Gen GenECPA
set of "standard" basis sets is stored internally in Gaussian (see the
"Basis Sets" section earlier in this chapter); these basis sets may be specified
by including the appropriate keyword within the route section for the calculation.
The Gen keyword allows a user-specified basis set to be used in a Gaussian
calculation. It is used in the place of a basis set keyword or a density fitting
basis set keyword. In this case, the basis set description must be provided as
input (in a separate basis set input section). Gen may be used in
a completely analogous way to specify an alternate density fitting basis set (see
the examples). The GenECP variation may be used to read in both basis
functions and ECPs; it is equivalent to Gen Pseudo=Read.
It is designed for use in ONIOM calculations
in which you want to use a general basis set with ECPs within one ONIOM layer. The
GFPrint keyword may be used to include the
gaussian function table within the output file. The GFInput
keyword may be used to have the table printed in a form which is suitable for
input to Gen. The ExtraBasis keyword
may be used to make additions to standard basis sets. Similarly, the ExtraDensityBasis
keyword may be used to make additions to standard density fitting basis sets BASIS
FUNCTION OVERVIEWA single basis function is composed of
one or more primitive gaussian functions. For example, an s-type basis
function φ_{μ}(r) is:
N is the number of primitive functions composing the basis function, and it
is called the degree-of-contraction of the basis function. The coefficients
d_{iμ} are called contraction coefficients. The
quantities α_{iμ} are the exponents, and f is the
scale factor for the basis function. The maximum degree-of-contraction
permitted in Gaussian is 100.
A shell is a set of basis functions
φ_{μ} with shared exponents. Gaussian supports shells of
arbitrary angular momentum: s, p, d, f, g, h, and so on. An s-shell contains a
single s-type basis function. A p-shell contains the three basis functions p_{X},
p_{Y}, and p_{Z}. An sp-shell contains four basis functions with
common gaussian exponents: one s-type function and the three p-functions p_{X},
p_{Y }and p_{Z}. A d-shell may be defined to contain either
the six second-order functions (d_{X}^{2}, d_{Y}^{2},
d_{Z}^{2}, d_{XY}, d_{XZ}, d_{YZ}), or
the five "pure d" basis functions (d_{ z}^{2}_{-r}^{2},
d_{x}^{2}_{-y}^{2}, d_{xy}, d_{xz},
d_{yz}). Likewise, an f-shell may contain either the 10 third-order gaussians
or the 7 "pure f" functions. Higher order shells function similarly. Note that
the contraction coefficients in a shell must be the same for all functions of
a given angular momentum, but that s and p contraction coefficients can be different
in an sp-shell. A scale factor is also defined for each shell. It is used to scale
all the exponents of primitives in the shell. The program has the ability to convert
between the two types of functions [391]. Consider
the series of basis sets STO-3G, 6-31G, and 6-311G(d) for the carbon atom. With
the STO-3G, basis there are two shells on a carbon atom. One is an s-shell composed
of 3 primitive gaussian functions (which are least-squares fit to a Slater 1s
orbital). The other sp-shell is a least-squares fit of 3 gaussians to Slater 2s
and 2p orbitals with the constraint that the s and p functions have equal exponents.
These expansions are the same for all atoms. Only the scale factors for each shell
differ from atom to atom. For carbon atoms, the 1s- and 2sp-shells have scale
factors of 5.67 and 1.72, respectively. The 6-31G basis on a first row atom has
three shells. One shell is a contraction of six primitive s-type gaussians. The
second shell is a combination of three primitive sp-shells. The third shell consists
of a single sp-function. These functions were optimized for the atom. Scale factors
of 1.00, 1.00, and 1.04, respectively, for each shell for carbon were then determined
by molecular calculations. As its name implies, the 6-311G(d) basis has 5 shells:
an s-shell with 6 primitives, 3 sp-shells with 3, 1, and 1 primitives, and an
uncontracted d-shell. All shells are "unscaled" (have unit scale factor). BASIS
SET INPUT FORMATExternal basis sets are read into Gaussian by specifying
Gen (for general basis) in the route section. The keywords 5D, 6D,
7F, and 10F are used to specify use of Cartesian or pure d and f
(and higher) functions; the defaults are 5D and 7F. All d-shells
in a calculation must have the same number of functions. Similarly, f- and higher
shells must either be all Cartesian or all pure. Defining a shell.
External basis input is handled by the routine GenBas in Link 301. The
basic unit of information that it reads from the basis set input section is the
shell definition block. A shell definition block, together with the global
specification of pure vs. Cartesian functions, contains all necessary information
to define a shell of functions. It consists of a shell descriptor line,
and one or more primitive gaussian lines:
IType NGauss Sc Shell descriptor line: shell type, # primitive gaussians, and scale factor.
α1 d_{1μ} Primitive gaussian specification: exponent and contraction coefficient.
α2 d_{2μ}
...
α_{N} d_{Nμ} There are a total of NGauss primitive gaussian lines.
IType defines the shell
type and shell constraint and may be S, P, D, SP, SPD, F, G, ..., for an
s-shell, p-shell, d-shell, sp-shell, f-shell, g-shell, and so on. NGauss
specifies the number of primitive gaussian shells (the degree of contraction)
for the shell being defined. The shell scale factor is given by Sc (i.e.,
all primitive exponents are scaled by Sc^{2}). The subsequent
NGauss primitive gaussian lines define the exponents α_{k}
and contraction coefficients, d_{k}_{μ}. Each line provides
the exponent for one primitive, followed by its contraction coefficient (or s
and p coefficients for an sp-shell). A second format also exists to specify
a shell as a least-squares gaussian expansion of a Slater orbital. This is requested
by a shell descriptor line of the form STO, IOrb, NGauss,
Sc. IOrb is one of 1S, 2S, 2P, 2SP, 3S, 3P, 3SP, 3D, 4SP, and specifies
which expansion is requested. Note that 2SP requests the best least-squares
fit simultaneously to S and P slater orbitals and is not equivalent to separately
specifying the best S and the best P expansions. NGauss is the same as
above. Gaussian expansions of Slater functions having from 1 to 6 primitives are
available. Sc is the scale factor and hence the exponent of the slater function
being expanded. No primitive gaussian lines are required after a shell descriptor
line requesting an STO expansion.
Defining the basis for an atom or atom
type. One customarily places at least one, and often several, shells on any
given nuclear center ("atom"), via a center definition block. A center
definition block consists of a center identifier line, and one shell
definition block for each shell desired on the center(s) specified. It is
terminated by a line with either asterisks or plus signs in columns 1 through
4:
c_{1} c_{2} ... 0 Center identifier line: specifies applicability for these shells.
IType NGauss Sc First shell definition block.
α_{2} d_{2μ}
...
α_{N} d_{Nμ}
... Additional shell definition blocks.
IType NGauss Sc Final shell definition block.
α_{2} d_{2μ}
...
α_{N} d_{Nμ}
**** Separator: terminates the center definition block.
The center identifier
line specifies a list of centers on which to place the basis functions in the
center definition block, terminated by a 0. It can contain one or more integers,
which are used to indicate the corresponding atom(s) in the molecule specification;
more commonly, it contains a list of atomic symbols to refer to all atoms of a
specific type. Center numbers and atomic symbols may be freely intermixed within
a single center identifier line. To help detect input mistakes, if a center
definition block specifies an atom that is not present in the molecule, the run
is aborted. If the center is preceded by a minus sign (e.g. -H), the basis
set information is simply skipped if no atom of that type is present in the molecule
specification (the terminal zero may also be omitted in this case). The latter
syntax is intended for creating basis set include files that specify a standard
basis set for many atoms; once built, it can be included in its entirety in the
input stream when the basis set is desired, via the include (@) function (as described
earlier in this chapter). A center or atom type may be specified in more
than one center definition block. For example, in the Gaussian 03 basis
set directory—$g03root/g03/basis on UNIX systems—there is one
file which specifies 6-31G as a general basis set (631.gbs), and another
file containing d exponents which would be included as well to specify 6-31G*
(631s.gbs). Every atom from H through Cl is specified in both files, and
in practice both of them would be included (most often along with additional basis
set specifications for those atoms in the molecule for which the 6-31G basis set
is not available). Drawing on Pre-Defined Basis Sets in Gen Input.
Gaussian adds flexibility to general basis set input by allowing them to
include pre-defined basis sets within them. Within a center definition block for
an atom type (or types), an entire shell definition block may be replaced by a
line containing the standard keyword for a pre-defined basis set. In this case,
all of the functions within the specified basis set corresponding to the specified
atom type(s) will be used for all such atoms within the molecule. The SDD,
SHF, SDF, MHF, MDF, MWB forms may be used to specify Stuttgart/Dresden basis
sets/potentials within Gen basis input. Note that the number of core electrons
must be specified. Here is a portion
of the Gen input corresponding to the 6-31+G(d) basis set:
H 0 Applies to all hydrogen atoms.
S 3 1.00
0.1873113696D+02 0.3349460434D-01
0.2825394365D+01 0.2347269535D+00
0.6401216923D+00 0.8137573262D+00
S 1 1.00
0.1612777588D+00 0.1000000000D+01
****
C 0 Applies to all carbons.
S 6 1.00 6-31G functions.
0.3047524880D+04 0.1834737130D-02
0.4573695180D+03 0.1403732280D-01
0.1039486850D+03 0.6884262220D-01
0.2921015530D+02 0.2321844430D+00
0.9286662960D+01 0.4679413480D+00
0.3163926960D+01 0.3623119850D+00
SP 3 1.00
0.7868272350D+01 -0.1193324200D+00 0.6899906660D-01
0.1881288540D+01 -0.1608541520D+00 0.3164239610D+00
0.5442492580D+00 0.1143456440D+01 0.7443082910D+00
SP 1 1.00
0.1687144782D+00 0.1000000000D+01 0.1000000000D+01
D 1 1.00 Polarization function.
0.8000000000D+00 0.1000000000D+01
****
C 0 Applies to all carbons.
SP 1 1.00 Diffuse function.
0.4380000000D-01 0.1000000000D+01 0.1000000000D+01
****
The following Gen input uses the 6-31G(d,p) basis set for the
carbon and hydrogen atoms and the 6-31G†† basis set for the fluorine atoms in
the molecule, and places an extra function only on center number 1 (which happens
to be the first carbon atom in the molecule specification for 1,1-difluoroethylene):
C H 0
6-31G(d,p)
****
F 0
6-31G(d',p')
****
1 0 Place a diffuse function on just one carbon atom.
SP 1 1.00
0.4380000000D-01 0.1000000000D+01 0.1000000000D+01
****
The following job uses the Gaussian include file mechanism
to specify the basis functions for chromium:
# Becke3LYP/Gen Opt Test
HF/6-31G(*) Opt of Cr(CO)6
molecule specification
C O 0
6-31G(d)
****
@/home/gwtrucks/basis/chrome.gbs/N
Note that .gbs is the conventional extension for basis set files
(for gaussian basis set). The following example uses general basis
set input to specify both the basis set and the density fitting basis set.
# RBLYP/GEN/GEN 6D
HCl: reading in 6-31g* AO basis and DGA1 fitting set.
6D is specified because the default for general basis
input is 5D but the 6-31g* basis is defined to use 6D
0,1
cl
h,1,1.29
! here are the 6-31g* basis sets for Cl and H
cl 0
S 6 1.00
0.2518010000D+05 0.1832959848D-02
0.3780350000D+04 0.1403419883D-01
0.8604740000D+03 0.6909739426D-01
0.2421450000D+03 0.2374519803D+00
0.7733490000D+02 0.4830339599D+00
0.2624700000D+02 0.3398559718D+00
SP 6 1.00
0.4917650000D+03 -0.2297391417D-02 0.3989400879D-02
0.1169840000D+03 -0.3071371894D-01 0.3031770668D-01
0.3741530000D+02 -0.1125280694D+00 0.1298800286D+00
0.1378340000D+02 0.4501632776D-01 0.3279510723D+00
0.5452150000D+01 0.5893533634D+00 0.4535271000D+00
0.2225880000D+01 0.4652062868D+00 0.2521540556D+00
SP 3 1.00
0.3186490000D+01 -0.2518280280D+00 -0.1429931472D-01
0.1144270000D+01 0.6158925141D-01 0.3235723331D+00
0.4203770000D+00 0.1060184328D+01 0.7435077653D+00
SP 1 1.00
0.1426570000D+00 0.1000000000D+01 0.1000000000D+01
D 1 1.00
0.7500000000D+00 0.1000000000D+01
****
h 0
S 3 1.00
0.1873113696D+02 0.3349460434D-01
0.2825394365D+01 0.2347269535D+00
0.6401216923D+00 0.8137573261D+00
S 1 1.00
0.1612777588D+00 0.1000000000D+01
****
! here are the DGA1 fitting sets for Cl and H
cl 0
S 1 1.00
0.2048000000D+05 0.1000000000D+01
S 1 1.00
0.4096000000D+04 0.1000000000D+01
S 1 1.00
0.1024000000D+04 0.1000000000D+01
S 1 1.00
0.2560000000D+03 0.1000000000D+01
S 1 1.00
0.6400000000D+02 0.1000000000D+01
SPD 1 1.00
0.2000000000D+02 0.1000000000D+01 0.1000000000D+01 0.1000000000D+01
SPD 1 1.00
0.4000000000D+01 0.1000000000D+01 0.1000000000D+01 0.1000000000D+01
SPD 1 1.00
0.1000000000D+01 0.1000000000D+01 0.1000000000D+01 0.1000000000D+01
SPD 1 1.00
0.2500000000D+00 0.1000000000D+01 0.1000000000D+01 0.1000000000D+01
****
h 0
S 1 1.00
0.4500000000D+02 0.1000000000D+01
S 1 1.00
0.7500000000D+01 0.1000000000D+01
S 1 1.00
0.1500000000D+01 0.1000000000D+01
S 1 1.00
0.3000000000D+00 0.1000000000D+01
****
If you wanted to specify the density fitting basis
set with general basis set input, then you would use a route section like this
one (substituting the appropriate basis set for your problem):
# RBLYP/6-31G(d,p)/Gen 6D
ExtraBasis,
ExtraDensityBasis, GFInput,
GFPrint, Pseudo |