

Hi
The way this was done in MacroModel was to identify equilavent atoms and then
check for identical conformers by doing rms superimposition with the
equilivalent atoms. For example in your n-butane case (C1-C2-C3-C4), if you
made atom one equivalent to atom four, and atom two equivalent to atom three
and then do the rms superpositions, you would find the redundant conformers.
Tom Hendrickson  

__________________________________________________________________________
From: [email-masked] (Leif Norskov)

  > Is there a simple way of testing if two given conformational isomers
  > are equivalent?
  > E.g., how can you know the gauche (+) conformer of n-butane is
  > equivalent to the gauche (-) conformer?
  > My idea is [ to superimpose the conformers ]...

If speed is a problem (and it could well be - consider for example
the matching of the protons in butane) then it might be advantageous
to first compare the moments of inertia, which of course are invariant
to atom labelling and rotation/translation, before proceeding
with superpositioning.

__________________________________________________________________________
From: "E. Lewars" <[email-masked]>

Dongchul Lim asked how one can tell if two conformers are the same.  This is
a special case of how to tell if two isomers are really the same species.
It seems to me a simple approach is (after looking to see that they are
not obviously different) to have your program (MOPAC, GAUSSIAN etc) 
calculate the total internuclear repulsions.  Two species that look the same
and have the same internuclear repulsions (to 6 or more decimals--Hartrees)
are, I would think, extremely unlikely not to be the same.  Many comp.
chem programs calculate internucl. repulsions; if a check job wn't give
that number, then ask for a single-point calc. using a fast method like 
a semiempirical routine.  The actual internuclear repulsin calc. is 
trivial.
Errol Lewars

__________________________________________________________________________
From: [email-masked] (Per-Ola Norrby)

        Your proposal is of course the only final test, but there are some
ways to do a quick screening to avoid having to test a lot of conformations
by superimposition.  If your structures are output from some calculation,
several commonly calculated criteria have to be equal for the two
conformers.  Two simple ones are calculated energy (only if you have fair
convergence) and moment of inertia (very sensitive to conformational
changes).  You only need to superimpose structures that differ "very
little" in these two test.

__________________________________________________________________________
From: <[email-masked]> (sandeep kumar)
           I think one way to test the conformational equivalence esp.
for small structures like n-butane is to calculate or measure the energies
of the two isomers.  For example, in case of n-butane both g+ and g- have
almost equal energies i.e. both of them are almost equally stable while
trans isomer has lower energy than any of the two and is much more stable
than any of the two.
                  I restrict myself to recomend its usage with small organic
molecules with simple geometries only.
  for further disscussion on the matter please refer to organic chemistry
text book by Morrison and Boyd.
                         yours' cordially
                          sandeep kumar
                       [email-masked]

   P.S. I shall be grateful to you if you summarize what you find.

__________________________________________________________________________
From: Garcia Edgardo <[email-masked]>

About the conf. isomers question of Dongchul Lim, my opinion
is that first we should ask if we want to compare IDENTICAL or
EQUIVALENT isomers (concerning energy for example).
In the first case a simple superpossition will probably work.
In the second we can make a non-bonding energy calculation
and compare the energies or compare the distance matrix of the structures
(or some kind of invariant of them) within some allowed range of values.

__________________________________________________________________________
From: [email-masked] (Joel Polowin)
> From: "E. Lewars" <[email-masked]>
> Subject: CCL:TELLING IF TWO CONFORMERS ARE IDENTICAL
> 
> Dongchul Lim asked how one can tell if two conformers are the same.  This is
> a special case of how to tell if two isomers are really the same species.
> It seems to me a simple approach is (after looking to see that they are
> not obviously different) to have your program (MOPAC, GAUSSIAN etc) 
> calculate the total internuclear repulsions.  Two species that look the same
> and have the same internuclear repulsions (to 6 or more decimals--Hartrees)
> are, I would think, extremely unlikely not to be the same.  Many comp.
> chem programs calculate internucl. repulsions; if a check job wn't give
> that number, then ask for a single-point calc. using a fast method like 
> a semiempirical routine.  The actual internuclear repulsin calc. is 
> trivial.

I don't think the situation is quite so simple -- possibly depending on
what is meant by conformers being "the same".  If I have a large structure
and alter a torsional angle in the middle by a fraction of a degree, it's
probably still "the same structure".  If the structure was energy-
optimized before, it's very likely that trying to optimize it again
won't do much to change it back unless there are other steric effects.
But the atoms at the ends of this large structure will probably move a
*lot* as the result of that tiny bend in the middle, and the internuclear
repulsions are likely to change significantly too.  Maybe only a little,
or maybe some other local minimum would be found, but I don't think the
internuclear repulsions would likely be the same to 6 or more decimals.

I think that the matter depends critically on: What sort of structures
are you trying to compare, and what do you mean by "the same"?

Regards,
Joel
 
__________________________________________________________________________
From: [email-masked] (Dr. Golender Valery)

Dear Lim,
You asked on CCL how one can tell if two conformers are 
the same. I already saw some responses on the net advising to 
solve the problem from the molecular modeling point of view. 
In fact,  there exist a strict mathematical formulation of this 
problem called isomorphism of 3D objects. It is a common 
problem arising in a number of applications including 3D 
database search, ligand design, spanning of conformational 
space and etc. A number of different algorithms and programs 
were proposed to solve this problem. Simple superposition 
suggested in the original posting is not working because of 
molecular symmetry. We recently developed an efficient 
algorithm incorporated into the conformer clustering utility of 
Apex-3D activity prediction system marketed by Biosym. I can 
provide more detailed information if you are interested in 
this functionality.

__________________________________________________________________________
From: [email-masked]

Sounds about right to me, but, if your program doesn't do so already, you 
should first provide a "standard" orientation such as placing the origin at 
the center of mass and orienting the molecule along the principal moment axes 
or dipoles, if you include charges.  But, depending on your code, you may 
still have to consider reversed orientation, i.e., check if x1(a) = x1(b) or 
x1(a) = -x1(b), if the latter, reverse the orientation, ditto for y and z.

Besides exact superposition, quick screens are the total energy, dipole (if 
you include charges), and moments.  For larger molecules, end-to-end or 
selected interatomic distances afford quick checks.  And, if you're checking a 
series of molecules, molecular weight or elemental composition are effective 
screens.

It's suprising that some/many molecular mechanics packages do not 
support/generate "standard" orientations since it would be helpful not only 
for your problem but also as a start for CoMFA alignments.  However, you could 
easily write your own starting from MOPAC or GAMESS subroutines, if you have 
them.  There may also be a program/subroutine available from QCPE which you 
could modify.  A few years ago I had modified the GAMESS subroutine for 
determining the principal moments to generate standard orienetations for 
Tripos "*.mol" files. It was very fast, requiring only a several seconds to 
reorient lysozyme on an SGI 4D/35.  Unfortunately I no longer have the code 
and would be prohibited from redistributing it even if I did.  My original 
interest was to subsequently compute the 3 principal cross-sectional areas, 
and/or solvent cross-sectioanl areas, to try to relate them to diffusivities 
but I didn't get that far.

Good luck!

__________________________________________________________________________
From: Mick Kappler <[email-masked]>

> Is there a simple way of testing if two given conformational isomers
> are equivalent?

Yes. The Stereochemical Extended Morgan Algorithm (SEMA) developed by Wipke
and Dyott provides a stereochemical canonical name.  Comparison of the
structure SEMA names is straight forward.

__________________________________________________________________________
From: [email-masked] (Marvin Waldman)
> Is there a simple way of testing if two given conformational isomers
> are equivalent?

This is, in fact, quite a difficult and subtle question.  The SEMA
algorithm which Mick Sappler proposed can be used to detect if
two CONFIGURATIONAL isomers are equivalent (ie. they have the
same or different stereochemistry).  However, it will not detect
if the same configurational isomers are equivalent or not in
a CONFORMATIONAL sense.  SEMA cannot detect the difference between
the gauche and trans forms of n-butane.  These are CONFORMATIONAL
isomers.

The issue of the equivalence of two conformations is further complicated
by the problem of topological symmetry.  This makes an RMS comparison
of atoms problematic for detecting equivalent conformations.  For
example, if I do an RMS comparison of corresponding atoms between
two conformers in which the hydrogens of a methyl group are rotated
by 120 degrees, I will detect an RMS difference because I am now
comparing the wrong set of atoms.  One needs to compare all combinations
of topologically equivalent atoms in the molecule to see if they
have a (virtually) zero RMS.  If one proposes to do an RMS comparison
of heavy atoms only, then you only need to replace the methyl group
with a t-butyl group, and the problem remains.  If one proposes to
compare only energies (and not RMS), then, of course, the symmetry
will be correctly handled for the energy, and you only need to
worry about the somewhat unlikely case of two different conformers
having (almost?) the same energy.  Since these conformers are likely
to come from some energy optimization procedure, roundoff error
and tolerances used for the minimization implies that one needs to
use some kind of tolerance in comparing energies, which always leads
to the (remote?) possibility that nearly equal energies may not
correspond to the same conformer.  The larger the molecule and the
more conformational flexibility (and therefore conformers) it has,
the more likely that this somewhat theoretical problem may manifest
itself in a real example.  The ideal/correct solution would be to
compare both the energy as well as all combinations of RMS comparisons
of topologically equivalent atoms until the RMS difference found
for a given comparison pair fell below some threshold.  I am not
aware of a software package that has actually implemented such
an algorithm, and would be very interested to hear about one that
does.

So, the bottom line answer to the question, is: No, I don't think
there is a SIMPLE way to do this.

__________________________________________________________________________
From: "E. Lewars" <[email-masked]>

When I suggested using the internuclear repulsion E to check if two isomers
are identical, I should have pointed out that enantiomers have precisely
the same energies--internuclear, electronic, etc (in the absence of a 
chiral perturbation; physicists may quibbl, too, that the negation of
parity by the weak nuclear force causes a miniscule difference in enantiomer
E's).  
Joel Polowin of HyperChem pointed out that as a practical matter identity
isn't an all-or-nothing phenomenon: how similar do two species have to be 
for a chemist to call them the same thing?  As several people said, there
are sophisticated algorithms for matching up two molecules and looking
at, e.g., RMS differences in geometric parameters.  I think the widely-
used MM program PCModel can do something like this; one or two other
programs were mentioned.  Joel's idea about a small tweak in one part
of a molecule causing a ratcheting effect that's amplified elsewhere
(cf. allosteric effects in enzymes?) is interesting.
Errol Lewars
===============================
Regarding  internucl rep.--one could calc it for some test cases, alter
these geometries slightly, and see if it might be useful for the problem
at hand.
===============

__________________________________________________________________________
From: "CBAS25 ::P_BLADON ::CBAS25" <[email-masked]>

Dear Dongchul Lim,

With regard to the conparisons of conformers.

There are several points to consider.

(1) If the problem involves small molecules like butane where the number 
of stable conformers is known, then simply superimposing the "unknown" 
structure on each of the "known" conformers in turn will give an answer.
The rms deviation of atom positions or some other figure of merit will afford
an answer even when an exact match is not achieved.

(2) If the structures are more complex, perhaps involving large membered rings,
then the number of conformers could be large.  But suppose that you have a set
of such structures, and wish to test which of them your "unknown" most 
resembles. You would still get an answer. 
If the "unknown" were a crystal structure and the "knowns" derived 
from a conformer generating program, you would not expect a good match 
necessarily.  What you could do then is to take the pair of best matched 
structures and refine them with your favourite MM or MO package, and see if 
they both decend into the same energy well.  

(3) To do the matching you could use atom to atom matching, or alternatively
use the icosahedral matching algorithm in programs like COMPARISONS or
CORRELATE.  The first of these programs will match an "unknown" against a
series of "unknowns", while the second would allow the correlation of a whole 
series of conformers. The matching of mirror-image forms is taken care of.   
Both programs are available from QCPE as part of the INTERCHEM package.  

__________________________________________________________________________
From: "Victor M. Rosas Garcia" <[email-masked]>

Some people have mentioned algorithms for comparison of conformers and evidently
the solution to this problem is far from simple.  The best implementation I
have seen to solve this problem is in the program GMMX, a global minimum search
utility by Serena Software.  As I understand it, the program calculates the RMS
of the conformers by using identical numbering in the atoms of both conformers
and, if necessary, checks for planes of symmetry and for the so-called
numerical isomers.  The idea is that making the atoms distinguishable by
numbering them will introduce artificial conformers that differ only in the
numbering but that are really "the same" conformer e.g. a product of a rotation
or reflection or some other symmetry operation.

__________________________________________________________________________
From: [email-masked] (Graham Hurst)
>> Is there a simple way of testing if two given conformational isomers
>> are equivalent?

[good stuff deleted]

>The ideal/correct solution would be to
>compare both the energy as well as all combinations of RMS comparisons
>of topologically equivalent atoms until the RMS difference found
>for a given comparison pair fell below some threshold.  I am not
>aware of a software package that has actually implemented such
>an algorithm, and would be very interested to hear about one that
>does.

The Conformational Search module of the ChemPlus set of extensions
for HyperChem uses energy and RMS compairisons of topologically
equivalent atom pairings.

I've been following this discussion with some interest.  When I
wrote the Conformational Search module of ChemPlus, I implemented
the following tests to compare for equivalent conformations that
might result from the search.  The comparisons available are (in
the order that the program can optionally execute them) are:

1. Changed chirality (R or S) of chiral centers with 4 bonded
   neighbours. (Chiral centers are determined by HyperChem.)

2. Energy (from HyperChem) within a user adjustable range.

3. Varied torsions within a user adjustable range.  This test is
   turned off by default, since it doesn't handle topologically
   equivalent dihedral angles.

4. R.M.S. deviation for a least-squares overlay of atoms.  As Marvin
   Waldman pointed out, one needs to compare with all topologically
   equivalent permutations of atom order and this option (discussed
   further below) is available in ChemPlus.  A subset of atoms can
   also be specified for the comparision.

I initially included an option for comparison of inertial moments
(suggested earlier by Leif Norskov <[email-masked]>) but I abandoned it
because it seemed too sensitive a measure, with suitable tolerances
varying widely with the number of atoms.

If the option to use equivalent atoms in the RMS comparison is
turned on, the program generates all equivalent atom order
permutations.  The algorithm I used for this is basically brute
force, O(N!) at worst, but being able to compare element type
and number of bonds for each topological "node" allows considerable
trimming of the paths.  Further trimming results from only considering
a subset of atoms (eg. no hydrogens or only backbone atoms) so
that permutations of ignored atoms are unnecessary (assuming
equivalent sets are either all included or all excluded).

>So, the bottom line answer to the question, is: No, I don't think
>there is a SIMPLE way to do this.

I agree!  It took me about a month to puzzle out and implement an
algorithm for generating equivalent atom orders!  As Valery
Golender <[email-masked]> pointed out, the conformational
isomer problem is a specific instance of isomorphism of 3D objects.

Cheers,

Graham

P.S. If you want more ChemPlus or HyperChem product info, please
send email to [email-masked], not to me because I don't work
there anymore.

__________________________________________________________________________
From: Matt Stahl <[email-masked]>
Greetings,
	The problem of duplicate conformer removal certainly is 
challenging, especially to anyone doing extensive conformational 
searches.  The "easy" method of detection is to compare a unique 
identifier based on atomic coordinates.  Shape descriptors such as the 
sum of interatomic distances, or the sum of all triangles in a molecule 
provide a single number to identify a conformation.  In this sense, 
energy is also a "shape descriptor" because it is simply a function 
operated on a set of coordinates.  As pointed out by Dr. Waldman, there 
is always the possibility of ambiguity when using this kind of 
descriptor.  I have seen cases in larger bicyclo alkanes where very 
different conformations had the same mechanics energy to the 5th or 
6th decimal place!
	There are several matters that must be addressed with regard to 
comparing conformations.  Rms fitting may not be the best measure of 
similarity when comparing long acyclic chains because of the 'torque' 
effect.  Torsional comparisons certainly have valid applications.  In 
general, rms fits work well with the exception of the problems of 
automorphism and enantiomeric coordinates.  Generating enantiomers is 
trivial.  Simply multiply all of the x, y, or z coordinates by -1 to 
generate the mirror image.  Automorphisms can be more of a problem.  They 
can be discovered by connectivity matrix manipulations (see 
balasubramanian in j. chem. inf. comp. sci. may/june 1994).  A much 
quicker approach is to effectively do an atom-by-atom max common 
substructure search using comparisons of atom types.  Once the 
automorphisms are discovered they can be used in both torsional and rms 
comparisons.
	Pat Walters and i have written a program called Padre (Population
Analysis and Duplicate REmoval) that will read multi-structure files,
automatically generate the automorphisms (and enantiomers if desired), and
do rms or torsional comparisons and identify duplicate conformers.  It
will also map rings onto each other and compare all possible overlays.  
Padre is FAR from completion, but the features currently implemented are 
solid.  Please contact me directly if you are interested in this software.

__________________________________________________________________________
From: Mick Kappler <[email-masked]>
> Is there a simple way of testing if two given conformational isomers
> are equiva
lent?

This question can be interpreted in two ways, as Joel Polowin indicated.

On Wed, 22 Feb 95 10:29:54 -0500, Joel Polowin wrote:

> I don't think the situation is quite so simple -- possibly depending on
> what is meant by conformers being "the same".

If one is interested in structural equivalency independent of conformation,
the SEMA algorithm (JACS, 96, 4834, 1974) is a solution.  If one is interested
in structural equivalency dependent of conformation, the solution is more
complex, as Marvin Waldman pointed out.

On Wed, 22 Feb 1995 14:47:42 -0800, Marvin Waldman wrote:

> This is, in fact, quite a difficult and subtle question.  The SEMA
> algorithm which Mick Sappler proposed can be used to detect if
> two CONFIGURATIONAL isomers are equivalent (ie. they have the
> same or different stereochemistry).  However, it will not detect
> if the same configurational isomers are equivalent or not in
> a CONFORMATIONAL sense.  SEMA cannot detect the difference between
> the gauche and trans forms of n-butane.  These are CONFORMATIONAL
> isomers.

This is correct.  The ultimate solution to the structural equivalency dependent
of conformation problem will depend on analytical features of the two
structures only.

On Thu, 23 Feb 1995 01:47:29 EST, CBAS25 ::P_BLADON ::CBAS25 wrote:

> There are several points to consider.
>
> (1) If the problem involves small molecules like butane where the number
> of stable conformers is known...

We can not assume we have anything but the two conformations that we wish to
compare.  Given a hypothetical structure, who knows the set of stable
conformers?

> (2) If the structures are more complex... then the number of conformers
> could be large.  But suppose that you have a set of such structures...

Again, let's not assume we know.

> (3) To do the matching you could use atom to atom matching...

This could take a long time, considering the size of the set of structures to
compare.  Is time an issue?  I imagine it is if you have a large set of
structures to compare.

On Wed, 22 Feb 1995 23:36:21 -0800, Victor M. Rosas Garcia wrote:

> ...The best implementation I have seen to solve this problem is in the
> program GMMX, a global minimum search utility by Serena Software.

If this works for you, this is great.  Unfortunately, this technique is only
as good as the software and comparison of conformation A by software X to
conformation B by software Y is impossible.  Hence, comparisons between
research groups may be a problem.  This is not to mention the multiple minima
problem, as E. Lewars pointed out.

On Wed, 22 Feb 1995 17:10:28 -0500, E. Lewars wrote:

> ...enantiomers have precisely the same energies...

On Wed, 22 Feb 1995 23:32:59 -0500, Graham Hurst wrote:

> The Conformational Search module of the ChemPlus set of extensions
> for HyperChem uses energy and RMS compairisons of topologically
> equivalent atom pairings.

RMS comparisons look promising at first.  Unfortunately, before the comparison
can be made, the conformations need to be superimposed, which is independent of
the conformation itself.  Although the superimposition can be solved
analytically, it is sometimes solved iteratively, and can be a source of
contention.  Can we solve this problem indepedent of transformation?

I would love to hear more from experts in this field.  This is an interesting
problem and this discussion has increased our interest in publishing our latest
work relating to conformational comparisons.

__________________________________________________________________________
From: Ramesh Gopalaswamy <[email-masked]>

I have been working with steroid conformational analysis in connection
with receptor modeling. I have generated several (typically 100) structures
(conformers) for each steroid using DGEOM program. Now I need to pick out
those conformers that are unique. (DGEOM generated structures might converge
to same minimum upon minimization). Any ideas on how to do that using
commercial modeling software or other shareware programs?
   Also, how to run minimizations (for 100 or so structures) as a background
job, instead of having to read in each structure on to the graphics 
interface? I have access to Quanta, Cerius2 and Sybyl. Thanks a lot.
Ramesh ([email-masked])

__________________________________________________________________________
From: Harold Helson <[email-masked]>

Hi DC, I hope you are well!
If I remember Wipke & Dyott's paper on SEMA ("Stereochemically extended Morgan 
algorithm") correctly, they propose some modifications to treat conformers.

Here is an idea that's not too carefully thought out, and would take more time

than you probably want to invest, but -- hell, it's an interesting problem.

    Canonicalization algorithms, which deliver a unique description of a
     molecule, incorporate some representation of a given bond's environment.

     In topological algorithms, this may merely be the bond order.  In con-
     figurational algorithms, it is more complex, also including cis/trans
     and chiral parity information.  What you would do is append additional
     configurational information, such as dihedral relationships along the
     path being grown.  This might be all there is to this problem.

     So you would perform conventional canonicalization, using the more
     detailed bonding representation.  You end up with one or more paths
      of equal priority, the presence of more than one reflecting automor-
      phisms (symmetry).  The power in SEMA is that it
      is a trivial operation to enumerate all the enantiomers and geometric
       isomers.  I expect that you would similarly be able to trivially enu-
       merate all the conformations, provided (and it's a big proviso) that
       you limited the dihedral angles to, say, multiples of thirty degrees,
        or whatever number is small enough to be a good approximation,
        but large enough so that the number of possible conformations does
        not go rapidly to infinity.  This is certainly a valid approximation
        in the gauche butane example you cite.

        You would be able to tell a mirror image because its stereochemical
         parity table (see Wipke & Dyott) would contain an inversion, but the

         extra, appended conformational table would be the same for both
         structures.  You could tell configurational isomers because their
         stereochemical tables would be identical, but their conformational
         tables would differ.
__________________________________________________________________________