多孔材料孔结构表征方法：什么是DFT法、NLDFT法和GCMC法？
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多孔材料孔结构表征方法：什么是DFT法、NLDFT法和GCMC法？
（Mr. Jacek Jagiello
问答录）
Mr. Jacek Jagiello ，
Micromeritics, Norcross, GA,
USA
美国麦克仪器公司，世界著名的DFT理论方面的科学家
关键词：
Adsorption 吸附；
Adsorption isotherms 等温吸附线；
Pore size distribution
(简称：PSD) 孔分布；
Density functional theory
(简称：DFT) 密度函数理论 ；
Non-local density functional theory
(简称：NLDFT) 非定域密度函数理论 ；
Grand canonical Monte Carlo
(简称：GCMC)巨正则蒙特卡罗；
Question : What are DFT, NLDFT, and GCMC?
Mr. Jacek Jagiello answered:
There are many books and original publications where one can
find the answers to this
question on different levels. Here, I keep my answers short
and simple. They should be
regarded only as introductory highlights to these
subjects.
问题：什么是DFT，NLDFT和GCMC？
你可以在很多书籍和原始出版物找到答案。
这是一个可以在不同级别上进行论述的问题。在这里，我仅会简单扼要地回答此问题。这些答复应该是入门级别的重点问题。
1．DFT is a general term for the
density functional theory, while there are many versions of this
theory.
1．DFT是密度函数理论的通用简化语，目前这一理论有了很多版本。
2．There are two levels of the
density functional theory (DFT):
a. Quantum DFT: Computational quantum mechanical modelling
method used to describe the electronic structure of atoms,
molecules and the condensed phases in terms of the electron density
rather than wave functions (orbitals).
b. Classical DFT for fluids: Molecular modeling method used
to describe properties of fluid systems in terms of the fluid
density.
2．密度函数理论（DFT）涉及两个层次理论版本：
a. 量子密度函数理论(Quantum
DFT)：一种计算量子力学建模方法，用于根据电子密度而不是波函数（轨道）来描述原子，分子和凝聚相的电子结构。
b. 经典流体密度函数理论（Classical
DFT）：用流体密度描述流体系统性质的分子建模方法。
3．By the density of electrons or
fluids we mean the density profile as a function of (x, y,
z).
3. 我们所说的电子或流体的密度是指密度分布作为(x, y,
z)的函数。
4. The density profile for systems of electrons or fluids is
obtained by minimization of
the energy functional or grand potential functional. The
density profile represents the
structure a system of electrons or fluids.
4．电子或流体系统的密度分布剖面是通过使表面能量函数或表面巨势函数最小化而获得的。密度分布剖面表示电子或流体系统的结构。
5．Nonlocal DFT (NLDFT) or local DFT
refers to a version of DFT where the nonlocal (smoothed) or local
density approximation is used. Various weighting (smoothing)
functions have been proposed for the density approximations. In our
NLDFT model calculations we apply the Tarazona [1, 2] prescription
for the weighting function. Nonlocal DFT is considered more
accurate than local for describing adsorption systems.
5．非定域DFT（即：NLDFT）或定域DFT（即：DFT）是指使用非局部（平滑处理）或局部密度近似处理的DFT版本。在密度近似中，人们提出了各种加权（或者平滑）函数。在我们的NLDFT模型计算中，我们使用了加权函数的Tarazona[1，2]公式。在描述吸附体系时，非定域DFT（NLDFT）被认为比定域DFT（DFT）更准确。
6. Grand Canonical Monte Carlo (GCMC) is a computer
simulation method. It was shown [3] that the GCMC and NLDFT give
similar results for model calculation of adsorption isotherms and
pore size distributions (PSD) from adsorption data.
6.
巨正则蒙特卡罗(GCMC)是一种计算机仿真方法。结果表明，GCMC和NLDFT对等温吸附线和孔径分布(PSD)的模型计算结果相似，详见文献[3]。
References: 参考文献
[1] P. Tarazona,
Free-energy density functional for hard spheres,
“用于硬球的自由能密度函数”
Physical Review A, (1985) .
[2] C. Lastoskie, K.E. Gubbins, N. Quirke,
Pore size distribution analysis of microporous carbons: a
density functional theory approach,
“微孔炭的孔径分布分析：一种密度函数理论方法”
The Journal of Physical Chemistry, (1993)
[3] A.D. Lueking, H.-Y. Kim, J. Jagiello, K. Bancroft, J.K.
Johnson, M.W. Cole,
Tests of Pore-Size Distributions Deduced from Inversion of
Simulated and Real Adsorption Data,
“将仿真的和真实的吸附数据反演推导出孔径分布的测试”
Journal of Low Temperature Physics, (2009) .
