Dunning contraction

Figure 1.27 The matchings of Huzinaga s sto-ng ls) basis sets to the Is [Slater] function for hydrogen. Note, in particular, the match of the sto-4g) linear combination and the H 2s radial function for later comparison with the Dunning contraction of this basis set.

Figure 1.29 Detail from the interactive spreadsheet and the graph for the matches of the Huzinaga and Dunning contracted bases with the Is orbital function for hydrogen from Table 1.1. This diagram presents the results for the c and c starting choices of 0.1 and 0.929.

Many basis sets are just identihed by the author s surname and the number of primitive functions. Some examples of this are the Huzinaga, Dunning, and Duijneveldt basis sets. For example, D95 and D95V are basis sets created by Dunning with nine s primitives and hve p primitives. The V implies one particular contraction scheme for the valence orbitals. Another example would be a basis set listed as Duijneveldt 13s8p . 

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 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. 

Gaussian Basis Functions for use in Molecular Calculations III Contraction of (10s, 6p) Atomic Basis Sets for the First-Row Atoms T. FI. Dunning, Jr... 

Take note of Dunning s notation. He writes the primitives (10s6p) and the contracted basis functions in square brackets [5s3p]. To give a detailed example, consider the oxygen atom set in Table 9.7. 

Table 9.7 Dunning s [5s3p] contraction scheme for Huzinaga s (10s6p)...

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. 

The atomic basis consists in a double-zeta set expanded with polarization functions (DZP) and augmented by diffuse functions (DZPR). Exponents and contraction coefficient are from McLean and Chandler 1980 [18] diffuse functions, centered on the heavy atoms with exponents of 0.023 for the s orbitals and 0.021 for the p orbitals are from Dunning and Hay 1977 [34]. Extension of the DZP basis set with two sets of diffuse s (0.0437, 0.0184) and p (0.0399, 0.0168) functions (DZPRR) has also been tested. 

HF molecule we use the Dunning s contraction [As2pl2s [24] of Huzinaga s 9s5p As) [25] primitive set, augmented with a d polarization function with exponent 1.6 for F, and a set of p functions for H with exponent 0.75. We run different calculations for the equilibrium distance Re = 1.733 bohr), 1.5 Re, 2.0 Re and 3.0 Re. In this case, Cartesian Gaussians with 6fil-functions are used. Comparison is made with nearFCI (nFCI, up to sextuple excitation, i.e. CISDTQQS) [26]. 

H2O we also use the Dunning s contraction of Huzinaga s basis. Polarization exponent for oxygen is 1.2, while for the set of p orbitals of H a = 0.8. Water molecule is stretched symetrically, with the equilibrium geometry defined in [27]. Calculations are made at Re, 1.5 Re and 2.0 R . Spherical Gaussians (5 7-orbitals) were used. 

Department of Chemistry, Washington State University Current address Molecular Research Institute, 845 Page Mill Road, Palo Alto CA 94304, USA Electronic mail addresses t vanmourik pnl.gov, ak wilson pnl.gov, ka peterson pnl.gov, woon hecla.molres.gov, and th dunning pnl.gov The Pacific Northwest National Laboratory is operated for the U.S. Department of Energy by Battelle Memorial Institute under Contract No. DE-AC06-76RLO 1830. 

These are SCF results obtained with the GTO(9i 5p 6i) [5i 3p 3i] basis using Dunning s exponents [85] and optimum contraction vectors [85]. The error (A ) represents the difference between our calculation using Eqs. (4.1) and (3.27) and the genuine SCF result it is positive whenever E/7] >2 and negative when... 

In recent years a compromise has been found which presently dominates polyatomic calculations. Each function fj is expanded as a linear combination of gaussian orbitals (f is then called a contracted gaussian function). Since this is basically a numerical fitting procedure, various choices have been suggested for the contraction scheme. The most popular choices are presently Pople s approximations (15) to Slater orbitals and Dunning s approximations (16) to free atom Hartree-Fock orbitals. 

Dunning-type contractions are characterized by considerable flexibility in the valence part of the primitive space. Typically, the outermost primitive functions are not contracted at all, contraction being reserved for the inner parts of the valence orbitals and the core orbitals. The commonest contracted set of this type is probably the [4s 2p] contraction of the (9s 5p) set. Unfortunately, there are at least two such double zeta contraction schemes in use, as well as an erroneous one. Some care may be required to reproduce results asserted to be obtained with a Huzinaga-Dunning [4s 2p] basis . Because of the relatively flexible contraction scheme these basis sets usually perform well, especially when large primitive sets such as van Duijneveldt s (13s 8p) sets are used. However, it should be noted that such primitive sets are difficult to contract this way without significant loss of accuracy at the atomic SCF level, unless very large contracted sets are used. 

The correlation-consistent basis sets of Dunning axe only beginning to appear, but they show great promise as a way to achieve accuracy similar to that of ANOs, at less computational expense in the integral evaluation (they axe generally the same size, in terms of contracted functions, as the ANO sets). It is interesting to contrast... 

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