Double-zeta

A double-zeta (DZ) basis in which twice as many STOs or CGTOs are used as there are core and valence AOs. The use of more basis functions is motivated by a desire to provide additional variational flexibility so the LCAO-MO process can generate MOs of variable difhiseness as the local electronegativity of the atom varies. 

Because ol Lhe use of Lwo double-precision words for each in tegral. IlyperCbem needs, for example, ahoiil 44 MByles of computer mam memory and/or disk space Lo store the elecLroii repulsion inlejrrals for benzene wilh a double-zeta 6-i lG basis set. 

Double zeta valence or triple zeta valence calculations can be carried out by putting DZV or TZV in place of STO NGAUSS = 3 in the second line of the INPUT file in the GAMESS implementation. The calculated energies become progressively lower (better) for double and triple zeta basis sets... 

Plot the curve of the bond energy of H2 vs. intemuclear distance for the H2 molecule using the STO-3G, double zeta valence (DZV), and triple zeta valence (TZV) basis sets in the GAMESS implementation. 

A double-zeta (DZ) basis in which twice as many STOs or CGTOs are used as there are... 

An older, but still used, notation specihes how many contractions are present. For example, the acronym TZV stands for triple-zeta valence, meaning that there are three valence contractions, such as in a 6—311G basis. The acronyms SZ and DZ stand for single zeta and double zeta, respectively. A P in this notation indicates the use of polarization functions. Since this notation has been used for describing a number of basis sets, the name of the set creator is usually included in the basis set name (i.e., Ahlrichs VDZ). If the author s name is not included, either the Dunning-Hay set is implied or the set that came with the software package being used is implied. 

SBKJC VDZ Available for Li(4.v4/>) through Hg(7.v7/ 5d), this is a relativistic basis set created by Stevens and coworkers to replace all but the outermost electrons. The double-zeta valence contraction is designed to have an accuracy comparable to that of the 3—21G all-electron basis set. Hay-Wadt MB Available for K(5.v5/>) through Au(5.v6/ 5r/), this basis set contains the valence region with the outermost electrons and the previous shell of electrons. Elements beyond Kr are relativistic core potentials. This basis set uses a minimal valence contraction scheme. These sets are also given names starting with LA for Los Alamos, where they were developed. 

LANL2DZ Available for H(4v) through Vu ls6p2d2f), this is a collection of double-zeta basis sets, which are all-electron sets prior to Na. 

Since the basis set is obtained from atomic calculations, it is still desirable to scale exponents for the molecular environment. This is accomplished by defining an inner valence scale factor and an outer valence scale factor ( double zeta ) and multiplying the corresponding inner and outer a s by the square of these factors. Only the valence shells are scaled. 

Because of the use of two double-precision words for each integral, HyperChem needs, for example, about 44 MBytes of computer main memory and/or disk space to store the electron repulsion integrals for benzene with a double-zeta 6-3IG basis set. 

The double zeta basis sets, such as the Dunning-Huzinaga basis set (D95), form all molecular orbitals from linear combinations of two sizes of functions for each atomic orbital. Similarly, triple split valence basis sets, like 6-3IIG, use three sizes of contracted functions for each orbital-type. 

Optimize these three molecules at the Hartree-Fock level, using the LANL2DZ basis set, LANL2DZ is a double-zeta basis set containing effective core potential (ECP) representations of electrons near the nuclei for post-third row atoms. Compare the Cr(CO)5 results with those we obtained in Chapter 3. Then compare the structures of the three systems to one another, and characterize the effect of changing the central atom on the overall molecular structure. 

We refer to such a basis set as a double zeta basis set. Where the minimal basis set for atomic lithium had a 1 s exponent of 2.6906, the double zeta basis set has two Is orbitals with exponents 2.4331 and 4.5177 (the outer and inner orbitals). 

A selection of dementi s double zeta basis sets is given in Table 9.4. 

Dunning valence double zeta Dunning (1975) Dunning and Hay (1976)... 

Durming full double zeta. References as above... 

Barone also introduces two new basis sets, EPR-Il and EPR-llI. These are optimized for the calculation of hyperfine coupling constants by density functional methods. EPR-Il is a double zeta basis set with a single set of polarization functions and an enhanced s part. EPR-III is a triple zeta set including diffuse functions, double d polarization functions and a single set off functions. 

The chemical bonding occurs between valence orbitals. Doubling the 1 s-functions in for example carbon allows for a better description of the 1 s-electrons. However, the Is-orbital is essentially independent of the chemical environment, being very close to the atomic case. A variation of the DZ type basis only doubles the number of valence orbitals, producing a split valence basis. In actual calculations a doubling of tire core orbitals would rarely be considered, and the term DZ basis is also used for split valence basis sets (or sometimes VDZ, for valence double zeta). 

Figure 5.1 A double zeta basis allows for different bonding in different directions...

Like Daw and Baskes, we use the double-zeta wave functions of Clementi and Roetti for the calculation of the effective electronic densities... 

DZ double-zeta STO HF Hartree-Fock limit STO AE all electrons PP pseudopotential, this calculation. Energies are in a.u., and DZ and HF results are from Reference 4. 

The starting point to obtain a PP and basis set for sulphur was an accurate double-zeta STO atomic calculation4. A 24 GTO and 16 GTO expansion for core s and p orbitals, respectively, was used. For the valence functions, the STO combination resulting from the atomic calculation was contracted and re-expanded to 3G. The radial PP representation was then calculated and fitted to six gaussians, serving both for s and p valence electrons, although in principle the two expansions should be different. Table 3 gives the numerical details of all these functions. 

More definite evidence comes from an MO study of the S—O stretching in dimethyl sulphoxide9, where three basis sets were employed a STO-3G one (I), a 4-31G one (double-zeta, II) and a 3G + d one (III). Table 6 reports the main results the small effect of the double-zeta, and the dramatic effect of the 3d functions, are clearly visible. Notice also how the C—S bond length and the bond angles are by far less sensitive to basis set changes. 

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