Exchange Constants Research Articles

Tuning of exchange constants and magnetic anisotropy for terahertz antiferromagnetic resonance frequencies in cation-doped NiO

Tuning of exchange constants and magnetic anisotropy for terahertz antiferromagnetic resonance frequencies in cation-doped NiO

Investigation of Zinc and Chromium Substitution Nickel-rich LiNi1−x−yZnyCrxO2 Cathode Materials to Improve the Redox Reaction of Lithium-ion Battery: A First-principles Study

First-principles calculations are employed to investigate the structural, electronic, magnetic, thermoelectric, and electrochemical characteristics of Nickel-rich layered cathodes by substitution of Zn and Cr such as LiNi1−x−yZnyCrxO2 (with x = 0.00, 0.16 and 0.32, y = 0.00 and 0.16). The structure of pure LiNiO2 and substituted are organized in a trigonal arrangement inside the P3m1 space group. Using PBE-GGA approximation, the spin-polarized calculation of pure LiNiO2 in a spin-down channel exhibits a band gap of 0.48 eV. Whereas, Zn and Cr substitution results in the band gap reduction to zero, and metallic behavior is observed. Electronic charge density calculation Ni(Zn, Cr)-O reveals covalent bonding. In electrochemical investigation, by the increasing substitution concentration of Zn and Cr in LiNi1−x−yZnyCrxO2 significant improvements are observed at 4.65–3.89 V potential with a good theoretical discharge capacity of 48–246 mAhg−1. The exchange constants N∘α and N∘β demonstrate negative values that validate the ferromagnetic nature of substituted material. The thermoelectric parameters have been determined using the BoltzTraP code and the highest ZT value of 0.35 is obtained for LiNi0.52Zn0.16Cr0.32O2. These results offer a new perspective on the potential of doping techniques for Nickel-rich cathode materials, providing helpful insight for the development of high-performance cathodes for Lithium-ion battery applications.

Trinuclear nickel (II) string complexes and copper (II) coordination polymer with pyrazine modulated unsymmetrical dipyridylamino ligand: Synthesis, structure and bioactivity properties with molecular docking

The unsymmetrical pyrazine-modulated ligand, N-(pyridine-2-yl)pyrazin-2-amine (Hppza) (1), its 1D straight-chain copper (II) coordination polymer [Cu2(Hppza)2∙(NO3)4]n (2) and trinuclear metal string [Ni3(µ3-ppza)4Cl2] (3) and [Ni3(µ3-ppza)4(NCS)2] (4) complexes have been successfully synthesized and structurally characterized. The free ligand Hppza (1) exhibits anti-syn conformation. In an asymmetric unit of 2, there are two kinds of Cu(II) atoms, both of which have elongated octahedral coordination geometry, and the copper(II) centers are linked by oxygen atoms of one nitrate anion. There are only minor differences in Ni…Ni bond lengths between pyrazine-modulated ligand complexes of [Ni3(μ3-ppza)4×2] (X = Cl− (3), NCS− (4)) and their unmodulated analogs, while the distances between the terminal nickel atoms and the axial ligands 3 and 4 are shorter. The results of magnetic susceptibility measurements showed an antiferromagnetic exchange constant (J) of about J = –199.2 cm–1 for 3 and J = –178.0 cm–1 for 4. The electrochemical properties of nickel strings of Hppza differ significantly from their unmodulated counterparts. The activities of ligands and their metal complexes against various proteins that are AChE (PDB ID: 4M0E), BChE (PDB ID: 5NN0), α-Gly (PDB ID: 1UAS), hCA I (PDB ID: 2CAB), and hCA II (PDB ID: 3DC3) were compared, and then the ADME/T properties of molecules were examined. Afterward, the interactions occurring in the docking calculation were examined in detail with the Protein-Ligand Interaction Profiler (PLIP) service. These complexes were inhibitors of BChE, hCA I and II, α-glycosidase and AChE enzymes for complex 3 and 5 with Ki values of 12.65 and 42.95 μM for hCA I, 3.64 and 15.84 μM for hCA II, 5.44 and 50.07 μM for BChE, 15.85 and 4.77 μM for α-glycosidase and 8.58 and 86.24 μM for AChE, respectively.

Study of the spin-polarized electronic, exchange constant, and thermoelectric characteristics of spinels LiFe2(O/S)4 for spintronic and energy-harvesting applications

Spintronics is a rapidly developing field in advanced technology. It focuses on manipulating the spin of electrons to achieve high-speed data transfer, handling, and storage in order to enhance its capabilities. We conducted a systematic investigation of the ferromagnetism, electronic, and thermoelectric characteristics of spinel compounds LiFe2(O/S)4. Our analysis for optimization demonstrates that ferromagnetic states exhibit great energy release compared to the antiferromagnetic states, indicating the presence of ferromagnetic behavior in the studied compounds. To evaluate the presence of ferromagnetism above room temperature, we employ the Heisenberg model to calculate the Curie temperature and spin polarization to evaluate the presence of ferromagnetism above room temperature. Additionally, a concise overview of the nature of ferromagnetism, including band structures, density of states, exchange energies and constants, hybridization double exchange model, and crystal-field energy, is provided in this research. The absorption of a shift in magnetic moment from Fe to the Li and O/S sites suggests that the ferromagnetic behavior is primarily due to the spin of electrons. Furthermore, we explore the impact of the thermal parameters on the electro-spin as well as the thermoelectric characteristics for both spin-down and spin-up states, providing insights into the energy-harvesting potential.

Nano-Magnonic Crystals by Periodic Modulation of Magnetic Parameters

Magnonic crystals are metamaterials whose magnon behavior can be controlled for specific applications. To date, most magnonic crystals have relied on nanopatterning and magnetostatic waves. Here, we analytically and numerically investigate magnonic crystals defined by modulating magnetic parameters at the nanoscale, which predominantly act on exchange-dominated, sub-100 nm magnons. We focus on two cases: the variation in the exchange constant, and the DMI constant. We found that the exchange constant modulation gives rise to modest band gaps in the forward volume wave and surface wave configurations. The modulation of the DMI constant was found to have little effect on the magnonic band structure, leading instead to a behavior expected for unpatterned thin films. We believe that our results will be interesting for future experimental investigations of nano-designed magnonic crystals and magnonic devices, where material parameters can be locally controlled, e.g., by thermal nano-lithography.

Magnetic structure and pressure-induced spin-crossover in Me3B2O6 (Me = Mn, Fe, Co, Ni) kotoites: Representation analysis and DFT calculations

The magnetic and electronic properties of transition metal borates Me3B2O6 (Me = Mn, Fe, Co, Ni) with kotoite structure have been investigated at ambient and high pressures via a combination of representation analysis and density functional theory (DFT + U) calculations. Several magnetic configurations corresponding to the different irreducible representations have been considered. The total-energy calculations reveal that the magnetic ground state of Me3B2O6 kotoites is composition-dependent. The lowest energy magnetic phase of manganese and nickel kotoites is characterized by the antiferromagnetic ordering of the transition metal magnetic moments along the c- axis and along the b-axis for cobalt and iron kotoites. The magnetic cell of Ni3B2O6 kotoite corresponds to k = (1/2, 0, 1/2) vector and four time larger than the unit cell. The calculated exchange constants indicate the competition between ferromagnetic and antiferromagnetic interactions. At a critical pressure, Me ions undergo a high-spin to low-spin state crossover. This magnetic moments collapse is analyzed in terms of change in electronic structure under pressure.

Magnetic ordering in strong anisotropic ferromagnetic bilayers with dipolar and antiferromagnetic interlayer exchange interactions: Monte Carlo approach.

In this work, multilayer films consisting of two strong-anisotropic ferromagnetic layers antiferromagnetically coupled by a nonmagnetic spacer are studied by Monte Carlo simulations. The system is modeled by an Ising-based Hamiltonian that depends on both the intralayer exchange and dipolar constants and on the interlayer exchange constant (IEC). The ground state of the monolayers (null IEC) corresponds to alternate stripe domains with width h defined by the ratio between the exchange and dipolar constants (δ). The results show that IEC alters the energy balance that controls the stripe domain formation, leading to a ground state characterized by in-plane stripes out-plane antiferromagnetically coupled. When temperature increases two regimes are identified: an IEC-dominated regime where the orientational and positional orders are simultaneously lost in both layers, driving the system to the tetragonal liquid (TL) phase, and a dipolar-dominated one where signs of layers decoupling and the onset of positional disorder are observed. The last could be related with an intermediate nematic phase (NM). From the study of the nonequilibrium dynamics, the phase transitions to TL phase are characterized as continuous and those to the NM one as Kosterlitz-Thouless type. Also, for both layers the critical temperatures are the same and increase with IEC magnitude. Furthermore, the obtained critical exponents depend on the IEC values, which is indicative of a weak universality. For the dipolar-dominated regime, the decoupling between layers is also evidenced by the difference between their critical exponents.

Magnetic properties of the frustrated Ising chain

Using the Kramers–Wannier transfer matrix method, we studied several decorated Ising chains. The exact expressions for thermodynamic characteristics, including the ground state characteristics, were obtained. We considered several modeling chains with different signs and absolute values of exchange constants for the nearest- and the next-nearest neighbors. For these models, we calculated the magnetization curves. The critical values of magnetic fields and corresponding magnetization plateau parameters were obtained. Analytic expressions for the ground state entropy were obtained for the chains with different interaction constants. The dependencies of the number of states with minimum energy (the degeneration of the ground state) as the function of the number of particles were found. It was shown that these dependencies are expressed in terms of well-known numerical sequences, namely Lucas numbers and Pell numbers, which, in the limit of a large number of particles, are proportional to the powers of the golden and silver sections. Therefore, the ground state entropy (per particle) of the systems under consideration can be described in terms of these sections and, therefore, is nonzero.

Rare earth based Mg- chalcogenides MgDy2(S/Se)4 as an emerging aspirant for spintronic and thermoelectric applications

The magnesium based spinel chalcogenides are outstanding materials for spintronic technology and energy applications. Herein, the modified Becke Johnson potential (TB-mBJ) was employed to investigate the electrical, ferromagnetism, and thermoelectric properties of MgDy2(S/Se)4 spinels comprehensively. The energy emitted during optimization as well as formation energy has both been used to demonstrate the stability of the cubic phase. The density of states, Curie temperature, exchange coupling, and spin polarization are elaborated to address the nature of ferromagnetism. Further, half metallic ferromagnetism is studied in terms of hybridization, exchange energies, and exchange constants. In contrast to the clustering effect of the internal magnetic of Dy atoms in the structure, the lowering of Dy's magnetic moment and its transferring on Mg, and S/Se sites demonstrate that the ferromagnetism is caused by the exchange of electron spin. Furthermore, thermoelectric properties were studied and various thermoelectric parameters such as electrical and thermal conductivities, Seebeck coefficient (S), and power factor (PF) of the examined spinels have been determined.

Physical properties of ferromagnetic Mn-doped double perovskites (DPs) Cs2AgInCl/Br6 for spintronics and solar cell devices: DFT calculations.

A computational framework based on density functional theory (DFT) has been effectively employed to investigate the wide-ranging physical characteristics of ferromagnetic manganese (Mn)-substituted double perovskites (DPs) with composition Cs2AgIn1-xMnxCl/Br6 (x = 0.0, 0.25). This research covers a systematic exploration of the mentioned DPs for potential applications in the domains of spintronics and energy conversion devices. The physics concerning ferromagnetic (FM) Cs2AgIn0.75Mn0.25Cl/Br6 DPs was studied computationally using the modified Becke-Johnson (mBJ-LDA) potential and the generalized gradient approximation (PBEsol GGA) method introduced by Perdew, Burke, and Ernzerhof. The structural, electronic, magnetic, and transport behavior of materials were investigated using these computations. Structural parameters for both perovskite materials were computed subsequent to their optimization in FM phase. According to evaluations of the electronic band structure and density of states (DOS), the incorporation of Mn ions into the host lattice causes exchange splitting induced by p-d hybridization, consequently stabilizing the FM state. Probing the sharing of magnetic moment, charge, and spin between the substituent cations and the host anions led to the comprehensive elaboration of this exchange splitting of bands. Important parameters such as exchange constants (N0α, N0β), and direct spin-exchange splitting Δx(d), support the stability of the FM state. Finally, we briefly explored the spin effect on other aspects of electronic transport, the Seebeck coefficient, and the power factor, using the conventional Boltzmann transport theory.

Physical properties of vacancy-ordered double perovskites K2TcZ6 (Z = Cl, Br) for spintronics applications: DFT calculations.

Vacancy-ordered double perovskites (DPs) are emerging materials for spintronics due to their stable structures and non-toxic properties. In this study, we conducted a comprehensive investigation into the role of 4d electrons in Tc to understand their impact on the ferromagnetic properties of K2TcY6 (Y = Cl, Br). We have employed a modified Back and Johnson potential to assess electronic and magnetic characteristics and utilized the BoltzTraP code to investigate thermoelectric effects. Experimental lattice constants confirmed the presence of stable structures and formation energy estimates affirmed their thermodynamic stability. The Heisenberg model and density of electron states (DOS) at the Fermi level provides insights into Curie temperature and spin polarization. The presence of ferromagnetism is evident in the density of states, reflecting the transition of electron spins that support the exchange mechanism. The study delves into how electron functionality influences the control of ferromagnetism, considering exchange constants, exchange energies, hybridization process and the crystal field energies. Moreover, the exploitation of magnetic moments from Tc to K and Cl/Br sites takes precedence in driving ferromagnetism by exchanging electron spins rather than forming magnetic clusters. Additionally, to explore the optical characteristics of the compounds, we investigated their optical absorption, dielectric constants and refractive index within the energy range of 0-10 eV, ensuring absorption across both the visible and ultraviolet regions. Finally, we delve into the impact of the thermoelectric effect on both thermoelectric performance and spin functionality, taking into account factors such as the Seebeck coefficient, power factor, and electronic conductivity.

Study of the magnetism of C-doped MgO based on first-principles calculations and the Ising model.

The electronic and magnetic properties of d0 dilute magnetic semiconductors formed by rock-salt structured magnesium oxide (MgO) doped with C are systematically studied based on first-principles calculations and the Ising model. It is shown that the electronic holes of p states are generated due to the impurity carbon replacing oxygen in MgO, and the magnetic moment of 2μB is introduced by each C impurity. The polarization energy and formation energy of C-doped MgO are calculated, and the magnetization energy of C-doped MgO is also calculated which is used to obtain the exchange constant between C impurities. By means of the Ising model, we simulated the magnetization and the susceptibility of the doped system with increasing temperature and obtained the Curie temperature of C-doped MgO.

Consistent interpretation of isotope and chemical oxygen exchange relaxation kinetics in SrFe0.85Mo0.15O3-δ ferrite.

This paper is devoted to the study of phase composition and kinetic and thermodynamic characteristics of Mo-doped strontium ferrite SrFe0.85Mo0.15O3-δ (SFM15) under oxygen-conducting membrane working conditions. Single-phase SFM15 with a cubic Pm3̄m structure was synthesized using a ceramic method. It was shown that the molybdenum introduction stabilizes the perovskite cubic structure over a wide range of oxygen pressures and temperatures, preventing the bulk phase transition at high temperatures. Oxygen exchange constants, diffusion coefficients and activation energy of oxygen exchange were obtained using oxygen relaxation and isotopic exchange techniques, and the obtained values are consistent with known literature data. It was shown that the surface reaction rates obtained using chemical and tracer relaxation methods are quantitatively comparable with each other, despite significantly different experimental conditions. This result not only confirms the reliability of the data obtained by independent methods, but also allows one to expand the area of physical conditions for studying the kinetics of oxygen transfer where another method has technical or methodological limitations.

Study of half-metallic ferromagnetism and transport characteristics of double perovskites Sr2AIrO6 (A = Y, Lu, Sc) for spintronic applications.

The precise manipulation of electromagnetic and thermoelectric characteristics in the miniaturization of electronic devices offers a promising foundation for practical applications in quantum computing. Double perovskites characterized by stability, non-toxicity, and spin polarization, have emerged as appealing candidates for spintronic applications. This study explores the theoretical elucidation of the influence of iridium's 5d electrons on the magnetic characteristics of Sr2AIrO6 (A = Y, Lu, Sc) with WIEN2k code. The determined formation energies confirm the thermodynamic stability while an analysis of band structure and the density of states (DOS) reveals a half-metallic ferromagnetic character. This characteristic is comprehensible through the analysis of exchange constants and exchange energies. The current analysis suggests that crystal field effects, a fundamental hybridization process and exchange energies contribute to the emergence of ferromagnetism due to electron-spin interactions. Finally, assessments of electrical and thermal conductivities, Seebeck coefficient, power factor, figure of merit and magnetic susceptibility are conducted to assess the potential of the investigated materials for the applications in thermoelectric devices.

Magnetic and dielectric properties of the Co-defective Ca3Co2-xO6 compounds

The Ca3Co2-xO6 (x = 0, 0.02, 0.04, 0.06, 0.08, 0.1) samples were prepared by reducing the stoichiometric ratio of Co atoms. Their structure, magnetic properties, dielectric and magnetodielectric properties were investigated. XRD results show that the presence of a small number of vacancies does not change the crystalline structure. The positive Curie-Weiss temperature θ and interchain exchange constants J indicate that ferromagnetic interactions are stronger than the antiferromagnetic interactions in Co-defective Ca3Co2-xO6. The Co-vacancies could weaken the Co-Co exchange interactions, it has an obvious dilution effect on the ferromagnetic interactions within the chain. The magnetization steps move to low field accompanying the defects increase. Simultaneously, Co defects could also release part of the magnetic frustration. The competition of the released magnetic frustration and the dilution effect of the vacancies to the ferromagnetic chains and low doping concentration make the Co-defective Ca3Co2-xO6 present similar magnetic property with the parent Ca3Co2O6. At the positions of magnetic phase transition and the critical magnetic field of magnetization steps, clear dielectric anomalies can be detected. This result suggests the strong magnetodielectric coupling effect in Ca3Co2-xO6 (x = 0, 0.02, 0.04, 0.06, 0.08, 0.1) samples.

Study of ferromagnetism, and thermoelectric behavior of double perovskites K2Z(Cl/Br)6 (Z = Ta, W, Re) for spintronic, and energy application

Spintronic is the developing technology which probes the properties of quantum devices with spin of electrons which reduce the size and enhance its speed. Therefore, here the role of 5d electrons and thermoelectric characteristics of double perovskites (DPs) K2ZCl/Br6 (Z = Ta, W, Re) elaborated comprehensively by density functional theory (DFT). The Heisenberg model spin polarization density (SP) has been applied to evaluate the Curie temperature (Tc) and spin polarization factor. The tolerance factor (tF) and formation energy (ΔH) have been calculated to confirm the stability of structures. Ferromagnetism has been discussed in terms of spin polarization, crystal field energy (ΔCF) and exchange energies (Δ(d), Δ(pd)). The double exchange mechanism, and exchange constants ensure the role of electrons spin in ferromagnetism instead of segregation of transition metal ions. The transferring of magnetic moments of transitions metals to nonmagnetic sites (K, Cl, Br) show the exchange of spin of electrons and integer values of total magnetic moment show 100 % spin polarization. Finally, the transport properties are studied in standings of electrical and thermal conductivities. The large value of Seebeck coefficient and power factor ensure the importance of studied DPs for thermoelectric generators.

Effect of the surface anisotropy on the magnetic behavior of ultra-thin films single-domain on the spin reorientation transition regime by monte carlo simulation

In this work, Monte Carlo simulations allowed for studying the effect of the surface anisotropy on the Spin Reorientation Transition regime for single-domain ultra-thin films. The simulations included spin moments (1), exchange constant (10 meV), magnetocrystalline anisotropy (0.5 meV), and dipolar magnetic interaction (0.05 meV). We evaluated the surface anisotropy constant for K S = 0.5, 1, and 2 meV and thicknesses ranging from 3 to 11 cells. We determined the magnetothermal and hysteresis loop in- and out-plane at different angles to the plane. Analysis of Variance allows for modeling the coercivity as a function of the thickness and the applied field direction (in- and out-plane). Under these simulation conditions, the Spin Reorientation Transitions appear only at a thickness of 7 cells with K S =1 meV. The main contribution to magnetization rises out-plane at low thicknesses and in-plane at high values. However, the dominant magnetization contribution is in-plane for the thickness of 7 cells and low surface anisotropy. The magnetization is mainly oriented, out-plane for the high surface anisotropy case. However, hysteresis loops were observed independent of the applied magnetic field direction and thickness. Analysis of Variance results suggests that the thickness and the applied magnetic field direction allowed for tunning the coercivity (hard or soft magnetic materials). Sample simulated ignoring the magnetocrystalline and the surface anisotropies produce magnetic components in- and out-plane with slight differences as angle function. The combination of dipolar interactions and magnetocrystalline anisotropy showed two magnetic behaviors, a hard magnetic phase at low angles and a soft one at high angles in-plane direction. The inverse behavior results in the out-plane component. We observed the same behavior when surface anisotropy is considered. The differences are the transition angle of 50° in the first case and 30° in the second.

Role of 4d electrons in room temperature ferromagnetism, and thermoelectric properties of Sr2CrXO6 (X = Nb, Mo) for spintronic applications

The spintronic is an emerging technology which controls the properties of multifactional devices with spin of electrons. In present manuscript, Wien2k and Boltz Trap codes are used to explore electronic, magnetic, and thermoelectric characteristics of Sr2CrXO6 (X = Nb, Mo) double perovskites (DPs). The evaluation of energies released in paramagnetic (PM), antiferromagnetic (AFM), and ferromagnetic (FM) states assure the stability of FM states. Both the negative formation energy and the tolerance factor confirm structural and thermodynamic stability in FM states. The 100 % spin polarization was confirmed by both integer values of magnetic moment (MM) and the spin polarization factor. The values of exchange energy, double exchange model, hybridization of p-d states, and exchange constants are calculated to explore the nature of ferromagnetism and spin functionality. The effect of thermoelectric parameters on spin of electrons and thermoelectric performance are elaborated by thermal to electrical conductivity ratio, Seebeck coefficient and power factor.

Semiempirical Magnetostructural Correlation for High-Nuclearity MnIII-Oxo Complexes: Accommodation of Different Relative Jahn-Teller Axis Orientations.

The previous development of a magnetostructural correlation (MSC) for polynuclear FeIII/oxo clusters has now been extended to one for polynuclear MnIII/oxo clusters. A semiempirical model estimating each pairwise Mn2 exchange constant (Jij) from the Mn-O bond lengths and Mn-O-Mn angles has been formulated based on the angular overlap model. The extra complication, compared with the FeIII/oxo MSC, of different relative orientations of the Jahn-Teller distortion axes typical of high-spin MnIII in near-octahedral geometry was accommodated by developing a separate MSC variant for each possible situation. The final coefficients of the three MSC variants were determined by using reliable crystal structure data and experimentally determined Jij values from the literature. The estimated JMSC values from the new MnIII/oxo MSC have been employed to successfully rationalize the magnetic properties of a number of MnIII clusters in the nuclearity range Mn3-Mn10. These properties include relative spin vector alignments in the ground state, the presence of spin frustration effects, and the resulting overall ground state spin. In addition, the JMSC values can be used to simulate the direct-current magnetic susceptibility versus temperature data and provide realistic input values for fits of these data to minimize false-fit problems. A protocol for the use of the new MSC is also reported.

Elucidating Events within the Black Box of Enzyme Catalysis in Energy Metabolism: Insights into the Molecular Mechanism of ATP Hydrolysis by F1-ATPase.

Oxygen exchange reactions occurring at β-catalytic sites of the FOF1-ATP synthase/F1-ATPase imprint a unique record of molecular events during the catalytic cycle of ATP synthesis/hydrolysis. This work presents a new theory of oxygen exchange and tests it on oxygen exchange data recorded on ATP hydrolysis by mitochondrial F1-ATPase (MF1). The apparent rate constant of oxygen exchange governing the intermediate Pi-HOH exchange accompanying ATP hydrolysis is determined by kinetic analysis over a ~50,000-fold range of substrate ATP concentration (0.1-5000 μM) and a corresponding ~200-fold range of reaction velocity (3.5-650 [moles of Pi/{moles of F1-ATPase}-1 s-1]). Isotopomer distributions of [18O]Pi species containing 0, 1, 2, and 3 labeled oxygen atoms predicted by the theory have been quantified and shown to be in perfect agreement with the experimental distributions over the entire range of medium ATP concentrations without employing adjustable parameters. A novel molecular mechanism of steady-state multisite ATP hydrolysis by the F1-ATPase has been proposed. Our results show that steady-state ATP hydrolysis by F1-ATPase occurs with all three sites occupied by Mg-nucleotide. The various implications arising from models of energy coupling in ATP synthesis/hydrolysis by the ATP synthase/F1-ATPase have been discussed. Current models of ATP hydrolysis by F1-ATPase, including those postulated from single-molecule data, are shown to be effectively bisite models that contradict the data. The trisite catalysis formulated by Nath's torsional mechanism of energy transduction and ATP synthesis/hydrolysis since its first appearance 25 years ago is shown to be in better accord with the experimental record. The total biochemical information on ATP hydrolysis is integrated into a consistent model by the torsional mechanism of ATP synthesis/hydrolysis and shown to elucidate the elementary chemical and mechanical events within the black box of enzyme catalysis in energy metabolism by F1-ATPase.