24小时热门版块排行榜

返回列表

【奖励】本帖被评价6次，作者yongleli增加金币 5.5 个

yongleli

木虫 (正式写手)

应助: 93 (初中生)
金币: 3769.1
帖子: 764
在线: 101.3小时
虫号: 303595

[资源] 【原创】多参考自洽场方法及相关概念

所谓MC(multi configuration，这里的configuration指电子的不是分子的)，
是要在CI框架下处理问题。但是Full CI又太费时了，怎么办呢？

于是，划定一个子空间，即model space，这个space里边，轨道又分三种：
frozen orbital，它们的初始猜测选定之后，就不变化了。相当于一批观众。
inactive orbital，它们的初始猜测选定之后，还要用变分法优化组合系数。
               但是它们始终双占据，不参与激发。
active orbital，这些轨道根据CI的思想，计算各种不同的激发
         （就是考虑很多个Slater行列式）。但是，
            实际计算的时候，并非所有的组合都考虑。根据体系的特点，
            只计算几种组合。比如，

-----  ----- --|--
-----  --|-- -----
--|--  ----- -----
            一个电子，3个轨道的活性空间，只计算前两个。

CAS是一种MC。这时不设置frozen orbital，所有的orbital都参与优化。
但是划出一大块作为inactive space。留一部分做为active space。而
active space中的轨道，做Full CI，即考虑所有的组合。
比如上图三个configuration都会考虑到。

===================================================
Configuration严格定义：
A configuration (CSF, i.e. Configuration State Function) is a linear
combination of determinants which is an eigenfunction of the operators:
Sˆ2 and Sˆz, and belongs to the proper irreducible representation of the
symmetry group of the Hamiltonian. We say that this is a linear
combination of the (spatial and spin) symmetry adapted determinants.
Sometimes we refer to the spin-adapted configurations which are
eigenfunctions only of the Sˆ2 and Sˆz operators.

===================================================
MC的问题：Intruder states

There is another trouble known as intruder states,
i.e. states which are of unexpectedly low energy.

How can these states appear?

Firstly, the CI states known as “front door intruders”
appear, if some important (low-energy)
configurations were for some reason not included into the model space.

Secondly, we may have the “back door intruder”
states. When the energy gaps between the model space and the
other configurations are too small (quasi-degeneracy),
some CI states became low energy states (enter the model space energy
zone) even if they are not composed of the model space configurations.
所谓“前门驱虎，后门进狼”，哈哈
===================================================

两种关联：static & dynamical correlation
Dynamical correlation, i.e. correlation of electronic motion.

Certain determinants (or, in other words: configurations) absolutely
need to be present (“static correlation”) in the correct wave function
===================================================

参考文献：
IDEAS OF
QUANTUM CHEMISTRY

LUCJAN PIELA
Department of Chemistry University of Warsaw
Warsaw, Poland

Elsiver, 2007
目前，北师大的方维海老师是这方面的专家，
他们组用CASSCF方法计算过大量体系，甚至用QM/MM的方法研究了生物大分子。

[ Last edited by zeoliters on 2010-1-5 at 15:47 ]

回复此楼