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[Masayoshi Mikami <mmikami@rc.m-kagaku.co.jp>]

Dear Hongyi Zhao,

This is just a mathematical issue.
Suppose y=f(x) has a local minimum at x=x0.
At x=x0, df/dx=0 (first derivative should be zero)
Thus, remembering Taylor series,
f(x) = f(x0) + (f''(x0)/2!)*x^2 + O(x^3)
if |x-x0| is small enough, everything can be
described as "parabola" (so called, harmonic approximation).

In passing, you want to know the equation-of-state:
Try googling with "Murnaghan" (or "Birch-Murnaghan")
You will find, for example,
http://en.wikipedia.org/wiki/Birch-Murnaghan_equation_of_state

Good luck,
Masaysohi

P.S.
Before posting, you might want to have "physics/math mentors"
available around you (physically), if you could not find a good
textbook such as
Electronic Structure: Basic Theory and Practical Methods
Cambridge University Press, New York, 2004
ISBN 0 521 78285 6
(as suggested by Paul)

On 2007/04/16, at 18:51, Hongyi Zhao wrote:

> Hi all,
>
> I am wondering Why the Etotal has the parabola-function- 
> relationship in
> respect to the increasment of the parameter *acell*?  For detail of my
> problem, I describe it as follows:
>
> The input file for abinit is like this:
>
> -----------------
> ndtset   15
> acell:   9.6  9.6  9.6
> acell+   0.1  0.1  0.1
> kptopt   1
> ngkpt   6  6  6
> toldfe   1.0d-6
> iscf   5
> nstep   15
> diemac   12.0
> ecut   9.0
> enunit   2
> nband   5
> ixc   1
> typat   1  1
> znucl   14
> natom   2
> rprim   0.0  0.5  0.5
>        0.5  0.0  0.5
>       0.5  0.5  0.0
> xred   0.0  0.0  0.0
>       0.25 0.25 0.25
> -----------------
>
> Then, I find that the the Etotal has the parabola-function- 
> relationship
> in respect to the increasment of the parameter *acell*, in detail, the
> Etotal will take its minimum vaule when the *acell* is about 10.2  
> bohr.
> Dut to my poor theoretical background, I can't understand this
> phenomena.  Who can give me some hints on this thing?
>
> Thanks in advance.
>
> ---
> Hongyi Zhao
> GnuPG DSA: 0xD108493B