Different formula in manual for improper_style from the original paper

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1

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.

2

Tod implemented this for LAMMPS, who is familiar with

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

Steve

3

Trying again with a different email for Tod.

Steve

4

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

5

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.​

6

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

7

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

the change in the doc page …

Steve