Basis set valence triple zeta

We now examine the results when a set of larger Pople-type basis sets is used. These are based on a triple-zeta valence description. The effects of adding diffuse functions and using multiple sets of polarization effects are considered. The 6-311G basis set is a triple-zeta valence basis set, augmented with a set of polarization functions for all atoms. 6-311++G includes in addition a set of diffuse functions on aU atoms. In the 6-311++G(2df,2pd) and 6-3U++G(3df,3pd), multiple sets of polarizations are used on all atoms. 

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. 

The next step up in basis set size is a Triple Zeta (TZ). Such a basis contains three times as many functions as tire minimum basis, i.e. six s-functions and three p-functions for the first row elements. Some of the core orbitals may again be saved by only splitting the valence, producing a triple split valence basis set. Again the term TZ is used to cover both cases. The names Quadruple Zeta (QZ) and Quintuple Zeta (5Z, not QZ) for the next levels of basis sets are also used, but large sets are often given explicitly in terms of the number of basis functions of each type. 

All calculations were performed with the Gaussian 98 suite of programs [4] using the hybrid DFT/HF B3LYP method. The all-electron 6-311+G(2df) basis set was used for H, O, Si, and Ge, whereas the valence triple zeta pseudopotential basis set of Stoll et al. [5] was used for Sn. The Sn basis set was augmented with diffuse function exponents one-third in size of the outermost valence exponents, the two-membered d-polarization set of Huzinaga, [6] and f(QSn = 0.286. This basis set combination will be called (v)TZ throughout this paper. 

Triple-zeta STF basis sets were used for the valence shells, extended by single-zeta STF to accurately represent the nodal structure of the core. For the transition metals, (n-l)d and ns were considered as valence shells and one np polarization function was added. For C and O, 2s and 2p were the valence shells and a 3d polarization function was added. For H one 2p polarizaition function was added. Core shells were frozen. 

Relativistic all-electron calculations on F2, CI2, Br2,12, and At2 using various correlation methods found that the relativistic corrections were approximately independent of the level of theory used, except for At2 [L. "V sscher and K. G. Dyall, /. Chem. Phys., 104,9040 (1996)]. For example, with a valence triple-zeta polarized basis set, the changes in on going from a nonrelativistic to a relativistic calculation were -8,-7 -7, -7, -7 kcal/mol for Br2 using the HF, MP2, CISD, CCSD, CCSD(T) methods, respectively for I2, these changes were -15, -13, -12.5, -13, -13 kcal/mol for At2, they were -30, -27, -24, -25, -24 kcal/mol. 

Abbreviations used t(0)dzp - basis set is double-zeta polarization on all atoms except oxygen for which it is valence triple-zeta svp - basis set is split-valence plus polarization. B3LYP, BP86, and PW are all gradient-corrected density functionals. See the original papers for references. 

The remarkable structural properties of cubane greatly motivate us to investigate its underlying driving force. We employ an ab initio method to calculate its bond structure for a pure cubane. All the calculations are performed at the Hartree-Fock level by the Molpro package [9]. The basis set used for hydrogen is (4S 1 P)/[2S 1P], whereas for carbon (9S 4P 1D)/[3S 2P ID] is used. The basis functions are all valence triple zeta correlated 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... 

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. 

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. 

The starting point is our previously performed calculations [3] using the Huzinaga basis set [20] (9s) for Be and (4s) for H, triple-zeta contracted, supplemented by the three 2p orbitals proposed for Be by Ahlrichs and Taylor [21] with exponents equal to 1.2, 0.3 and 0.05 respectively. This initial basis set, noted I, includes one s-type bond-function the exponent of which is equal to 0.5647. Several sets of diffuse orbitals have then been added to this basis I. Their corresponding exponents were determined by downward extrapolation from the valence basis set, using the Raffenetti [22] and Ahlrichs [21] procedure. Three supplementary basis sets noted II, III and IV containing respectively one, two and three... 

Stuttgart pseudopotential for Au with a uncontracted (lls/10p/7d/5f) valence basis set and a Dunning augmented correlation consistent valence triple-zeta sets (aug-cc-pVTZ) for both C and N, but with the most diffuse f function removed, was used. 

Schaefer, A. Huher, C. Ahlrichs, R. Fully optimized contracted Gaussian basis sets of triple zeta valence quality for atoms Li to Kr. J. Chem. Phys. 1994, 100, 5829-5835. 

Each CGTO can be considered as an approximation to a single Slater-type orbital (STO) with effective nuclear charge f (zeta). The composition of the basis set can therefore be described in terms of the number of such effective zeta values (or STOs) for each electron. A double-zeta (DZ) basis includes twice as many effective STOs per electron as a single-zeta minimal basis (MB) set, a triple-zeta (TZ) basis three times as many, and so forth. A popular choice, of so-called split-valence type, is to describe core electrons with a minimal set and valence electrons with a more flexible DZ (or higher) set. 

The ECP basis sets include basis functions only for the outermost one or two shells, whereas the remaining inner core electrons are replaced by an effective core or pseudopotential. The ECP basis keyword consists of a source identifier (such as LANL for Los Alamos National Laboratory ), the number of outer shells retained (1 or 2), and a conventional label for the number of sets for each shell (MB, DZ, TZ,...). For example, LANL1MB denotes the minimal LANL basis with minimal basis functions for the outermost shell only, whereas LANL2DZ is the set with double-zeta functions for each of the two outermost shells. The ECP basis set employed throughout Chapter 4 (denoted LACV3P in Jaguar terminology) is also of Los Alamos type, but with full triple-zeta valence flexibility and polarization and diffuse functions on all atoms (comparable to the 6-311+- -G++ all-electron basis used elsewhere in this book). 

Further improvements in the flexibility with which the AOs in Eq. 4 are described mathematically can be obtained by adding a third independent basis function to a split valence basis set. In an anion, electrons are likely to be spread over a greater volume than in a neutral molecule, so adding very dijfuse basis functions to the basis set for a negatively charged molecule is usually important. A fiuther improvement in the basis set for a molecule would be to use two or three independent basis functions to describe, not only the valence AOs, but also the core AOs. Such basis sets are called, respectively, double-zeta or triple-zeta basis sets. 

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