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Hi all,
I'm seeking some help for obtaining the analytical derivatives of the
dihedral angle defined by 4 points with respect to the cartesian
coordinates of these points.
Instead of trying to explain the problem with poor ascii, I think it's
better to give a pointer. It's explained clearly in the paper J. Chem.
Phys. 117, 9160, the relevant part of it I have uploaded to:
<http://djelibeibi.unex.es/files/diedro.pdf>. What I'm looking for is the
right form for equations 34 and 35.
I have some reasons to believe the minus sign in eq. 34 should actually be a
plus. Comparing with similar expressions in other books and computer
programs, sometimes there's a minus and sometimes there's a plus, but
things work better with a plus and at least in one case the minus was later
corrected, as it was a typo.
Eq. 35 is a bigger monster. I'd say the "u_j" in the fourth term should be
"v_j" (nothing else in that term is related to u, but to v), and the very
last "zeta" factor should be zeta_(bon) instead of zeta_(bom) for similar
reasons. However, even with those changes, the second derivatives are not
symmetrical due the the last two terms, which are symmetrical with respect
to the a<->b interchange but antisymmetrical with respect to i<->j; and the
sum of all second derivatives does not vanish, which I believe it should,
due again to these last two terms.
So, I'm almost sure these equations are not fully correct, probably just
because of a couple of typos, but I can't get the right expressions. I have
written to the paper's author but have got no reply yet. Could anyone help
me pinpoint the mistakes in eqs. 34 and 35?
Thanks in advance
--
Ignacio __ Fernández Galván
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