. The results include electronic energy bands, densities of states, and effective masses. The calculated band gap of 2.02 eV, for the room temperature lattice constant of a=4.5383 Å, is in excellent agreement with the experimental value of 2.02±0.05 eV. Our result for the bulk modulus, 155.7 GPa, agrees with experiment (152–155 GPa). Our predictions for the equilibrium lattice constant and the corresponding band gap, for very low temperatures, are 4.5269 Å and 2.01 eV, respectively.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2018

Effect of Oxygen on the Quantum, Magnetic, and Thermodynamic Properties of Co Nanowires on the Reconstructed Anisotropic (1 × 2)/Au(110) and (1 × 2)/Pt(110) Surfaces: Ab Initio Approach

Ab initio theoretical study of the quantum magnetic properties of Co nanowires on the pure and oxygen-reconstructed (1 × 2)/Au(110) and (1 × 2)/Pt(110) surfaces is performed. Their structures and electronic configurations are calculated using the electron density functional theory. High values of magnetic moment and magnetic anisotropy energies of Co atoms are found on both pure and oxygen-reconstructed (1 × 2)/Au(110) and (1 × 2)/Pt(110) surfaces. The adsorption of oxygen atoms on the (1 × 2)/Au(110) substrate is shown to affect the structural arrangement of Co nanowire atoms on this substrate and to increase the magnetic anisotropy energy (by 1.91 meV per nanowire atom). The adsorption of oxygen on the Pt(110) substrate substantially decreases the magnetic anisotropy energy of the Co nanowire on it (by 5.98 meV per atom). The origin of these changes is revealed by analyzing the local densities of states of the d electrons of nanowire atoms. The temperature ranges of the states with the lowest free surface energy are determined using the atomistic thermodynamics methods. These data and the available experimental data are used to predict the possibility of observing the structures under study in experiments.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Band and Impurity States in Dimond with the (MV){sup –} (M = Si, Ge, Sn) Centers Based on ab Initio Calculations

Ab initio calculations were used to determine the structure, electronic zone dispersion, partial (atomic and orbital) densities of states, and levels of impurity–vacancy cluster (MV){sup –} (M = Si, Ge, Sn) in diamond. Wavefunctions were determined in the density functional theory approximation using hybrid exchange-correlation functional, localized basis set of Gaussians, and a supercell consisting of 192 atoms. Results are compared with data on undoped diamond and with experimental results. The dependence of the direct and indirect energy gap on the cluster type is discussed. Calculations are carried out taking into account the spin–orbit interaction to identify impurity levels in the valence band. The effect of electron–electron interaction on the position of impurity levels is discussed. The dominant contribution of the d orbitals to the density of states at the impurity level in all clusters is detected.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2018

Electronic Structure, Mechanical and Dynamical Stability of Hexagonal Subcarbides M{sub 2}C (M = Tc, Ru, Rh, Pd, Re, Os, Ir, and Pt): Ab Initio Calculations

Ab initio calculations were used to study the properties of a series of hexagonal (Fe{sub 2}N-like) subcarbides M{sub 2}C, where M = Tc, Ru, Rh, Pd, Re, Os, Ir, and Pt, and to calculate their equilibrium structural parameters, electronic properties, phase stability, elastic constants, compression modulus, shear modulus, Young’s modulus, compressibility, Pugh’s indicator, Poisson ratio, elastic anisotropy indices, and also hardness, Debye temperature, sound velocity, and low-temperature heat capacity. It is found based on these results that all the subcarbides are mechanically stable; however, their formation energies E{sub form} are positive with respect to a mixture of d-metal and graphite. In addition, the calculation of the phonon spectra of these subcarbides shows the existence of negative modes, which indicates their dynamical instability. Thus, a successful synthesis of these subcarbides at normal conditions is highly improbable.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗