上次写了一点 Surface dipole moment and work function change , 下面再谈一点相关的问题，即表面计算中的偶极修正. 在第一原理计算建模中，表面通常是由一个若干层的slab加上一定厚度的真空层来模拟。真空层的存在是周期性边界条件决定的。周期性边界条件决意味着slab的images 会周期性的重复，而真空层的作用就是保证这一artificial的重复不会对真正模拟的表面产生影响。当真空层厚度大于10Å时，总能一般已经收敛。不过work function远没有收敛，原则上也不会收敛(周期性边界条件决定的)。很多计算中work function是很重要的，为了得到"收敛"的work function, 就要使用偶极修正. 原理是在真空层中央引入一个artificail偶极子（与表面偶极大小相同，符号相反) 来抵消表面偶极引起的势能梯度. 原则上，知道表面偶极的大小后，可以不做偶极修正就可以得到表面两侧work function 的大小, 即: phi_m_axis = -d_phi/2 - efermi # 负轴侧表面work function phi_p_axis = d_phi/2 - efermi # 正轴侧表面work function efermi 为fermi level d_phi的计算见 Surface dipole moment and work function change
SAJG_110_combrinck1.pdf Earth-tide as parameter of crustal motion correction for SLR station displacement Ludwig Combrinck and Vasyl Suberlak Space Geodesy Programme, HartRAO, PO. Box 443, Krugersdorp, 1740, South Africa e-mail:ludwig@hartrao.ac.za; vasyl@hartrao.ac.za 2007 September Geological Society of South Africa ABSTRACT A new Satellite Laser Ranging (SLR) analysis program is being developed at Hartebeesthoek Radio Astronomy Observatory (HartRAO) that can model satellite orbits with high accuracy utilising advanced modelling and SLR data. We introduce the background to SLR analysis to an interdisciplinary audience and present the results of processing one month of LAGEOS-1 and LAGEOS-2 data in combined and separate solutions. The inclusion of Earth-tide modelling is shown to be necessary to reduce range bias and to minimise observed minus computed (O-C) residuals. The combined solution shows a reduction in range bias when allowance is made for the SLR station displacement vector due to solid Earth-tide and the effect of the Earth-tide on the static gravity field. In order to make the comparison it is necessary to set the a-priori estimation error of unmodelled forces to a low value as it tends to absorb range biases and improve O-C residuals if included as an additional solve-for parameter. A comparison between the SLR station position perturbation resulting from solid Earth-tide and range bias indicates a correlation, which probably results from an overestimate of the Earth-tide vector and indicates that SLR will be able to differentiate between and evaluate different Earth-tide models. These are preliminary results and further improvement is envisaged due to the planned inclusion of additional advanced modelling procedures.
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