密度泛涵理论最初来源于对下面这个问题的考虑: 在量子化学从头算中,对于一个N电子体系,N电子波函数依赖于3N个空间变量及N个自旋变量共4N个变量,我们是否能用其它相对简单的变量来替换这4N个变量以达到简化计算的目的,比如用体系的电子密度?因为,对于波函数实验上无法准确测定,而电子密度却可以,电子密度同波函数模的平方相联系.另一方面,对于依赖4N个变量的波函数,将随着体系变大电子数增多使计算变得越来越困难,而体系的哈密顿只不过由单电子和双电子算符组成,同时只跟体系中的单个电子和双电子的信息有关,因此对我们的计算目的而言，波函数中4N个变量已经包含了多余的信息.因此,以电子密度为变量,Thomas-Fermi Model作了最初的尝试,将能量表示为密度的泛函,这里有个问题要注意的是泛函和复合函数的区别.TFM虽然是一个很粗糙的模型,但是它的意义非常重要,因为它将电子动能第一次明确地以电子密度形式表示.至此,说简单些,密度泛函方法就是以体系的电子密度为变量的方法.
随后,Hohenberg-Kohn定理证明了external potentail是密度的唯一泛函,多电子体系的
基态也是电子密度的唯一泛函.因此,对于多电子体系非简态基态而言有一基态电子密度相
对应,正是这个基态电子密度也决定了体系的基态的其它性质,寻找基态的电子密度同样利
医院感染管理制度用变分方法.有关这个定理的内容可以参考其它资料.
在此定理的基础上,Kohn and Sham引入了"无相互作用参考系统"的概念,这个思想和传
统的从头算不同,我们推导的HF方程是建立在真实的系统基础上的,而无相互作用参考系统
是不存在的,只是KS为计算真实体系的设立的一个参照系统,它和真实系统的联系就在于有
相同的电子密度.因此,我们也可以看出,DFT能获Nobel Prize也是完全在于它是一个全新的
创造性的思想.这个无相互作用系统中,粒子间无相互作用,它的哈密顿算符就只有两项,动能算符和势能算符,这个形式和HF方法的形式比起来就简单多了,同HF方程一样,根据单电子近似也得到了KS单电子算符.接下来就是将这个参照系统同真实系统联系起来.HF方法完全
忽略了相关能的计算,在DFT中,这部分能量考虑了进去,因此从原理上讲,Kohn-Sham方法是
弗吉尼亚联邦大学
严格的,未作任何近似,但是同交换相关能相联系的交换相关势的形式却是无法确定的,因此
DFT的中心问题更是寻找更好的泛函形式.
PW91，PBE，BLYP都属于GGA泛函（广义梯度近似Generalized gradient approximations），一般来说其计算结果不如杂化泛函(hybrid functionals，如B3LYP、PBE0等)。B3LYP和BLYP的区别是加入了20%的Hartree-Fock交换项（exchange），所以对于体系的一般性质计算更准确。PBE0相比PBE区别是加入了25%的Hartree-Fock交换项（exchange）。如果只是简单的优化结构或计算单点，推荐B3LYP或者PBE0。以上并不局限于dmol软件。
100个原子以内很轻松就能优化，100-200个原子花点时间也是可以做优化的。如果只做单点能计算的话，建议从晶体结构入手，如果没有晶体结构，那就没办法保证你的结构是合理的，也就无法保证单点能是合理的。这种情况下至少用低水平的算法做个优化吧，例如HF/3-21G或B3LYP/3-21G或PM3或AM1，等等。
∙ LDA局域密度近似（LDA）：局域密度近似（LDA）是第一阶梯。它仅仅采用空间点r处的电子密度n（r）来决定那点交换-相关能密度的形式。交换-相关能密度由密度相同的均匀电子气完全确定。泛函的交换部分就准确的用均匀电子气的微分表达。各种不同的局域密度近似（LDA）仅仅是相关部分表示方法不同，所有现代应用的局域密度泛函都基于Ceperly和Alder`s在８０年代对均匀电子气总能量的Monte Carlo模拟。
广义梯度近似（ＧＧＡ）：ＧＧＡ是Jacob阶梯的第二个台阶，将电子密度的梯度也作为一个独立的变量（|∇n(r)|），在描述交换－相关能方面，梯度引入了非定域性。ＧＧＡ泛函包含了两个主要的方向：一个称为“无参数”，泛函中新的参数通过已知形式中参数或在其它准确理论帮助下得到。另外一个就是经验方法，未知参数来自于对实验数据的拟和或通过对原子和分子性质准确的计算。Perdew,Burke and Emzerhof(PBE)以及Perdew-Wang from 1991(PW91)是无参数的，在量子化学中广泛采用的GGA，比如Becke,Lee,Parr and Yang(BLYP)是经验性。LYP校正采用了密度的二阶Laplace算符，因此严格上讲属于Jacob阶梯的第三阶，但通常仍然归类为GGA.
PW91 Perdew-Wang generalized-gradient approximation Perdew and Wang (1992)
BP Becke exchange plus Perdew correlation Becke (1988), Perdew and Wang (1992)
PBE Perdew-Burke-Ernzerhof correlation Perdew et al. (1996)
RPBE Revid PBE functional by Hammer et al. Hammer et al. (1999)
HCTH Hamprecht, Cohen, Tozer and Handy functional Boe and Handy (2001)
BLYP Becke exchange plus Lee-Yang-Parr correlation Becke (1988), Lee et al. (1988)
BOP Becke One Parameter functional Tsuneda et al. (1999)
羽绒服油渍怎么洗VWN-BP BP functional with the local correlation replaced by the VWN functional. Vosko et al. (1980), Becke (1988), Perdew and Wang (1992)
VWN: The Vosko-Wilk-Nusair (VWN) functional is the most popular LSD correlation potential. It us a fit to accurate numerical results (by Ceperly and Alder) of a uniform electron gas. Ceperley and Alder performed quantum Monte Carlo calculations on a uniform electron gas at low and high spin limits for veral electron densities. VWN us the Pade interpolation procedure to fit the CA results for both the para and ferro states and for low and high densities. DMol3 us the best VWN (so called "Fit") parameters.
PWC: The Perdew-Wang (PWC) functional is a recent parameterization of the Ceperley and Alder data, which corrects some VWN problems with fitting. PWC is the default functional for DMol3 calculations.
咫尺读音
removeThe local spin-density (LSD) approximation accurately predicts structures, vibrations, and relative energies of covalent systems; however, bond energies are riously overestimated. The local DFT should not be ud for systems with weak bonds, such as hydrogen bonds. The problems with the LSD method can be corrected to a large extent by using the so-called gradient-corrected (or nonlocal) functionals.
P91, BP, BLYP, BOP: DMol3 supports veral nonlocal exchange and correlation functionals. The most popular, the Becke exchange functional (B88) is ud in conjunction with the Perdew-Wang correlation functional (BP) or the Lee-Yang-Parr correlation functional (BLYP). The so-called generalized gradient corrected (GGA) functional, by Perdew and Wang (P91) was derived by considering low and high density regimes and by enforcing various summation rules.
jiaoanPBE: The PBE (Perdew, Burke and Enzerhof) functional (1996, 1997) is another GGA functional in which all the parameters (other then tho in its LDA component) are funda
mental constants. The exchange part of this functional is similar to the Becke formula (1986), and the correlation part is clo to the Perdew-Wang functional (1986).This functional has a strong physical background, reliable numerical performance and it is frequently ud in DFT calculations.
自我评价材料
寻找答案RPBE: More recently, Hammer, Hann and Norskov (1999) propod a modified version of the PBE formula that improves considerably thermochemical results. So far this functional, called RPBE, has been mainly ud for solids.
HCTH: The HCTH functional, named for the authors' initials (Hamprecht et al., 1998), reprents a "pragmatic" philosophy in designing a DFT functional. Assuming that the exact functional will never be found, they propo a flexible form of gradient corrected functional that is fitted to the training t of molecules. The default for the current implementation, the so called HCTH/407 functional, that was obtained by fitting to the t of the 407 atomic and molecular systems (Boe and Handy, 2001). This functional was f
ound to predict a much improved thermochemistry for inorganic and hydrogen bonded systems. The standalone keyword for this functional is hcth407. The original HCTH-type functionals can be activated by keyword hcth93 (Hamprecht et al, 1998) and hcth147 (Boe et al. 2000).
Although the NLSD methods are significantly better than the LSD method, particularly in studying chemical reactions, the NLSD methods may still lead to reaction barriers that are too low.
VWN-BP: The VWN-BP functional is recommended for COSMO and COSMO-RS studies.
