From jkl@ccl.net Fri Mar 15 15:25:51 1991 Date: Fri, 15 Mar 91 15:10:10 EST From: jkl@ccl.net Subject: More bugs in basis set intro To: chemistry@ccl.net Status: R Mike Zerner (zerner@qtp.ufl.edu Thu Mar 7 19:06:08 1991) found more bad stuff in my basis set intro. I am really glad that the person of his experience took the time to read it and write the comments to correct me. Here are his comments and my "answers": Jan Labanowski jkl@ccl.net -------------------------------------------------------------------------- MZ> One of the reasons that core orbitals make their appearance in valence MZ> and other higher energy orbitals is due to the fact that all mo's must be MZ> orthogonal. If one examines these coefficients they are very much like MZ> those you would get from simple Schmidt orthogonalisation to the lower MZ> lying core orbitals. JL> Hi Mike, JL> JL> I aggree with you that some of my statements in the "Basis Sets Trilogy" JL> are at least misleading, if not plain wrong. Only after I heard people's JL> comments I realised that what I wanted to say and what I actually said are JL> two different things. Of course, there are two major reasons for this: JL> 1) I am truly ignorant is many of these issues, 2) I wanted to be brief, JL> JL> My statement that core orbitals are present in HOMO. JL> What I wanted to imply was: if the basis functions were "true" atomic JL> orbitals (i.e. all atomic orbitals on a given center were orthogonal to JL> each other and overlap between "core" orbitals on different centers was JL> negligible) we would not have large participation of core orbitals in HOMO. JL> But it seems that I am totally wrong on this. Please help me,since I simply JL> do not know. Of course, I probably should go and retake a course "Quantum JL> Chemistry for Psychologists 100" but I do not have time. This perception JL> comes from my early years when they showed me this diagram for homonuclear JL> molecule. If what I said above is not true than these molecular JL> orbital diagrams are totally misleading and should be abolished. JL> I would really appreciate your comment on this. ---------------------------------------------------------------------------- MZ> I don't understand the discusion above the 66-31 basis set for Si Table. MZ> If a primitive occurs contracted in a 3 combo , say, x+y+z, and appears MZ> by itself, say z, why is this linearly dependent? I.e think of three MZ> dimensional space. DId I read this wrong? JL> Linear independence. Yes, I did say something else than I wanted to say. JL> Basis functions: JL> phi_1 = a_1*g_1 + a_2*g_2 + a_3*g_3 (set I) JL> phi_2 = g_3 JL> are not linearly dependent. JL> What I wanted to say is that basis functions JL> phi_1' = a_1'*g_1 + a_2'*g_2 (set II) JL> phi_2 = g_3 JL> would yield the basis set of exactly the same quality with the following JL> relationship between coefficients in resulting molecular orbitals: JL> JL> ... c_1*phi_1 + c_2*phi_2 ... (set I) JL> and JL> ... c_1*phi_1' + (c_1*a_3 + c_2)*g_3 (Set II) JL> JL> However, since set with "doubled" g_3 (set I) whould take more time at JL> integral calculation stage (assuming no support for general JL> contractions), it would be wasteful not to use basis set II. ---------------------------------------------------------------------------- MZ> under 66-31G means that there is :" should this not be S(6/6/3/1) rather MZ> than S(6/6/3/2) ? JL> 66-31G -> is s(6/6/3/1) and not s(6/6/3/2) and it is a typo (another one). ---------------------------------------------------------------------------- MS> The difference between the 2p function on Li, and the 3d on S, is that the MS> former is needed for hybridization, and ignoring it ignores all of first MS> year chemistry! (The first solid state calculations on Li and alkali MS> halides were done by physists, and of course, did not contain the 2p!). MS> The 3d function on sulfur is usually polarization, but even this is MS> somewhat controversial. JL> p's for Li and d's for S. What I wanted to say is, that designating JL> a function as "polarization" or "basic" should not be based on how JL> obvious or not obvious it is. I would welcome some more precise criterion, JL> since "accuracy of the results" and "correctness of physical picture" is JL> very subjective (depends on the investigator) and depends on the particular JL> system studied. ---------------------------------------------------------------------------- ---