Energy Matrices Research Articles

Life cycle cost analysis of HPVT air collector under different Indian climatic conditions

In this communication, a study is carried out to evaluate an annual thermal and exergy efficiency of a hybrid photovoltaic thermal (HPVT) air collector for different Indian climate conditions, of Srinagar, Mumbai, Jodhpur, New Delhi and Banglore. The study has been based on electrical, thermal and exergy output of the HPVT air collector. Further, the life cycle analysis in terms of cost/kWh has been carried out. The main focus of the study is to see the effect of interest rate, life of the HPVT air collector, subsidy, etc. on the cost/kWh HPVT air collector. A comparison is made keeping in view the energy matrices. The study reveals that (i) annual thermal and electrical efficiency decreases with increase in solar radiation and (ii) the cost/kWh is higher in case of exergy when compared with cost/kWh on the basis of thermal energy for all climate conditions. The cost/kWh for climate conditions of Jodhpur is most economical.

Study on the local structure of (CrO 6) 9− complex in garnet crystals by optical and EPR spectrum

The local lattice structure distortions for YAG and YGG systems doped with Cr 3+ have been investigated by the d 3 configuration complete energy matrices which contain the Zeeman energy besides the electron–electron interaction, the trigonal crystal field as well as the spin–orbit coupling interaction. The local lattice structure parameters R and θ of (CrO 6) 9− complex are determined for Cr 3+ in YAG and YGG systems, respectively. The calculated results show that the local lattice structures have expansion distortions, which almost tend to the same after distortions. Meanwhile, the EPR parameter D, g factors ( g ||, g ⊥) and optical spectrum of these systems have been interpreted uniformly by quantitative calculation. It is shown that the effect of the orbit reduction factor k on g factors ( g ||, g ⊥) cannot be ignored.

A ULFC Method for d4(D2d) Ions and a Study of the Spin Singlets Contributions to Zero-Field Splitting of Cr2+ Ions in Zinc Sulfide Crystals

A simple theoretical method is shown to yield a detailed explanation of numerous EPR parameters for a d4 configuration ion in tetragonal ligand field. Using the unified ligand-field-coupling (ULFC) scheme, the formulas relating the microscopic spin Hamiltonian parameters with the crystal structure parameters are derived. On the basis of the theoretical formulas, the 210 x 210 complete energy matrices including all the spin states are constructed within a strong field representation. By diagonalizing the complete energy matrices, the local lattice structure and Jahn-Teller energy of Cr(2+) ions in ZnS:Cr(2+) system have been investigated. It is found that the theoretical results are in good agreement with the experimental values. Moreover, the contributions of the spin singlets to the zero-field splitting (ZFS) parameters of Cr(2+) ions in ZnS crystals are investigated for the first time. The results indicate that the spin singlets contributions to ZFS parameter b(0)(4) is negligible, but the contributions to ZFS parameters b(0)(4) and b(4)(4) cannot be neglected.

A Diabatic Representation Including Both Valence Nonadiabatic Interactions and Spin−Orbit Effects for Reaction Dynamics

A diabatic representation is convenient in the study of electronically nonadiabatic chemical reactions because the diabatic energies and couplings are smooth functions of the nuclear coordinates and the couplings are scalar quantities. A method called the fourfold way was devised in our group to generate diabatic representations for spin-free electronic states. One drawback of diabatic states computed from the spin-free Hamiltonian, called a valence diabatic representation, for systems in which spin-orbit coupling cannot be ignored is that the couplings between the states are not zero in asymptotic regions, leading to difficulties in the calculation of reaction probabilities and other properties by semiclassical dynamics methods. Here we report an extension of the fourfold way to construct diabatic representations suitable for spin-coupled systems. In this article we formulate the method for the case of even-electron systems that yield pairs of fragments with doublet spin multiplicity. For this type of system, we introduce the further simplification of calculating the triplet diabatic energies in terms of the singlet diabatic energies via Slater's rules and assuming constant ratios of Coulomb to exchange integrals. Furthermore, the valence diabatic couplings in the triplet manifold are taken equal to the singlet ones. An important feature of the method is the introduction of scaling functions, as they allow one to deal with multibond reactions without having to include high-energy diabatic states. The global transformation matrix to the new diabatic representation, called the spin-valence diabatic representation, is constructed as the product of channel-specific transformation matrices, each one taken as the product of an asymptotic transformation matrix and a scaling function that depends on ratios of the spin-orbit splitting and the valence splittings. Thus the underlying basis functions are recoupled into suitable diabatic basis functions in a manner that provides a multibond generalization of the switch between Hund's cases in diatomic spectroscopy. The spin-orbit matrix elements in this representation are taken equal to their atomic values times a scaling function that depends on the internuclear distances. The spin-valence diabatic potential energy matrix is suitable for semiclassical dynamics simulations. Diagonalization of this matrix produces the spin-coupled adiabatic energies. For the sake of illustration, diabatic potential energy matrices are constructed along bond-fission coordinates for the HBr and the BrCH(2)Cl molecules. Comparison of the spin-coupled adiabatic energies obtained from the spin-valence diabatics with those obtained by ab initio calculations with geometry-dependent spin-orbit matrix elements shows that the new method is sufficiently accurate for practical purposes. The method formulated here should be most useful for systems with a large number of atoms, especially heavy atoms, and/or a large number of spin-coupled electronic states.

EPR theoretical study of hydrostatic pressure and temperature dependence of local lattice structure for [Mn(H 2O) 6] 2+ octahedral complex in the Zn(BF 4) 2 · 6H 2O:Mn 2+ system

The effect of hydrostatic pressure and temperature on the local molecular structure for Mn 2+ ions in the Zn(BF 4) 2 · 6H 2O:Mn 2+ system have been investigated by diagonalizing the complete energy matrices for a d 5 configuration ion in a trigonal ligand-field. By simulating the EPR parameters D and ( a − F), the local lattice structure parameters R and θ under different conditions have been determined. The results show that the local lattice structure of the [Mn(H 2O) 6] 2+ octahedron has a compressed distortion with increasing the pressure, and a elongated distortion with the temperature rising. Moreover, the electronic transition energies for Mn 2+ ions in the Zn(BF 4) 2 · 6H 2O crystal at 293 K are reported for the first time.

Prediction of Ras-effector interactions using position energy matrices

One of the more challenging problems in biology is to determine the cellular protein interaction network. Progress has been made to predict protein-protein interactions based on structural information, assuming that structural similar proteins interact in a similar way. In a previous publication, we have determined a genome-wide Ras-effector interaction network based on homology models, with a high accuracy of predicting binding and non-binding domains. However, for a prediction on a genome-wide scale, homology modelling is a time-consuming process. Therefore, we here successfully developed a faster method using position energy matrices, where based on different Ras-effector X-ray template structures, all amino acids in the effector binding domain are sequentially mutated to all other amino acid residues and the effect on binding energy is calculated. Those pre-calculated matrices can then be used to score for binding any Ras or effector sequences. Based on position energy matrices, the sequences of putative Ras-binding domains can be scanned quickly to calculate an energy sum value. By calibrating energy sum values using quantitative experimental binding data, thresholds can be defined and thus non-binding domains can be excluded quickly. Sequences which have energy sum values above this threshold are considered to be potential binding domains, and could be further analysed using homology modelling. This prediction method could be applied to other protein families sharing conserved interaction types, in order to determine in a fast way large scale cellular protein interaction networks. Thus, it could have an important impact on future in silico structural genomics approaches, in particular with regard to increasing structural proteomics efforts, aiming to determine all possible domain folds and interaction types. All matrices are deposited in the ADAN database (http://adan-embl.ibmc.umh.es/). Supplementary data are available at Bioinformatics online.

Studies of EPR theory and trigonal distortion of the [Cr(H 2O) 6] 3+ cluster in ferroelectric guanidinium aluminum sulfate hexahydrate (GASH): Cr 3+ system at different temperatures

For a d 3 configuration ion, a theoretical method for studying the inter-relationships between electronic and molecular structure is investigated by diagonalizing the 120 × 120 complete energy matrices. The theoretical results show the following: (i) the local distortion structure for the Cr 3+ occupying the Al 3+ sites I and II exhibits an expansion distortion and the EPR parameters ( D, g ∥, g ⊥) are in good agreement with the experimental results at different temperatures. (ii) The | D| values decrease with the increasing temperature. (iii) The sign of the zero-field splitting parameter D is negative for the two trigonal Cr 3+ centers I and II in guanidinium aluminum sulfate hexahydrate (GASH) at 295.5, 78.45 and 1.61 K.

Local structure and EPR studies of octahedral (MnO 6) 2+ cluster in the series of zinc fluoride hexahydrate

The EPR zero-field splitting of Mn 2+ ions doped in single crystals of zinc fluoride hexahydrate series is studied by diagonalizing the complete energy matrices for d 5 configuration ions in a trigonal ligand field. By simulating the EPR parameters D and ( a − F) simultaneously, the local structure parameters R = 2.252 Å, θ = 52.6006° for ZnTiF 6 · 6H 2O:Mn 2+, R = 2.266 Å, θ = 52.5466° for ZnGeF 6 · 6H 2O:Mn 2+, and R = 2.226 Å, θ = 52.9195° for ZnNbOF 5 · 6H 2O:Mn 2+ are determined, respectively, in which R is the Mn–O bond length and θ is the angle between the Mn–O bond length and C 3 axis. From our calculations, it is found that when Mn 2+ doped in the isomorphous crystals there have a similar local distortion.

Theoretical investigation of zero-field splitting and local structure distortion for a substitution of Fe 3+ ion in CdCl 2 crystal

A theoretical method for studying the inter-relation between electron and molecule structure is proposed on the basis of the complete energy matrices of the electron–electron repulsion, the ligand-field and the spin–orbit coupling for d 5 configuration ion in a trigonal ligand-field. As an application, the local distortion structure of ( FeCl 6 ) 3 - coordination complex for Fe 3+ ions doped into CdCl 2 is investigated. Both the second-order zero-field splitting parameter b 2 0 and fourth-order zero-field splitting parameter b 4 0 are considered simultaneously in the structural investigation. By diagonalizing the complete energy matrices, the local structure distortion parameters Δ R=−0.24 Å, Δ θ=2.137° at 26 K and Δ R=−0.203 Å, Δ θ=2.515° at 225 K for Fe 3+ ions in CdCl 2 are determined. These results elucidate a microscopic origin of various ligand-field parameters which are usually used empirically for the interpretation of electron paramagnetic resonance results. It is found that the theoretical results are in good agreement with the experimental values.

Theoretical study on local lattice structure distortion for octahedral Fe 3+ center in several germanate garnets

Local lattice structure distortion study of octahedral Fe 3+ center in garnets Ca 3M 2Ge 3O 12 (M = Al, Ga, Sc, In, Lu) has been performed systematically based on the diagonalization of the complete energy matrices of the electron–electron repulsion, the spin–orbit coupling and the trigonal ligand–field interaction for a d 5 configuration ion in a trigonal ligand field. From the EPR calculation, the local structure distortion parameters Δ R and Δ θ are determined, respectively. These results illuminate a microscopic origin of various ligand field parameters used empirically for the interpretation of electron paramagnetic resonance experiments. It is found that the theoretical results of the electron paramagnetic resonance spectra for Fe 3+ center in garnets Ca 3M 2Ge 3O 12 (M = Al, Ga, Sc, In, Lu) are in good agreement with the experimental findings. Although the local lattice structures around the M 3+ (M = Al, Ga, Sc, In, Lu) ions are obviously different, the local lattice structures around the dopants are rather similar. Moreover, it is noted that the empirical impurity–ligand distance R ≈ R H + 1 2 ( r i - r h ) is not suitable for Fe 3+ in garnets Ca 3M 2Ge 3O 12 (M = Al, Ga, Sc, In, Lu).

A model approach for analysing trends in energy supply and demand at country level: Case study of industrial development in China

Ideally, national energy supply and demand choices would be based on comprehensive models and predictions of the energy sources, energy transformations, energy carriers and energy end-uses expected to play major roles into the foreseeable future (20–40 years). However, in many cases, the necessary detailed, high quality, consistent and timely data is not available for such comprehensive models to be constructed, in particular in large and complex developing economies expected to be major energy users in the near future. In the developing countries that are the focus of UNIDO's work, attention has been concentrated on making progress simultaneously on two fronts: (a) a dramatic decrease in energy intensity, particularly in activities linked to industrial production and (b) a major increase in the contribution of local renewable energy to limit growth in fossil fuel use. National policies need to be oriented towards a strict and strategic monitoring of the respective energy matrices with a simultaneous focus on both fronts. Robust assessments of industrial development trends throughout the whole 20–40 year transition phase are needed to achieve both objectives. Until more comprehensive energy-related models can be built up, to overcome the limited availability of data at country level it is proposed that a simple energy supply and demand model analysis consisting of three phases be used for identifying the consistency of future scenarios and corresponding policy requirements. This model analysis, which is a dynamic exercise, consists, first, of an analysis at aggregate level of the current and future national energy matrices; secondly, an analysis of perspectives for decreasing the energy intensity of the most inefficient systems or industrial sectors; and thirdly, an analysis of perspectives for increasing the supply and cost-effectiveness of sustainable energy sources. As an illustration of this model approach, the case of China is analysed with emphasis on the industrial sector, followed by a discussion of some of the structural change policies indicated for China to reach its planned energy supply and demand objectives for 2020.

Theoretical investigation of local lattice structure of the tetragonal FeF 5O cluster in KMgF 3:Fe 3+ crystal

The relationship between the electronic and molecular structure has been established based on the complete energy matrices for a 3d 5 configuration ion in a tetragonal ligand-field. By diagonalizing the complete energy matrices, the zero-field splitting parameters and the local lattice structure of the tetragonal FeF 5O cluster in KMgF 3:Fe 3+ crystal have been studied. The distortion of local lattice distortion structure parameters Δ R 1 = 0.10464 Å and Δ R 2 = 0.10094 Å are determined. Simultaneously, the local lattice structure parameters R 1 = 1.88936 Å and R 2 = 1.89306 Å, which reflect the interactions between impurity and crystal lattice, are determined from our calculation.

Theoretical Investigation of Electron Paramagnetic Resonance Spectra and Local Structure Distortion for Mn2+ Ions in CaCO3:Mn2+ System: A Simple Model for Mn2+ Ions in a Trigonal Ligand Field

This paper reports on a novel application of a ligand field model for the detection of the local molecular structure of a coordination complex. By diagonalizing the complete energy matrices of the electron-electron repulsion, the ligand field and the spin-orbit coupling for the d5 configuration ion in a trigonal ligand field, the local distortion structure of the (MnO6)10- coordination complex for Mn2+ ions doped into CaCO3, have been investigated. Both the second-order zero-field splitting parameter b(0)2 and the fourth-order zero-field splitting parameter b(0)4 are taken simultaneously in the structural investigation. From the electron paramagnetic resonance (EPR) calculations, the local structure distortion, DeltaR=-0.169 A to -0.156 A, Deltatheta=0.996 degrees to 1.035 degrees for Mn2+ ions in calcite single crystal, DeltaR=-0.185 A to -0.171 A, Deltatheta=3.139 degrees to 3.184 degrees for Mn2+ ions in travertines, and DeltaR=-0.149 A to -0.102 A, Deltatheta=0.791 degrees to 3.927 degrees for Mn2+ ions in shells are determined, respectively. These results elucidate a microscopic origin of various ligand field parameters which are usually used empirically for the interpretation of EPR and optical absorption experiments. It is found that the theoretical results of the EPR and optical absorption spectra for Mn2+ ions in CaCO3 are in good agreement with the experimental findings. Moreover, to understand the detailed physical and chemical properties of the doped CaCO3, the theoretical values of the fourth-order zero-field splitting parameters b(0)4 for Mn2+ ions in travertines and shells are reported first.

An investigation of the EPR zero-field splitting of Fe 3+ ions at tetragonal sites in Tl 2MgF 4 and Tl 2ZnF 4 crystals

By analyzing the EPR zero-field splitting parameters of Fe 3+ located at tetrahedral site in Tl 2MgF 4 and Tl 2ZnF 4 crystals, the local lattice structure for Fe 3+ doped in Tl 2MgF 4 and Tl 2ZnF 4 crystals is theoretically studied by diagonalizing the complete energy matrices for a d 5 configuration ion in a tetragonal ligand-field. From the calculation, the local lattice structure parameters R ⊥ = 1.8914 Å, R ∥ = 1.84699 Å and R ⊥ = 1.88229 Å, R ∥ = 1.84490 Å for tetragonal Fe 3+ center in Tl 2MgF 4 and Tl 2ZnF 4 crystals are determined, respectively. This result suggests that the ligand-fluorines on the C 4 axis deviate easily in both two crystals, which is consistent with the conclusion drawn by earlier workers.

Local molecular structure and thermal expansion coefficient for octahedral Fe 3+ center in AlF 3:Fe 3+system

A theoretical method for studying the inter-relation between electronic and molecular structure has been proposed by diagonalizing the complete energy matrices for d 5 configuration ion in a trigonal ligand-field. Based on this method, the local lattice distortion of Fe 3+ in AlF 3:Fe 3+ system (AlF 3 is the component of fluoride glasses or is the single crystal) has been studied by considering the second-order and fourth-order EPR parameters D and ( a − F), simultaneously. The results indicate that the local lattice structure around octahedral Fe 3+ center has an expansion distortion whether AlF 3:Fe 3+ is the component of fluoride glasses or Fe 3+ is doped in the AlF 3 single crystal. The expansion distortion may be ascribed to the fact that the radius of Fe 3+ ion is larger than that of Al 3+ ion, and the Fe 3+ ion will push the fluoride ligand outwards, respectively. Furthermore, the thermal expansion coefficient of Fe 3+ in the single crystal AlF 3:Fe 3+ depending on the temperature are reported and some characteristics of it are also analyzed.

EPR Theoretical Study of the Local Lattice Structure of Fe3+ Doped in MgTiO3 and LiTaO3

The EPR zero-field splittings of Fe3+ doped in MgTiO3 and LiTaO3 are studied by diagonalizing the complete energy matrices of the electron-electron repulsion, ligand-field and spin-orbit coupling interactions for a d5 configuration ion in a trigonal ligand-field. It is shown that, when Fe3+ is doped in aMgTiO3 or LiTaO3 crystal, the local lattice structure around the octahedral Fe3+ center has an obvious distortion along the C3 axis. By simulating the second- and fourth-order EPR parameters D and (a−F) simultaneously, the local structure parameters of Fe3+ doped inMgTiO3 and LiTaO3 crystals are determined, which reveal that Fe3+ occupies both the Mg2+ and Ti4+ sites in the MgTiO3:Fe3+ system and occupies the Li+ site rather than the Ta5+ site in the LiTaO3:Fe3+ system. The results accord with the ENDOR and EPR experiments. - PACS numbers: 71.70.Gm; 75.30.Et; 71.70.Ch.

Effect on the EPR and site symmetry of Cr 3+ ions doping spinel crystals: A complete energy matrices study

The EPR parameters ( D, g ∥, g ⊥) for chromium doped in spinels (MgAl 2O 4, ZnAl 2O 4 and ZnGa 2O 4) have been calculated by diagonalizing the 120 × 120 complete energy matrices for d 3 configuration ion in trigonal ligand field. The Zeeman effect of Cr 3+ ion in the trigonally distorted octahedral site of spinels has been studied, suggesting that there is a nonlinear relation between the Δ g (Δ g = g ∥ − g ⊥) and orbital reduction factor k. Both the site symmetries D 3 d and C 3 v of this impurity have been discussed for the three host lattices, and the local lattice structure around the impurity has also been determined.

Optical spectrum and local lattice structure for ruby

By diagonalizing the 120 x 120 complete energy matrices for d(3) ion in trigonal crystal field, which contains the electrostatic interaction, the trigonal field as well as the spin-orbit interaction, the unified calculation of the whole optical and EPR spectra for ruby are made. And matrix elements of the Zeeman energy with the magnetic field parallel or perpendicular to the trigonal axis are introduced into the complete energy matrices for obtaining the g factors of the energy levels. It is concluded that zero-field splitting and optical spectra as well as g factors are in good agreement with the experimental data and the distorted local lattice structure is determined firstly results from a stretching of the O2- ions along the C-3 axis. The pressure-induced shifts of energy levels, g factors and local lattice structure are also discussed. In particular, all the calculations are carried out successfully within the framework of the crystal-field model which is consistent with the opinion of Macfarlane and Sturge that if all terms within the d(3) configuration are included, one need not go outside conventional crystal-field theory.

Theoretical study of local lattice structure of Mn 2+ in perovskite fluorides A 2MF 4 (A=K, Rb; M=Mg, Zn, Cd) series

A theoretical method for investigating the inter-relation between the molecular structure and electronic structure has been established on the basis of the 252×252 complete energy matrices for a 3d 5 configuration ion in a tetragonal ligand field. By means of this method, which is independent of the X-ray diffraction, the local structure of the paramagnetic Mn 2+ ion in perovskite fluorides A 2MF 4 (A=K, Rb; M=Zn, Mg, Cd) are determined directly by analyzing the EPR spectrum of octahedral Mn 2+ center in A 2MF 4 crystals and the optical absorption spectrum of the (MnF 6) 4− cluster. It is shown that, comparing with the octahedral cubic structure, the local micro-structure in the vicinity of Mn 2+ displays an elongated distortion when b 2 0 > 0 and a compressed distortion when b 2 0 < 0 , and Δ R vs. 1 0 4 b 2 0 as well as Δ R vs. 1 0 4 b 4 0 in the distortion region is, respectively, approximately linear. Simultaneously, the theoretical zero-field-splitting parameters b 2 0 , b 4 0 and b 4 4 are in good agreement with the experimental values.

Study of optical absorption and EPR spectra of Mn2+ ion in cadmium maleate dihydrate

The optical absorption and EPR spectra of Mn2+ ion doped in cadmium maleate dihydrate have been theoretically investigated by diagonalizing the complete energy matrices for a d5 configuration ion in a trigonal ligand-field. According to the suggestion of the optical absorption studies, we assume that the Mn2+ ion enters the host lattice interstitially and the distorted octahedral symmetry for the impurity ion is trigonal. Moreover, the local lattice structure parameters of the system are determined. The results show that the six oxygen ions around the Mn2+ ion are at the same distance R=2.115 A, and there are three Mn-O bonds forming an angle θ1 of 66.26° with the C3-axis and three others forming an angle θ2 of 43.40°.