From chemistry-request at.at server.ccl.net Mon May 17 00:54:27 1999 Received: from ccl.net (atlantis.ccl.net [192.148.249.4]) by server.ccl.net (8.8.7/8.8.7) with ESMTP id AAA29798 for ; Mon, 17 May 1999 00:54:26 -0400 Received: from krakow.ccl.net (krakow.ccl.net [192.148.249.195]) by ccl.net (8.8.6/8.8.6/OSC 1.1) with ESMTP id AAA04146; Mon, 17 May 1999 00:48:29 -0400 (EDT) Date: Mon, 17 May 1999 00:48:29 -0400 (EDT) From: Jan Labanowski To: Eric German cc: chemistry %! at !% ccl.net, Jan Labanowski Subject: ab initio basis sets In-Reply-To: Message-ID: krakow.ccl.net> MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Hi CCL, can you give better answers than my naive explanations? I did not look at these issues of ages... Jan jkl : at : ccl.net Actually, your question is a good one for CCL, and you may want to send it there to get opinions from experts in basis sets (I am not an expert in any way). Also, I did not look at the papers... My short comment: 1) Getting the good basis set is a a black art. While there is a systematic ways to get good basis sets (e.g., Dunning's correlation consistent basis sets), these sets are usually much larger than "ad hoc" (sorry, should be "intuitively optimized") basis sets. 2) You contract the inner s/p orbitals for at least 2 reasons: a) they usually do not change much on bonding, since most changes are in the valence orbitals b) to prevent core collapse -- the inner orbitals have VERY low energy (very large negative), and if uncontracted, the SCF optimization would first try to optimize coefficients for these orbitals rather than valence ones. 1% change in core orbital coefficient can make larger energy change for heavier elements than 50% change in a valence orbital coefficient. So, it is safer to keep them contracted, since they are not optimial for molecular calculations as they are derived from atomic calculations. 3) How contractions are done... Again, it is an art... But in short, people can get accurate numeric Hartree-Fock atomic calculations and fit exponents and coefficients for gaussian expansion of numeric AOs. They can also vary exponents and coefficients for atomic calculations since these computations are computationally feasible. But when we go to molecules, we have to limit the basis set size, or it would not finish in our lifetime, and also, there are many molecules to try. So what people do, they try to pull together some basis functions (contract them) and redo the calculations using either atomic (most often) or simple/representative/ molecular calculations to see how much energy they loose on going from uncontracted -> contracted. If energy change is small, contraction scheme is acceptable, if energy change is big, they try to come with different contraction scheme. And the big/small is in the eye of the beholder, and also depends on particular varian of ab initio (HF vs plethora of MCSCF and correlated methods) so often there are different contractions schemes for the same set of primitive gaussians. Note also that even for, say 20 primitive gaussians, you have a lot of possible contractions (factorials are involved), and rarely all possible contraction schemes are tried to see which one gives the lowest energy. So in many cases, there is a chance to design some new contraction scheme for the old set of primitive (i.e., uncontracted) gaussians. On Sun, 16 May 1999, Eric German wrote: > > > > Dear Dr. Lobanowski, > I have not any experience in using of ab initio basis sets but I > would like calculate complexes involving atoms of Pd. > I would greatly appreciate if you could clear me the following > problems with the contracted basis. Hay and Wadt have published > (JCP,1985) the basis (3s3p4d) for Pd (see 1-st and 2-nd columns of > table below. > > (3s3p4d) [2s2p2d] [2s1p1d] > --------- > alpha_i C_i C_i C_i > > 5s-orbitals > 1 1 1 > .4496 -.3594574 -1.166 -.3594574 > .1496 .5467561 1.6763 .5467561 > 2 2 > .0436 .7414499 1.00 .7414499 > 5p-orbitals > 2-4 3-5 3-5 > .7368 .03491 .0763285 .03491 > .0899 .4454769 .974006 .4454769 > 6-8 > .0262 .6611266 1.00 .6611266 > 4d-orbitals > 5-9 9-13 6-10 > 6.091 .0447293 .0511957 .0447293 > 1.719 .4425814 .5506564 .4425814 > .6056 .5051035 .578125 .5051035 > 14-18 > .1883 .2450132 1.00 .2450132 > > 9 basis funct., 18 basis funct., 10 basis funct., > 32 Gaussians 32 Gaussians 32 Gaussians > > 2) There is the standard basis LANL1DZ in Gaussian94 for Pd. It is the > contracted basis (3s3p4d)/[2s2p2q] (column 3 above). We see that this > contraction increases the number of basis functions and increases CPU > time. So, my question is: why this contraction is done and what is idea > to do the contraction of the first and the second Gaussians but not, for > example, of the first and the third for 5s-orbitals, and so for 5p > Gaussians? Are the corresponding coefficients in column 3 obtained by the > optimization procedure? > 3) In Column 4 is given the contracted basis (3s3p4d)/[2s1p1d] > of Akinaga et al (J.Chem.Phys,109 (1988) 11010 ). We can see that the > coefficients of this basis is the same as of the uncontracted basis > (3s3p4d). How do you think, what could be idea of this contraction? > Many thanks in advance > > Best wishes > Sicerely > E.D. German > > Jan K. Labanowski | phone: 614-292-9279, FAX: 614-292-7168 Ohio Supercomputer Center | Internet: jkl ( ( at ) ) ccl.net 1224 Kinnear Rd, | http://www.ccl.net/chemistry.html Columbus, OH 43212-1163 | http://www.ccl.net/