Basis set label in input:
8.49.0.2.4 Polarized basis setsThe socalled polarized basis sets are purpose oriented, relatively small GTO/CGTO sets devised for the purpose of accurate calculations of dipole electric properties of polyatomic molecules [166,167,168,169,170]. For each row of the periodic table the performance of the basis sets has been carefully examined in calculations of dipole moments and dipole polarizabilities of simple hydrides at both the SCF and correlated levels of approximation [166,167,168,169,170]. The corresponding results match within a few percent the best available experimental data. Also the calculated molecular quadrupole moments turn out to be fairly close to those computed with much larger basis sets. According to the present documentation the polarized basis GTO/CGTO sets can be used for safe accurate predictions of molecular dipole moments, dipole polarizabilities, and also molecular quadrupole moments by using highlevel correlated computational methods. The use of the polarized basis sets has also been investigated in calculations of weak intermolecular interactions. The interaction energies, corrected for the basis set superposition effect (BSSE), which is rather large for these basis sets, turn out to be close to the best available data. In calculations for molecules involving the 4th row atoms, the property data need to be corrected for the relativistic contribution. The corresponding finite perturbation facility is available [171,172]. It is recommended to use these basis sets with the contraction given in the library. It is of course possible to truncate them further, for example by deleting some polarization functions, but this will lead to a deterioration of the computed properties.

/label 
where ``label'' is the basis set label, as defined below in the input description to SEWARD. Then follows two lines with the appropriate literature reference for that basis set. These cards are read by SEWARD and must thus be included in the library, and may not be blank. Next is a set of comment lines, which begin with an asterisk in column 1, giving some details of the basis sets. A number of lines follow, which specifies the basis set:
The following is an example of an entry in a basis set library.
* This is the Huzinaga 5s,2p set contracted to 3s,2p  Comment
* according to the Dunning paper.  Comment
/H.TZ2P.Dunning.5s2p.3s2p.  Label
Exponents : S. Huzinaga, J. Chem. Phys., 42, 1293(1965).  First ref line
Coefficients: T. H. Dunning, J. Chem. Phys., 55, 716(1971).  Second ref line
1.0 1  Charge, sp
5 3  5s>3s
52.56 7.903 1.792 0.502 0.158  sexponents
0.025374 0.0 0.0  contr. matrix
0.189684 0.0 0.0  contr. matrix
0.852933 0.0 0.0  contr. matrix
0.0 1.0 0.0  contr. matrix
0.0 0.0 1.0  contr. matrix
2 2  2p>2p
1.5 0.5  pexponents
1.0 0.0  contr. matrix
0.0 1.0  contr. matrix
MOLCAS is able to perform effective core potential (ECP) calculations and embedded cluster calculations. In ECP calculations, only the valence electrons of a molecule are explicitly handled in a quantum mechanical calculation, at a time that the core electrons are kept frozen and are represented by ECP's. (An example of this is a calculation on HAt in which only the 5d, 6s and 6p electrons of Astatine and the one of Hydrogen are explicitly considered.) Similarly, in embedded cluster calculations, only the electrons assigned to a piece of the whole system (the cluster) are explicitly handled in the quantum mechanical calculation, under the assumption that they are the only ones relevant for some local properties under study; the rest of the whole system (the environment) is kept frozen and represented by embedding potentials which act onto the cluster. (As an example, calculations on a TlF_{12}^{11} cluster embedded in a frozen lattice of KMgF_{3} can be sufficient to calculate spectroscopical properties of Tl^{+}doped KMgF_{3} which are due to the Tl^{+} impurity.)
In order to be able to perform ECP calculations in molecules, as well as embedded cluster calculations in ionic solids, with the Ab Initio Model Potential method (AIMP) [173,174,175,176,177,178] MOLCAS is provided with the library ECP which includes nonrelativistic and relativistic core ab initio model potentials and embedding ab initio model potentials representing both completecations and completeanions in ionic lattices [174,179].
Before we continue we should comment a little bit on the terminology used here. Strictly speaking, ECP methods are all that use the frozencore approximation. Among them, we can distinguish two families: the `pseudopotential' methods and the `model potential' methods. The pseudopotential methods are ultimately based on the PhillipsKleinman equation [180] and handle valence nodeless pseudo orbitals. The model potential methods are based on the Huzinaga equation [181,182] and handle nodeshowing valence orbitals; the AIMP method belongs to this family. Here, when we use the general term ECP we will be referring to the more particular of AIMP. According to its characteristics, the AIMP method can be also applied to represent frozenions in ionic lattices in embedded cluster calculations; in this case, we will not be very strict in the nomenclature and we will also call ECP's to the frozenion (embedding) ab initio model potentials.
The effective potentials in the libraries include the effects of the atomic core wave functions (embedding ion wave functions) through the following operators:
Given the quality and nonparametric nature of the operators listed above, the flexibility of the basis sets to be used with the AIMP's is crucial, as in any ab initio method.
The valence basis sets included in the libraries have been obtained by energy minimization in atomic valenceelectron calculations, following standard optimization procedures. All the experience gathered in the design of molecular basis sets starting from allelectron atomic basis sets, and in particular from segmented minimal ones, is directly applicable to the AIMP valence basis sets included in the libraries. They are, for nonrelativistic and relativistic CowanGriffin AIMPs, minimal basis sets with added functions, such as polarization and diffuse functions; in consequence, the minimal sets should be split in molecular calculations in order to get reasonable sets (a splitting pattern is recommended in the library for every set); the splitting can be done by means of `the basis set label'. For the relativistic nopair DouglasKroll AIMPs contracted valence basis sets are given directly in a form which is recommended in molecular calculations, i.e. they are of triple zeta quality in the outer shells and contain polarization functions. In both cases these valence basis sets contain very inner primitive GTF's: They are necessary since, typical to a model potential method, the valence orbitals will show correct nodal structure. Finally, it must be noted that the core AIMP's can be safely mixed together with allelectron basis sets.
In AIMP embedded cluster calculations, the cluster basis set, which must be decided upon by the user, should be designed following high quality standard procedures. Very rigid cluster basis sets should not be used. In particular, the presence of the necessary embedding projection operators, which prevent the cluster densities from collapsing onto the crystal lattice, demands flexible cluster bases, including, eventually, components outside the cluster volume.[183] The use of flexible cluster basis sets is then a necessary requirement to avoid artificial frontier effects, not ascribable to the AIMP embedding potentials. This requirement is unavoidable, anyway, if good correlated wave functions are to be calculated for the cluster. Finally, one must remember that the AIMP method does exclude any correlation between the cluster electronic group and the embedding crystal components; in other words, only intracluster correlation effects can be accounted for in AIMP embedded cluster calculations. Therefore the clusterenvironment partition and the choice of the cluster wave function must be done accordingly. In particular, the use of oneatom clusters is not recommended.
Core and embedding AIMP's can be combined in a natural way in valenceelectron, embedded cluster calculations. They can be used with any of the different types of wave functions that can be calculated with MOLCAS.
The list of core potentials and valence basis sets available in the ECP library follows. Although AIMP's exist in the literature for different core sizes, this library includes only those recommended by the authors after numerical experimentation. Relativistic CGAIMP's and NPAIMP's, respectively, and nonrelativistic NRAIMP's are included. Each entry of the CGAIMP's and the NRAIMP's in the list is accompanied with a recommended contraction pattern (to be used in the fifth field). The NPAIMP basis sets are given explicitly in the recommended contraction pattern. For the thirdrow transition metals two NPAIMP basis sets are provided which differ in the number of primitive and contracted f GTFs. For further details, please refer to the literature.[178] For more information about a particular entry consult the ECP library.
The ECP libraries have also been extended to include the socalled nodeless ECPs or pseudo potentials based on the PhillipsKleinman equation [180]. These are included both as explicit and implicit operators. Following the work by M. Pelissier and coworkers [184] the operators of nodeless ECPs can implicitly be fully expressed via spectral representation of operators. The explicit libraries are the ECP.STOLL and ECP.HAYWADT files, all other files are for the implicitly expressed operator. In the list of nodeless ECPs the Hay and Wadt's family of ECPs (LANL2DZ ECPs) [185,186,187] has been included in addition to the popular set of the socalled Stoll and Dolg ECPs [188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212]. Both of them in either the explicit form labeled as HAYWADT and STOLL, or in the implicit form labeled as HW and DOLG. The latter include the recently developed ANObasis sets for actinides [212].
The start of a given basis set and AIMP is identified by the line
where ``label" is defined below,
in the input description to seward.
Then, comment lines, effective charge, and basis set follow,
with the same structure that the allelectron Basis Set Library
(see items 1. to 4. in Sec. .)
Next, the AIMP/ECP/PP is specified as follows:
Below is an example of an entry in the ECP library for an AIMP.
/S.ECP.Barandiaran.7s6p1d.1s1p1d.6eCGAIMP.  label (note that type is ECP) Z.Barandiaran and L.Seijo, Can.J.Chem. 70(1992)409.  1st ref. line core[Ne] val[3s,3p] (61/411/1*)=2s3p1d recommended  2nd ref. line *SQRSP(7/6/1) (61/411/1)  comment line 6.000000 2  eff. charge & highest ang.mom.  blank line 7 1  7s > 1s 1421.989530  sexponent 211.0266560  sexponent 46.72165060  sexponent 4.310564040  sexponent 1.966475840  sexponent .4015383790  sexponent .1453058790  sexponent .004499703540  contr. coeff. .030157124800  contr. coeff. .089332590700  contr. coeff. .288438151000  contr. coeff. .279252515000  contr. coeff. .700286615000  contr. coeff. .482409523000  contr. coeff. 6 1  6p > 1p 78.08932440  pexponent 17.68304310  pexponent 4.966340810  pexponent .5611646780  pexponent .2130782690  pexponent .8172415400E01  pexponent .015853278200  contr. coeff. .084808963800  contr. coeff. .172934245000  contr. coeff. .420961662000  contr. coeff. .506647309000  contr. coeff. .200082121000  contr. coeff. 1 1  1d > 1d .4210000000  dexponent 1.000000000000  contr. coeff. *  comment line * Core AIMP: SQR2P  comment line *  comment line * Local Potential Parameters : (ECP convention)  comment line * A(AIMP)=Zeff*A(ECP)  comment line M1  M1 operator 9  number of M1 terms 237485.0100  M1 exponent 24909.63500  M1 exponent 4519.833100  M1 exponent 1082.854700  M1 exponent 310.5610000  M1 exponent 96.91851000  M1 exponent 26.63059000  M1 exponent 9.762505000  M1 exponent 4.014487500  M1 exponent  blank line .019335998333  M1 coeff. .031229360000  M1 coeff. .061638463333  M1 coeff. .114969451667  M1 coeff. .190198283333  M1 coeff. .211928633333  M1 coeff. .336340950000  M1 coeff. .538432350000  M1 coeff. .162593178333  M1 coeff. M2  M2 operator 0  number of M2 terms COREREP  CoreRep operator 1.0  CoreRep constant PROJOP  Projection operator 1  highest ang. mom. 8 2  8s > 2s 184.666320 18.1126960  1s,2s proj. op. constants 3459.000000  sexponent 620.3000000  sexponent 171.4000000  sexponent 58.53000000  sexponent 22.44000000  sexponent 6.553000000  sexponent 2.777000000  sexponent 1.155000000  sexponent .018538249000 .005054826900  contr. coeffs. .094569248000 .028197248000  contr. coeffs. .283859290000 .088959130000  contr. coeffs. .454711270000 .199724180000  contr. coeffs. .279041370000 .158375340000  contr. coeffs. .025985763000 .381198090000  contr. coeffs. .005481472900 .621887210000  contr. coeffs. .001288714400 .151789890000  contr. coeffs. 7 1  7p > 1p 13.3703160  2p proj. op. constant 274.0000000  pexponent 70.57000000  pexponent 24.74000000  pexponent 9.995000000  pexponent 4.330000000  pexponent 1.946000000  pexponent .8179000000  pexponent .008300916100  cont. coeff. .048924254000  cont. coeff. .162411660000  cont. coeff. .327163550000  cont. coeff. .398615170000  cont. coeff. .232548200000  cont. coeff. .034091088000  cont. coeff. *  comment line Spectral Representation Operator  SR operator Valence primitive basis  SR basis specification Exchange  Exchange operator 1stOrder Relativistic Correction  massvel + Darwin oper. SQR2P  label in QRPLIB End of Spectral Representation Operator  end of SR operator
Below is an example of an entry in the ECP library for a pseudo potential.
/Hg.ECP.Dolg.4s4p2d.2s2p1d.2eMWB  label (note the type ECP) W. Kuechle, M. Dolg, H. Stoll, H. Preuss, Mol. Phys. ref. line 1 74, 1245 (1991); J. Chem. Phys. 94, 3011 (1991).  ref. line 2 2.00000 2  eff. charge & highest ang.mom. *s functions  comment line 4 2  4s > 2s 0.13548420E+01  sexponent 0.82889200E+00  sexponent 0.13393200E+00  sexponent 0.51017000E01  sexponent 0.23649400E+00 0.00000000E+00  contr. coeff. 0.59962800E+00 0.00000000E+00  contr. coeff. 0.84630500E+00 0.00000000E+00  contr. coeff. 0.00000000E+00 0.10000000E+01  contr. coeff. *p functions  comment line 4 2  4p > 2p 0.10001460E+01  pexponent 0.86645300E+00  pexponent 0.11820600E+00  pexponent 0.35155000E01  pexponent 0.14495400E+00 0.00000000E+00  contr. coeff. 0.20497100E+00 0.00000000E+00  contr. coeff. 0.49030100E+00 0.00000000E+00  contr. coeff. 0.00000000E+00 0.10000000E+01  contr. coeff. *d functions  comment line 1 1  1d > 1d 0.19000000E+00  dexponent 0.10000000E+01  contr. coeff. *  comment line PP,Hg,78,5;  PP operator, label, # of core elec., L 1; ! H POTENTIAL  # number of exponents in the H potential 2, 1.00000000,.000000000;  power, exponent and coeff. 3; ! SH POTENTIAL  # number of exponents in the SH potential 2,0.227210000,.69617800;  power, exponent and coeff. 2, 1.65753000,27.7581050;  power, exponent and coeff. 2, 10.0002480,48.7804750;  power, exponent and coeff. 2; ! PH POTENTIAL  # number of exponents in the PH potential 2,0.398377000,2.7358110;  power, exponent and coeff. 2,0.647307000,8.57563700;  power, exponent and coeff. 2; ! DH POTENTIAL  # number of exponents in the DH potential 2,0.217999000,.01311800;  power, exponent and coeff. 2,0.386058000,2.79286200;  power, exponent and coeff. 1; ! FH POTENTIAL  # number of exponents in the FH potential 2,0.500000000,2.6351640;  power, exponent and coeff. 1; ! GH POTENTIAL  # number of exponents in the GH potential 2,0.800756000,13.393716;  power, exponent and coeff. *  comment line Spectral Representation Operator  SR operator End of Spectral Representation Operator  end of SR operator