From shubin@email.unc.edu Mon Apr 10 12:28:39 1995 Received: from email.unc.edu for shubin@email.unc.edu by www.ccl.net (8.6.10/930601.1506) id MAA25585; Mon, 10 Apr 1995 12:17:57 -0400 Received: by email.unc.edu (AIX 3.2/UCB 5.64/4.03) id AA54129; Mon, 10 Apr 1995 12:17:50 -0400 Date: Mon, 10 Apr 1995 12:17:49 -0400 (EDT) From: Shubin Liu X-Sender: shubin@isisa.oit.unc.edu To: chemistry@ccl.net Cc: chemistry@ccl.net Subject: CCL:Summary of the question: Does optimized structure depend on the input? In-Reply-To: <9504101118.AA05409@tci002.uibk.ac.at> Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Dear all CCLers: Last Friday, I posted the question of whether the optimized structure depends on the input. I recieved a number of reponses from you guys. Thanks are due to all of you who promptly responsed my qusetion. Following are the answers: ------------------------------------------------------------------------- From TANG@kitten.chem.uh.eduMon Apr 10 09:51:49 1995 There is no optimization method to my knowledge that can GUARRANTEE to reach a global minimum. Searching a global minimum becomes more difficult with increase of the number of variables. For small molecules, chemical (or any) intuition is at times the only guide for searching what is desired. For instance, when dealing with TiCl_6 complex, it's good to try Oh symmetric geometry first. The "best" way other than the Good luck. -------------------------------------------------------------------------- From: David Close Part of what you say is true. But part of the answer depends on the types of problems your are dealing with. A good example of a local minimum would be trying to do a calculation on an isolated molecule. As torsion angles vary there are going to be geometries encountered where strong intra-molecular hydrogen bonds form. Often times the calculation stops at this local minima. However in a more realistic situation, the atoms forming the intra-molecular bond are most likely tied up with H-bonds to neighboring molecules. But few of us can afford the computer time to add very many neighboring molecules. One trick here is to use small neighboring molecules like waters of hydra- tion. But there are many other things that one can do. First of all, what systems are you studying, and what are you trying to learn? --------------------------------------------------------------------------- From lim@rani.chem.yale.eduMon Apr 10 09:52:30 1995 Most geometry optimization algorithms find a nearby local minimum, as opposed to a global minimum. In general, it is not an easy task to find out the global minimum of a molecule, especially when the molecule becomes larger. But there are mothods for locating global minima. The simulated annealing method is one example. However, in general, we don't know how many conformers there will be in a given molecule. So we try to find out as many (low-energy) conformers as possible in a conformational space. This is called 'conformational searching'. There are two major categories in the conformational searching: 1) deterministic method 2) stochastic method Method 1) is used in small to medium systems and method 2) in medium to large systems. You can get more information from A. R. Leach "A Survey of Methods for Searching the Conformational Space of Small and Medium-Sized Molecules" in Reviews in Computational Chemistry, Ed. K. B. Lipkowitz and D. B. Boyd, Vol. 2, VCH, 1991. -Dongchul Lim -------------------------------------------------------------------------- From sbl@linus.herl.epa.govMon Apr 10 09:52:42 1995 To the best of my knowledge there is no direct way to find a global minima apart from a reasonably exhaustive search for all degrees of freedom. The approaches may include systematic conformational searches ro random sampling of conformational space using a molecular mechanics force field level of theory followed by a more focused search using semi-empirical methods (for poorly parameterized chemical species) and ab initio calculations at selected local minima to verify the global minima at a given level of theory. You should talk with Alex Tropsha with the Pharmacy School Modelling Laboratory, tropsha@gibbs.oit.unc.edu. -------------------------------------------------------------------------- From ccl@cric.chemres.huMon Apr 10 09:52:54 1995 As far as I know, there are numerous tricks, methods and practical recipes, but neither has strict guaranties that you will find the global minimum and not only a local one. --------------------------------------------------------------------------- From montero@coch01.chm.tu-dresden.deMon Apr 10 09:53:27 1995 G92, as all other geometry optimizing theoretical procedures, looks for minimal energy in a function of the nuclear coordinates. This func- tion is the electronic hamiltonian of the molecule. If you start from a geometry very near or very far from the absolute minimum, the result could be a partial minimum. Gradients are calculated analiticaly, and very accurate input data can give a first gradient displacement going farther than the right amount. In such a case, a van der Waals minimum could be attained (in a predisociative state, for example) in place of the equilibrium geometry. A too distorted input can conduct to unpredicatable results. It is a matter of experience and doing it many times. If not, theore- tical chemistry research is meaningless, because programs and computers are doing all things. ---------------------------------------------------------------------------- From elewars@alchemy.chem.utoronto.caMon Apr 10 09:53:42 1995 Shubin Liu (shubin@email.unc.edu) asked how one can be sure he has found the global, rather than merely a local, minimum. I think there is no short answer to this question. If you are looking at something like water or methane, where everyone knows in a general way what the answer looks like, there is no ambiguity (what's the n-fold analog of an ambiguity?), and you might even dispense with the frequency job which is usually considered prudent to characterize a stationary state. But note that even very simple molecules can have PES's with >1 minimum. If you are working with proteins I suspect that at the current state of the art you may as well forget about nailing down the global minimum. Somewhere between water and a peptide you can worry about finding the global min. If, as is usually the case, the various possible minima you are concerned about arise from conformational possibilities, the systematic way to look for the global one is with a conformational search program as implemented in several commercial packages, e.g. Spartan. If you have no hangups about gambling, there is at least one stochastic search program, PCGlobal, from Serena Software, which randomly generates a slew of input structures, hopefully including some you may not have thought of. If your molecule is not too big you could do the job by hand, using input structures corresponding to all reasonable-looking possibilities for minima; your computational chemistry program should slide each one into the nearest minimum for the level you're using; if size doesn't make it impractical then do a freq job to see if the lowest-E stationary point is really a min. ------------------------------------------------------------------------------ From FOX@cmchem.chem.cmu.eduMon Apr 10 09:53:50 1995 There are a number of possibilities raised by your question about how the Gaussian input can give rise to a local minimum, 1) You could have symmetry constrained the input and the true minimum does not have the initial symmetry 2) You could have started near a local minimum and the global minimum is separated by a barrier. 3) You supplied a Z-matrix which does not span the full conformational space, either by restricting some internal coordinates, i.e. having too few coordinates, or by supplying a set with a redundancy so that it effectively has too few variables. Only the third would get close to being an input error. The first two qualify as constrained solutions and local solutions respectively. Check to see that your input spans the full conformational space with the keyword FOPT in place of OPT. It does not change the algorithm, simply adds a check that the coordinate supplied are linearly independent and sufficient in number to span the space. If you have symmetry constraing then the frequency result will guide you in reducing the symmetry and displacing toward the true minimum. If you simply have located a local minimum try SCAN'ing the surface, possibly with a lower cost method, to locate other potential minima. ---------------------------------------------------------------------------- From GOVENDEM@che.und.ac.zaMon Apr 10 09:54:01 1995 To obtain a global minimum, the entire PES has to be scanned, and not a region..this is however difficult in some cases where there is little experimental support. ---------------------------------------------------------------------------- From bouyer@ext.jussieu.frMon Apr 10 09:54:12 1995 About local and global minimum, there is a simple answer: we cannot be sure of the minimum is local or global. All optimizer converge to an local minimum. To be sure of a global one, try others geometries (a little distorted) and calculate the energy. Within gaussian, there is a keyword (I don't remember, perhaps SCAN, see the documentation) that scan the potential energy surface. So gaussian can do that for you. -------------------------------------------------------------------------- From noy@tci002.uibk.ac.atMon Apr 10 09:54:19 1995 Gaussian 92 will locate to the next (closet) minima using various methods, steepest descent, conjugated gradient and so on. Therefore, you are right that the optimized geometrical structure definitely depends on the initial input. To my limit knowledge, there is no ultimate method to locate the global minimum, especially when the potential hypersurface is rather complicated. The most promising method in the modern days is "simulated annealing" [1] with the help of statistical mechanics, molecular dynamics and Monte Carlo simulations to find the global minimum. The idea is to search all the energetically possible areas as much as possible by increasing temperature so that molecular complexe can wander over the energy barrier (Gaussian can't do that since it always goes downhill) and then gradually decrease the temperature to allow the molecular complex to relax to the lowest minimum. Statistical mechanics tools are used to search the possible potential hypersurface. Somebody believes that this is the ONLY gauranteed method to find the global minimum.[2,3] The method is applied in connection with DFT and HF theory for mimization of geometry and wave-function paremeters on the fly. This approach is so-called Car-Parinello molecular dynamics [4] (see review in [5]) which successfully works with solid-state but now extends to organic chemistry [6]. Reference ========= 1. S. Kirkpatrick, C. D. Gelatt Jr. and M. P. Vecchi, Science 220: 4598 (1983) 2. P. J. M. van Laarhoven and E. H. L. Aarts, Simulated Annealing: Theory and Applications (Reidel, Dordrecht, 1987). 3. B. Hartke and E. A. Carter, J. Chem. Phys. 97: 6569 (1992). 4. R. Car and M. Parinello, Phys. Rev. Letters 55: 2473 (1985). 5. D. K. Remler and P. A. Madden, Mol. Phys. 70: 921 (1990). 6. U. C. Singh and P. A. Kollman, J. Comput. Chem. 7: 718 (1986). ---------------------------------------------------------------------------- Best regards, Shubin ............................................................................. Shubin Liu Department of Chemistry Email: shubin@email.unc.edu University of North Carolina sliu@mulliken.chem.unc.edu Chapel Hill, NC 27599-3290 Tel : (919) 962-0150(O) USA (919) 914-6923(H) .............................................................................