# Which type of spline interpolation is used in EAM

Dear Steve and LAMMPS users,

Recently I read the code of EAM potential section in LAMMPS (pair_eam.cpp). The spline interpolation is used to calculate the energy and interaction force from the tabulated values. I want to know the type (or name) of spline and its reference. Could you please give me some help?

I compared the formula used in the code with cubic spline, Hermite spline, B-spline and Akima spline (http://www.alglib.net/interpolation/spline3.php). It looks like the Akima spline, they are all local interpolation (http://www.iue.tuwien.ac.at/phd/rottinger/node60.html). Except that the slope of the curve at point 3 (x1<x2<x3<x4<x5) in EAM is determined by

s = ((y1-y5)* + 8*(y4-y2))/dx

(The code in pair_eam.cpp:

spline[m][5] = ((spline[m-2][6]-spline[m+2][6]) + 8.0*(spline[m+1][6]-spline[m-1][6])) / 12.0;)

While the slope of the curve at point 3 in Akima is determined by

s = (|g4-g3|*g2 + |g2-g1|*g3)/(|g4-g3| + |g2-g1|)

g(i)=y(i+1)- y(i)/ x(i+1)- x(i)

On the other hand, the interpolation curve looks like the cubic one as shown in the attachment.

Any help is appreciated greatly. Thank you.

Sincerely yours,

Zhenhai Xu

I want to know the type (or
name) of spline and its reference. Could you please give me some help?

I don't know the answer to this. It is inherited from the original EAM DYNAMO
code. So you could ask one of its authors, like Stephen Foiles
(foiles at sandia.gov).

Steve