More bugs in basis set intro

 Mike Zerner (zerner' at \` 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' at \`
 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> I aggree with you that some of my statements in the "Basis Sets
 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
 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> My statement that core orbitals are present in HOMO.
 JL> What I wanted to imply was: if the basis functions were "true"
 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
 JL> But it seems that I am totally wrong on this. Please help me,since I
 JL> do not know. Of course, I probably should go and retake a course
 JL> Chemistry for Psychologists 100" but I do not have time. This
 JL> comes from my early years when they showed me this diagram for
 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
 JL>    relationship between coefficients in resulting molecular orbitals:
 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>    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)
 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
 MS> The difference between the 2p function on Li, and the 3d on S, is that
 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
 JL> since "accuracy of the results" and "correctness of
 physical picture" is
 JL> very subjective (depends on the investigator) and depends on the
 JL> system studied.