K-shell Research Articles

Enhanced stability of the Nb3O6- and Nb4O6+ clusters: the nxcπ rule versus superatomic nature.

This study examines the chemical reactivity of niobium clusters with carbon dioxide (CO2), with an emphasis on the analysis of the ensuing products Nb4O6+ and Nb3O6-, which show up in the cationic and anionic mass spectra, respectively. Using density functional theory (DFT) calculations, we demonstrate the reactivity of the Nbn± clusters with CO2 and reveal distinct stabilization mechanisms for the two prominent products. The stability of Nb3O6- is determined by the existence of ten π bonds pertaining to π-electron delocalization, which conforms to the nxcπ electron configuration model. Despite having only a one-atom distinction, Nb4O6+ exhibits superatomic electron shells embodying superatom stability. The divergent stabilizing mechanisms found in Nb4O6+ and Nb3O6- illustrate the intricate nature of cluster chemistry and the significance of electronic structure in governing cluster stability and reactivity.

The smallest triple-ring tubular gold clusters M2@Au15 with M = Mo, W: stability, electronic properties and nonlinear optical response.

The smallest triple ring tube-like gold clusters M2@Au15q with M = Mo, W and q = 1, 0, -1 are reported for the first time. Incorporation of an M2 dimer results in a remarkable modification of both atomic and electronic structures of the gold host. While the bare Au15 cluster exhibits a 3D cage shape, the doubly doped clusters M2@Au15 in all charge states are found to prefer a tubular form composed of three five-membered Au rings in an anti-prism arrangement and stabilized by an M2 unit placed inside the tube-like Au15 gold framework. The equilibrium geometry of both M2@Au15 and M2@Au15- is not much modified upon electron detachment from or attachment to their pure gold counterpart. The anion M2@Au15- with 28 itinerant electrons establishes an electron shell configuration of 1S21P61D102S21F8, in which the 1F shell splits into four different sub-levels. These stable clusters are thus not magic. Computed results on the first and second hyper-polarizability parameters of the doped clusters show a strong dependence on the charge. Overall, the neutral M2@Au15 is found to exhibit a particularly strong nonlinear optical (NLO) response. These clusters can also be extended to 1D nanowires, providing helpful guidance for the design of novel gold-based nanowires with rich optoelectronic properties.

Extending the Chevrel-type superatoms to the nitrogen family.

Chevrel-type superatoms refer to the ligated transition metal chalcogenide clusters M6E8L6, where the octahedral M6 is face-capped with cubic chalcogen E8 (E = S/Se/Te). Most transition metals can form such superatoms and many organic and inorganic ligands can be substituted in solution reactions, which allows these atomic precision species to be easily functionalized and their properties to be tunable. No test was reported for substituting the chalcogens with pnicogens in this class of materials. In this article, we try to discover if such substitutions are possible. Combining different transition metals and ligands, theoretical computations show that [M6Q8(CN)6]2- (Q = P, As, Sb) for M = Co, Rh, Ir, and Ni, Pd, Pt have closed electronic shells and possess enhanced thermal and chemical stabilities. Analyses of the electronic structures indicate high similarity between the M-M and M-Q/M-S interactions in these species.

A superatom-assembled B8N2 monolayer acting as an electronic sponge for high-capacity anode materials for Na/K-ion batteries.

Rechargeable sodium/potassium-ion batteries (SIBs/PIBs) have emerged as appealing alternatives for lithium-ion batteries due to their earth-abundance and economic benefits. However, exploring high-capacity anode materials for SIBs/PIBs is still challenging. Superatoms with delocalized electronic shells possess high flexibility as electron-acceptors/donors, making them ideal candidates for anode materials. Here, a superatom-assembled boron nitride monolayer (B8N2) was theoretically predicted using first principles calculations. The B8 core is assembled with two B4 superatoms, and further linked by nitrogen atoms in a graphene-like lattice. The B8N2 monolayer has an undirected bandgap (0.82 eV/HSE06) with an ultra-high carrier mobility of 13 × 104 cm2 V-1 s-1, where Na/K ions can be effectively adsorbed on its surface. The remarkably high theoretical storage capacities (924 mA h g-1/1115 mA h g-1), and low open-circuit voltages (0.08 V/0.21 V) are also revealed for the B8N2 monolayer with Na/K ions. Intriguingly, adsorption of Na/K ions causes little geometric deformation of the B8N2 monolayer, which ensures a promising cell operating cycle during the adsorption of Na/K ions at high concentrations. This work reveals the potential of superatoms as an efficient "electronic sponge", providing impetus for the design of superatomic electrode materials for metal ion batteries.

Reconstructing perspectives: investigating how molecular geometry cards (MGCards) and molecular model building (MMB) disrupt students' alternative notions of molecular structure – a qualitative study

The range of abstract concepts encountered when learning chemistry and the inability of students to make connections between the macroscopic, sub-microscopic, and symbolic representations, used in chemistry teaching, are believed to be the main reasons for students’ difficulty when learning chemistry. Prediction and determination of molecular geometry using the theory of valence shell electron pair repulsion (VSEPR) is a sample of the abstract concept that is hard to understand by students who learn chemistry. Students may comprehend these ideas better if the learning process is supplemented with cutting-edge, interactive learning aids. To address the conceptual difficulties that students encounter when learning how to predict the shapes of molecules, a card game (MGCards) has been developed which is supported by simple molecular model building (MMB). The card game allows students to work through the steps required to predict the shape of a molecule in an engaging format. The student learning process is supported by feedback at all stages (if students make a mistake, they receive hints that will help them in the next step of the game). Action research with qualitative methods has been used to design, develop, and evaluate the MGCards. The MGCards and MMB were piloted at the University of Leicester with year one Natural Sciences students and modified based on the feedback received. Both MGCards and MMB were then used as part of the first-year chemistry education programme at Tanjungpura University in Indonesia. The findings of students’ answer analysis (pre- and post-test) in both cycles showed that students had a better understanding after learning with MGCards and MMB. The positive feedback for MGCards and MMB confirmed that these resources were effective in delivering an engaging learning experience. The results suggest that MGCards and MMB play a significant role in enhancing students’ understanding while also keeping them engaged.

Study of electronic structure and optical transition properties of low-lying excited states of AuB molecules based on configuration interaction method

High-level configuration interaction method including the spin-orbit coupling is used to investigate the low-lying excited electronic states of AuB that is not reported experimentally. The electronic structure in our work is preformed through the three steps stated below. First of all, Hartree-Fock method is performed to compute the singlet-configuration wavefunction as the initial guess. Next, we generate a multi-reference wavefunction by using the state-averaged complete active space self-consistent field (SACASSCF). Finally, the wavefunctions from CASSCF are utilized as reference, the exact energy point values are calculated by the explicitly correlated dynamic multi-reference configuration interaction method (MRCI). The Davidson correction (+Q) is put forward to solve the size-consistence problem caused by the MRCI method. To ensure the accuracy, the spin-orbit effect and correlation for inner shell electrons and valence shell electrons are considered in our calculation. The potential energy curves of 12 Λ-S electronic states are obtained. According to the explicit potential energy curves, we calculate the spectroscopic constants through solving radial Schrödinger equation numerically. We analyze the influence of electronic state configuration on the dipole moment by using the variation of dipole moment with nuclear distance. The spin-orbit matrix elements for parts of low-lying exciting states are computed, and the relation between spin-orbit coupling and predissociation is discussed. The predissociation is analyzed by using the obtained spin-orbit matrix elements of the 4 Λ-S states which spilt into 12 Ω states. It indicates that due to the absence of the intersections between the curves of spin-orbit matrix elements related with the 4 low-lying Λ-S states, the predissociation for these low-lying exciting states will not occur. Finally, the properties of optical transition between the ground Ω state <inline-formula><tex-math id="M3">\begin{document}$ {\rm A}^{1}{{{\Pi}}}_{1} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231347_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231347_M3.png"/></alternatives></inline-formula> and first excited Ω state <inline-formula><tex-math id="M4">\begin{document}$ {{\mathrm{X}}}^{1}{{{\Sigma }}}_{{0}^{+}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231347_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231347_M4.png"/></alternatives></inline-formula> are discussed in laser-cooling filed by analyzing the Franck-Condon factors and radiative lifetime. And the transition dipole moment is also calculated. But our results reveal that the AuB is not an ideal candidate for laser-cooling. In conclusion, this work is helpful in deepening the understanding of AuB, especially the structures of electronic states, interaction between excited states, and optical transition properties. All the data presented in this paper are openly available at <ext-link ext-link-type="uri" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://www.doi.org/10.57760/sciencedb.j00213.00009">https://www.doi.org/10.57760/sciencedb.j00213.00009</ext-link>.

Ligand-enforced geometric constraints and associated reactivity in p-block compounds.

The geometry at an element centre can generally be predicted based on the number of electron pairs around it using valence shell electron pair repulsion (VSEPR) theory. Strategies to distort p-block compounds away from these predicted geometries have gained considerable interest due to the unique structural outcomes, spectroscopic properties or reactivity patterns engendered by such distortion. This review presents an up-to-date group-wise summary of this exciting and rapidly growing field with a focus on understanding how the ligand employed unlocks structural features, which in turn influences the associated reactivity. Relevant geometrically constrained compounds from groups 13-16 are discussed, along with selected stoichiometric and catalytic reactions. Several areas for advancement in this field are also discussed. Collectively, this review advances the notion of geometric tuning as an important lever, alongside electronic and steric tuning, in controlling bonding and reactivity at p-block centres.

Recent advances in the chemistry of isolable carbene analogues with group 13-15 elements.

Carbenes (R2C:), compounds with a divalent carbon atom containing only six valence shell electrons, have evolved into a broader class with the replacement of the carbene carbon or the RC moiety with main group elements, leading to the creation of main group carbene analogues. These analogues, mirroring the electronic structure of carbenes (a lone pair of electrons and an empty orbital), demonstrate unique reactivity. Over the last three decades, this area has seen substantial advancements, paralleling the innovations in carbene chemistry. Recent studies have revealed a spectrum of unique carbene analogues, such as monocoordinate aluminylenes, nitrenes, and bismuthinidenes, notable for their extraordinary properties and diverse reactivity, offering promising applications in small molecule activation. This review delves into the isolable main group carbene analogues that are in the forefront from 2010 and beyond, spanning elements from group 13 (B, Al, Ga, In, and Tl), group 14 (Si, Ge, Sn, and Pb) and group 15 (N, P, As, Sb, and Bi). Specifically, this review focuses on the potential amphiphilic species that possess both lone pairs of electrons and vacant orbitals. We detail their comprehensive synthesis and stabilization strategies, outlining the reactivity arising from their distinct structural characteristics.

Calculation of Nuclear Stopping Power

Fast charged particles interact with matter mainly by interaction with the electron shell of the atoms causing ionization and excitation, i.e. inelastic scattering. However, for lower velocity projectiles an important part of the energy loss is due to elastic scattering on the nuclei, which is called nuclear stopping. In the present paper we calculate the nuclear stopping cross section of protons and antiprotons in different materials. The obtained results are compared with calculations by other groups and with the electronic stopping cross sections. The difference between the results for protons and antiprotons is explained. Keywords: interaction of charged particles with matter, nuclear stopping, Barkas effect.

Carbon-Free, Connected Core-Shell Nanoparticle Catalysts with Advanced Oxygen-Reduction Performances for PEFCs

As the world faces diminishing non-renewable energy sources and a surge in global pollution, establishing a hydrogen and low-carbon economy has become crucial. Polymer electrolyte fuel cells (PEFCs) hold great promise as a sustainable energy source with the potential for high efficiency, and clean power generation in both stationary and mobile applications. However, the conventional platinum nanoparticle catalysts on carbon support (Pt/C) used for the oxygen reduction reaction (ORR) at the cathode shows sluggish ORR activity, leading to high cost and inferior PEFC performance. Moreover, the carbon-supports used for the Pt catalysts are susceptible to degradation caused by carbon-corrosion during start-stop operations, which can severely compromise the overall performance of the PEFCs. Hence, in order to significantly enhance the commercial viability of PEFCs, considerable progress must be made in terms of cost, performance, and durability.Previously our group has reported carbon-free, connected Pt-alloy catalysts to address the above issues. This catalyst is composed of connected Pt-alloy nanonetworks with high electronic conductivity and exhibits enhanced ORR activity, high start-stop durability, and thin catalyst layers. Specifically, this catalyst exhibited 9 times higher specific activity than that of the commercial Pt/C, making it an excellent candidate for cathode catalyst applications.[1,2] However, high-temperature annealing process is required to develop connected networks between the Pt-alloy nanoparticles, resulting in larger crystallite sizes and reduced surface areas. This limitation has prevented connected Pt-alloy catalysts from achieving significant improvement in mass activity.In this work, we have proposed a novel synthesis method that enables the development of connected core-shell nanoparticle catalysts without any high-temperature treatment. This method eliminates the particle growth and exhibit a high surface area, making it highly effective for ORR applications. Here, a carbon-free catalyst with a core-shell nanonetwork structure having a non-Pt (Pd) core and Pt shell was developed. Additionally, the relationship between the thickness of the Pt-shell layer and ORR activity was investigated.Connected core-shell catalysts with Pd nanoparticles as core and Pt as atomic shell (Pd@Pt) were synthesized in a one-pot polyol process that does not require high-temperature annealing as shown in Fig. 1. The formation of connected Pd@Pt core-shell nanonetworks (< 10 nm) was confirmed by TEM and STEM-EDX analysis. Also, the structure of Pt shell on core metals was successfully tuned by controlling the reaction temperature and time, precursor ratio, etc. Here, the number of the Pt layers on the surface of the connected Pd@Pt core-shell catalysts were varied from 1–6 atomic layers and the results show that the ORR mass activity was notably enhanced in the catalyst with a moderate shell thickness ranging from 2.5 to 3.5 Pt atomic layers. This suggests that connected Pd@Pt catalyst with a moderate Pt layer achieves both high surface area and ORR specific activity. The high surface area of the developed catalysts is attributed to a new synthesis method that does not use high temperature annealing and a low Pt core-shell structure. The improvement in ORR specific activity can be attributed to the more suitable d-band center position of the Pt shell, which is influenced by strain and ligand effects resulting from the Pd core. The ORR performance of the carbon-free connected Pd@Pt catalyst showed 2–4 times enhancement in electrochemical surface area (ECSA) and 1.5–3 times improvement in ORR mass activity compared to the connected Pt-alloy catalysts prepared using high-temperature annealing. Further, high durability of the connected core-shell catalyst against load cycles (0.6 ↔1.0 V) at 60 °C in acidic electrolyte solution was also demonstrated, indicating that a high stability nanonetwork connected by Pt atomic shell.In summary, we have successfully demonstrated a new synthesis method for the formation of connected core-shell nanoparticles by Pt atomic shell without high-temperature annealing and prepared a carbon-free, connected Pd@Pt core-shell catalyst with advanced ORR performance, highlighting its great potential as a cathode catalyst. Acknowledgement The part of this presentation is based on results obtained from a project, JPNP20003, commissioned by the New Energy and Industrial Technology Development Organization (NEDO).

Analysis of electron configurations in terms of parity-supporting rotations returns the hydrogen spectrum with consequences for the orbital model

A centrally symmetric variant of Bohr’s atomic model was constructed according to first geometric principles, and entanglement of pairs of subatomic particles through invariant rotations that stabilize the system. Its base symmetry was constrained to 2-fold rotational symmetry corresponding to 2 electrons associated with the atomic ground energy state. The theory was constructed using two sets of invariant rotations of distinguishable and indistinguishable type, derived from spherical approximations, with information regarding the initial state of the system preserved throughout the geometric transformation. Superposition of alternating structures of the two types indicates that closing of electron shells may take place via formation of mirror symmetry through rotational invariance, and quantization of energy can be reconciled with observables in quantum mechanics. The resulting solution correlates subshells s-g with unique parity-supporting states, and subsequent subshells with their imitations, having double the number of electrons of the preceding subshell of a corresponding type.

Atomic Electron Shell Excitations in Double-β Decay

The problem of the transition of electron shells of atoms to excited states in the process of neutrinoless double-βdecay is investigated. This subject is crucial for modeling the energy spectrum ofβ-electrons, which is sensitive to the mass and Majorana nature of neutrinos. The dependence of the obtained results on the atomic number indicates an important role of the Feinberg–Migdal effect in the electron shell excitations. We report the overlap amplitudes of the electron shells of the parent atom and the daughter ion for eleven atoms, the two-neutrino double-βdecay of which was observed experimentally. In around one-fourth of the cases where the structure of the electron shells is inherited from the parent atom, there is a transition to the ground state or the excited state with the lowest energy. The de-excitation of the daughter ion in the latter scenario is accompanied by the emission of photons in the ultraviolet range, which can serve as an auxiliary signature of double-βdecay. The average excitation energy of the electron shells ranges between 300 and 800 eV, with the variance ranging from (1.7 keV)2in calcium to (14 keV)2in uranium.

Phenalenyl-substituted stilbenes as the basis for spin switches: quantum-chemical modeling

Isomers of stilbenes containing phenalenyl substituents in the para - and meta -positions of phenyl rings were studied by means of density functional theory method. Exchange coupling in structures with the trans -form of stilbenes is absent. In the cis -isomer of a meta -substituted compound, the state with a closed electron shell is stabilized due to two-electron multicenter interactions, which is confirmed by CASSCF calculations. The predicted transition between the triplet and singlet states as a result of trans-cis isomerization opens up prospects for using the discovered effect in the development of organic spin switches.

Structural and electrochemical performance of (Sr1.8Ln0.2)FeMoO6 (Ln = Sr, La, Sm, Eu) anode for solid oxide fuel cell

Different electronic structure on 4 f shell endows rare earth with variable of catalytic activity. In order to explore the catalytic effect of rare earth on solid oxide fuel cell (SOFC) electrode, we prepare electrolyte-supported (Sr1.8Ln0.2)FeMoO6/SDC/LSGM/SBCO single cell with Ln = Sr, La, Sm and Eu, and investigate their electrochemical performance based on X-ray diffraction (XRD), DC four-point probe, I-V and electrochemical impedance spectra. XRD results show that (Sr1.8Ln0.2)FeMoO6 are of single phase and belong to I4/m space group. Owing to the increased density of states, electronic conductivity of (Sr1.8La0.2)FeMoO6 (SLFM), (Sr1.8Sm0.2)FeMoO6 (SSFM) and (Sr1.8Eu0.2)FeMoO6 (SEFM) increases significantly, where SEFM exhibits the highest value in the measuring range. The higher conductivity and the smaller activation energy favor the power output of the investigated cell. The maximum power density of Sr2FeMoO6 (SFMO)-based cell is 772 mW·cm−2 at 850 ℃, that of SLFM- and SSFM-based cell increases to 890.8 mW·cm−2 and 861.6 mW·cm−2, while SEFM-based cell exhibits the highest value of 964.6 mW·cm−2. Electrochemical Impedance Spectroscopy (EIS) finds that SEFM-based cell possesses the smallest electrode resistance, charge transfer resistance, the fastest surface exchange and oxygen diffusion process, which favors its highest power output. These results demonstrate that the synergistic reaction in catalytic activity between rare earth atoms and SFMO lattice is different to a large degree, and our innovative discovery is the good catalytic activity of SEFM anode, which is conducive to comprehensively understanding the catalytic properties of rare earth for SOFC electrodes.

Değişen Sıcaklık Koşullarının LiNi2Sn Malzemesinin Elektronik Seviyeleri Üzerine Etkilerinin Araştırılması: Bir Ab-Initio Çalışması

In this study, the electronic and crystal structures of the LiNi2Sn material—reported to have a stable crystal structure but not yet thoroughly studied—were examined at various temperatures, and traces of the thermoelectric property were looked for in light of the results. A test research was carried out with a fresh perspective on the thermoelectric property traces on the electrical and crystal structures in order to promote the studies of thermoelectric materials, and the results were provided with complete analysis. Theoretical investigations using X-ray absorption fine structure (XAFS) spectroscopic calculations were made into the electronic structural characteristics of the LiNi2Sn material. Calculations were made with XAFS code FEFF 8.20 under increasing temperature conditions of 300 K, 323 K, 373 K, and 423 K. Findings from the study included the quantity and potency of the atoms' outer shell electrons, which are where the photoelectrons are directed. The results of the study are compatible with the literature data.

Atomic Structure: Validation of the Electron Phase Transformation Theory

The current consensus on the atomic structure was formulated about a hundred years ago. In the enlightenment of the newly developed instrumentations and theories the electronic structure of the atoms is reconsidered. It has been concluded that in order to comply with experiments the electron must go through phase transformation from point to surface charge when captured by the nucleus. The surface charge electron shell model of the atoms is consistent with all the known features of the atoms and offers a physical explanation for Schrodinger`s wave equation.

Alloy splitting of the FeGa acceptor level in dilute AlxGa1−xN

The results of conventional deep-level transient spectroscopy (DLTS) and high-resolution Laplace DLTS measurements of the FeGa(0/−) acceptor level in dilute AlxGa1−xN layers (x ≤ 0.05) grown by MOVPE technique (metal–organic vapor phase epitaxy) on native ammono-GaN substrates are analyzed and discussed. It is shown that the electron emission signal related to the FeGa acceptor level in AlxGa1−xN splits into individual components due to aluminum fluctuations in the second-nearest neighbor (2NN) shell around the FeGa impurity atoms. The calculations of the probability of finding a given number of aluminum atoms in the 2NN shell of the FeGa defect agree well with the experimental concentrations determined from Laplace DLTS peak intensities. This finding shows that in dilute AlxGa1−xN layers grown by MOVPE, aluminum and iron atoms are randomly distributed in the material. Finally, we demonstrate that the energy level of the FeGa acceptor with no Al atoms in the 2NN shell in the AlxGa1−xN samples shifts linearly with the aluminum content and the shifts are 28 and 55 meV relative to that in GaN for the samples with x = 0.025 and 0.05, respectively.

Identification of the optimal doping position of hetero-atoms in chalcogen-doped Fe–N–C catalysts for oxygen reduction reaction

The excellent oxygen reduction reaction (ORR) activity of Fe–N–C catalysts in acidic media makes them potential for low-cost proton exchange membrane fuel cells. In recent years, it has been shown that heteroatoms (B, O, S, P, Cl, F, etc.) can be used as electron-withdrawing groups to modulate the planar structure and electron distribution of the Fe–Nx active sites to achieve simultaneous improvement of catalytic activity and stability. However, the optimal location of the heteroatoms remains unclear. Here, taking chalcogen heteroatoms (S and Se) as an example, we control the doping positions and investigate their effect on the ORR performance of the Fe–N–C catalysts. The first coordination shell of the iron single atom is identified as the optimal doping position. The optimized catalyst Fe–N3S1/NC and Fe–N3Se1/NC demonstrate improved activity and stability in both half cells and fuel cells. This work provides insights into the enhancement mechanism of heteroatom doping of single-atom catalysts.

Establishment of descriptor for screening high-performance catalysts for hydrogen peroxide production through surface stress modulation induced by metal atom doping

Metal atoms doped onto the catalyst surface form surface alloys, enabling the modulation of surface electronic and geometric structures, consequently exerting control over the catalytic reactions occurring on the catalyst surface. However, as the concentration and placement of metal atom doping vary, makes the activity of surface reaction centers ambiguous. Herein, we demonstrate a methodology to describe the catalytic activity of hydrogen peroxide on the metal doped surface of Pd(111) by constructing a structural descriptor. By integrating the work function, d-band center, electronegativity of elements, number of electron shells, and surface compression/extension stress resulting from metal atom doping, this descriptor enables the discrimination of catalyst performance. This work provides novel insights for the screening of high-performance surface alloy catalysts and the development of catalyst descriptor studies.

Photoionization cross-sections of valence ns and np (n = 2,3) atomic shells in soft x-ray region

Theoretical photoionization cross-sections for average of configuration terms of valence ns- and np- shells of atoms C, N, O, F, Ne, Si, P, S, Cl and Ar are calculated with account for intrachannel and interchannel interactions for the energy region from threshold to 400 eV. The many-electron effects were accounted for within the framework of RPAE (random phase approximation with exchange) method, which is extended for average terms of unfilled shells. Calculations demonstrate for open-shell atoms similar effects as that were known for noble gas atoms Ne and Ar, namely a strong decrease of photoionization cross-sections of ns- subshell due to the interaction of transitions ns→εp and np→εd.