Summary of 5d and 6d functions in basis set

Dear CCLers;
 I summarized answers to following question of mine.
 Dear CCLers;
 According to Gaussian and other program manuals, some basis sets employ
 6d, and others do 5d. For example, 6-31G* basis set use 6d (Cartesian d
 function) but 6-311G* basis set use 5d (pure d function). And in
 GaussianXX program, when the keyword of "Gen" is applied, using 5d is
 default.
 Is any particular reason for that?
 I would appreciate it if anyone could kindly give some advice on this
 maater.
 Thank you very much for your attention.
 The answers are;
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 Date: Wed, 10 Dec 2003 17:04:20 -0000
 From: Herbert Fruechtl <h.fruchtl|at|fle.fujitsu.com>
 To: 'Ohyun Kwon' <ok16|at|mail.gatech.edu>
 Subject: CCL: RE: 5d and 6d functions in basis set
 Parts/Attachments:
    1 Shown    71 lines  Text
    2   OK     20 lines  Text
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 The "correct" treatment of the angular part of the basis set
 (cartesian or
 spherical) is generally the one that was used for its development, so you
 would have to look up the original reference (unless you just trust
 Gaussian
 to get it right).
 Generally, older basis sets tend to be of the cartesian variety, because
 this is easier to program, and integral codes for these basis functions
 were
 available earlier. Spherical harmonics are mathematically cleaner, because
 they don't introduce additional functions of lower angular momentum.
 Differences in speed vary between programs. Some calculate spherical
 functions from the cartesians by projecting out the additional functions,
 which is obviously slower than just the cartesian functions. Others are
 optimised for spherical functions, and you pay a penalty if you use
 cartesian functions. For post-HF methods, often the number of basis
 functions determines the cost of calculations, which also favours
 spherical
 functions.
 HTH,
   Herbert
 ---------------------------------------------------------------------------------
 Date: Wed, 10 Dec 2003 12:26:25 -0500 (EST)
 From: Joslyn Y Kravitz <jyudenfr|at|umich.edu>
 To: Ohyun Kwon <ok16|at|mail.gatech.edu>
 Subject: Re: CCL:5d and 6d functions in basis set
 I've just been dealing with this. If you use 5D, you get the orbital
 information in a form that translates directly to the regular 5 d orbitals
 you usually think of, dxy, dz^2, etc. I think this is preferrable if you
 are looking at atomic orbital contributions to MO's. The 6D puts the
 electron density into 6 d-type orbitals, which is probably more
 "accurate"
 since more basis functions give a better approximation and the dz^2 is
 really a linear combination of two orbitals anyway. But I think the 5D way
 is more "intuitive." One note of caustion, if you use a basis set that
 defaults to (6D, 10F) but you want to use 5D, you also may have to specify
 7F or else the orbitals don't come put right. While this explanation is
 not the most scientific, I hope it helps.
 Joslyn Kravitz
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 Date: Wed, 10 Dec 2003 13:05:16 -0500
 From: Stefan Fau <fau|at|qtp.ufl.edu>
 To: Ohyun Kwon <ok16|at|mail.gatech.edu>
 Cc: CCL - all <CHEMISTRY|at|ccl.net>
 Subject: CCL: Re: 5d and 6d functions in basis set
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 Hi Ohyun,
 my speculation on this is as follows:
 cartesian d-functions are linear combinations of the five
 "pure" d-functions and an s-function of the same exponent.
 Therefore, using cartesian d-functions introduces an
 additional s-function into the basis set. This may lead to
 near linear dependence problems in larger basis sets.
 Since many smaller basis sets are part of Gaussians basis
 set library, it is probably more likely that the GEN keyword
 is used to specify large basis sets. Hence the 5D default.
 Stefan
 ______________________________________________________________________
 Dr. Stefan Fau                    |      fau|at|qtp.ufl.edu
 University of Florida             |     (352) 392-6714
 Quantum Theory Project
 2319 NPB #92, P.O.Box 118435
 Gainesville, FL 32611-8435
 ------------------------------------------------------------------------------------
 Date: Wed, 10 Dec 2003 14:26:51 -0500 (EST)
 From: Doug Fox <gaussian.com!fox|at|gaussian.com>
 Reply-To: gaussian.com!help%gaussian.com|at|gaussian.com
 To: Ohyun Kwon <uunet!mail.gatech.edu!ok16%gaussian.com|at|uunet.uu.net>
 Subject: Re: CCL:5d and 6d functions in basis set
   Dr. Kwon,
    The 6d case is easier to code but less satisfying if you compare with
 the hydrogenic solution where there are only 5 angular momentum functions
 with l=2.  Second, that 6th function is sort of a 2S function, spherically
 symmetric with a node, and as an s function it overlaps strongly with the
 other s functions in the basis set.  This can cause linear dependence
 problems
 and if you have carefully chosen the set of s functions adding a random
 function is unlikely to be an improvement.  So eliminating these functions
 cuts down the cost slightly while achieving the goal of adding
 polarization
 functions to the basis set.
 >