Basis Set FAQ

  1. What do the basis set names mean?
  2. How do the basis sets affect the energy?
  3. What does the 'pseudopotential' button do?
  4. What is the LACVP* basis set?
  5. Are there other effective core basis sets available?

  1. 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 complexity and increasing calculation time.
    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 results. Available for elements H - Cs.
    6-31G* A significant improvement on 3-21G(*), 6-31G* adds polarization to all 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 extra 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 - Kr and I.
    6-311G** Adds polarization functions to hydrogens of the 6-311G* basis set. Available for elements H - Kr and I.
    6-311++G** Add diffuse functions to 6-311G**. Available for elements H - Kr and I.
    6-311++G(2df,2pd) Improve the polarization to the 6-311++G** basis set. Available for elements H - Kr and I.
    cc-pVTZ Similar to 6-311++G(2df,2pd) but with a more descriptive core (7s) and different S/P splitting; (7-711S, 311P). The 'cc' stands for 'correlation consistent' and has been designed specifically for post HF methods. Available for elements H - Ca and Ge - Kr.
    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-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 some diffuse (aug: spdf) and some core polarization functions (C: 3s3p2d1f, 9s). Available for elements H - Ar.

  2. 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

  3. What does the 'pseudopotential' button do?

    Checking the 'pseudopotential' button extends the basis set by adding atom definitions containing 'effective cores'. Currently only the 6-31G series of basis sets can be extended this way in Spartan. When extending the 6-31G basis set with effective cores the new basis set is called LACVP

  4. 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.

    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 : __ __ __ __ __ __ __ __ __ __ __ __ __ __
        Actinides   : __ __  U Np Pu __ __ __ __ __ __ __ __ __

    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... :
  5. Are there other effective core basis sets available?

    Yes. Spartan ships with the LANL2DZ basis set as well as the SBKJC basis set. These can be entered by typing in the basis set name in the option field of the calculation dialogue.

    It is important to note that Spartan has been optimized for the LACVP basis set and the performance of SBKJC is noticeably slower.

    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 SBKJC basis set uses effective core for all atoms except H and He.

  6. Suggested Reference

Author: Phil Klunzinger
Last modified: Mon Aug 11 14:42:04 PDT 2008