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futiliu

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[交流] 投影态密度有负值

本人用smeagol算两电极系统的投影态密度时，某些原子上的PDOS出现负值，请问有人碰到这种情况吗？又如何解释呢？谢谢！

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1楼 2012-02-28 08:38:16

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zhangguangping

木虫 (著名写手)

★
futiliu(金币+1):谢谢参与
WDD880227(金币+1): 感谢交流提示 2012-02-28 15:35:57

这个是由于基组的不正交性导致的。严格说来，如果投影的时候采用一个已经正交的基组来定义的话，就会避免这个问题，但是那个时候PDOS的物理意义没有现在明确。所以有点“鱼和熊掌不可兼得”。

更加详细的解释，我下面引用如下：

http://www.mail-archive.com/sies ... am.es/msg02951.html

------------------------------------------

Dear Siesta users,

I have a problem understanding the output in a .PDOS output file for my
system.  I am getting negative values in the PDOS for the projection
onto a lot of the basis functions.  Perhaps my understanding is wrong,
but surely this should not be?  According to my understanding the PDOS
onto a specific basis function should have peaks at  the energies
corresponding  to the eigenfunctions to which it contributes.

I restarted the PDOS calculation from the output files of a converged
calculation and used 1 SCF iteration with 50x50x50 Monkhorst Pack grid.

Regards,
Rainer

-------------------------------------------

Dear Rainer:

When you are working with a non-orthogonal basis set,
as is the case in Siesta, neither the PDOS nor the Mulliken
population analysis are positive definite magnitudes.

The reason is due to the fact that the PDOS is defined
as:

g_mu(eps) = sum_nu rho_mu,nu S_nu,mu delta(eps-eps_i)

rho_mu,nu = sum_i C_mu,i C*_nu,i

(i stands for the bands, S stands for the overlap matrix,
and C stands for the coefficients of the wave function)
and the non-diagonal elements of the density matrix
might be negative.

However, the term in the diagonal IS positive definite,
and it is usually larger than the rest of the terms.
Therefore, when the PDOS is negative the value should be
small in absolute value.

Hope this helps,

   Javier

---------------------------------------

Dear Javier

Thanks very much for your reply.  This certainly helps me understand
why there can be negative values in the PDOS, at least mathematically.
But these negative values of PDOS are not physically meaningful, right?
So how should I interpret them?  Can one just invert them? I am
getting negative values that are roughly the same size as the positive
values, so I dont feel comfortable just disregarding them.

Regards,
Rainer
-----------------------------------------

Dear Rainer:

I do not think you can give any physical meaning
to a large negative Projected Density Of States.

The problem is rather fundamental.
The solution should come from a redefinition
of the PDOS as the projection over a basis of
orthogonalized orbitals. That would imply
a first transformation from our
non-orthogonal basis set to a orthogonal one
(I guess that you will have to multiply
by the inverse of the overlap matrix somewhere).

Hope this helps,

      Javier
=================================