Questions About Basis Sets

  • What do the basis set names mean?

    The names of the basis sets come from a specialized field of quantum chemistry, and reflect abbreviations used in this field. A more complete description of what these abbreviations mean can be found in Spartan's "Tutorial and User's Guide", as well as " A Guide to Molecular Mechanics and Quantum Chemical Calculations". Below is a qualitative description of the most common basis sets. These are listed in order of increasing complexity and calculation time. Basis set names which are shaded are not available in Spartan Student but are shown here for completeness.
    STO-3G A minimal basis set. The fastest, but the least accurate basis set in common use. Available for elements H - I.
    3-21G(*) A simple basis set with added flexibility and polarization functions on atoms heavier than Ne. This is the simplest basis set that gives reasonable energies and geometries. Available for elements H - Cs.
    6-31G* A significant improvement on 3-21G(*), 6-31G* adds polarization to all (non-hydrogen) atoms, and improves the modeling of core electrons. 6-31G* is often considered the best compromise of speed and accuracy, and is the most commonly used basis set. Available for elements H - Kr.
    6-31G** Adds polarization functions to hydrogens. This can improve the total energy of the system. Available for elements H - Kr.
    6-31+G* Adds diffuse functions to heavy atoms. This can sometimes improve results for systems with large anions. Available for elements H - Kr.
    6-311G* Adds more flexibility to the basis set. Available for elements H - Ca, Ga - Kr and I.
    6-311G** Adds polarization functions to hydrogens of the 6-311G* basis set. Available for elements H - Ca, Ga - Kr and I.
    6-311+G** Adds diffuse functions to heavy atoms in 6-311G**. Available for elements H - Ca, Ga - Kr and I. This has been shown to be helpful for anions.
    6-311++G** The same as 6-311+G**, but also adds a diffuse 'S' orbital to Hydrogens.
    6-311++G(2df,2pd) Improves the polarization of the 6-311++G** basis set. Available for elements H - Ca, Ga - Kr and I.
    G3Large An extension of 6-311G** with more flexible polarization functions (2df on Li-Ne, 3d2f on Na-Ar) and polarization of the core electrons (pd on Li-Ne, df on Na-Kr) . This basis set is used as the 'limiting HF' basis set in the G3 method. Available for elements H - Ca and Ge - Kr.
    cc-pVTZ Similar to 6-311G(2df,2pd) but with a more descriptive core (7s) and different S/P splitting; (7-711S, 311P). The 'cc' stands or 'correlation consistent' and has been designed specifically for post HF methods. Available for elements H - Ca and Ge - Kr. The largest use of this basis set (aug-cc-pVQZ) is in extrapolating basis set energy results to the basis set limit.
    def2-TZVPPD Another triple-eta basis set of similar performance to cc-pVTZ. This has been extended to most of the periodic table and is arguably more efficient that cc-pVTZ.
    cc-pVQZ A systematic extension of cc-pVTZ with more flexible valence orbital (8-8111S, 3111P), more polarization functions (3d2fg) and a more accurate description of the core (8s). Available for elements H - Ca and Ge - Kr.
    aug-cc-pCVQZ Expands cc-pCVQZ with diffuse (aug: spdf) and some core polarization functions (C: 3s3p2d1f, 9s). Available for elements H - Ar. The largest use of this basis set is in extrapolating basis set energy results to the basis set limit.

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  • How do the basis sets affect the energy?

    As an example of the basis sets we show the Hartree-Fock energy for different basis sets of acetone at the 6-31G* geometry. (Note that some of the very large basis sets have a difficult time converging and thus require tighter tolerances than the commonly used basis sets and often require the SCFTOLERANCE=HIGH keyword. For consistency, this keyword was used in each example below.)

    # basis
    Energy (au)
    STO-3G 26 -189.534 688 6914 0.05
    3-21G 48 -190.886 407 5414 0.2
    6-31G 48 -191.874 189 8214 0.3
    6-31G* 72 -191.960 613 3115 1
    6-311G* 90 -192.001 883 1215 3
    6-311+G* 106 -192.005 994 0815 6
    6-311++G** 130 -192.015 295 5615 25
    6-311++G(2df,2pd)226 -192.029 578 6115 88
    6-311++G(3df,3pd)264 -192.031 627 8831235
    cc-pVTZ 204 -192.032 898 4615 82
    cc-pVQZ 400 -192.046 642 88303400
    aug-cc-pCVQZ 712 -192.047 735 331941000

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  • How do I use a basis if it is not in the pull-down menu?

    Spartan offers more basis sets than are available from the pull-down menu. Additional basis sets are accessible from the Basis Selector> dialogue, accessed by clicking on the "More.." entry in the pull-down menu. For common usage we recommend the basis sets accessible from the Calculation dialogue as they are well studied and optimized for Spartan. To access basis sets not available from the pull-down menu or the Basis Selector dialogue, open the later and click on the "Other..." tab, type the name of the basis set you wish to use and click the OK button. The specified basis set will be reflected in the Calculations dialogue.

    The complete list of basis sets which Spartan supports is:
    It is also possible to build your own basis set but this is rather difficult and is not "fully supported". (i.e. it is possible to build basis sets which do not converge)

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  • What is the LACVP basis set?

    The LACVP series of basis sets is a combination of the successful 6-31G basis set with the LANL2DZ effective core basis set. Specifically the atoms H - Ar are described with the 6-31G (or 6-31G*, 6-31+G** etc.) basis set while heavier atoms are modeled using the LANL2DZ basis set.

    Beginning with Spartan'14 Lanthanides have been added to LACVP basis with the constraint that they must be in the +3 oxidation state. (This is based on the Dolg, Stoll and Preuss ECP, [Theoret. Chim. Acta, 75 , 173 (1989) and 85, 441 (1993)], where the f-electron are placed in the core.)

    The atoms available in LACVP are shown in the following periodic table:

      H                                                                   He
     Li  Be                                            B   C   N   O   F  Ne
     Na  Mg                                           Al  Si   P   S  Cl  Ar
      K  Ca  Sc   Ti   V  Cr  Mn  Fe  Co  Ni  Cu  Zn  Ga  Ge  As  Se  Br  Kr
     Rb  Sr   Y   Zr  Nb  Mo  Tc  Ru  Rh  Pd  Ag  Cd  In  Sn  Sb  Te   I  Xe
     Cs  Ba  La ^ Hf  Ta   W  Re  Os  Ir  Pt  Au  Hg  Tl  Pb  Bi  __  __  __
     __  __  __ ^ __  __
        Lanthanides : Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu
        Actinides   : __ __  *  *  *  __ __ __ __ __ __ __ __ __
    (* U, Np, and Pu are available in LACVP, but only for Single Point Energies)

    A summary of the shell splitting used in the basis set is as follows:

    [Symbol] [Splitting description] [C = core-electrons]
      H-He :    31 (SP)
     Li-Ne :  6-31 (SP)
     Na-Ar : 66-31 (SP)
      K-Ca : C3-41 (p=3-11)           C = Ne           (10e)
     Sc-Cu : C3-41 (p=3-11 d=41)      C = Ne           (10e)
     Zn    :  C-21 (p=11   d=41)      C = Ar           (18e)
     Ga-Kr :  C-21 (p=21)             C = Ar + 3d      (28e)
     Rb-Sr : C3-41 (p=3-21)           C = Ar + 3d      (28e)
      Y-Ag : C3-41 (p=3-21 d=31)      C = Ar + 3d      (28e)
     Cd    :  C-21 (p=21   d=31)      C = Kr           (36e)
     In-Xe :  C-21 (p=21)             C = Kr + 4d      (46e)
     Cs-Ba : C3-41 (p=3-21)           C = Kr + 4d      (46e)
     La    : C3-41 (p=3-21 d=21)      C = Kr + 4d      (46e)
     Ce-Lu :       
     Hf-Au : C3-41 (p=3-21 d=21)      C = Kr + 4d + 4f (60e)
     Hg    :  C-21 (p=21   d=21)      C = Xe + 4f      (68e)
     Tl-Rn :  C-21 (p=21   d=21)      C = Xe + 5d + 4f (78e)
     Fr-Ra :
     Ac    :
     Th-Lr : C4-51 (p=3-41 d=11 f=22) C = Xe + 5d + 4f (78e)
     Rf... :

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  • What effective core basis sets available?

    The 6-31G and 6-311G basis-set families have been extended in Spartan with effective core basis sets. For the 6-31G series we use the LACVP basis set. With 6-311G basis sets we've added the Def2-TZVP basis set, with the removal of 'f' polarization on the transition metals.

    The LANL2DZ basis uses effective core for all atoms larger than Ne. For atoms heavier than potassium [K] this is the same as LACVP. For [Na-Ar] a neon core is used.

    The Def2 series of basis sets from Ahlrichs and Weigend are also available in the basis set selector.

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  • How to work with Lanthanides?

  • In Spartan we have two ways of dealing with Lanthanides

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  • What is BSSE?

  • BSSE is an acronym for "Basis Set Superposition Error". BSSE can occur when calculating reaction energies. For example in the A + B = AB calculation, the energy of AB could be lower because B's basis sets may lower the A part (on the right hand side) and of course will not change the energy of A on the left hand side.

    If one worries about this error, the solution in Spartan is to do all three calculation (A, B, and AB) at a higher basis set. Typically this BSSE correction energy is small for large basis sets. Often smaller than other neglected terms such as incomplete basis, neglect of electron correlation, infinite gas phase, approximate geometries and zero-point energy.

    Another well-known way of dealing with BSSE is the 'counter poise' method. In this approach the calculations on the left hand side 'A' and 'B' have included in them the basis functions of 'B' and 'A' added respectively. Unfortunately this method is geometry dependent and assumes the geometry of A and B do not change much when going from A and B to AB.

    Spartan's preferred way of dealing with BSSE is to do a single point energy with a large basis set using the "dual-basis" approximation. This is typically more accurate than the usual small basis-set 'counter poise' method, includes a correction to finite basis set size, and is much quicker than the larger basis set calculation. As an example of the effect of different basis sets we summarize the results for an HF dimer of water. The dimer was optimized for each basis set.

    Hydrogen Bond Energy of the Water Dimer
    Total Energy

    CP Corrected


    Finite Basis

    3-21G -151.1894036-46.11-25.3520.8~2500
    6-31G* -152.0304565-23.61-19.743.4~300
    6-31G* -152.0214653-23.53 Optimized Monomer
    6-31+G** -152.0704856-21.16-18.582.6~200
    6-311++G(2df,p) -152.1157130-18.58-16.711.9~50
    cc-pVQZ -152.1374225-16.82-15.571.3~5
    aug-cc-pVQZ -152.1392919-15.65-15.540.1???
    aug-cc-pVQZ -152.1392919-15.60Optimized Monomer
    At 6-31G* Geometry
    -152.1083753-19.99dual basis
    -152.1305373-17.44dual basis
    -152.1312025-16.12dual basis
    aug-cc-pVQZ -152.1387935-15.26-15.140.1???
    Other Post HF Methods
    MP2/6-31G*-152.4102728 -30.61
    T1 -22.53 includes RI-MP2
    T1 + 4RT -12.62 includes Trans/Rot/PV
    G3(MP2)Ee -20.57 includes post-MP2
    G3(MP2)Ee + 4RT -10.66 includes thermodynamics
    G3(MP2)-0.18781194 -13.76 adds vibrations
    G3 -14.70 better electron correlation & basis
    Experiment -15.+-2 "Quantum Chemistry:
    Fundamentals to Applications",
    1999, pg 240; Vespremi, Feher

    Using this data to assign a rough approximation of the errors involved in an HF/6-31G* calculation of the interaction energy of two water molecules (1 hydrogen bond) we get

    Not surprisingly, G3 and G3(MP2) address all of these errors. For reactions where the number of bonds stays the same, we would expect the T1 theory to address these errors to some extent. In this non-isodesmic reaction (a hydrogen bond is created/broken) one would expect a dual-basis RI-MP2 calculation with a frequency correction to do well. This calculation is summarized below.

    Total Energy

    -152.0304565 -23.61Use this geometry
    -152.6283024 -25.46 includes better
    basis set and
     electron correlation
    "  "   + 4RT -15.55
      "  "   + Hv[6-31G*] -18.13  includes HF vibrations
    -152.70857-22.43 includes better
    basis set and
     electron correlation
    "  "   + 4RT -12.52
      "  "   + Hv[6-31G*] -15.10  includes HF vibrations

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  • How can I use the Counter Poise (CP) method to account for BSSE?

  • In Spartan we have a shortcut that can be used to calculate this 'Interaction Energy'. Note that this is available only as a single point energy. (Any geometry optimization must be done prior to this calculation.) Freeze one of the fragments with the freeze center tool (found in the Geometry menu) and type in the keyword INTERACTIONENERGY. This keyword will calculate all three parts of the 'reaction', for a total of three energy calculations. To calculate the "Counter-Poise" correction one may type INTERACTIONENERGY=CP. If you want to calculate/show the intermediate BSSE energies, type INTERACTIONENERGY=BSSE which will calculate a total of 5 energies. Example output for INTERACTIONENERGY=BSSE is shown below:

     Combined Energy     -152.06977558 (Hartrees)
     Parts               -152.06243373 [     -76.03122486 +     -76.03120887 ] 
     Interaction           -0.00734185 =     -19.27602192 kJ/mol 
     BSSE correction       -0.00082962 [      -0.00062318 +      -0.00020644 ]
     Interaction (CP)      -0.00651223 =     -17.09786380 kJ/mol 
    Our INTERACTIONENERGY method is implemented for energy only calculations, i.e. there is not geometry optimization. Currently, INTERACTIONENERGY works only for cases when the combined system is a singlet and the reaction is not a "charge separation" reaction. If there is a net charge Spartan attempts to put the charge on the appropriate fragment, while the other fragment will be set as neutral with no unpaired electrons. If we detect a bond breaking reaction (i.e. the creation of a radical on each fragment, each fragment is set to a doublet state.

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  • How do I convert energy units in Spartan?
  • Below are some common energy conversion factors:
       1 kcal/mol    =       6.948 e-21            J
                     =       4.184                 kJ/mol
       1 au (Hartree)=       me*e^4/h-bar^2
                     =       4.3597482(26) 10^-18  J              *
    	         =       4.35974381(34)10^-18  J      (1998 CODATA)
                     =    2625.5000                kJ/mol
                     =     627.510                 kcal/mol
                           627.5095602             kcal/mol       *
                           627.50947093            kcal/mol (1998 CODATA [new Na])
                     =      27.212                 ev
                     =      27.2113961(81)         ev             *
       1 ev          =       1.60217733(49) 10^-19 J              *
                     =      23.06                  kcal/mol
                     =      92.24                  kJ/mol
       4.184 J       =       1                     Calorie (a constant)
       1 kT (T=300K) =       0.595                 kcal
    *In places where multiple values are listed for a given conversion, the first is the approximation used in Spartan, the second is the 'exact' value (as of 1973, 1986 or 1998).

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