Zeta Basis Sets

A triple-zeta (TZ) basis in which tlnee times as many STOs or CGTOs are used as the number of core and valence AOs (and, yes, there now are quadniple-zeta (QZ) and higher-zeta basis sets appearing in the literature). 

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... 

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. 

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. 

Even larger basis sets are now practical for many systems. Such basis sets add multiple polarization functions per atom to the triple zeta basis set. For example, the 6-31G(2d) basis set adds two d functions per heavy atom instead of just one, while the 6-311++G(3df,3pd) basis set contains three sets of valence region functions, diffuse functions on both heavy atoms and hydrogens, and multiple polarization functions 3 d functions and 1 f function on heavy atoms and 3 p functions and 1 d function on hydrogen atoms. Such basis sets are useful for describing the interactions between... 

The experimental bond length is 1.476. Both the triple zeta basis set and multiple polarization functions are needed to produce a very accurate structure for this molecule. 

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. 

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. 

From a basis set study at the CCSD level for the static hyperpolarizability we concluded in Ref. [45] that the d-aug-cc-pVQZ results for 7o is converged within 1 - 2% to the CCSD basis set limit. The small variations for the A, B and B coefficients between the two triple zeta basis sets and the d-aug-cc-pVQZ basis, listed in Table 4, indicate that also for the first dispersion coefficients the remaining basis set error in d-aug-cc-pVQZ basis is only of the order of 1 - 2%. This corroborates that the results for the frequency-dependent hyperpolarizabilities obtained in Ref. [45] by a combination of the static d-aug-cc-pVQZ hyperpolarizability with dispersion curves calculated using the smaller t-aug-cc-pVTZ basis set are close to the CCSD basis set limit. 

The calculations were performed using a double-zeta basis set with addition of a polarization function and lead to the results reported in Table 5. The notation used for each state is of typical hole-particle form, an asterisc being added to an orbital (or shell) containing a hole, a number (1) to one into which an electron is promoted. In the same Table we show also the frequently used Tetter symbolism in which K indicates an inner-shell hole, L a hole in the valence shell, and e represents an excited electron. The more commonly observed ionization processes in the Auger spectra of N2 are of the type K—LL (a normal process, core-hole state <-> double-hole state ) ... 

In a previous work [1,2], we were interested in the calculation of second order hyperpolarizabilities of eonjugated systems including substituted benzenes, pyridine N-oxydes and vinyl oligomers, in relation with non linear optical activity [3]. We showed that MNDO ealeulations were in good agreement with SCF ab initio results obtained using a double zeta basis set plus polarization and diffuse orbitals. 

The Veillard basis set [23] (1 ls,9p) has been used for A1 and Si, and the (1 ls,6p) basis of the same author has been retained for Mg. However, three p orbitals have been added to this last basis set, their exponents beeing calculated by downward extrapolation. The basis sets for Al, Si and Mg have been contracted in a triple-zeta type. For the hydrogen atom, the Dunning [24] triple-zeta basis set has been used. We have extended these basis sets by mean of a s-type bond function. We have optimized the exponents a and locations d of these eccentric polarization functions, and the internuclear distance R of each of the studied molecules. These optimized parameters are given in Table 3. 

Details of the extended triple zeta basis set used can be found in previous papers [7,8]. It contains 86 cartesian Gaussian functions with several d- and f-type polarisation functions and s,p diffuse functions. All cartesian components of the d- and f-type polarization functions were used. Cl wave functions were obtained with the MELDF suite of programs [9]. Second order perturbation theory was employed to select the most energetically double excitations, since these are typically too numerous to otherwise handle. All single excitations, which are known to be important for describing certain one-electron properties, were automatically included. Excitations were permitted among all electrons and the full range of virtuals. 

Andzelm and Wimmer, 1992, published one of the first comprehensive studies on the performance of approximate density functional theory in which optimized molecular geometries were reported. These authors computed the geometries of several organic species containing the atoms C, N, O, H, and F at the local SVWN level, using a polarized double-zeta basis set optimized for LDA computations. Some trends have been discerned... 

The theory described in the previous section is now applied to beryllium metal. Accurate low temperature data was taken from the paper of Larsen and Hansen [20]. (But note that in (20) I used the structure factors multiplied by 1000, as given in then-paper.) For the orthogonalisation, all nearest neighbours we included within the first shell. There were 12 atoms. A triple zeta basis set from Ref. [21] was used. There are 182 basis functions and 361 independent parameters in the wave function, whereas there are 58 experimental measurements. Figure 1 shows a plot of the x2 agreement statistic as a function of the parameter X for k = 0.2. Larger values of k caused... 

Dunning has developed a series of correlation-consistent polarized valence n-zeta basis sets (denoted cc-pVnZ ) in which polarization functions are systematically added to all atoms with each increase in n. (Corresponding diffuse sets are also added for each n if the prefix aug- is included.) These sets are optimized for use in correlated calculations and are chosen to insure a smooth and rapid (exponential-like) convergence pattern with increasing n. For example, the keyword label aug-cc-pVDZ denotes a valence double-zeta set with polarization and diffuse functions on all atoms (approximately equivalent to the 6-311++G set), whereas aug-cc-pVQZ is the corresponding quadruple-zeta basis which includes (3d2flg,2pld) polarization sets. 

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