Keyword BASIS

This keyword specifies the basis set.
Options:
$<$Basis$>$ The basis set string $<$Basis$>$ defines the global basis set. If absent, the DZVP basis set is used by default.
Description:
The global basis set (DZVP) is used for all atoms not defined explicitly in the BASIS keyword body. In the BASIS keyword body, basis sets can be assigned to individual atoms by a specific atomic symbol (e.g. H4) or to atom groups by the element symbol (e.g. H). The assignment of the basis set by atomic symbols, element symbols, and global basis set definition has the hierarchy (highest to lowest):

$<$atomic symbol$>$
$<$element symbol$>$
$<$global basis set$>$

Thus any basis set definition for an atom can be overridden by the explicit assignment of the basis set using the atomic symbol. For example, for C$_2$H$_4$ (see input in 4.1.1), the following basis set definition

 
 Basis (DZVP)
 C     (TZVP)
 C1    (STO-3G)

assigns an STO-3G basis to atom C1, a TZVP basis to the other carbon and the DZVP basis to all other atoms. Instead of using basis set strings, the basis set of an atom may also be specified by the Huzinaga notation given in the BASIS file. In that notation, the foregoing basis set definition would read

 
 Basis (DZVP)
 C     (7111/411/1*)
 C1    (33/3)

The file BASIS contains the basis sets listed in Table 7. Other basis sets can be obtained from the Extensible Computational Chemistry Environment Basis Set Database [131] at https://bse.pnl.gov/bse/portal by choosing the deMon2k basis set format.


Table 7: Basis sets available in the deMon2k BASIS file.
Basis Set Elements Description
DZV H, C LDA double $\zeta$ basis set.
DZV-GGA H, C GGA double $\zeta$ basis set.
DZVP H-Xe LDA double $\zeta$ polarization$^a$ basis set [132].
DZVP-GGA H-Xe GGA double $\zeta$ polarization$^a$ basis set [133].
DZVP2 Be-F, Al-Ar, Sc-Zn Modified DZVP basis set.
TZVP H, Li, C-F, Si-Cl LDA triple $\zeta$ polarization basis set.
TZVP-GGA Sc-Cu GGA triple $\zeta$ polarization basis set.
TZVP-FIP1 H, C-F, Na, P, S, Cl, Cu TZVP with field-induced polarization [134,135].
TZVP-FIP2 H, C-F, Na, P, S, Cl, Cu for $\alpha$, $\beta$ (FIP1) and $\gamma$ (FIP2) calculations.
EPR-III H-F EPR basis set [136].
IGLO-II H, Li, B-F, Si NMR basis set [137].
IGLO-III H, B-F, Si, Cr, Fe NMR basis set [137].
aug-PCJ-X H, B-F, Si, P J-Coupling basis set [138].
STO-3G H-Ar HF single $\zeta$ basis set [139].
6-31G** H-Ar HF double $\zeta$ polarization basis set [140].
6-311G** H-Ar MP2 triple $\zeta$ polarization basis set [141].
SAD H, C-F Sadlej FIP basis set [142].
LIC H-Ne Lie-Clementi basis set [143].
WACHTERS Sc-Cu Wachters basis set without $f$ functions [144].
DZ-ANO H-Zn Double $\zeta$ ANO basis set from Roos [145].
def2-TZVPP H-Ar Enlarged triple $\zeta$ polarization basis set [146]
aug-cc-pVXZ H, Li-F, Na, Al, Cl,
Cr, Zn, Mo, Ru, Au Augmented correlation consistent basis [147].
ECP$\vert$SD See Figure 7, top Valence basis for SD ECPs [148].
RECP$\vert$SD See Figure 7, middle Valence basis for SD RECPs [148].
QECP$\vert$SD See Figure 7, bottom Valence basis for SD QECPs [148].
ECP$\vert$LANL2DZ See Figure 8, top Valence basis for LANL ECPs [131].
QECP$\vert$LANL2DZ See Figure 8, bottom Valence basis for LANL QECPs [131].
ECP$\vert$HW K-Cu Hay-Wadt basis for LANL ECPs [149,150,151].
QECP$\vert$HW Rb-Ag, Cs-La, Hf-Au Hay-Wadt basis for LANL QECPs [149,150,151].
MCP$\vert$LK See Figure 9, top Valence basis for LK MCPs [152,153].
RMCP$\vert$LK See Figure 9, bottom Valence basis for LK RMCPs [152,153].
XAS-I Li-F XAS augmentation basis for first row [154].
XAS-II Na-Cl XAS augmentation basis for second row [154].

$^a$Modified for Li and Na [155].


Instead of reading the basis set from the BASIS file, the user can define the basis directly in the input file according to the format:

 Basis
 SYMBOL Read
 N  L  K
    EXPONENT  COEFFICIENT
       :          :
    EXPONENT  COEFFICIENT

Here SYMBOL can be an element (e.g. OXYGEN) or atomic symbol (e.g. O), N and L are the principal and angular momentum quantum numbers of this shell and K is the degree of contraction. A shell collects all contracted orbitals of the same angular momentum quantum number, such as $p_x$, $p_y$, $p_z$ or $d_{xx}$, $d_{xy}$, $d_{xz}$, $d_{yy}$, $d_{yz}$ and $d_{zz}$. The contracted orbitals, $\mu(\bf r)$, are linear combinations of (atom-centered) Gaussian type orbitals (LCGTO), which are called the primitive orbitals, $g(\bf r)$:

$\displaystyle \mu(\bf r)$ $\textstyle =$ $\displaystyle \sum_{k=1}^K d_{\mu k} \, g_k(\bf r)$ (5)
$\displaystyle g_k(\bf r)$ $\textstyle =$ $\displaystyle (x - A_x)^{a_x} \, (y - A_y)^{a_y} \, (z - A_z)^{a_z} \,
e^{- \alpha_k ({\bf r} - {\bf A})^2}$ (6)

The exponents $\alpha_k$ and contraction coefficients $d_{\mu k}$ are listed in free format under the shell definition line, one line for each primitive orbital (EXPONENT and COEFFICIENT). Here is an example for a user-defined basis set input for the oxygen molecule:

 Multiplicity 3
 SCFType ROKS
 VxcType Basis BLYP
 Mixing 0.4
 PRINT GTO CGTO AUXIS
 Geometry Z-Matrix
 O
 O  O  r
 #
 Variables
 r  1.207
 BASIS
 O Read
 1    0    2
 49.98097100        0.4301280000
 8.896588000        0.6789140000
 2    0    2
 1.945237000        0.4947200000E-01
 0.493363000        0.9637820000
 2    1    2
 1.945237000        0.5115410000
 0.493363000        0.6128200000
 AUXIS (GEN-A2)

In this example the basis set was taken from https://bse.pnl.gov/bse/portal using the deMon2k format (see Figure 6). The first line in this format (here 3) must be deleted in the user-defined basis set input. This line defines the number of contractions and is only needed for the basis set definition in the file BASIS. The basis set in this example contains a $1s$, $2s$ and $2p$ shell. Each shell has a contraction degree of two. The $2s$ and $2p$ shells share a common set of exponents. However, in deMon2k both those shells have to be listed independently, as shown here.

Figure 6: STO-2G basis set for oxygen, taken from https://bse.pnl.gov/bse/portal

\includegraphics[width=13.0cm]{/home/gerald/guide.5.0/Figures.5.0/Basis_Set_STO-2G.eps}

The specification of ECP and MCP valence basis sets will also trigger the use of the corresponding effective or model core potential if the ECP and MCP keywords are not specified. Thus, their specification usually is not necessary. An exception is the Hay-Wadt valence basis sets (ECP$\vert$HW and QECP$\vert$HW), which represent alternative choices to the corresponding LANL (Los Alamos National Laboratory) double $\zeta$ valence basis sets. If the Hay-Wadt basis sets are used, the ECP must be specified explicitly with the ECPS keyword. This is a special case of the more general capability of defining basis sets and ECPs or MCPs independently by the BASIS and ECPS or MCPS keywords. Be aware that you can mix any ECPs/MCPs with any basis set, including all-electron ones! Thus, care must be taken if the keywords BASIS and ECPS/MCPS are used together in the deMon2k input. For less experienced users, we recommend using the PRINT keyword with the BASIS options ECPS and MCPS (see example [*] on page [*] of the tutorial) in order to obtain full information about the basis sets and ECPs/MCPs actually utilized. If the ECP or MCP valence basis sets are obtained from external resources like https://bse.pnl.gov/bse/portal, the principal quantum number indexing may be wrong. As a result the tight-binding start density cannot be generated correctly. As a quick fix, we suggest switching to a CORE start density by GUESS CORE (see 4.5.5).