5.2.1. Extra information about basis sets and integrals¶
5.2.1.1. Basis set format¶
The Inline option for a basis set will read the basis set as defined by the following pseudo code.
Read Charge, lAng
Do iAng = 0, lAng
Read nPrim, nContr
Read (Exp(iPrim),iPrim=1,nPrim)
Do iPrim=1,nPrim
Read (Coeff(iPrim,iContr),iContr=1,nContr)
End Do
End Do
where Charge
is the nuclear charge, lAng
is the highest angular
momentum quantum number, nPrim
is the number of primitive functions
(exponents) for a given shell, and nContr
is the number of contracted
functions for a given shell.
The following is an example of a DPZ basis set for carbon. Normally, however, the basis set will be read from a library file following the specified label (like, e.g., C.DZP…4s2p1d.), and not be inserted inline at the input file.
Basis set  Start defining a basis set
C.DZP.Someone.9s5p1d.4s2p1d. / inline  Definition in input stream
6.0 2  charge, max lquantum no.
9 4  no. of prim. and contr. sfunctions
4232.61  sexponents
634.882
146.097
42.4974
14.1892
1.9666
5.1477
0.4962
0.1533
.002029 .0 .0 .0  scontraction matrix
.015535 .0 .0 .0
.075411 .0 .0 .0
.257121 .0 .0 .0
.596555 .0 .0 .0
.242517 .0 .0 .0
.0 1.0 .0 .0
.0 .0 1.0 .0
.0 .0 .0 1.0
5 2  no. of prim. and contr. pfunctions
18.1557  pexponents
3.98640
1.14290
0.3594
0.1146
.018534 .0  pcontraction matrix
.115442 .0
.386206 .0
.640089 .0
.0 1.0
1 1  no. of prim. and contr. dfunctions
.75  dexponents
1.0  dcontraction matrix
C1 0.00000 0.00000 0.00000  atomlabel, Cartesian coordinates
C2 1.00000 0.00000 0.00000  atomlabel, Cartesian coordinates
End Of Basis  end of basis set definition
5.2.1.2. The basis set label and the ECP libraries¶
The label within the ECP library is given as input in the line following the keyword BASIS SET. The label defines either the valence basis set and core potential which is assigned to a frozencore atom or the embedding potential which is assigned to an environmental frozeion. Here, all the comments made about this label in the section The basis set label and the basis set library for allelectron basis sets stand, except for the following changes:
The identifier
type
must beECP
orPP
.The identifier
aux
specifies the kind of the potential. It is used, for instance, to choose between nonrelativistic, Cowan–Griffin, or nopair Douglas–Kroll relativistic core potentials (i.e.Pt.ECP.Casarrubios.13s10p9d5f.1s2p2d1f.16eNRAIMP.
orPt.ECP.Casarrubios.13s10p9d5f.1s2p2d1f.16eCGAIMP.
orPt.ECP.Rakowitz.13s10p9d6f.5s4p4d2f.18eNPAIMP.
) and to pick up one among all the embedding potentials available for a given ion (i.e.F.ECP.LopezMoraza.0s.0s.0eAIMPKMgF3.
orF.ECP.LopezMoraza.0s.0s.0eAIMPCsCaF3.
).The identifier
contracted
is used here in order to produce the actual basis set out of the basis set included in the ECP library, which is a minimal basis set (in general contraction form) augmented with some polarization, diffuse, … function. It indicates the number of s, p, … contracted functions in the actual basis set, the result being always a manyprimitive contracted function followed by a number of primitives. As an example,At.ECP.Barandiaran.13s12p8d5f.3s4p3d2f.17eCGAIMP.
will generate a (13,1,1/12,1,1,1/8,1,1/5,1) formal contraction pattern which is in this case a (13,1,1/12,1,1,1/7,1,1/5,1) real pattern. Other contraction patters should be input “Inline”.The user is suggested to read carefully Section 5.2.2 of the tutorials and examples manual before using the ECP utilities.
5.2.1.3. OneElectron Integral Labels¶
The storage of oneelectron integrals on disk is facilitated by the oneelectron integral I/O facility. The internal structure of the oneelectron file and the management is something which the user normally do not need to worry about. However, for the general input section of the FFPT, the user need to know the name and structure of the internal labels which the oneelectron integral I/O facility associates with each type of oneelectron integral. The labels are listed and explained here below for reference. The component index is also utilized by the oneelectron integral I/O facility to discriminate the various components of the oneelectron integrals of a certain type, for example, the dipole moment integrals have three components (1=xcomponent, 2=ycomponent, 3=zcomponent). The component index is enumerated as a canonical index over the powers of the Cartesian components of the operator (e.g. multipole moment, velocity, electric field, etc.). The order is defined by following pseudo code,
Do ix = nOrder, 0, 1
Do iy = nOrderix, 0, 1
iz = nOrderixiy
End Do
End Do,
where nOrder
is the total order of the operator, for example, nOrder=2
for
the electric field gradient and the quadrupole moment operator.
Label 
Explanation 


the 

the overlap matrix used in the semiempirical NDDO method. 

the kinetic energy integrals. 

the electron attraction integrals. 

the electron attraction integrals used in the semiempirical NDDO method. 

the projection integrals used in ECP calculations. 

the M1 integrals used in ECP calculations. 

the M2 integrals used in ECP calculations. 

the spectrally resolved operator integrals used in ECP calculations. 

the external electric field integrals. 

the massvelocity integrals. 

the Darwin oneelectron contact integrals. 

the velocity integrals. 

the electric potential at center 

the electric field at center 

the electric field gradient at center 

the angular momentum integrals. 

the diamagnetic shielding integrals. 

the 

the oneelectron Hamiltonian. 

the hermitized product of angular momentum integrals. 

the atomic mean field integrals. 