From chemistry-request@ccl.net Mon Mar 2 16:58:36 1992 Date: Mon, 2 Mar 1992 14:45 CST From: Andy Holder Subject: Oh, boy, oh, boy! Real scientific controversy! To: CHEMISTRY@ccl.net Status: R I would like to take the opportunity to bore you yet again with one of my sermons. This diatribe is ostensibly in response to a request for comparing AM1 and PM3 charges. I'll come back to that via a roundabout route. It is quite long and involved, so want to save it and read it later. Let me once again precede this message with the information that I spent time with Michael Dewar at the U. of Texas as a post-doc., so my opinions are "tarnished" by that experience. As a person whose major research emphasis is development of semi- empirical parameters, I have had occasion to directly examine the MNDO, AM1, and PM3 parameters in close detail. I am also familiar with many of the principal people involved in the der- ivation of these methods. The basic contention, that I will hopefully support to some extent below, is that PM3 has left chemistry behind in a quest for improved results. At first, this statement may seem a bit strange, but stay with me. 1. The HF quantum mechanical method is based on a series of rel- atively crude approximations that fortuitously give results that are not too far off from experiment. If we operate on the assumption that the model has chemical validity (and we must to proceed further), it must be explainable in terms of chemical trends and phenomena. In the present case, this means that the parameter values themselves must be reasonable in the context of other elements: the parameters must exhibit PERIODICITY. It should be possible to derive a set of trial parameters given an understanding of the implementation of the scheme within the NDDO approximation and the values of nearby elements. This has indeed formed the basis of the Dewar approach to parameterization. For the great majority of cases, the parameters from Dewar and coworkers follow more or less periodic trends. The values are not exactly periodic, but vary due to the crudity of the model and the variety of chemistry described. (This variance is easy to rationalize if one realizes that, for example, the AM1 sulfur parameters must accomodate two valence states without the help of d orbitals for handling the hypervalent case.) 2. The quantum mechanical model for MNDO and AM1 (and PM3) is identical. The only differences in the methods are, that due to limtations in computer time, the lighter elements in MNDO had active two assumption: A. The Slater orbital exponent for s and p orbitals were close enough to be set equal (zetas and zetap). B. The beta values for s and p orbitals of the lighter elements are also set equal. These are used in a function that results in the resonance integral, and is hence responsible for bonding. (For a detailed discussion of the MNDO/PM3/AM1 parameterization model see: Dewar, M. J. S.; Thiel, W. J. Am. Chem. Soc. 1977, 99, 4907.) Both of these have been allowed to attain different values in AM1 and PM3. Additionally, AM1 and PM3 added gaussian functions to directly correct the core-core repulsion function. It must be emphaiszed that gaussians are a purely empirical correction, and are in programmer's terms, a PATCH. They hold no chemical significance in and of themselves. The Dewar group has traditionally used gaussians to correct for particular types of molecules or effects. These include particular bond energies (Al-Cl), hypervalency (P, S), minimal basis set, and/or the lack of d orbitals. Gaussians must be added very carefully, as they effect the energy in a direct manner and will "drag" the other parameters during procedure is best, followed by careful optimization. A stepwise examination of the results after each parameterization run. To summarize: Gaussians should not be part of the CHEMISTRY of the system, but should act to correct the parameters for the specific deficiencies mentioned above. 3. PM3 was parameterized using a vast amount of experimental data, and many elements were parameterized simulateneously. For the most part, AM1 and MNDO parameterization proceeded one element at a time using only a SUBSET of the BEST data for a parameterization basis. By carefully selecting the mole- cules used in the basis set, it is possible to reproduce the important and significant chemistry of an element. By using ALL experimental data of any quality, the parameterization becomes a prisoner to more easily obtained experimental data. This is most evident in the plethora of data available for halogenated molecules and the relative paucity of results for organometallic compounds. Chemical judgement must be used to balance the molecular basis against this type in influence. When I joined the Dewar group in 1987, I moved into an office with a sign that said "Human Factors" on the door. It took me some time to realize that this was not a computer nerd joke, but a philosophical statement. The above points are both philosophical and practical. Given the manner in which PM3 was parameterized and the results of the par- ameterization, I am doubtful of its utility as a quantum chemical model for general application. As an example of what can happen, The parameters for aluminum are compared across the three methods. I am using aluminum, because I developed the AM1 parameters for this element and I am most familiar with it. Similar trends can be found in many of the other PM3 elements. Parameter AM1 MNDO PM3 Units ----------------------------------------------------- Uss -24.353585 -23.807097 -24.845404 eV Upp -18.363645 -17.519878 -22.264159 eV zetas 1.516593 1.702885 au } 1.444161 zetap 1.306347 1.073269 au betas -3.866822 -0.594301 eV } -2.670284 betap -2.317146 -0.956550 eV alpha 1.976586 1.868834 1.521073 1/A Gaussians: Intensity #1 0.090000 - -0.473090 eV Width #1 12.392443 - 1.915825 A^2 Position #1 2.050394 - 1.451728 A Intensity #2 - - -0.154051 eV Width #2 - - 6.005086 A^2 Position - - 2.51997 A The point on the potential surface located by PM3 is significantly different than that located by AM1. This is immediately apparent from the large discrepancy between the Upp values. These are the important one-electron energy values and they have strong influence on the parameter hypersurface. Also, the difference between Uss and Upp for both MNDO and AM1 is about 6 eV (roughly the same value as for all elements on this period according to AM1/MNDO). This has been reduced to 2.5 eV in PM3. The realdifficulty, however, is in the beta values. These parameters are the two-center/one-electron resonance terms and are responsible for bonding interactions between atoms. The PM3 values are almost zero, resulting in the conclusion that there is very little bonding between atoms of aluminum! (Note that the AM1 values for betas and betap spread out around the single MNDO value for beta. This suggests that the MNDO values were reasonable and AM1 simply adds greater flexibility.) PM3 regains the bonding interactions lost due to the low beta values with two strongly attractive Gaussians spanning the bonding region. One result of such difficulties as discussed above is poor quantum mechanical descriptions of molecules. A prime example is formamide. The PM3 parameters were developed with an eye toward reproducing -NO2 compounds, a somewhat severe test of such a min- imal basis set approach. Focusing on these types of compounds has caused the parameters to perform somewhat oddly. Below is a table listing the charge on atoms in formamide as predicted by PM3 and AM1. For purposes of comparison, also listed are charges from a Mulliken analysis at the HF/6-31G* level and NBO charges at the same level. I have chosen to present this data because it such a finely tuned barometer of chemical significance. The fact of the matter is that there is no real way to experimentally determine charge routinely, so this should conform to your chemical intuition more than anything else. Method C O N H H(N) ---------------------------------------------- AM1 0.26 -0.37 -0.45 0.12 0.22 PM3 0.21 -0.37 -0.03 0.08 0.05 Mullik. 0.67 -0.70 -0.93 0.12 0.41 NBO 0.51 -0.55 -0.88 0.14 0.39 Note that AM1 is in general qualitative agreement with the NBO (probably the most reliable in this set). The PM3 charge on nitrogen is simply beyond any chemical reason. The carbon and oxygen parameters appear to offer a good model. Examination of the PM3 nitrogen parameters indicates several conceptual problems, such as p orbitals that are more contracted than s orbitals and very strong gaussians spanning the bonding range. The overall heat of formation results for N are better in PM3 than in AM1, but the cost appears to be loss of an accurate chemical description of the electronic structure. Thus, the essence of the difference between the two philosophies can be directly stated: the theoretical basis for the method is either accepted or denied. Significant approximations are made to gain the speed advantage that semiempirical methods enjoy over their ab initio quantum mechanical brethren. But both the ab initio and semiempirical models are finally, in the end based on the Hartree-Fock set of ideas. These ideas possess theoretical rigor as regards solution of the Schrdinger Equation. If one simply views the semiempirical parameters as adjustables within a curve-fit scheme rather than as components of a theoretical model, little faith resides in the meaning of their final values. Simply put, the method of parameterization described above and used so successfully with AM1 and MNDO expresses confidence in the theory. With a firmer footing in chemical reality, AM1 parameters are more likely to yield useful results for situations not specifically included in the parameter- ization. End of Sermon. One of my colleagues that read this called it "preachy". I hope that it didn't come over too much that way. Dr. James J.P. Stewart of course has arguments to counter these and I hope that many of you are aware of them. Every- one has an opinion and this is mine. I hope that the above discourse is taken in the spirit of scientific disagreement as it is intended. Andy Holder =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= DR. ANDREW HOLDER Assistant Professor of Computational/Organic Chemistry Department of Chemistry || BITNET Addr: AHOLDER@UMKCVAX1 University of Missouri - Kansas City || Internet Addr: aholder@vax1.umkc.edu Spencer Chemistry, Room 502 || Phone Number: (816) 235-2293 Kansas City, Missouri 64110 || FAX Number: (816) 235-1717 =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=