Gen
GenECP

DESCRIPTION

A set of standard basis sets is stored internally in Gaussian (see theBasis Setssection earlier in this chapter); these basis sets may be specified by including the appropriate keyword within the route section for the calculation. TheGenkeyword 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).

Genmay be used in a completely analogous way to specify an alternate density fitting basis set (see the examples).

TheGenECPvariation may be used to read in both basis functions and ECPs; it is equivalent toGen Pseudo=Read. It is designed for use inONIOMcalculations in which you want to use a general basis set with ECPs within one ONIOM layer.

TheGFPrintkeyword may be used to include the gaussian function table within the output file. TheGFInputkeyword may be used to have the table printed in a form which is suitable for input toGen. TheExtraBasiskeyword may be used to make additions to standard basis sets. Similarly, theExtraDensityBasiskeyword may be used to make additions to standard density fitting basis sets.

A brief general overview of basis functions is provided as the final subsection of this discussion.

BASIS SET INPUT FORMAT

External basis sets are read into Gaussian by specifyingGen(for general basis) in the route section. The keywords5D,6D,7F, and10Fare used to specify use of Cartesian or pure d and f (and higher) functions; the defaults are5Dand7F. 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 routineGenBasin Link 301. The basic unit of information that it reads from the basis set input section is theshell 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 ashell descriptorline, and one or moreprimitive gaussianlines:

ITypedefines the shell type and shell constraint and may beS,P,D,SP,SPD,F,G, …, for an s-shell, p-shell, d-shell, sp-shell, f-shell, g-shell, and so on.NGaussspecifies the number of primitive gaussian shells (the degree of contraction) for the shell being defined. The shell scale factor is given bySc(i.e., all primitive exponents are scaled bySc²).

The subsequentNGaussprimitive gaussian lines define the exponents α_kand contraction coefficients, d_kμ. 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 formSTO,IOrb,NGauss,Sc. IOrbis one of1S,2S,2P,2SP,3S,3P,3SP,3D,4SP, and specifies which expansion is requested. Note that2SPrequests 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.NGaussis the same as above. Gaussian expansions of Slater functions having from 1 to 6 primitives are available.Scis 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 acenter definition block. A center definition block consists of acenter identifier line, and oneshell definition blockfor 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:

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 09 basis set directory—$g09root/g09/basison 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).

Basis set transformation option to the Integral keyword.Several options to theIntegralkeyword control whether/how generalized contraction basis sets are transformed to reduce the number of primitives.Int=BasisTransform=Nsays to transform generalized contraction basis sets to reduce the number of primitives, neglecting primitives with coefficients of 10^-Nor less. This is the default, withN=4.Int=ExactBasisTransformsays to transform generalized contraction basis sets to reduce the number of primitives, but using only transformations which are exact (do not change the computed energy). Finally,Int=NoBasisTransformsays not to transform generalized contraction basis sets to reduce the number of primitives.

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.

TheSDD,SHF,SDF,MHF,MDF,MWBforms may be used to specify Stuttgart/Dresden basis sets/potentials withinGenbasis input. Note that the number of core electrons must be specified. The ECP potential namedef2or the synonymQZVcan be used inGenECPinput to request the potentials which are used with both the def2 and QZV basis sets.

EXAMPLES

Here is a portion of theGeninput corresponding to the 6-31+G(d) basis set:

H 0Applies 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 0Applies to all carbons.S 6 1.006-31G 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 1.00Polarization function.0.8000000000D+00 0.1000000000D+01 **** C 0Applies to all carbons.SP 1 1.00Diffuse function.0.4380000000D-01 0.1000000000D+01 0.1000000000D+01 ****

The followingGeninput 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 0Place 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)6molecule specificationC O 0 6-31G(d) **** @/home/gwtrucks/basis/chrome.gbs/N

Note that.gbsis the conventional extension for basis set files (forgaussian 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 000000D+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

RELATED KEYWORDS

ExtraBasis,ExtraDensityBasis,GFInput,GFPrint,Integral,Pseudo

BASIS FUNCTION OVERVIEW

A singlebasis functionis composed of one or moreprimitive gaussian functions. For example, an s-type basis function φ_μ(r) is:

S-Type Basis Function

Nis the number of primitive functions composing the basis function, and it is called thedegree-of-contractionof the basis function. The coefficientsd_iμare calledcontraction coefficients. The quantities α_iμare the exponents, andfis thescale factorfor the basis function. The maximum degree-of-contraction permitted in Gaussian is 100.

Ashellis a set of basis functions φ_μwith 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_Yand p_Z.

A d-shell may be defined to contain either the six second-order functions (d_X², d_Y², d_Z², d_XY, d_XZ, d_YZ), or the five so-called “pure d” basis functions (d_z²_-r², d_x²_-y², 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[Schlegel95a].

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).

Last update: 2 May 2013