# Different formula in manual for improper_style from the original paper

Dear all,

it seems that the formula for the improper_style umbrella in the manual

E = 0.5 * K ((1+cos(w0)/sin(w0))^2 * (cos(w) - cos(w0)), when w0 != 0

is different from the one in the original paper:

E = 0.5 * K (1/sin(w0))^2 * (cos(w) - cos(w0))^2.

I took a quick peek into the code, and it seems to be using the formula from the paper.

What is the reason for this difference?

Thank you for your time.

Tod implemented this for LAMMPS, who is familiar with

the Dreiding FF. I’ve CCd - hopefully he can answer.

Steve

Trying again with a different email for Tod.

Steve

Hi Steve/Donatas:
As Donatas pointed out, the formula in the manual is incorrect and should be updated to be consistent with the code and the paper:
E = 0.5 * K (1/sin(w0))^2 * (cos(w) - cos(w0))^2

Best,
–Tod

Hi Steve/Donatas:
As Donatas pointed out, the formula in the manual is incorrect and should
be updated to be consistent with the code and the paper:
E = 0.5 * K (1/sin(w0))^2 * (cos(w) - cos(w0))^2

​i've included that in my branch and will forward it to steve at the next
occasion when he has time again to incorporate patches.

what about the second expression for w0 = 0?
shouldn't that be 0.5 * K *(1 - cos(w))^2 ?
that looks more similar to the w0 != 0 expression for small w0

​axel.​

Hi Axel:
No, if the equilibrium angle is 0 (i.e. the atoms bonded to the central atom I are coplanar), the potential is replaced with
E = K(1-cos(w))
as written (note the 1/2 factor is removed)

–Tod

Thanks for the quick response Tod - as Axel said, we’ll make

the change in the doc page …

Steve