Basis Set References

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

  1. W.J.Hehre, R.F.Stewart, J.A.Pople J.Chem.Phys. 51, 2657-2664(1969).
  2. W.J.Hehre, R.Ditchfield, R.F.Stewart, J.A.Pople J.Chem.Phys. 52, 2769-2773(1970).
  3. M.S.Gordon, M.D.Bjorke, F.J.Marsh, M.S.Korth J.Am.Chem.Soc. 100, 2670-2678(1978).
    ** the valence scale factors for Na-Cl are taken from this paper, rather than the "official" Pople values in Ref. 2.
  4. W.J.Pietro, B.A.Levi, W.J.Hehre, R.F.Stewart, Inorg.Chem. 19, 2225-2229(1980).
  5. W.J.Pietro, E.S.Blurock, R.F.Hout,Jr., W.J.Hehre, D.J. DeFrees, R.F.Stewart Inorg.Chem. 20, 3650-3654(1980).
  6. W.J.Pietro, W.J.Hehre J.Comput.Chem. 4, 241-251(1983).

  7. MINI/MIDI H-Xe Ref. 9
  8. "Gaussian Basis Sets for Molecular Calculations" S.Huzinaga, J.Andzelm, M.Klobukowski, E.Radzio-Andzelm, Y.Sakai, H.Tatewaki Elsevier, Amsterdam, 1984.

    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
     
  9. J.S.Binkley, J.A.Pople, W.J.Hehre J.Am.Chem.Soc. 102, 939-947(1980).
  10. M.S.Gordon, J.S.Binkley, J.A.Pople, W.J.Pietro, W.J.Hehre J.Am.Chem.Soc. 104, 2797-2803(1982).
  11. K.D.Dobbs, W.J.Hehre J.Comput.Chem. 7,359-378(1986)
  12. K.D.Dobbs, W.J.Hehre J.Comput.Chem. 8,861-879(1987)
  13. K.D.Dobbs, W.J.Hehre J.Comput.Chem. 8,880-893(1987)
     
              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
     
  14. R.Ditchfield, W.J.Hehre, J.A.Pople J.Chem.Phys. 54, 724-728(1971).
  15. W.J.Hehre, R.Ditchfield, J.A.Pople J.Chem.Phys. 56, 2257-2261(1972).
  16. W.J.Hehre, J.A.Pople J.Chem.Phys. 56, 4233-4234(1972).
  17. W.J.Hehre, W.A.Lathan J.Chem.Phys. 56,5255-5257(1972).
  18. J.D.Dill, J.A.Pople J.Chem.Phys. 62, 2921-2923(1975).
  19. J.S.Binkley, J.A.Pople J.Chem.Phys. 66, 879-880(1977).
  20. M.S.Gordon Chem.Phys.Lett. 76, 163-168(1980) ** - Note that the built in 6-31G basis for Si is not that given by Pople in reference 22. The Gordon basis gives a better wavefunction, for a ROHF calculation in full atomic (Kh) symmetry,
    6-31G Energy virial
    Gordon -288.828573 1.999978
    Pople -288.828405 2.000280
    See the input examples for how to run in Kh.
  21. M.M.Francl, W.J.Pietro, W.J.Hehre, J.S.Binkley, M.S.Gordon, D.J.DeFrees, J.A.Pople J.Chem.Phys. 77, 3654-3665(1982).
  22. Unpublished, copied out of GAUSSIAN82.
  23. For Li and Be, 4-31G is actually a 5-21G expansion.

    Extended basis sets

    6-311G
  24. R.Krishnan, J.S.Binkley, R.Seeger, J.A.Pople J.Chem.Phys. 72, 650-654(1980).

    valence double zeta "DZV" sets:

    "DH" basis - DZV for H, Li-Ne, Al-Ar
  25. T.H.Dunning, Jr., P.J.Hay Chapter 1 in "Methods of Electronic Structure Theory", H.F.Shaefer III, Ed. Plenum Press, N.Y. 1977, pp 1-27.
    Note that GAMESS uses inner/outer scale factors of 1.2 and 1.15 for DH's hydrogen (since at least 1983). To get Thom's usual basis, scaled 1.2 throughout: HYDROGEN 1.0 x, y, z DH 0 1.2 1.2 "BC" basis - DZV for Ga-Kr
  26. R.C.Binning, Jr., L.A.Curtiss J.Comput.Chem. 11, 1206-1216(1990)

    valence triple zeta "TZV" sets:

    TZV for Li-Ne
  27. T.H. Dunning, J.Chem.Phys. 55 (1971) 716-723. TZV for Na-Ar - also known as the "MC" basis
  28. A.D.McLean, G.S.Chandler J.Chem.Phys. 72,5639-5648(1980). TZV for K,Ca
  29. A.J.H. Wachters, J.Chem.Phys. 52 (1970) 1033-1036. (see Table VI, Contraction 3). TZV for Sc-Zn (taken from HONDO 7)
    This is Wachters' (14s9p5d) basis (ref 42) contracted to (10s8p3d) with the following modifications
    1. the most diffuse s removed;
    2. additional s spanning 3s-4s region;
    3. two additional p functions to describe the 4p;
    4. (6d) contracted to (411) from ref 43, except for Zn where Wachter's (5d)/[41] and Hay's diffuse d are used.
  30. A.K. Rappe, T.A. Smedley, and W.A. Goddard III, J.Phys.Chem. 85 (1981) 2607-2611

    Valence only basis sets (for use with corresponding ECPs)

    SBK -31G splits, bigger for trans. metals (available Li-Rn)
  31. W.J.Stevens, H.Basch, M.Krauss J.Chem.Phys. 81, 6026-6033 (1984)
  32. W.J.Stevens, H.Basch, M.Krauss, P.Jasien Can.J.Chem, 70, 612-630 (1992)
  33. T.R.Cundari, W.J.Stevens J.Chem.Phys. 98, 5555-5565(1993)

    HW -21 splits (sp exponents not shared)

    transition metals (not built in at present, although they will work if you type them in).
  34. P.J.Hay, W.R.Wadt J.Chem.Phys. 82, 270-283 (1985) main group (available Na-Xe)
  35. W.R.Wadt, P.J.Hay J.Chem.Phys. 82, 284-298 (1985) see also
  36. P.J.Hay, W.R.Wadt J.Chem.Phys. 82, 299-310 (1985)

    Polarization exponents

    STO-NG*
  37. J.B.Collins, P. von R. Schleyer, J.S.Binkley, J.A.Pople J.Chem.Phys. 64, 5142-5151(1976).

    3-21G*. See also reference 12. 61) W.J.Pietro, M.M.Francl, W.J.Hehre, D.J.DeFrees, J.A. Pople, J.S.Binkley J.Am.Chem.Soc. 104,5039-5048(1982)

    6-31G* and 6-31G**. See also reference 22 above.
  38. P.C.Hariharan, J.A.Pople Theoret.Chim.Acta 28, 213-222(1973)

    multiple polarization, and f functions
  39. M.J.Frisch, J.A.Pople, J.S.Binkley J.Chem.Phys. 80, 3265-3269 (1984).

    STO-NG*
    means d orbitals are used on third row atoms only. The original paper (ref 60) suggested z=0.09 for Na and Mg, and z=0.39 for Al-Cl. At NDSU we prefer to use the same exponents as in 3-21G* and 6-31G*, so we know we're looking at changes in the sp basis, not the d exponent.
    3-21G*
    means d orbitals on main group elements in the third and higher periods. Not defined for the transition metals, where there are p's already in the basis. Except for alkalis and alkali earths, the 4th and 5th row zetas are from Huzinaga, et al (ref 9). The exponents are normally the same as for 6-31G*.
    6-31G*
    means d orbitals on second and third row atoms. We use Mark Gordon's z=0.395 for silicon, as well as his fully optimized sp basis (ref 21). This is often written 6-31G(d) today.
    6-31G**
    means the same as 6-31G*, except that p functions are added on hydrogens. This is often written 6-31G(d,p) today.
    6-311G**
    means p orbitals on H, and d orbitals elsewhere. The exponents were derived from correlated atomic states, and so are considerably tighter than the polarizing functions used in 6-31G**, etc. This is often written 6-311G(d,p) today.

    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.
  40. T.Clark, J.Chandrasekhar, G.W.Spitznagel, P. von R. Schleyer J.Comput.Chem. 4, 294-301(1983)
  41. G.W.Spitznagel, Diplomarbeit, Erlangen, 1982.

    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  0.0294
    
    Additional 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.

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