Questions About Basis Sets

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.

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.)

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 Pople STO series: STO-2G, STO-3G and STO-6G
• The Pople double-eta series: 3-21, 4-31, and 6-31 with the common polarization and diffuse options
• The Pople triple-eta 6-311G series
• Two G3 basis sets: G3large and G3MP2large
• Dunning basis sets: SV, DZ, TZ
• Ahlrichs basis sets: VDZ, pVDZ, TZV, VTZ
• correlated corrected basis sets: cc-pVDZ, cc-pVTZ, cc-pVQZ, cc-pV5Z
• correlated corrected basis sets: cc-pCVDZ, cc-pCVTZ, cc-pCVQZ, cc-pCV5Z
• augmented basis sets aug-cc-pVDZ, aug-cc-pCVDZ, aug-cc-pVDZ, aug-cc-pCVTZ, aug-cc-pVQZ, aug-cc-pCVQZ, aug-cc-pV5Z, aug-cc-pCV5Z
• LANL2DZ based pseudopotentials, including LANL2DZ and LACVP
• the def2 basis sets of Ahlrichs and Weigend, including def2-SV(P), dev2-SVPD, def2-TZVP, def2-TZVPPD, def2-QZVP, and def2-QZVPPD

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... :

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.