# Summary of 5d and 6d functions in basis set

• From: Ohyun Kwon <ok16|at|mail.gatech.edu>
• Subject: Summary of 5d and 6d functions in basis set
• Date: Fri, 12 Dec 2003 15:55:11 -0500 (EST)

```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.
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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
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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
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
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Date: Wed, 10 Dec 2003 14:26:51 -0500 (EST)
From: Doug Fox <gaussian.com!fox|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.
>
```