programming languages really are languages

Just thought I would forward this interesting note to the net, since
 it came to me directly.  I like the debate - it really is interesting
 to see and hear what others think about this issue.  I will have some
 more and final comments in a day or two.
 Doug Smith
 From:	IN%"ornitz;at;Kodak.COM" 11-JUN-1992 06:06:10.00
 To:	IN%"dsmith;at;"
 Subj:	Programming "languages"
 Return-path: <ornitz;at;Kodak.COM>
 Date: 10 Jun 1992 10:10:43 -0400 (EDT)
 From: ornitz;at;Kodak.COM (Barry Ornitz)
 Subject: Programming "languages"
 To: dsmith;at;
 Date: Thu, 11 Jun 1992 16:22 -0500
 From: Katrina Werpetinski <WERPETIN;at;>
 Subject: 3-D Integration grids (again)
 To: chemistry;at;
 Status: RO
 [ Please pardon my ignorance.  I'm just a lowly chemical engineer
   pretending to be a computational chemist. :) ]
 I'm struggling with a problem in an LCGTO-LDF-SCF code concerning the
 numerical integration for the fitting of the exchange potential.  The
 present code uses 26 angular points, randomly rotated(1) at each of
 the Gauss-Legendre radial points.  This is insufficient for the
 problems I'm interested in studying (dihedral angles and torsional
 energy barriers).
 I've bumped it up to 110 points thanks to a couple of people who sent
 me the code to generate the additional angular points and weights.
 This takes care of the accuracy problem, but the program now takes
 significantly longer to run.  I know I can get rid of many of the
 angular points in the core region.  I'm also thinking of changing the
 radial grid.
 Does anyone have a favorite method of forming a grid (ie which radial
 quadrature to use, what criterion to use for when to increase the # of
 angular points, how many angular points to use, etc) and any reasoning
 behind it?
 Delly(2) doesn't specify what order angular grids or what sort of
 radial grid Dmol uses.  Andzelm and Wimmer(3) use up to 302 angular
 points (randomly rotated) and Gauss-Chebyshev quadrature for the
 radial points in DGauss.  Becke(4) uses up to 194 angular points and
 Gauss-Chebyshev for the radial points.  Fournier and DePristo(5) say
 deMon uses a grid like Becke's with rotation of the angular points.
 Dunlap(6) uses 26 angular points and a logaritmically increasing grid
 that starts at the first Herman-Skillman point.
 1 R.S.Jones, J.W.Mintmire, and B.I.Dunlap, IJQCS 22, 77-84 (1988)
 2 B.Delly, J. Chem. Phys. 92, 508-517 (1990)
 3 J.Andzelm and E. Wimmer, J. Chem. Phys. 96, 1280-1303 (1992)
 4 A.D.Becke, J. Chem. Phys. 88, 2547-2553 (1988)
 5 Rene Fournier and Andrew E. DePristo, J. Chem. Phys. 96, 1183-1193 (1992)
 6 Brett Dunlap, J. Phys. Chem 90, 5524-5529 (1986)