According to this:
https://en.wikipedia.org/wiki/List_of_moments_of_inertia
The moments of inertia of a disk (something like benzene) are:
Iz = mr^2/2
Ix = Iy = mr^2/4
None of them is zero. The smallest moment of inertia of a rod-like molecule
(e.g. C#C) is zero.
Best,
Peter
On Sun, Jan 15, 2017 at 8:15 AM Greg Landrum <greg.land...@gmail.com> wrote:
> Hi Guillaume,
>
> I think it this case it's something else. According to the Todeschini
> article the smallest moment of inertia of a planar molecule like benzene
> should be zero. The eigenvalues of the inertia matrix for benzene, however,
> are definitely not zero (and not close enough that it's likely to be
> round-off error).
> It would be very nice if you could run the three files I mention through
> Dragon and let me know what it calculates for those descriptors.
>
> -greg
>
>
> _____________________________
> From: Guillaume GODIN <guillaume.go...@firmenich.com>
> Sent: Sunday, January 15, 2017 1:11 PM
> Subject: RE: [Rdkit-discuss] PMI API
> To: Greg Landrum <greg.land...@gmail.com>, RDKit Discuss <
> rdkit-discuss@lists.sourceforge.net>, Chris Earnshaw <cgearns...@gmail.com
> >
>
>
>
> Dear Greg,
>
>
> I suspect that it's a precision error or eigen algorithm shift between
> rdkit c++ & dragon.
>
>
> To obtain good value, I suggest to try to implement a test on the eigen
> values like i did in gateway.cpp implementation.
>
>
>
> JacobiSVD<MatrixXd> getSVD(MatrixXd A) {
>
> JacobiSVD<MatrixXd> mysvd(A, ComputeThinU | ComputeThinV);
>
> return mysvd;
>
> }
>
>
> // get the A-1 matrix using
>
> MatrixXd GetPinv(MatrixXd A){
>
> JacobiSVD<MatrixXd> svd = getSVD(A);
>
> double pinvtoler=1.e-2;// choose your tolerance wisely!
>
> VectorXd vs=svd.singularValues();
>
> VectorXd vsinv=svd.singularValues();
>
>
> for (unsignedint i=0; i<A.cols(); ++i) {
>
> if ( vs(i) > pinvtoler )
>
> vsinv(i)=1.0/vs(i);
>
> else vsinv(i)=0.0;
>
> }
>
>
> MatrixXd S = vsinv.asDiagonal();
>
> MatrixXd Ap = svd.matrixV() * S * svd.matrixU().transpose();
>
> return Ap;
>
> }
>
>
> If it's not solve the problem, I would like to test it in Matlab. can you
> provide me the 3 (3d xyz matrix) of your example please ?
>
>
> I also have Dragon 6
>
>
> best regards,
>
> *Dr. Guillaume GODIN*
> Principal Scientist
> Chemoinformatic & Datamining
> Innovation
> CORPORATE R&D DIVISION
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> MOBILE +41 (0)79 536 1039 <079%20536%2010%2039>
> Firmenich SA
> RUE DES JEUNES 1 | CASE POSTALE 239 | CH-1211 GENEVE 8
>
> ------------------------------
> *De :* Greg Landrum <greg.land...@gmail.com>
> *Envoyé :* dimanche 15 janvier 2017 11:50
> *À :* Chris Earnshaw; RDKit Discuss
> *Objet :* Re: [Rdkit-discuss] PMI API
>
> I managed to make some time to look into this this weekend and I've found
> a bug and something I don't understand. Hopefully the community can help
> out here.
> On Sun, Jan 8, 2017 at 11:17 AM, Chris Earnshaw <cgearns...@gmail.com>
> wrote:
>
> 4) The big one! The returned results look very odd. They appear to relate
> more to the dimensions of the molecule than the moments of inertia. For a
> rod-like molecule (dimethylacetylene) I'd expect two large and one small
> PMI (e.g. PMI1: 6.61651 PMI2: 150.434 PMI3: 150.434 NPR1: 0.0439828
> NPR2: 0.999998) but actually get PMI1: 0.061647 PMI2: 0.061652 PMI3:
> 25.3699 NPR1: 0.002430 NPR2: 0.002430.
> For disk-like (benzene) the result should be one large and two medium
> (e.g. PMI1: 89.1448 PMI2: 89.1495 PMI3: 178.294 NPR1: 0.499987 NPR2:
> 0.500013) but get PMI1: 2.37457e-10 PMI2: 11.0844 PMI3: 11.0851 NPR1:
> 2.14213e-11 NPR2: 0.999933.
> Finally for a roughly spherical molecule (neopentane) the NPR values look
> reasonable (no great surprise) but the absolute PMI values may be too
> small: old program - PMI1: 114.795 PMI2: 114.797 PMI3: 114.799
> NPR1: 0.999966 NPR2: 0.999988, new program - PMI1: 6.59466 PMI2:
> 6.59488 PMI3: 6.59531 NPR1: 0.999902 NPR2: 0.999935
>
>
> Your expectations are correct: the current RDKit implementation is wrong.
> The corresponding github entry is here:
> https://github.com/rdkit/rdkit/issues/1262
> This is due to a mistake in the way the principal moments are calculated
> (which is due to the fact that I don't spend a lot of time working
> with/thinking about 3D descriptors). Instead of using the
> eigenvectors/eigenvalues of the inertia matrix (the tensor of inertia) the
> RDKit is currently using the covariance matrix. There's some more on the
> relationship between these two here:
> http://number-none.com/blow/inertia/deriving_i.html
>
> The problem is easy to fix (and I have something working here:
> https://github.com/greglandrum/rdkit/tree/fix/github1262), but it screws
> up the values of the descriptors that are derived from here:
> Todeschini and Consoni "Descriptors from Molecular Geometry" Handbook of
> Chemoinformaticshttp://dx.doi.org/10.1002/9783527618279.ch37
> These include the radius of gyration, inertial shape factor, etc.
> Within that article they state that Ic = 0 for planar molecules. Ignoring
> the inequality on page 1010, which says that Ic is the largest moment and
> is contradicted by the rest of the text (particularly the inequalities on
> page 1011), Ic corresponds to the smallest principal moment : PMI1.
>
> So now I'm confused, but I'm hoping this is obvious to someone versed in
> the field: I'd like to reproduce the descriptors described in the
> Todeschini article, but I clearly can't do that using the actual moments of
> inertia. I could keep using the eigenvalues of the covariance matrix there,
> but that doesn't match what's described in the text.
>
> Two things that would be extremely helpful:
> 1) an explanation of the disconnect here from someone who knows this
> stuff, I would guess that it's pretty simple
> 2) The results of running the files github1262_1.mol, github1262_2.mol,
> and github1262_3.mol from here:
> https://github.com/greglandrum/rdkit/tree/fix/github1262/Code/GraphMol/MolTransforms/test_data
> through Dragon and calculating the radius of gyration, inertial shape
> factor, eccentricity, molecular asphericity, and spherocity index.
>
> Best,
> -greg
>
>
>
>
>
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