*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. The answers are; --------------------------------------------------------------------------------------- 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 ---------------------------------------- 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 ---------------------------------------------------------------------------------- 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 [ The following text is in the "iso-8859-1" character set. ] [ Your display is set for the "US-ASCII" character set. ] [ Some characters may be displayed incorrectly. ] 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. >