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1.
A theorem reported for Hartree-Fock SCF theory is shown to be valid for general MC SCF and open-shell RHF theories - a sufficient condition for these wavefunctions to satisfy the Hellmann-Feynman theorem is that the basis set includes the derivative AO ?Xr/?Xrfor any basis Xr. The new force approach is applicable to wider fields including electronic processes in chemical reactions. Test calculations are given for some simple systems. 相似文献
2.
The force constants of the molecules LiH, BH, and H2O have been calculated by means of the Hellmann-Feynman theorem on the basis of the Hartree-Fock-Roothan wave functions in the one-determinant approximation. The results obtained have been compared with the results previously calculated on the basis of the same functions by means of the virial theorem. 相似文献
3.
《Journal of Chemical Sciences》1997,107(2):139-154
The problem considered here can be viewed as the analogue in higher dimensions of the one variable polynomial interpolation
of Lagrange and Newton. Let x1,...,x
r be closed points in general position in projective spacePn, then the linear subspaceV ofH
0 (⨑n,O(d)) (the space of homogeneous polynomials of degreed on ⨑n) formed by those polynomials which are singular at eachx
i, is given by r(n + 1) linear equations in the coefficients, expressing the fact that the polynomial vanishes with its first derivatives at x1,...,x
r. As such, the “expected” value for the dimension ofV is max(0,h
0(O(d))−r(n+1)). We prove thatV has the “expected” dimension for d≥5 (theorem A). This theorem was first proven in [A] using a very complicated induction
with many initial cases. Here we give a greatly simplified proof using techniques developed by the authors while treating
the corresponding problem in lower degrees. 相似文献
4.
5.
The properties of manganites can be tuned by changing the doping level x in Ln1−xMxMnO3. A second mechanism allows tuning of magnetic and electronic properties, for fixed x values, by varying the average A-cation radius, 〈rA〉. Moreover, for fixed x and 〈rA〉 values, the changes in the A-cation size variance, σ2, also modify the ferromagnetic and metal-insulator transition temperatures. Here, we investigate the influence of the number of A-site cations on Ln5/8M3/8MnO3 manganites, where x, 〈rA〉 and σ2 values are kept constant, and in the absence of phase separation phenomena. We have found that the number of cation species at the A site (NA) has a strong influence on the width of the ferromagnetic and metal-insulator transitions, and a small influence on the average transition temperature. This behavior is opposite to that observed for increasing values of the variance σ2 in manganites, with the same x and 〈rA〉 values, where average transition temperatures are strongly reduced. 相似文献
6.
The effect of inert additives on the explosive mechanochemical synthesis of some metal chalcogenides
《Journal of solid state chemistry》1987,71(2):522-529
The effect of different inert additives on the mechanochemical synthesis of SnS was studied. A transition from explosive to nonexplosive mechanochemical reaction was observed. It was shown that this change takes place only when a critical volume xc is occupied by inert material. The critical volume for a transition from an explosive to nonexplosive mechanochemical synthesis were determined for the chalcogenides of Zn, Cd, and Sn. The xc values obtained are discussed. On the basis of the new data concerning the critical dimensions rc of the exploding mechanical aggregates and the percolation phenomena, a mechanism for the transition from an explosive to nonexplosive mechanochemical synthesis is suggested. 相似文献
7.
Calculations on the ground states of the helium isoelectronic series are carried out using variational wavefunctions of the form ψ (x,y), in which x and y are the combinations r1 + r2 ± r12 occurring in the Coulomb Green's function. The results for helium are the most accurate to date using a two-variable wavefunction accounting for 71.5% of the correlation energy. 相似文献
8.
The passage of D3dC2H6 and B2H6 toward a D2 h bridged structure, and the motion of a methyl proton maintaining C symmetry in C2H inf5 sup+ and CH3BH2 are described by integral Hellmann-Feynman computations in a Frost floating spherical Gaussian basis. Marron and Weare's variational corrections to the integral Hellmann-Feynman formula forAE between statesA andB are evaluated with variational functions of the form η(ψA/SAB-ψB)) used to refine the stateB. An analogous function ξ(ψB/SAB-ψA) refines state A. Both η and ξ are chosen variationally to minimize Marron and Weare's functional. No obvious advantage of the variational method became apparent in this simple application. 相似文献
9.
Structural, magnetic and transport properties of La0.6−xPrxSr0.4MnO3 with x=0.0, 0.03, 0.06, 0.18, 0.3, 0.42, 0.54 and 0.6 are studied. The system exhibits a rhombohedrally distorted perovskite structure for x?0.3. A rhombohedral-orthorhombic (Pnma) structure transition is detected in the doping range from x=0.42 to 0.6. The structure refinement by Rietveld analysis of the X-ray powder diffraction data shows that the average distance Mn-O increases in the rhombohedral phases and decreases in the orthorhombic phases. Results show that the Curie temperature decreases from 374 to 310 K when 〈rA〉 varies from 1.254 to 1.231 Å. Electrical measurements show that all samples exhibit a metallic to semiconducting transition with increasing temperature. Meanwhile, the size of the resistivity ρ increases near TC. This phenomenon is interpreted as a gradual bending of the Mn-O-Mn bond angle, with decreasing 〈rA〉, which causes the narrowing of the electronic bandwidth and the effect of the A-site variance σ2. 相似文献
10.
Dielectric and conducting properties of Tb1−xAlxMnO3 (x = 0, 0.05) synthesized by the solid–state reaction method have been investigated. The Al ion has the same valence as substituted Tb but is nonmagnetic and its small size gives rise to microstructural strain which affects the multiferroic properties of the parent compound. Samples were characterized by means of complex impedance spectroscopy (CIS) in the frequency range from 40 Hz to 5 MHz, at temperatures above room temperature. The conductivity curves for the two samples are well fitted by the Jonscher law σ(ω) = σdc + Aωn. Results of the fitting procedure indicate that for the studied samples, the hopping motion involves localized hopping without the species leaving the neighbors. Frequency dependence of the dielectric constant (ε″) and tangent loss (tan δ) display a dispersive behavior at low frequencies that can be explained on the basis of the Maxwell–Wagner model and Koop's theory. The relaxation dynamics of charge carriers has been studied by means of the electric modulus formalism. In turn, the variation of the imaginary part of the complex impedance, Z″, shows a peak at a relaxation angular frequency (ωr) related to the relaxation time (τ) by τ = 1/ωr. The complex impedance spectra (Nyquist plots) show well-defined semicircles which are strongly dependent on the Al-doping level and temperature. The complex impedance data have been modeled using electrical equivalent circuits. 相似文献
11.
Magnesium is a key determinant in calcite (CaCO3) mineralization having a notable significance upon the carbonate growth. Magnesium is also present in CaCO3 mineral scale formation which is a persistent and expensive problem in oil and gas production. In the present work, we attempt to treat CaCO3 calcite mineral bulk inducing different concentrations of Mg impurity. The study is done using a quantum‐chemical computer code based on the Hartree–Fock method. It is found that small Mg impurity concentrations produce a significant distortion of the defect‐closest O atoms thus developing local microstructures being distinct to those of the original calcite structure. This structural alteration is accompanied by the electron density redistribution from the O 2pz atomic orbitals (AOs) toward the O 2px and 2py AOs for impurity nearest oxygens. On the other hand, the high Mg impurity concentrations make the chemical bonding in calcite more ionic. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011 相似文献
12.
《Spectrochimica Acta Part B: Atomic Spectroscopy》2007,62(6-7):529-532
A different approach to X-ray stress analysis has been developed. At the outset, it must be noted that the material to be analyzed is assumed homogeneous and isotropic. If a sphere with radius r within a specimen is subjected to a state of stress, the sphere is deformed into an ellipsoid. The semi-axes of the ellipsoid have the values of (r + εx), (r + εy), and (r + εz), which are replaced by dx, dy, and dz, or for the cubic case, ax, ay, and az. In this technique, at a particular ϕ angle (see Fig. 1), the two-theta position of a high angle (hkl) peak is determined at ψ angles of 0, 15, 30, and 45°. These measurements are repeated for 3 to 6 ϕ angles in steps of 30°. The dϕψ or aϕψ values are then determined from the peak positions. The data is then fitted to the general quadratic equation for an ellipsoid by the method of least squares. From the coefficients of the quadratic equation, the angle between the laboratory and the specimen coordinates (direction of the principle stress) can be determined. Applying the general rotation of axes equations to the quadratic, the equation of the ellipse in the x–y plane is determined. The ax, ay, and az values for the principal axes of the lattice parameter ellipsoid are then evaluated. It is then possible to determine the unstressed a0 value from Hooke's Law using ax, ay, and az. The magnitude of the principal strains/stresses is then determined. 相似文献
13.
《Solid State Sciences》2012,14(6):668-672
Using a high-temperature standard solid-state reaction (i.e., mixed oxide) method several yttrium modified ferroelectric ceramics of type Pb1−xYx(Fe0.5Nb0.5)1−x/4O3 (PYFN)with different concentration (x = 0.00, 0.02, 0.04, 0.06, 0.08) were prepared. Preliminary X-ray structural analysis reveals that all the samples were crystallized in monoclinic crystal system. The crystal structure is almost invariant with small Y-concentration. Microstructure of the samples exhibits grain growth on increasing Y content. Curie temperature of Y-substituted samples decreases slightly as compared to that of PFN (Pb(Fe1/2Nb1/2)O3). However, Y substitution results in a notable enlargement of remnant polarization (2Pr). The 2Pr of PYFN (x = 0.02) reaches to a large value (23 μC/cm2) which is nearly 5 times greater than that of x = 0.00 (4.6 μC/cm2). A phenomenological model (i.e., ferroelectric capacitor model) used to simulate hysteresis loops was found to be suitable to explain experimental results. Jonscher's single power law (σac(ω) = σ(0) + Aωn) was well fitted to the frequency dependence of conductivity for all the samples. 相似文献
14.
T. D. Alieva G. J. Abdinova N. M. Akhundova D. Sh. Abdinov 《Russian Journal of Physical Chemistry A, Focus on Chemistry》2008,82(11):1967-1968
The effect of annealing of Pb1 ? x Mn x Te crystals at ~690 K and structures on their basis at ~383 K on the adhesive and electric properties of the interface in the Pb1 ? x Mn x Te-(In-Ag-Au) structure was studied over the temperature range ~77–300 K. The contacts possessed high adhesive strength. The effect of annealing on contact resistance r c was determined by a change in the specific resistance of crystals, diffusion of Ag atoms into the near-contact area of crystals, and the formation of intermediate phases of the Ag2Te type at the interface. 相似文献
15.
《Journal of solid state chemistry》1986,62(2):133-137
Four ternary phases MPtSi (M = Ca, Eu, Sr, Ba) have been shown to crystallize in the LaIrSi-type structure (space group P213). This ternary structure is a derivative structure of the binary SrSi2-type structure (space group P4332 or P4132). In the MPtSi series the LaIrSi-type structure has a stability range for metals with radii from rCa = 1.973 Å to rBa = 2.243 Å in contrast to MSi2 compounds which exist with the SrSi2-type structure only from rSr = 2.151Å to rBa 2.243 Å. From a single-crystal investigation on CaPtSi remarkably short PtSi distances of 2.30 Å (3x) are obtained. Structural relations are discussed. 相似文献
16.
Rajuru R. Reddy Agarala S. R. Reddy Vanka Krishna Reddy 《Theoretical chemistry accounts》1985,67(3):187-191
The bond dissociation energies for Alkali halides have been estimated based on the derived relations: $$\begin{gathered} D_{AB} = \bar D_{AB} + 31.973{\text{ e}}^{0.363\Delta x} {\text{ and}} \hfill \\ D_{AB} = \bar D_{AB} (1 - 0.2075\Delta xr_e ) + 52.29\Delta x, \hfill \\ \end{gathered} $$ where \(\bar D_{AB} = (D_{AA} \cdot D_{BB} )^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0em} 2}} \) , Δx represents Pauling electronegativity differences x(A ?xB) and r e is the internuclear distance. A simplified formula relating bond orders, q, to spectroscopic constants is suggested. The formula has the form q = 1.5783 × 10?3 (ω e 2 re/ Be)1/2. The ambiguity arising from the Parr and Borkman relation is discussed. The present study supports the view of Politzer that q/(0.5r e)2 is the correct definition of bond order. The estimated bond energies and bond orders are in reasonably good agreement with the literature values. The bond energies estimated with the relations we suggested, for alkali halides give an error of 4.5% and 5.3%, respectively. The corresponding error associated with Pauling's equation is 40.2%. 相似文献
17.
《Solid State Sciences》2004,6(6):561-564
Magnetic and electron transport properties of La0.7−xLnxSr0.3MnO3 with Ln=Gd and Dy have been investigated over a wide range of compositions to explore the effects of the radius of the A-site cation, 〈rA〉, and the size-disorder as measured by σ2. These manganates exhibit ferromagnetism and insulator–metal transitions up to a critical value of x (xc), with the Tc (TIM) values decreasing with 〈rA〉. When x⩾xc, however, the manganates cease to be ferromagnetic and instead they show an abrupt decrease in magnetization and increase in resistivity, suggesting the likely occurrence of electronic phase separation. 相似文献
18.
The integrated Hellmann-Feynman theorem is used to derive a rigorous relation between the energy and the electron density in momentum space. Choosing the electron mass as a differential parameter, we obtain a formula corresponding to the Wilson-Frost formula in coordinate space. Analysing the mass-dependence of momentum density, we then show that the present formula is equivalent to one of the previous results deduced from the virial theorem. Use of the integral Hellmann-Feynman theorem is also discussed. Several illustrative examples are given for the calculation of energy from momentum density. 相似文献
19.
The evaluation of data from DTA and calorimetric measurements is still, in most cases, made by hand. This is not only a highly time-consuming procedure, but also includes subjective errors. This is especially true for the determination of starting points and end points of DTA peaks. Via integration between these limits, errors are introduced into the calculation of peak areas, i.e. thermal energies. Since many research groups possess high-performance microcomputers or desktop computers, which are able to perform measurements with subsequent data evaluation by suitable software, we developed a computer-controlled DTA/DMC equipment.In the present paper, we first describe the hardware coupling of a desktop computer to a DTA/DMC apparatus. We proceed with a discussion of the capabilities of both the apparatus and the data evaluation methods. A calorimetric measurement of the melting point of tin is the basis for a rating of the proposed numeric procedure for finding the peak limits and for peak integration in contrast to the evaluation of data by hand. With the argyrodite—cuprodite system. Ag8?xCuxGeS6, O?x?4, as an example, we present a proposed method for obtaining phase diagrams. 相似文献
20.
GPS patch antenna performance by modification of Zn(1−x)CaxAl2O4-based microwave dielectric ceramics
Wan Nasarudin Wan Jalal Huda Abdullah Mohd Syafiq Zulfakar Mohammad Tariqul Islam Badariah Bais Sahbudin Shaari 《Journal of Sol-Gel Science and Technology》2014,71(3):477-489
This study reports the characterization, fabrication, and performance of global positioning systems (GPS) patch antennas as a function of calcium (Ca) concentration and dielectric constant (? r ). Zn(1?x)CaxAl2O4 (x = 0.00, 0.05, 0.10, 0.20, 0.25, and 0.30) thin films were prepared through a sol–gel method. The effects of added Ca on the nanostructures and dielectric properties of ZnAl2O4 ceramics were investigated. The addition of Ca increased the crystallite size, grain size, and surface morphology, thereby increasing the density and dielectric constant. As the Ca content increased, the ? r values linearly increased. However, the Q u values decreased (at x = 0.25 to x = 0.25) after achieving the optimum values at x = 0.20. Finally, GPS patch antennas were successfully fabricated using the Zn(1?x)CaxAl2O4 material. The patch antenna sizes decreased as ? r increased from 2.88 × 4.37 cm (? r ≈ 8.52) to 2.88 × 4.37 cm (? r ≈ 10.16). The performance (return loss analysis) and operating frequencies of the GPS patch antennas were measured using the PNA series network analyzer. Results show that the patch antenna resonates at frequency of 1.570 GHz and produces a return loss bandwidth between ?16.6 and ?27.5 dB. The optimal performance of GPS patch antenna with ? r ≈ 9.95, Q u ≈ 6,186, and return loss = ?27.5 dB was obtained from specimen using Zn0.80Ca0.20Al2O4 (x = 0.20) ceramics. 相似文献