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【求助】英译汉 【有效期至2009年2月22日】
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【求助】英译汉 【有效期至2009年2月19日】 [ Last edited by telomerase on 2009-2-20 at 08:06 ] |
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现把要翻译的内容直接放在上面，并请版主顺延有效期2天，谢谢！
telomerase(金币+0,VIP+0):好的，到22号，可以吧！！ 2-20 08:06
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(II) Density functional theory (DFT) Density functional theory begins with a theorem by Hohenberg and Kohn (later generalized by Levy) [139, 140], which states that all ground-state properties are functionals of the charge density . Specifically, the total energy Et can be written as: , (1) where T[] is the kinetic energy of a system of non-interacting particles of density , U[] is the classical electrostatic energy due to Coulombic interactions, and Exc[] includes all many-body contributions to the total energy, in particular the exchange and correlation energies. Eq. (1) emphasizes the explicit dependence of these quantities on (in subsequent equations, this dependence is not always indicated). We construct the charge density from a wavefunction . As in other molecular orbital methods, the wavefunction is taken to be an antisymmetrized product (Slater determinant) of one-particle functions, i.e. molecular orbitals (MOs): (2) When the molecular orbitals are orthonormal: . (3) The charge density is given by the simple sum , (4) where the sum is overall occupied MOs, i. The density obtained from this expression is also known as the charge density. The MOs may be occupied by spin-up (alpha) electrons or by spin-down (beta) electrons. Using the same i for both alpha and beta electrons is known as a spin-restricted calculation; using different i’s for alpha and beta electrons results in a spin-unrestricted or spin-polarized calculation. In the unrestricted case, it is possible to form two different charge densities: one for alpha MOs and one for beta MOs. Their sum gives the total charge density and their difference gives the spin density, the amount of excess alpha over beta spin. This is analogous to restricted and unrestricted Hartree-Fock calculations. From the wavefunctions (Eq. 1) and the charge density (Eq. 4), the energy components can be written (in atomic units) as: , (5) . (6) In Eq. (6), Z refers to the charge on nucleus of an N-atom system. The first term, VN, represents the electron-nucleus attraction. The second, Ve/2, represents the electron-electron repulsion. The final term, VNN , represents the nucleus-nucleus repulsion. The final term in Eq. 1, the exchange-correlation energy, requires a degree of approximation for this method to be computationally tractable. A simple and surprisingly good approximation is the local density approximation, which is based on the known exchange-correlation energy of the uniform electron gas. Analytical representations have been made by several researchers. The local density approximation assumes that the charge density varies slowly on an atomic scale (i.e. each region of a molecule actually looks like a uniform electron gas). The total exchange-correlation energy can be obtained by integrating the uniform electron gas result: , (7) where xc [] is the exchange-correlation energy per particle in a uniform electron gas and is the number of particles. The simplest form of the exchange-correlation potential is the form derived by Slater, which uses simply xc [] = 1/3. In this approximation, the correlation is not included. The next step in improving the local spin-density (LSD) model is to take into account the inhomogeneity of the electron gas that naturally occurs in any molecular system. This can be accomplished by a density gradient expansion, sometimes referred as the nonlocal spin-density approximation (NLSD). Over the past few years, it has been well documented that the gradient corrected exchange-correlation energy Exc[, d(  /dr] is necessary for studying the thermochemistry of molecular processes. The total energy can now be written as: . (8) To determine the actual energy, variations in Et must be optimized with respect to variations in , subject to the orthonormality constraints in Eq. (2): , (9) where ij are Lagrangian multipliers. (III) DFT/MD overlap multiscale method In the proposed project, we will adopt a concurrent and seamless multiscale technique, which is conceptually similar to that developed by the present authors in Yeak et al. [102] to couple MD with semi-empirical tight binding. That approach will be adopted to couple MD and DFT. Here we describe three region types: the pure MD region, the DFT near region, and the DFT far region. As shown in Fig 3.5(a), the DFT domain comprises the near and far regions. The DFT far region, which is a relatively small sub-domain, is an overlap region used to achieve a seamless coupling between the MD and DFT regions. The MD method is applied to both the pure MD and DFT far regions. The resultant forces and velocities of the atoms in these two regions are determined by the MD method. The DFT method is applied to both the DFT near and far regions but only the forces and velocities of the atoms in the near region are determined by the DFT method. The average width of the far region is 2.6 Å. As shown in Fig 3.5(b), the periodic boundary condition (PBC) is adopted for near and far DFT regions by applying the supercell concept. Based on the supercell approach, the model is thus not affected by the PBC because the near region is non-PBC whereas the near and far regions as a whole are PBC-confined. For the DFT analysis of the DFT near and far regions, the forces acting on the atoms at the boundary of the DFT far region are derived from the MD analysis. For the multiscale model between MD and DFT, the entire energy can be written as , (10) where the superscripts pure, far, and near indicate the pure MD region, far DFT region, and near DFT region. The subscripts indicate the computational method used. The force on each atom can be written as , (11) where the atom is located at nucleus RI. Fig 3.5. (a) Terminology for regions used in the overlap MD/DFT multiscale model; (b) schematic of DFT and non-periodic regions. |
7楼2009-02-19 20:35:54
2楼2009-02-18 20:35:42
caitikuan
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3楼2009-02-19 08:44:01
wanglu3353
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168yjh(金币+1,VIP+0):谢谢提示！ 2-24 12:28
168yjh(金币+1,VIP+0):谢谢提示！ 2-24 12:28
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4楼2009-02-19 08:51:34
