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 to 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 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.
   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.
   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.
   6-31G**	Adds polarization functions to hydrogens. This can improve the total energy of the system.
   6-31+G*	Adds extra diffuse functions to heavy atoms. This can sometimes improve results for systems with large anions.
   6-311G*	Adds more flexibility to the basis set.
   6-311G**	Adds polarization functions to hydrogens of the 6-311G* basis set.
   6-311++G**	Add diffuse functions to 6-311G**.
   6-311++G(2df,2pd)	Improve the polarization to the 6-311++G** basis set.
   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.
   G3Large	An extension of 6-311G** with more flexible polarization functions (2df) and polarization of the core electrons. (3d2f on Na-Ar). This basis set is used as the 'limiting HF' basis set in the G3 method.
   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).
   aug-cc-pCVQZ	Expands cc-pCVQZ with some diffuse (aug: spdf) and some core polarization functions (C: 3s3p2d1f, 9s).

   
   

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	# basis functions	Energy (au)	SCF cycles	Relative time
   STO-3G	26	-189.534 688 69	14	0.05
   3-21G	48	-190.886 407 54	14	0.2
   6-31G	48	-191.874 189 82	14	0.3
   6-31G*	72	-191.960 613 31	15	1
   6-311G*	90	-192.001 883 12	15	3
   6-311+G*	106	-192.005 994 08	15	6
   6-311++G**	130	-192.015 295 56	15	25
   6-311++G(2df,2pd)	226	-192.029 578 61	15	88
   6-311++G(3df,3pd)	264	-192.031 627 88	31	235
   cc-pVTZ	204	-192.032 898 46	15	82
   cc-pVQZ	400	-192.046 642 88	30	3400
   aug-cc-pCVQZ	712	-192.047 735 33	19	41000

   
   
   
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 noticably 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
   • "6-31G* Basis Set for Third-Row Atoms", V. Rassolov, J. A. Pople, M. Ratner, P. C. Redfern, and L. A. Curtiss, J. Comp Chem., 22 (9) 976-984