Artykuły w czasopismach: „D-band Theory”

1

Natori, A., i H. Kamimura. "Theory of a D- Band". Progress of Theoretical Physics Supplement 69 (14.05.2013): 353–64. http://dx.doi.org/10.1143/ptp.69.353.

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Moriarty, John A. "Generalized pseudopotential theory of d-band metals". International Journal of Quantum Chemistry 24, S17 (9.07.2009): 541–54. http://dx.doi.org/10.1002/qua.560240859.

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Jiao, Jun Rong, Jia Heng Wang, Chang Wei Gong, Yue Sheng Chai i Wei Shao. "Structural, Optical and Magnetic Properties of W-Doped TiO₂". Applied Mechanics and Materials 556-562 (maj 2014): 330–34. http://dx.doi.org/10.4028/www.scientific.net/amm.556-562.330.

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Based on the density functional theory method, the ab initio calculation with GGA+U was performed to investigate the electronic structure and properties of W-doped TiO2. The results indicated that W-doping induced ferromagnetism and shifted the absorption spectra to visible light region. The ferromagnetism derived from the spin-split of O 2p and W 5d caused by p–d orbit hybridization. Several impurity bands under the conduction band decreased the band gap.

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Fujisawa, Jun-ichi. "Highly-selective absorption control in photosynthetic chlorin dyes". Journal of Porphyrins and Phthalocyanines 19, nr 04 (kwiecień 2015): 601–9. http://dx.doi.org/10.1142/s1088424614501041.

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Selective chemical control of light-absorption bands of dye molecules in which the wavelengths of two or more absorption bands are individually controlled by chemical modifications is an ultimate challenge in chemistry and an important subject for their wide applications. Recently, selective absorption tuning was first reported in photosynthetic bacteriochlorin dyes. In the bacteriochlorin dyes, either the visible or near IR band is selectively shifted by the chemical modifications almost retaining the other band. Fujisawa et al. clarified that the selective absorption tuning is accomplished by chemical control of configuration interactions in the two two-level systems. This paper reports on more highly-selective absorption tuning in photosynthetic chlorin dyes, bacteriochlorophylls (BChls) d and e and the mechanism. In BChls d and e, the near UV band (so-called Soret band) is selectively red-shifted by the chemical modifications of BChl d involving the formylation and methylation perfectly retaining the visible band (so-called Qy). Density functional theory (DFT) and time-dependent DFT analyses showed that the red-shift of the Soret band is predominantly attributed to the large stabilization of the second lowest unoccupied molecular orbital induced by the formylation. In contrast, the Qy absorption retention results from the perfect cancellation between the positive excitation-energy change due to the formylation and negative excitation-energy change due to the methylation, both of which are significantly contributed by configuration interactions. This work reveals that the highly-selective absorption control in BChls d and e is accomplished by the complicated control of configuration interactions in the four-level system.

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Pan, Hongbo, Jia Tian, Taoyang Wang, Jing Wang, Chengbao Liu i Lei Yang. "Band-to-Band Registration of FY-1C/D Visible-IR Scanning Radiometer High-Resolution Picture Transmission Data". Remote Sensing 14, nr 2 (17.01.2022): 411. http://dx.doi.org/10.3390/rs14020411.

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The visible-IR scanning radiometer (VIRR) of FY1-C/D meteorological satellites consists of 10 bands with 4 different focal plane assemblies (FPAs). However, there are significant band-to-band registration (BBR) errors between different bands, which cannot be compensated for by a simple shift in the along-scan direction. A rigorous BBR frame was proposed to analyze the sources of misregistration in the whisk-broom camera. According to theory, the 45° scanning mirror introduces tangent function style misregistration in the along-track direction and secant function style misregistration in the across-track direction between different bands if the bands are not in the same optical axis. As proven by the experiments of both FY-1C and FY-1D, the image rotation caused by the 45° scanning mirrors plays a major role in the misregistration. However, misregistration between different FPAs does not strictly adhere to this theory. Therefore, a polynomial-based co-registration method was proposed to model the BBR errors for the VIRR. To achieve 0.1 pixel accuracy, a fourth-degree polynomial was used for BBR in the along-scan direction, and a fifth-degree polynomial was used for the along-track direction. For the reflective bands, the root-mean-square errors (RMSEs) of misregistration could be improved from 3 pixels to 0.11 pixels. Limited by matching accuracy, the RMSEs of misregistration between thermal bands and reflective bands were approximately 0.2 to 0.4 pixels, depending on the signal-to-noise ratio.

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Silva-Molina, R. A., R. Gámez-Corrales, J. M. Hernández-Cazares i I. G. Espinoza-Maldonado. "Study of Optical Vibrations Modes of Mineral Graphite by Micro Raman Spectroscopy". MRS Proceedings 1481 (2012): 37–43. http://dx.doi.org/10.1557/opl.2012.1630.

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ABSTRACTWe present experimental and theoretical Raman spectra of natural graphite mineral of Sonora, Mexico. In this work, we take the advantage of the utility of the RAMAN spectroscopy as a technique to determine the crystallinity and structure of graphite mineral. The RAMAN spectroscopy provides information that can be used to determine the degree of graphitization, which in turn can be used to know the metamorphic degree of the host rock. The resulting RAMAN spectra of graphite were divided in first and second order regions, in the first region (1100-1800cm-1) the E2gvibration mode with D6hcrystal symmetry occurs at 1580cm-1(G band) that indicates poorly organized graphite, additional bands appears in the first order region at 1350 cm-1(D band) called the defect band, and another at 1620 cm-1(D* band). The second-order region (2200-3400cm-1) shows several bands at ~2400 ~2700 ~2900 ~3300cm-1, all of them attributed to electron-phonon interactions or combination scattering. The density functional theory calculations were applied to determine the vibrational properties and the stacking layers of graphite.

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Kolev, S. K., D. V. Trifonov, H. A. Aleksandrov, V. A. Atanasov, V. N. Popov i T. I. Milenov. "DFT simulation of the Raman spectrum of single layer graphene". Journal of Physics: Conference Series 2487, nr 1 (1.05.2023): 012003. http://dx.doi.org/10.1088/1742-6596/2487/1/012003.

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Abstract Raman spectroscopy is one of the most suitable tools for studying few-layer graphene. The position of the G band and the defect-induced D and D' bands in the spectra of perfect single-layer graphene with sp2-hybridized carbon atoms and hydrogenated graphene with 27.7% sp3-hybridized carbon atoms are simulated using the Density Functional Theory (DFT) method with Perdew-Burke-Ernzerhof (PBE) functional. In the case of perfect graphene, the Raman G band is predicted at 1612 cm-1. In the case of the hydrogenated structure, a new feature appears. Namely, along with the G band, now shifted to 1591 cm-1, an additional feature, located at 1703 cm-1, is clearly seen. The latter is due to oscillations, involving six atomic benzene rings, containing two sp3-hybridized C atoms. According to our results, the presence of defects, related to sp3 hybridized carbon, gives rise to the appearance of the defect D' band in the Raman spectrum of defective graphene. This study shows that it is possible to simulate Raman spectra using the DFT method, with the results qualitatively matching the experimental data.

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Lobban, A. P., S. Zola, U. Pajdosz-Śmierciak, V. Braito, E. Nardini, G. Bhatta, A. Markowitz i in. "X-ray, UV, and optical time delays in the bright Seyfert galaxy Ark 120 with co-ordinated Swift and ground-based observations". Monthly Notices of the Royal Astronomical Society 494, nr 1 (4.03.2020): 1165–79. http://dx.doi.org/10.1093/mnras/staa630.

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ABSTRACT We report on the results of a multiwavelength monitoring campaign of the bright, nearby Seyfert galaxy Ark 120, using a ∼50-d observing programme with Swift and a ∼4-month co-ordinated ground-based observing campaign, pre-dominantly using the Skynet Robotic Telescope Network. We find Ark 120 to be variable at all optical, UV, and X-ray wavelengths, with the variability observed to be well correlated between wavelength bands on short time-scales. We perform cross-correlation analysis across all available wavelength bands, detecting time delays between emission in the X-ray band and the Swift V, B, and UVW1 bands. In each case, we find that the longer wavelength emission is delayed with respect to the shorter wavelength emission. Within our measurement uncertainties, the time delays are consistent with the τ ∼ λ4/3 relation, as predicted by a disc reprocessing scenario. The measured lag centroids are τcent = 11.90 ± 7.33, 10.80 ± 4.08, and 10.60 ± 2.87 d between the X-ray and V, B, and UVW1 bands, respectively. These time delays are longer than those expected from standard accretion theory and, as such, Ark 120 may be another example of an active galaxy whose accretion disc appears to exist on a larger scale than predicted by the standard thin-disc model. Additionally, we detect further inter-band time delays: most notably between the ground-based I and B bands (τcent = 3.46 ± 0.86 d), and between both the Swift XRT and UVW1 bands and the I band (τcent = 12.34 ± 4.83 and 2.69 ± 2.05 d, respectively), highlighting the importance of co-ordinated ground-based optical observations.

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Wang, Tianzuo, Lun Pan, Xiangwen Zhang i Ji-Jun Zou. "Insights into the Pt (111) Surface Aid in Predicting the Selective Hydrogenation Catalyst". Catalysts 10, nr 12 (16.12.2020): 1473. http://dx.doi.org/10.3390/catal10121473.

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The d-band center position of the metal catalyst is one of the most important factors for catalytic selective hydrogenation, e.g., the conversion of nitrostyrene to aminostyrene. In this work, we modulate the d-band center position of the Pt surface via H coverage manipulation in order to assess the highly efficient selective hydrogenation catalyst using density functional theory (DFT) calculation, which is validated experimentally. The optimal transition metal catalysts are first screened by comparing the adsorption energy values of two ideal models, nitrobenzene and styrene, and by correlating the adsorption energy with the d-band center positions. Among the ten transition metals, Pt nanoparticles have a good balance between selectivity and the conversion rate. Then, the surface hydrogen covering strategy is applied to modulate the d-band center position on the Pt (111) surface, with the increase of H coverage leading to a decline of the d-band center position, which can selectively enhance the adsorption of nitro groups. However, excessively high H coverage (e.g., 75% or 100%) with an insufficiently low d-band center position can switch the chemisorption of nitro groups to physisorption, significantly reducing the catalytic activity. Therefore, a moderate d-band center shift (ca. −2.14 eV) resulted in both high selectivity and catalytic conversion. In addition, the PtSn experimental results met the theoretical expectations. This work provides a new strategy for the design of highly efficient metal catalysts for selective hydrogenation via the modulation of the d-band center position.

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Jiao, Shilong, Xianwei Fu i Hongwen Huang. "Descriptors for the Evaluation of Electrocatalytic Reactions: d‐Band Theory and Beyond". Advanced Functional Materials 32, nr 4 (13.10.2021): 2107651. http://dx.doi.org/10.1002/adfm.202107651.

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Baquero, R., L. Quiroga i A. Camacho. "Analysis of the structure of the surface local density of states at the Fermi level: an application of the surface Green function matching method". Canadian Journal of Physics 67, nr 9 (1.09.1989): 841–44. http://dx.doi.org/10.1139/p89-145.

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We use a tight-binding description of the bands of bulk vanadium to set a surface-band structure. We show that knowledge of the s–d charge transfer in the surface layer is very important to be able to reproduce the ferromagnetic behavior of the (100) vanadium surface. We use the surface Stoner criterion of Allan to determine the acceptable values for the s–d charge transfer. There is no full agreement between theory and experiment on the magnetic properties of (100) vanadium at present.

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HUSSEIN, ABDULLAH M., i S. M. MUJIBUR RAHMAN. "PHASE STABILITY OF BCC TRANSITION METALS: ROLE OF d-ELECTRONS". International Journal of Modern Physics B 14, nr 06 (10.03.2000): 635–42. http://dx.doi.org/10.1142/s0217979200000571.

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The role of d-electrons in the structural phase stability of bcc transition metals viz. V, Fe, Cr and Mn are investigated. The underlying theory expresses the relevant structural part of the free energy in terms of the repulsion of the d-electron muffin-tin orbitals assigned to atomic sites and the attractive contribution arising from the band broadening effects of the d-bands in the total energy. The magnetic contribution arising from the population of magnetic moments in the systems is also included in the theory. The d-electronic contribution to entropy is written in terms of the density-of-electronic states at the respective Fermi level. The phase stability of the bcc transition metals is explained in terms of the population of atoms on the local and extended sites. It is observed that the d-electron energetics can precisely and correctly predict the crystal structure of the bcc transition metals.

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ALEXANDROV, A. S. "d-WAVE BIPOLARONIC STRIPES IN CUPRATES". International Journal of Modern Physics B 14, nr 29n31 (20.12.2000): 3298–305. http://dx.doi.org/10.1142/s0217979200003770.

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Two distinct energy scales, the d-wave superconducting order parameter, and the charge segregation in the form of stripes in cuprates are unified in the framework of the bipolaron theory as a result of the formation of mobile bipolarons in the normal state and their Bose-Einstein condensation. Within the theory both the d-wave superconducting order parameter and striped charge distribution result from the bipolaron (center-of-mass) energy band dispersion rather than from any particular interaction.

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Begunovich, Lyudmila V., i Maxim M. Korshunov. "Band Structure of Organic-Ion-Intercalated (EMIM)xFeSe Superconductor". Materials 15, nr 5 (2.03.2022): 1856. http://dx.doi.org/10.3390/ma15051856.

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The band structure and the Fermi surface of the recently discovered superconductor (EMIM)xFeSe are studied within the density functional theory in the generalized gradient approximation. We show that the bands near the Fermi level are formed primarily by Fe-d orbitals. Although there is no direct contribution of EMIM orbitals to the near-Fermi level states, the presence of organic cations leads to a shift of the chemical potential. It results in the appearance of small electron pockets in the quasi-two-dimensional Fermi surface of (EMIM)xFeSe.

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Vodnik, Vesna V., Dušan K. Božanić, Nataša Bibić, Zoran V. Šaponjić i Jovan M. Nedeljković. "Optical Properties of Shaped Silver Nanoparticles". Journal of Nanoscience and Nanotechnology 8, nr 7 (1.07.2008): 3511–15. http://dx.doi.org/10.1166/jnn.2008.144.

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The influence of shape and dielectric property of surrounding media on surface plasmon absorption band of silver nanoparticles was studied. Spherical silver nanoparticles (d = 5.6 nm) synthesized in water using NaBH4 as a reducing agent are transferred in non-polar solvent (chloroform) with phase-transfer reagent oleylamine. The absorption spectrum of oleylamine-capped silver nanoparticles dispersed in chloroform shows a strong surface plasmon resonance band that is 19 nm red-shifted compared to unmodified particles in water. The values for peak position and corresponding half widths are compared with theoretical calculations based on Mie theory. Prismatic and plate-like silver nanoparticles were synthesized in water using trisodium citrate as a reducing agent and cetyltrimethylammonium bromide as stabilizer. Due to structural anisotropy of prismatic and plate-like silver nanoparticles three surface plasmon resonance bands were observed in absorption spectrum. Nanocomposites consisting of non-spherical silver nanoparticles and polyvinyl alcohol exhibit different optical properties compared to water colloid. Instead of three surface plasmon bands, nanocomposite film has only one peak at 460 nm. Reason for appearance of single surface plasmon resonance band in nanocomposite film was discussed according to Maxwell-Garnet theory.

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Nguyen, Thi Thu Ha, Mane Sahakyan i Vinh Hung Tran. "The study of electronic structure and optical properties of Ba₂MnWO₆ within density functional theory". Low Temperature Physics 49, nr 3 (marzec 2023): 274–81. http://dx.doi.org/10.1063/10.0017260.

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Based on density functional theory, the electronic and optical properties of double perovskites Ba2MnWO6 were studied using the generalized gradient approximation. We have looked into four magnetic configurations, such as collinear antiferromagnetic AF-1, AF-2 and noncollinear antiferromagnetic AF-NC1, AF-NC2 structures. The obtained results show that the valence band maximum is mainly dominated by Mn-3 d orbitals, while the conduction band minimum is mainly composed of W-5 d orbitals. In addition, Ba2MnWO6 is shown as an indirect band gap semiconductor. The gap between two main t2 g,↑ and e2 g,↑ manifolds of Mn-3 d states, located at about 1.9 and 1 eV below Fermi level, is initiated as consequence of splitting in crystal field. From calculated optical results, Ba2MnWO6 indicates excellent light absorption in the ultraviolet range. Consequently, this material promises potential optical applications, such as solar cell functional in ultraviolet light.

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Sato, K., K. Hirata, S. Singh, K. Kuga, F. Ogawa, M. Matsunami i T. Takeuchi. "Electronic structure of silver chalcogenides investigated by hard x-ray photoemission spectroscopy and density functional theory calculations". Journal of Applied Physics 132, nr 4 (28.07.2022): 045104. http://dx.doi.org/10.1063/5.0095987.

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We have investigated the electronic structure of silver chalcogenides Ag2 X ( X = S, Se, Te) and their solid solutions using hard x-ray photoemission spectroscopy in combination with density functional theory calculations using generalized gradient approximation (GGA). By including the corrections for on-site Coulomb interactions (GGA + U), we successfully reproduced the valence band photoemission spectra, which consist mainly of the Ag 4 d band, by calculation. The estimated values for U = 4–6 eV are slightly high for Ag 4 d electrons but are consistent with those used in previously reported structural studies. On the other hand, the magnitude of the energy gap is virtually independent of U. These results suggest the strong correlation between Ag 4 d electrons in Ag2 X compounds to have surprisingly little impact on their electron transport properties.

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He, Cheng, i Wen Xue Zhang. "Effect of Size and Stress Field on Electronic Properties of ZnO Nanowires". Materials Science Forum 724 (czerwiec 2012): 209–12. http://dx.doi.org/10.4028/www.scientific.net/msf.724.209.

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The effects of external stress fieldfon band gapEg(D,f) of ZnO nanowires (NWs) in a diameter range ofD= 0.6 - 2.0 nm are investigated using first-principles density-function theory for the future application as nanogenerators. It is shown that theEg(D,0) values decreases with the increasing diameter of ZnO NWs without the stress field. Moreover,Eg(D, f) decreases with increasing offdue to the rapid drop of conduction band maximum of ZnO NWs whenDis constant. These findings imply thatEg(D,f) functions of ZnO NWs can be modulated by manipulatingDandf, which may be help for design of ZnO nanogenerators with a higher generation output voltage.

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Chiromawa, Idris Muhammad, Amiruddin Shaari, Razif Razali, Summanuwa Timothy Ahams i Mikailu Abdullahi. "Ab initio Investigation of the Structure and Electronic Properties of Normal Spinel Fe2SiO4". Malaysian Journal of Fundamental and Applied Sciences 17, nr 2 (29.04.2021): 195–201. http://dx.doi.org/10.11113/mjfas.v17n2.2018.

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Transition metal spinel oxides have recently been predicted to create efficient transparent conducting oxides for optoelectronic devices. These compounds can be easily tuned by doping or defect to adapt their electronic or magnetic properties. However, their cation distribution is very complex and band structures are still subject to controversy. We propose a complete density functional theory investigation of fayalite (Fe2SiO4) spinel, using Generalized Gradient Approximation (GGA) and Local Density Approximation (LDA) in order to explain the electronic and structural properties of this material. A detailed study of their crystal structure and electronic structure is given and compared with experimental data. The lattice parameters calculated are in agreement with the lattice obtained experimentally. The band structure of Fe2SiO4 spinel without Coulomb parameter U shows that the bands close to Fermi energy appear to be a band metal, with four iron d-bands crossing the Fermi level, in spite of the fact that from the experiment it is found to be an insulator.

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Pettersson, Lars Gunnar Moody, i Anders Nilsson. "A Molecular Perspective on the d-Band Model: Synergy Between Experiment and Theory". Topics in Catalysis 57, nr 1-4 (22.10.2013): 2–13. http://dx.doi.org/10.1007/s11244-013-0157-4.

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Chen, Lan Li, Hong Duo Hu i Zhi Hua Xiong. "Influence of Nd-Doping on Electronic Structure and Optical Properties of ZnO". Advanced Materials Research 941-944 (czerwiec 2014): 658–61. http://dx.doi.org/10.4028/www.scientific.net/amr.941-944.658.

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A detailed first-principles study of electronic structure and optical properties of Nd-doping ZnO with various concentrations of Nd was performed using density functional theory. The results show that the band gap of Nd-doping ZnO slightly widens with the increasing Nd concentration, this is because the conduction band undergoes a greater shift toward the lower-energy region than the valence band, which is agreement with experimental results. Furthermore, in comparison to pure-ZnO, the Fermi level shifts into the conduction band after Nd-doping ZnO. And the calculated result of imaginary part of dielectric function of Nd-doping ZnO shows that there is a sharp peak in the lower-energy region, which is due to the electrons transition between d-d orbital of Nd atom.

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Yan, Yibo, Zhengping Zhao, Jun Zhao, Wenfei Tang, Wei Huang i Jong-Min Lee. "Atomic-thin hexagonal CuCo nanocrystals with d-band tuning for CO2 reduction". Journal of Materials Chemistry A 9, nr 12 (2021): 7496–502. http://dx.doi.org/10.1039/d0ta12022g.

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Hexagonal CuCo nanocrystals are exploited for CO₂ reduction at high faradaic efficiency. Density functional theory calculates the structure-oriented binding energy of intermediates for catalyst optimization.

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Hu, Jing, Adel Al-Salihy, Bin Zhang, Siwei Li i Ping Xu. "Mastering the D-Band Center of Iron-Series Metal-Based Electrocatalysts for Enhanced Electrocatalytic Water Splitting". International Journal of Molecular Sciences 23, nr 23 (6.12.2022): 15405. http://dx.doi.org/10.3390/ijms232315405.

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The development of non-noble metal-based electrocatalysts with high performance for hydrogen evolution reaction and oxygen evolution reaction is highly desirable in advancing electrocatalytic water-splitting technology but proves to be challenging. One promising way to improve the catalytic activity is to tailor the d-band center. This approach can facilitate the adsorption of intermediates and promote the formation of active species on surfaces. This review summarizes the role and development of the d-band center of materials based on iron-series metals used in electrocatalytic water splitting. It mainly focuses on the influence of the change in the d-band centers of different composites of iron-based materials on the performance of electrocatalysis. First, the iron-series compounds that are commonly used in electrocatalytic water splitting are summarized. Then, the main factors affecting the electrocatalytic performances of these materials are described. Furthermore, the relationships among the above factors and the d-band centers of materials based on iron-series metals and the d-band center theory are introduced. Finally, conclusions and perspectives on remaining challenges and future directions are given. Such information can be helpful for adjusting the active centers of catalysts and improving electrochemical efficiencies in future works.

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Булычев, В. П., М. В. Бутурлимова i К. Г. Тохадзе. "Изотопные эффекты в спектрах комплексов с водородными связями. Ангармонические расчеты изотопологов комплекса [F(HF)-=SUB=-2-=/SUB=-]-=SUP=---=/SUP=-". Журнал технической физики 128, nr 8 (2020): 1077. http://dx.doi.org/10.21883/os.2020.08.49701.122-20.

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The frequencies and intensities of IR absorption bands of symmetric and asymmetric H-bonded complexes [FL1FL2F]- (L1, L2 = K-meson Ka, proton H, deuton D, and triton T) are calculated. The equilibrium configuration and potential energy and dipole moment surfaces of isotopologues [FL1FL2F]- were calculated by the MP2/6-311++G(3df,3pd) method with the basis set superposition error taken into account. The calculations of spectral parameters with allowance for anharmonic interactions of all vibrations were carried out using the second-order vibrational perturbation theory. Variation of Li and L2 masses in wide regions allowed significant changes in the forms of normal vibrations and values of anharmonic interaction constants upon isotopic substitution to be obtained. The trends in the changes of spectral parameters were determined upon transition from one symmetric isotopologue to another and upon transition from symmetric to asymmetric isotopologues. The D-F stretching band frequency predicted for [FHFDF]- is in good agreement with the experimental value. The assignment of this band was improved.

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Ummarino, Giovanni Alberto. "Standard Behaviour of Bi2Sr2CaCu2O8+δ Overdoped". Condensed Matter 6, nr 2 (25.03.2021): 13. http://dx.doi.org/10.3390/condmat6020013.

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I calculated the critical temperature and superconducting gap in the framework of one band d wave Eliashberg theory with only one free parameter in order to reproduce the experimental data relative to Bi2Sr2CaCu2O8+δ(BSCCO) in the overdoped regime. The theoretical calculations are in excellent agreement with the experimental data and indicate that cuprates in the overdoped regime are well described by standard d-wave Eliashberg theory with coupling provided by antiferromagnetic spin fluctuations.

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Esmaeili, Asghar, Mehdi Faraji i Somayyeh Karimi. "The conduction band non-parabolicity of degenerate AZO semiconductors: k.p method". European Physical Journal Applied Physics 83, nr 3 (wrzesień 2018): 30101. http://dx.doi.org/10.1051/epjap/2018180013.

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We present a discussion regarding the conduction band non-parabolicity and the Fermi energy of Al doped ZnO (AZO) degenerate semiconductors using the higher orders of Fermi–Dirac (F-D) integrals. We find an analytical expression for Fermi energy, based on two-band k.p theory and modified Boltzmann's classical equation. We examine the accuracy of resulted expression using absolute error value.

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SHI, LI BIN, SHUANG CHENG, RONG BING LI, LI KANG, JIAN WEI JIN, MING BIAO LI i CUI YAN XU. "A STUDY ON STRAIN AFFECTING ELECTRONIC STRUCTURE OF WURTZITE ZnO BY FIRST PRINCIPLES". Modern Physics Letters B 23, nr 19 (30.07.2009): 2339–52. http://dx.doi.org/10.1142/s0217984909020540.

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Density of states and band structure of wurtzite ZnO are calculated by the CASTEP program based on density functional theory and plane-wave pseudopotential method. The calculations are carried out in axial and unaxial strains, respectively. The results of density of states in different strains show that the bottom of the conduction band is always dominated by Zn 4s, and the top of valence band is always dominated by O 2p. The variation of the band gap calculated from band structure is also discussed. In addition, p-d repulsion is used in investigating the variation of the top of the valence band in different strains and the results can be verified by electron density difference.

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Seelmann, Albrecht, i Matthias Täufer. "Band Edge Localization Beyond Regular Floquet Eigenvalues". Annales Henri Poincaré 21, nr 7 (30.04.2020): 2151–66. http://dx.doi.org/10.1007/s00023-020-00911-7.

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Abstract We prove that localization near band edges of multi-dimensional ergodic random Schrödinger operators with periodic background potential in $$L^2({\mathbb {R}}^d)$$ L 2 ( R d ) is universal. By this, we mean that localization in its strongest dynamical form holds without extra assumptions on the random variables and independently of regularity or degeneracy of the Floquet eigenvalues of the background operator. The main novelty is an initial scale estimate the proof of which avoids Floquet theory altogether and uses instead an interplay between quantitative unique continuation and large deviation estimates. Furthermore, our reasoning is sufficiently flexible to prove this initial scale estimate in a non-ergodic setting, which promises to be an ingredient for understanding band edge localization also in these situations.

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Liu, Li, i Pingli Lv. "Understanding the enhanced catalytic activity of bimetallic AuCu/TiO2 in CO2 adsorption and activation: a density functional theory study". New Journal of Chemistry 44, nr 34 (2020): 14662–69. http://dx.doi.org/10.1039/d0nj02266g.

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Khan, Abdul Ahad, Aziz Ur Rehman, A. Laref, Masood Yousaf i G. Murtaza. "Structural, Optoelectronic and Thermoelectric Properties of Ternary CaBe2X2 (X = N, P, As, Sb, Bi) Compounds". Zeitschrift für Naturforschung A 73, nr 10 (25.10.2018): 965–73. http://dx.doi.org/10.1515/zna-2018-0204.

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AbstractThe structural, electronic, optical and thermoelectric properties of ternary CaBe2X2 (X = N, P, As, Sb and Bi) have been investigated comprehensively for the first time using density functional theory. All the compounds are optimized to obtain their ground states. Computed structural parameters agree to the available experimental results. Electronic band structure calculations reveal the semiconducting nature of the compounds, while bang gap decreases by changing the anion X from N to Bi the band gap decreases. In the valence band, major contribution is due to X-p state, while in conduction band (CB) the major contribution is mainly due to the Ca-d state. Furthermore, electron charge density plots reveal ionic bonding character with small covalent bonding. Optical properties are calculated in detail. Static value of refractive index shows inverse variation with band gap. The refractive indices of these compounds are high in the infrared region and gradually decreased in the visible and ultraviolet region. The thermoelectric properties are studied using Boltzmann statistics through BoltzTraP code. High optical conductivity peaks and figure of merits (ZT) for compounds reveal that they are good candidates for the optoelectronics and thermo-electric devices.

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31

Shan, Bing-Qian, Jia-Feng Zhou, Meng Ding, Xiao-Dan Hu i Kun Zhang. "Surface electronic states mediate concerted electron and proton transfer at metal nanoscale interfaces for catalytic hydride reduction of –NO2 to –NH2". Physical Chemistry Chemical Physics 23, nr 23 (2021): 12950–57. http://dx.doi.org/10.1039/d1cp01792f.

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Surface electronic states mediate concerted electron and proton transfer at metal nanoscale interfaces for catalytic hydride reduction of –NO₂ to –NH₂, beyond the conventional metal centered d-band theory

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32

Zdaniauskienė, Agnė, Ilja Ignatjev, Tatjana Charkova, Martynas Talaikis, Algimantas Lukša, Arūnas Šetkus i Gediminas Niaura. "Shell-Isolated Nanoparticle-Enhanced Raman Spectroscopy for Probing Riboflavin on Graphene". Materials 15, nr 5 (22.02.2022): 1636. http://dx.doi.org/10.3390/ma15051636.

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Graphene research and technology development requires to reveal adsorption processes and understand how the defects change the physicochemical properties of the graphene-based systems. In this study, shell-isolated nanoparticle-enhanced Raman spectroscopy (SHINERS) and graphene-enhanced Raman spectroscopy (GERS) coupled with density functional theory (DFT) modeling were applied for probing the structure of riboflavin adsorbed on single-layer graphene substrate grown on copper. Intense and detailed vibrational signatures of the adsorbed riboflavin were revealed by SHINERS method. Based on DFT modeling and detected downshift of prominent riboflavin band at 1349 cm−1 comparing with the solution Raman spectrum, π-stacking interaction between the adsorbate and graphene was confirmed. Different spectral patterns from graphene-riboflavin surface were revealed by SHINERS and GERS techniques. Contrary to GERS method, SHINERS spectra revealed not only ring stretching bands but also vibrational features associated with ribityl group of riboflavin and D-band of graphene. Based on DFT modeling it was suggested that activation of D-band took place due to riboflavin induced tilt and distortion of graphene plane. The ability to explore local perturbations by the SHINERS method was highlighted. We demonstrated that SHINERS spectroscopy has a great potential to probe adsorbed molecules at graphene.

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33

Wu, Feng, Xiaoqing Li, Xiufeng Fan, Ling Lin, Sofyan A. Taya i Abinash Panda. "Wide-Angle Absorption Based on Angle-Insensitive Light Slowing Effect in Photonic Crystal Containing Hyperbolic Metamaterials". Photonics 9, nr 3 (12.03.2022): 181. http://dx.doi.org/10.3390/photonics9030181.

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Light-slowing effect at band edges in photonic crystals (PCs) is widely utilized to enhance optical absorption. However, according to the Bragg scattering theory, photonic bandgaps (PBGs) in traditional all-dielectric one-dimensional (1-D) PCs shift towards shorter wavelengths as the incident angle increases. Therefore, light-slowing effect in traditional all-dielectric 1-D PCs is also angle-sensitive. Such angle-sensitive property of light-slowing effect in traditional all-dielectric 1-D PCs poses a great challenge to achieve wide-angle absorption. In this paper, we design an angle-insensitive PBG in a 1-D PC containing hyperbolic metamaterials based on the phase-variation compensation theory. Assisted by the angle-insensitive light-slowing effect at the angle-insensitive band edge, we achieve wide-angle absorption at near-infrared wavelengths. The absorptance keeps higher than 0.9 in a wide angle range from 0 to 45.5 degrees. Besides, the wide-angle absorption is robust when the phase-variation compensation condition is slightly broken. Our work not only provides a viable route to realize angle-insensitive light slowing and wide-angle light absorption, but also promotes the development of light-slowing- and absorption-based optical/optoelectronic devices.

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34

Chen, Wang, Ruijie Li i Yanhui Liu. "Effect of (0001) Strain on the Electronic and Magnetic Properties of the Half-Metallic Ferromagnet Fe2Si". Advances in Materials Science and Engineering 2017 (2017): 1–7. http://dx.doi.org/10.1155/2017/1853159.

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The electronic and magnetic properties of the half-metallic ferromagnet Fe2Si under (0001) strain have been evaluated by the first-principles density functional theory method. The spin-up band structure shows that bulk Fe2Si has metallic character, whereas the spin-down band structure shows that bulk Fe2Si is an S-L indirect band gap of 0.518 eV in the vicinity of Fermi surface. Indirect-to-direct band gaps and an unstable-to-stable transition are observed in bulk Fe2Si as strain is applied. In the range −11% to 11% (excluding zero strain), bulk Fe2Si has stable half-metallic ferromagnetism, the spin polarization at the Fermi surface is 100%, and the magnetic moment of the Fe2Si unit cell is 4.0 μB. The density distribution shows that the spin states of bulk Fe2Si mainly come from the Fe1-3d and Fe3-3d states, indicating that bulk Fe2Si has spin-polarized ferromagnetism. The half-metallic ferromagnetism of bulk Fe2Si is mainly caused by d–d exchange and p–d hybridization, which are not sensitive to strain. It is very important to investigate the effect of changes in the lattice constant on the half-metallic ferromagnetic properties of bulk Fe2Si.

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35

Quaino, P., E. Santos, G. Soldano i W. Schmickler. "Recent Progress in Hydrogen Electrocatalysis". Advances in Physical Chemistry 2011 (4.06.2011): 1–14. http://dx.doi.org/10.1155/2011/851640.

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Recently, we have proposed a unified model for electrochemical electron transfer reactions which explicitly accounts for the electronic structure of the electrode. It provides a framework describing the whole course of bond-breaking electron transfer, which explains catalytic effects caused by the presence of surface d bands. In application on real systems, the parameters of this model—interaction strengths, densities of states, and energies of reorganization—are obtained from density functional theory (DFT). In this opportunity, we review our main achievements in applying the theory of electrocatalysis. Particularly, we have focused on the electrochemical adsorption of a proton from the solution—the Volmer reaction—on a variety of systems of technological interest, such as bare single crystals and nanostructured surfaces. We discuss in detail the interaction of the surface metal d band with the valence orbital of the reactant and its effect on the catalytic activity as well as other aspects that influence the surface-electrode reactivity such as strain and chemical factors.

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36

Zhen, Li Ping, i Shao Wei Si. "Research of Chebyshev Equivalent Ripple Approximation Filter Based on DSP". Applied Mechanics and Materials 151 (styczeń 2012): 446–50. http://dx.doi.org/10.4028/www.scientific.net/amm.151.446.

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Abstract: Researched Chebyshev equiripple approximation FIR filter theory. In the algorithm process, we adopt direct remez algorithm, by a recursive formula to calculate the filter coefficients directly. Combined TMS320VC5502, we designed software and hardware system of Chebyshev equiripple band-pass filter to realize the voice signal filtering. In hardware system TLC320AC01 complete A/D and D/A converter, TMS320VC5502 complete data processing and filtering.

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37

Hao, Zhaopeng, Ran Liu, YiHang Fan i Yuan Qiu. "Ferromagnetic exchange mechanism and martensitic transformation of Heusler alloy based on d-band center theory". Journal of Magnetism and Magnetic Materials 523 (kwiecień 2021): 167627. http://dx.doi.org/10.1016/j.jmmm.2020.167627.

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38

Tran, Thi Nhan, Minh Triet Dang, Quang Huy Tran, Thi Theu Luong i Van An Dinh. "Band valley modification under strain in monolayer WSe₂". AIP Advances 12, nr 11 (1.11.2022): 115023. http://dx.doi.org/10.1063/5.0127204.

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We study the band valley modification induced by isotropic strain in monolayer WSe2 using the non-local van der Waals density functionals theory including the spin–orbit coupling effect. The dominant contributions of orbitals to the band extrema, spin splitting, and exciton diversity in monolayer WSe2 are visually displayed. The vertical shift of the d and p partial orbitals of W and Se atoms, respectively, at band edges under strain results in a notable reduction of the bandgap. Under tensile strain, the deformations of the band valleys lead to an additional appearance of optical excitons and the disappearance of momentum excitons. Therefore, the experimental observations of the changes in the radiation spectra such as the redshift of A and B excitons, blueshift of C and D excitons, enhancement of intensity, localization, and symmetrization of the exciton resonances can be explained thoroughly. Under compression, the band valley modification may lead to an additional appearance of momentum excitons and the disappearance of optical excitons. The compression is predicted to cause the blueshift of A and B excitons while it brings the redshift to C and D excitons. An asymmetric broadening and intensity de-enhancement of the exciton resonances are also found when a compression strain is applied. The modification of the band valleys can be explained by the enhancement/reduction of hybridization between orbitals under strain. These results offer new perspectives to comprehend the appearance/disappearance of the excitons in monolayer transition metal dichalcogenide materials upon mechanical perturbation.

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39

Supian, Faridah Lisa, Wong Yeong Yi, Nur Farah Nadia Abd Karim, Afiq Radzwan, Darvina Lim Choo Kheng i Abdullah Faisal Al Naim. "THE MOLECULAR BEHAVIORS OF CALIXARENES AT THE AIR-WATER INTERFACE: DENSITY FUNCTIONAL THEORY, SURFACE PRESSURE, POTENTIAL, AND EFFECTIVE DIPOLE MOMENT". Malaysian Journal of Science 41, nr 3 (31.10.2022): 63–68. http://dx.doi.org/10.22452/mjs.vol41no3.9.

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This study examined the behaviors of Langmuir-Blodgett ultrathin calixarene films at the air-water interface. The Langmuir trough was used to estimate the surface pressure, surface potential, and effective dipole moment of two calixarenes, namely, calix[4]arene (THC4) and calix[8]arene (THC8). The band gap was determined using the density functional theory (DFT). The DFT simulation gave a band gap of 2.28 eV for THC4, confirming that THC4 was an insulator. The surface pressure isotherms of THC4 and THC8 yielded the expected molecular behavior from the gaseous to the solid phases. THC4 and THC8 showed a perpendicular and a parallel orientation in the air-water subphase, respectively. The ∆Vmax values of TCH4 and THC 8 were 205 mV and 141mV, respectively, and their µ﬩max values were 0.147 D and 0.088 D, respectively.

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40

Hao, Zijun, Ling Guo, Minmin Xing i Qian Zhang. "Mechanistic study of ethanol steam reforming on TM–Mo6S8 clusters: a DFT study". Catalysis Science & Technology 9, nr 7 (2019): 1631–43. http://dx.doi.org/10.1039/c8cy02151a.

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The mechanism of ethanol steam reforming (ESR) on TM–Mo₆S₈ (TM = Pt, Pd) clusters is systematically investigated using a combination of the microscopic kinetic model, energetic span model (ESM) and d-band model under density functional theory (DFT) calculations.

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41

GUNES, M., E. KASAPOGLU, H. SARI, K. AKGUNGOR i I. SÖKMEN. "FINITE ELEMENT ANALYSIS OF VALENCE BAND STRUCTURE OF SQUARE QUANTUM WELL UNDER THE ELECTRIC FIELD". Surface Review and Letters 16, nr 05 (październik 2009): 689–96. http://dx.doi.org/10.1142/s0218625x09013177.

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Valence band structure with spin–orbit (SO) coupling of GaAs/Ga 1-x Al x As square quantum well (SQW) under the electric field by a calculation procedure based on a finite element method (FEM) is investigated using the multiband effective mass theory ([Formula: see text] method). The validity of the method is confirmed with the results of D. Ahn, S. L. Chuang and Y. C. Chang (J. Appl. Phys.64 (1998) 4056), who calculated valence band structure, using axial approximation for Luttinger–Kohn Hamiltonian and finite difference method. Our results demonstrated that SO coupling and electric field have significant effects on the valence band structure.

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42

Geertsma, W. "PERTURBATION THEORY OF THE PERIODIC ANDERSON LATTICE AND SUPERCONDUCTIVITY". International Journal of Modern Physics B 02, nr 05 (październik 1988): 681–87. http://dx.doi.org/10.1142/s0217979288000512.

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In this paper I develop a perturbation calculation of the second and fourth order interparticle interaction in band states, based on the Periodic Anderson Lattice. I show that 4th order interparticle interactions giving rise to the wellknown Kondo effect vanish in the superconducting ground state. This term survives in the presence of a magnetic field. Pair excitations can only give rise to an appreciable attractive contribution when the d states are less than half filled and the pair energy is near the Fermi level. The only important attractive interaction comes from the normal fourth order terms.

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43

Wang, Jin, Feng Li, Jing Ao, Ying Zhong i Zhi Qian Chen. "First Principle Study of the Optical Properties of Transition Metal Nitrides XN (X=Ti, Zr, Hf)". Advanced Materials Research 668 (marzec 2013): 710–14. http://dx.doi.org/10.4028/www.scientific.net/amr.668.710.

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The optical properties of face-centered cubic IVB group transition metal nitrides such as TiN, ZrN, and HfN were calculated using the plane wave pseudopotential method based on first-principle density function theory. The results of band structures show that conduction bands are mainly formed by the metal atom d-state, whereas valence bands are mainly formed by the N 2p-state. In optical properties research, the computed results of complex dielectric functions, absorptions, reflectivities, conductivities and loss functions of the three materials are analysed in terms of band structures. The results agree with experiment data. Analysis results show that the optical properties of these materials in low-energy regions are metallic because of the free electrons intraband-transition, and the transit to semiconducting properties in high-energy area is caused by valence electrons interband-transition. The sharp peaks of the transmissivity spectra indicate excellent optical selectivity in the visible light area. Moreover, lowering the starting energies of interband-transitions as a possible method to improve optical selectivities is discussed

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44

Wang, Yan Li, Ke He Su i Xin Wang. "A Density Functional Theory Study on the Ultra Long Single Walled Armchair (3, 3) (Bn)_Xc_y Nanotubes". Advanced Materials Research 463-464 (luty 2012): 1435–39. http://dx.doi.org/10.4028/www.scientific.net/amr.463-464.1435.

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The single walled armchair (3,3) (BN)xCy nanotubes with different ratios of B, C and N atoms were studied with density functional theory of B3LYP/3-21G(d) combined with the periodic boundary conditions in simulating the ultra long tube model. Different types of twelve models were examined and the diameter, energy, energy gaps and the band structures were obtained. The energy gaps were within 0.203eV to 2.620eV showing semiconductor conductivity. Results show that the energy gap and the band structure depend on both the atom ratio and arrangement.

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45

Makjan, Suppamat, Malinee Promkatkaew, Supa Hannongbua i Pornthip Boonsri. "Theoretical Study of the Electronic Structure and Properties of Alternating Donor-Acceptor Couples of Carbazole-Based Compounds for Advanced Organic Light-Emitting Diodes (OLED)". Key Engineering Materials 824 (październik 2019): 236–44. http://dx.doi.org/10.4028/www.scientific.net/kem.824.236.

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Generally, it is difficult to generate a high-performance pure blue emission organic light-emitting diode (OLED). That is because the intrinsically wide band-gap makes it hard to inject charges into the emitting layer in such devices. To solve the problem, carbazole derivatives have been widely used because they have more thermal stability, a good hole transporting property, more electron rich (p-type) material, and higher photoconductivity. In the present work, novel copolymers containing donor-acceptor-acceptor-donor (D-A-A-D) blue compounds used for OLEDs were investigated. The theory of the geometrical and electronic properties of N-ethylcarbazole (ECz) as donor molecule (D) coupled to a series of 6 acceptor molecules (A) for advanced OLEDs were investigated. The acceptors were thiazole (TZ), thiadiazole (TD), thienopyrazine (TPZ), thienothiadiazole (TTD), benzothiadiazole (BTD), and thiadiazolothienopyrazine (TDTP). The ground state structure of the copolymers were studied using Density Functional Theory (DFT) at B3LYP/6-31G(d) level. Molecular orbital analysis study indicated 3 investigated copolymers (ECz-diTZ-ECz, ECz-diTD-ECz, ECz-diBTD-ECz) have efficient bipolar charge transport properties for both electron and hole injection to the TiO2 conduction band (4.8 eV). In addition, the excited states electronic properties were calculated using Time-Dependent Density Functional Theory (TD-DFT) at the same level. Among these investigated copolymer ECz-diTZ-ECz and ECz-diTD-ECz showed the maximum absorption wavelengths (λabs) with blue emitting at 429 and 431 nm, respectively. The results suggested that selected D-A-A-D copolymers can improve the electron- and hole- transporting abilities of the devices. Therefore, the designed copolymers would be a promising material for future development of light-emitting diodes, electrochromic windows, photovoltaic cells, and photorefractive materials.

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46

Badrudin, F. W., M. S. A. Rasiman, M. F. M. Taib, N. H. Hussin, O. H. Hassan i M. Z. A. Yahya. "First Principles Study on Structural and Electronic Properties of LiFeSO₄OH Cathode Material for Lithium Ion Batteries". Applied Mechanics and Materials 510 (luty 2014): 33–38. http://dx.doi.org/10.4028/www.scientific.net/amm.510.33.

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Structural and electronic properties of a new fluorine-free cathode material of polyanionichydroxysulfates, LiFeSO4OH withcaminitestructure are studied using first principles density functional theory. From the calculated result, it reveals that antiferromagnetic configuration is more stable compared to ferromagnetic and non-magnetic configuration. Meanwhile, the density of state calculation divulges that this material exhibited large d-d type of band gap and would behave as a Mott-Hubbard insulator. Thus, this behaviour can lead to poor electronic conductivity.

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47

Kataoka, Yusuke, Raiki Fukumoto, Natsumi Yano, Daiki Atarashi, Hidekazu Tanaka, Tatsuya Kawamoto i Makoto Handa. "Synthesis, Characterization, Absorption Properties, and Electronic Structures of Paddlewheel-Type Dirhodium(II) Tetra-μ-(n-naphthoate) Complexes: An Experimental and Theoretical Study". Molecules 24, nr 3 (27.01.2019): 447. http://dx.doi.org/10.3390/molecules24030447.

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The reactions of [Rh2(O2CCH3)4(OH2)2] with n-naphthalenecarboxylic acids (n = 1: 1-HNC, n = 2: 2-HNC) afford the dirhodium tetra-μ-(n-naphthoate) complexes [Rh2(1-NC)4] (1) and [Rh2(2-NC)4] (2), respectively. Single crystal X-ray diffraction analyses of [1(OCMe2)2] and [2(OCMe2)2], which were obtained by recrystallization from acetone (OCMe2) solutions of 1 and 2, reveal that the dirhodium cores are coordinated by four equatorially bridging naphthoate ligands and two axial OCMe2 ligands. Density functional theory (DFT) calculation confirmed that (i) the single Rh–Rh bond is formed between the two Rh ions and (ii) the electronic structures between two Rh ions in [1(OCMe2)2] and [2(OCMe2)2] are best described as π4δ2σ2δ*2π*4 and δ2π4σ2δ*2π*4, respectively. Time-dependent DFT (TDDFT) calculations clarify the absorption band characters of [1(OCMe2)2] and [2(OCMe2)2]; the former shows the bands due to d–d and metal–to–metal-ligand charge transfer (MMLCT) excitations in the visible light region, whereas the latter shows the bands due to only d–d excitations in the same region. The electrochemical properties and thermal stabilities of [1(OCMe2)2] and [2(OCMe2)2] were also investigated in this study.

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48

Parajuli, D., G. C. Kaphle i K. Samatha. "First-Principles Study of Electronic and Magnetic Properties of Anatase and its Role in Anatase-Mxene Nanocomposite". Journal of Nepal Physical Society 5, nr 1 (29.12.2019): 42–53. http://dx.doi.org/10.3126/jnphyssoc.v5i1.26940.

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The electronic and magnetic properties of Titanium and one of its oxide Anatase are calculated by using Tight Binding Linear Muffin-Tin Orbital Atomic Sphere Approximation (TB-LMTO-ASA) method under Density Functional Theory (DFT). The lattice parameter, band structure, Density of States (DOS) and charge density distributions of Ti and TiO2 (Anatase) required for electronic structure are calculated respectively. The orbital contribution is analyzed by fat band structure; the d- orbital on conduction band and, s and p orbitals on valance bands. Consequently, their magnetic properties are checked. From our study, we found that the magnetic moments of Ti and TiO2 are found to be 2.2 μB and 0 respectively. The total Density of States for spin up and down electron have smaller difference in Ti and symmetric in TiO2 indicates that Ti slightly paramagnetic and Anatase is non magnetic in nature. The charge density plots reveals the concentration of electrons at the site under study. Anatase can be deposited onto Mxene to form Mxene-Anatase nanocomposite which has several excellent applications in the field of biosensors, biocompatible materials, energy storage devices, topological insulators etc.

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49

GA, Ummarino. "The link between s and d components of electron boson coupling constants in one band d wave Eliashberg theory for high Tc superconductors". Annals of Mathematics and Physics 6, nr 1 (7.04.2023): 048–51. http://dx.doi.org/10.17352/amp.000077.

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The phenomenology of overdoped high Tc uperconductors can be described by a one band d wave Eliashberg theory where the mechanism of superconducting coupling is mediated by antiferromagnetic spin fluctuations and whose characteristic energy Ω0 scales with Tc according to the empirical law Ω0 = 5.8 kBTc. This model presents universal characteristics that are independent of the critical temperature such as the link between the s and d components of electron boson coupling constants and the invariance of the ratio 2∆/kBTc. This situation arises from the particular structure of Eliashberg's equations which, despite being non-linear equations, present solutions with these simple properties.

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50

Turaeva, N. "SIZE EFFECTS IN THE D-BAND MODEL OF CO OXIDATION BY GOLD NANOPARTICLES". «Узбекский физический журнал» 20, nr 4 (21.07.2018): 236–42. http://dx.doi.org/10.52304/.v20i4.98.

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The volcano-type size dependence of the extraordinary catalytic activity of gold nanoparticles in CO oxidation is discussed on the basis of combination of the d-band model, the jellium model of metal clusters and the role of Fermi level in catalytic activity. The reaction rate depends non-monotonically upon the size of nanoparticles, due to exponential dependences of adsorption of reagents and desorption of products on the differences of the Fermi level of the metal cluster and antibonding states of CO and CO2 molecules forming chemical bonds with the nanoparticle, respectively. The origin of activation of the CO molecules towards the CO oxidation reaction by gold nanocatalysts is discussed in frame of the vibronic theory of chemical reactions based on the vibronic connection between charge transfer and nuclear processes.

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