Correcting the systematic error of the density functional theory calculation: the alternate combination approach of genetic algorithm and neural network

The alternate combinational approach of genetic algorithm and neural network (AGANN) has been presented to correct the systematic error of the density functional theory (DFT) calculation. It treats the DFT as a black box and models the error through external statistical information. As a demonstration, the AGANN method has been applied in the correction of the lattice energies from the DFT calculation for 72 metal halides and hydrides. Through the AGANN correction, the mean absolute value of the relative errors of the calculated lattice energies to the experimental values decreases from 4.93% to 1.20% in the testing set. For comparison, the neural network approach reduces the mean value to 2.56%. And for the common combinational approach of genetic algorithm and neural network, the value drops to 2.15%. The multiple linear regression method almost has no correction effect here.

A DFT study on isomorphously substituted MCM-22 zeolite

The density functional theory has been used to study the isomorphously substituted MCM-22 zeolite for the first time. The effect of the basis sets on the calculation results is discussed in details. Data of several index properties for characterizing the relative acidity of T-MCM-22 (T = B, Al, Ga, and Fe), including proton affinity, bond length and bond angle, OH stretching frequency, and charge on the acidic proton, show that the acidity of T-MCM-22 increases in the sequence of B-MCM-22 < Fe-MCM-22 < Ga-MCM-22 < Al-MCM-22. After making a correction, the calculated OH stretching frequencies for Al-MCM-22 and Fe-MCM-22 show a reasonable agreement with the experimental data. On the basis of an equilibrium structure of the B-MCM-22 zeolite, the effect of the B element in the synthesis of the Ti-MCM-22 is also discussed. The adding of the B element during the synthesis of the Ti-MCM-22 can decrease greatly the Ti substitution energy because of the forming of a structure quite similar to the terminal silanol group. The results can provide some constructively information for zeolite synthesis.

Different electronic structures and spectroscopic properties of cationic [M(ppy)2(N--N)]+ (M = Rh, Ir; N--N = Hcmbpy, H2dcbpy), a DFT study.

We report a comparative quantum-chemical study of the electronic structures and optical properties of a series of cationic complexes [M(ppy)(2)(N--N)](+) (N--N = Hcmbpy = 4-carboxy-4'-methylbpy, M = Rh (Rh1), Ir(Ir2); N--N = H(2)dcbpy = 4,4'-dicarboxy-bpy, M = Rh (Rh3) and Ir (Ir4)). The theoretical calculation reveals that the increased number of -COOH groups on the bpy ligand can decrease the energy levels of LUMO more than HOMO and narrow down the HOMO-LUMO energy gaps, which results in the red-shifted of the lowest-lying absorption and phosphorescent spectra. The lowest-lying singlet absorptions were categorized as d(M,M = Rh or Ir) + pi(ppy) -->pi*(bpy) with MLCT and LLCT characters.

Aminic nitrogen-bearing polydentate Schiff base compounds as corrosion inhibitors for iron in acidic media: A quantum chemical calculation

Quantum chemical calculations based on DFT method were performed on three polydentate Schiff base compounds (PSCs) used as corrosion inhibitors for iron in acid media to determine the relationship between the molecular structure of PSC and inhibition efficiency. The structural parameters, such as the frontier molecular orbital energy HOMO (highest occupied molecular orbital) and LUMO (lowest unoccupied molecular orbital), the charge distribution of the studied inhibitors, the absolute electronegativity (chi) values, and the fraction of electrons (Delta N) transfer from inhibitors to iron, were also calculated and correlated with inhibition efficiencies. The results showed that the inhibition efficiency of PSCs increased with the increase in E-HOMO and decrease in E-LUMO-E-HOMO; and the areas containing N atoms are most possible sites for bonding the metal iron surface by donating electrons to the metal. (C) 2007 Elsevier Ltd. All rights reserved.

Numerical approximation improves well survey calculation

It is now possible to improve the precision of well survey calculations by order of magnitude with numerical approximation.

Although the most precise method of simulating and calculating a wellbore trajectory generally requires more calculation than other, less-accurate methods, the wider use of computers in oil fields now eliminates this as an obstacle.

The results of various calculations show that there is a deviation of more than 10 m among the different methods of calculation for a directional well of 3,000 m.¹ Consequently, it is important to improve the precision and reliability of survey calculation-the fundamental, necessary work of quantitatively monitoring and controlling wellbore trajectories.

Hybrid Finite Compact-WENO Schemes for Shock Calculation

Hybrid finite compact (FC)-WENO schemes are proposed for shock calculations. The two sub-schemes (finite compact difference scheme and WENO scheme) are hybridized by means of the similar treatment as in ENO schemes. The hybrid schemes have the advantages of FC and WENO schemes. One is that they possess the merit of the finite compact difference scheme, which requires only bi-diagonal matrix inversion and can apply the known high-resolution flux to obtain high-performance numerical flux function; another is that they have the high-resolution property of WENO scheme for shock capturing. The numerical results show that FC-WENO schemes have better resolution properties than both FC-ENO schemes and WENO schemes. In addition, some comparisons of FC-ENO and artificial compression method (ACM) filter scheme of Yee et al. are also given.

Latin hypercube sampling used in the calculation of the fracture probability

The paper proposes Latin hypercube sampling combined with the stratified sampling of variance reduction technique to calculate accurate fracture probability. In the compound sampling, the number of simulations is relatively small and the calculation error is satisfactory.

An Approximate Method For Calculation Of Fluid Force And Response Of A Circular Cylinder At Lock-In

In this paper, equations calculating lift force of a rigid circular cyclinder at lock-in uniform flow are deduced in detail. Besides, equations calculating the lift force on a long flexible circular cyclinder at lock-in are deduced based on mode analysis of a multi-degree freedom system. The simplified forms of these equations are also given. Furthermore, an approximate method to predict the forces and response of rigid circular cyclinders and long flexible circular cyclinders at lock-in is introduced in the case of low mass-damping ratio. A method to eliminate one deficiency of these equations is introduced. Comparison with experimental results show the effectiveness of this approximate method.

Variation of added mass and its application to the calculation of amplitude response for a circular cylinder

In the present study, analyzed are the variation of added mass for a circular cylinder in the lock-in ( synchronization) range of vortex-induced vibration (VIV) and the relationship between added mass and natural frequency. A theoretical minimum value of the added mass coefficient for a circular cylinder at lock-in is given. Developed are semi-empirical formulas for the added mass of a circular cylinder at lock-in as a function of flow speed and mass ratio. A comparison between experiments and numerical simulations shows that the semi-empirical formulas describing the variation of the added mass for a circular cylinder at lock-in are better than the ideal added mass. In addition, computation models such as the wake oscillator model using the present formulas can predict the amplitude response of a circular cylinder at lock-in more accurately than those using the ideal added mass.

Stress intensity factors calculation in anti-plane fracture problem by orthogonal integral extraction method based on femol

For an anti-plane problem, the differential operator is self-adjoint and the corresponding eigenfunctions belong to the Hilbert space. The orthogonal property between eigenfunctions (or between the derivatives of eigenfunctions) of anti-plane problem is exploited. We developed for the first time two sets of radius-independent orthogonal integrals for extraction of stress intensity factors (SIFs), so any order SIF can be extracted based on a certain known solution of displacement (an analytic result or a numerical result). Many numerical examples based on the finite element method of lines (FEMOL) show that the present method is very powerful and efficient.

Numeric Calculation for Transient Thermal Stress Field in Wall-Shape Metal Part During Laser Direct Forming

In order to investigate the transient thermal stress field in wall-shape metal part during laser direct forming, a FEM model basing on ANSYS is established, and its algorithm is also dealt with. Calculation results show that while the wall-shape metal part is being deposited, in X direction, the thermal stress in the top layer of the wall-shape metal part is tensile stress and in the inner of the wall-shape metal part is compressive stress. The reason causing above-mentioned thermal stress status in the wall-shape metal part is illustrated, and the influence of the time and the processing parameters on the thermal stress field in wall-shape metal part is also studied. The calculation results are consistent with experimental results in tendency.