An excellent review of the relationship between
the atomic basis used, and the accuracy with which
various molecular properties will be computed is:
E.R.Davidson, D.Feller Chem.Rev. 86, 681-696(1986).
STO-NG H-Ne Ref. 1 and 2
Na-Ar, Ref. 2 and 3 **
K,Ca,Ga-Kr Ref. 4
Rb,Sr,In-Xe Ref. 5
Sc-Zn,Y-Cd Ref. 6
The MINI bases are three gaussian expansions of each atomic orbital. The exponents and contraction coefficients are optimized for each element, and s and p exponents are not constrained to be equal. As a result these bases give much lower energies than does STO-3G. The valence MINI orbitals of main group elements are scaled by factors optimized by John Deisz at North Dakota State University. Transition metal MINI bases are not scaled. The MIDI bases are derived from the MINI sets by floating the outermost primitive in each valence orbitals, and renormalizing the remaining 2 gaussians. MIDI bases are not scaled by GAMESS. The transition metal bases are taken from the lowest SCF terms in the s**1,d**n configurations.
3-21G H-Ne Ref. 10 (also 6-21G) Na-Ar Ref. 11 (also 6-21G) K,Ca,Ga-Kr,Rb,Sr,In-Xe Ref. 12 Sc-Zn Ref. 13 Y-Cd Ref. 14
N-31G references for 4-31G 5-31G 6-31G H 15 15 15 He 23 23 23 Li 19,24 19 Be 20,24 20 B 17 19 C-F 15 16 16 Ne 23 23 Na-Ga 22 Si 21 ** P-Cl 18 22 Ar 22
The definitions for 6-31G* for C-F are disturbing in that they treat these atoms the same. Dunning and Hay (ref 30) have recommended a better set of exponents for second row atoms and a slightly different value for H.
2p, 3p, 2d, 3p polarization sets are usually thought of as arising from applying splitting factors to the 1p and 1d values. For example, SPLIT2=2.0, 0.5 means to double and halve the single value. The default values for SPLIT2 and SPLIT3 are taken from reference 72, and were derived with correlation in mind. The SPLIT2 values often produce a higher (!) HF energy than the singly polarized run, because the exponents are split too widely. SPLIT2=0.4,1.4 will always lower the SCF energy (the values are the unpublished personal preference of MWS), and for SPLIT3 we might suggest 3.0,1.0,1/3. See ref 63 for more on this.
With all this as background, we are ready to present the table of polarization exponents built into GAMESS.
Built in polarization exponents, chosen by POLAR= in the $BASIS group. The values are for d functions unless otherwise indicated.
Please note that the names associated with each column are only generally descriptive. For example, the column marked "Pople" contains a value for Si with which John Pople would not agree, and that the K-Xe values in this column were actually originally from the Huzinaga group. The exponents for Ga-Kr are from the Binning and Curtiss paper, not Thom Dunning. And so on.
POPLE POPN311 DUNNING HUZINAGA HONDO7 ------ ------- ------- -------- ------ H 1.1(p) 0.75(p) 1.0(p) 1.0(p) 1.0(p) He 1.1(p) 0.75(p) 1.0(p) 1.0(p) 1.0(p) Li 0.2 0.200 0.076(p) Be 0.4 0.255 0.164(p) 0.32 B 0.6 0.401 0.70 0.388 0.50 C 0.8 0.626 0.75 0.600 0.72 N 0.8 0.913 0.80 0.864 0.98 O 0.8 1.292 0.85 1.154 1.28 F 0.8 1.750 0.90 1.496 1.62 Ne 0.8 2.304 1.00 1.888 2.00 Na 0.175 0.061(p) 0.157 Mg 0.175 0.101(p) 0.234 Al 0.325 0.198 0.311 Si 0.395 0.262 0.388 P 0.55 0.340 0.465 S 0.65 0.421 0.542 Cl 0.75 0.514 0.619 Ar 0.85 0.617 0.696 K 0.1 0.039(p) Ca 0.1 0.059(p) Ga 0.207 0.141 Ge 0.246 0.202 As 0.293 0.273 Se 0.338 0.315 Br 0.389 0.338 Kr 0.443 0.318 Rb 0.11 0.034(p) Sr 0.11 0.048(p) A blank means the value equals the "Pople" column. Common d polarization for all sets: In Sn Sb Te I Xe 0.160 0.183 0.211 0.237 0.266 0.297 Tl Pb Bi Po At Rn 0.146 0.164 0.185 0.204 0.225 0.247 f polarization functions, from reference 63: Li Be B C N O F Ne 0.15 0.26 0.50 0.80 1.00 1.40 1.85 2.50 Na Mg Al Si P S Cl Ar 0.15 0.20 0.25 0.32 0.45 0.55 0.70 --Anion diffuse functions 3-21+G, 3-21++G, etc.
Anions usually require diffuse basis functions to properly represent their spatial diffuseness. The use of diffuse sp shells on atoms in the second and third rows is denoted by a + sign, also adding diffuse s functions on hydrogen is symbolized by ++. These designations can be applied to any of the Pople bases, e.g. 3-21+G, 3-21+G*, 6-31++G**. The following exponents are for L shells, except for H. For H-F, they are taken from ref 70. For Na-Cl, they are taken directly from reference 71. These values may be found in footnote 13 of reference 63. For Ga-Br, In-I, and Tl-At these were optimized for the atomic ground state anion, using ROHF with a flexible ECP basis set, by Ted Packwood at NDSU.
H 0.0360 Li Be B C N O F 0.0074 0.0207 0.0315 0.0438 0.0639 0.0845 0.1076 Na Mg Al Si P S Cl 0.0076 0.0146 0.0318 0.0331 0.0348 0.0405 0.0483 Ga Ge As Se Br 0.0205 0.0222 0.0287 0.0318 0.0376 In Sn Sb Te I 0.0223 0.0231 0.0259 0.0306 0.0368 Tl Pb Bi Po At 0.0170 0.0171 0.0215 0.0230 0.0294Additional information about diffuse functions and also Rydberg type exponents can be found in reference 30.
The following atomic energies are from UHF calculations (RHF on 1-S states), with p orbitals not symmetry equivalenced, and using the default molecular scale factors. They should be useful in picking a basis of the desired energy accuracy, and estimating the correct molecular total energies.
Atom state STO-2G STO-3G 3-21G 6-31G H 2-S -.454397 -.466582 -.496199 -.498233 He 1-S -2.702157 -2.807784 -2.835680 -2.855160 Li 2-S -7.070809 -7.315526 -7.381513 -7.431236 Be 1-S -13.890237 -14.351880 -14.486820 -14.566764 B 2-P -23.395284 -24.148989 -24.389762 -24.519492 C 3-P -36.060274 -37.198393 -37.481070 -37.677837 N 4-S -53.093007 -53.719010 -54.105390 -54.385008 O 3-P -71.572305 -73.804150 -74.393657 -74.780310 F 2-P -95.015084 -97.986505 -98.845009 -99.360860 Ne 1-S -122.360485 -126.132546 -127.803825 -128.473877 Na 2-S -155.170019 -159.797148 -160.854065 -161.841425 Mg 1-S -191.507082 -197.185978 -198.468103 -199.595219 Al 2-P -233.199965 -239.026471 -240.551046 -241.854186 Si 3-P -277.506857 -285.563052 -287.344431 -288.828598 P 4-S -327.564244 -336.944863 -339.000079 -340.689008 S 3-P -382.375012 -393.178951 -395.551336 -397.471414 Cl 2-P -442.206260 -454.546015 -457.276552 -459.442939 Ar 1-S -507.249273 -521.222881 -524.342962 -526.772151 SCF * Atom state DH 6-311G MC limit H 2-S -.498189 -.499810 -- -0.5 He 1-S -- -2.859895 -- -2.861680 Li 2-S -7.431736 -7.432026 -- -7.432727 Be 1-S -14.570907 -14.571874 -- -14.573023 B 2-P -24.526601 -24.527020 -- -24.529061 C 3-P -37.685571 -37.686024 -- -37.688619 N 4-S -54.397260 -54.397980 -- -54.400935 O 3-P -74.802707 -74.802496 -- -74.809400 F 2-P -99.395013 -99.394158 -- -99.409353 Ne 1-S -128.522354 -128.522553 -- -128.547104 Na 2-S -- -- -161.845587 -161.858917 Mg 1-S -- -- -199.606558 -199.614636 Al 2-P -241.855079 -- -241.870014 -241.876699 Si 3-P -288.829617 -- -288.847782 -288.854380 P 4-S -340.689043 -- -340.711346 -340.718798 S 3-P -397.468667 -- -397.498023 -397.504910 Cl 2-P -459.435938 -- -459.473412 -459.482088 Ar 1-S -- -- -526.806626 -526.817528* M.W.Schmidt and K.Ruedenberg, J.Chem.Phys. 71, 3951-3962(1979). These are ROHF energies in Kh symmetry.