Minimum basis sets

Pisani [169] has used the density of states from periodic FIP (see B3.2.2.4) slab calculations to describe the host in which the cluster is embedded, where the applications have been primarily to ionic crystals such as LiE. The original calculation to derive the external Coulomb and exchange fields is usually done on a finite cluster and at a low level of ab initio theory (typically minimum basis set FIP, one electron only per atom treated explicitly). 

V. Hydrogen Molecule Minimum Basis Set Calculation VI. Conclusions Appendix A Useful Integrals Acknowledgments References... 

A projected CNDO/INDO guess uses th e com puted coefficien ts from a minimum basis set CXDCi/[NDO calculation and then... 

The Foek matriees (and orbital energies) were generated using standard ST03G minimum basis set SCF ealeulations. The Foek matriees are in the orthogonal basis formed from these orbitals. 

The orbital energies were generated using standard ST03G minimum basis set SCF ealeulations. 

A minimum basis set for molecules containing C, H, O, and N would consist of 2s, 2p, 2py, and 2p oibitals for each C, N, and O and a 1 j orbital for each hydrogen. The basis sets are mathematical expressions describing the properties of the atomic orbitals. 

The self-consistent field function for atoms with 2 to 36 electrons are computed with a minimum basis set of Slater-type orbitals. The orbital exponents of the atomic orbitals are optimized so as to ensure the energy minimum. The analysis of the optimized orbital exponents allows us to obtain simple and accurate rules for the 1 s, 2s, 3s, 4s, 2p, 3p, 4p and 3d electronic screening constants. These rules are compared with those proposed by Slater and reveal the need for the screening due to the outside electrons. The analysis of the screening constants (and orbital exponents) is extended to the excited states of the ground state configuration and the positive ions. 

The first step in reducing the computational problem is to consider only the valence electrons explicitly, the core electrons are accounted for by reducing the nuclear charge or introducing functions to model the combined repulsion due to the nuclei and core electrons. Furthermore, only a minimum basis set (the minimum number of functions necessary for accommodating the electrons in the neutral atom) is used for the valence electrons. Hydrogen thus has one basis function, and all atoms in the second and third rows of the periodic table have four basis functions (one s- and one set of p-orbitals, pj, , Pj, and Pj). The large majority of semi-empirical methods to date use only s- and p-functions, and the basis functions are taken to be Slater type orbitals (see Chapter 5), i.e. exponential functions. 

An ab initio HF calculation with a minimum basis set is rarely able to give more than a qualitative picture of the MOs, it is of very limited value for predicting quantitative features. Introduction of the ZDO approximation decreases the quality of the (already poor) wave function, i.e. a direct employment of the above NDDO/INDO/CNDO schemes is not useful. To repair the deficiencies due to the approximations, parameters are introduced in place of some or all of the integrals. 

Semi-empirical methods are zero-dimensional, just as force field mefhods are. There is no way of assessing the reliability of a given result within the method. This is due to the selection of a fixed (minimum) basis set. The only way of judging results is by comparing the accuracy of other calculations on similar systems with experimental data. 

It should be noted that in the spirit of the global simulation, all the interaction potentials used are obtained from ab initio computations, although at the present time only at the SCF level with minimum basis sets. 

Hamiltonian equation, 512-516 minimum basis set calculation, 542—550 integrals, 551-555... 

Force constants, crude Born-Oppenheimer approximation, hydrogen molecule, minimum basis set calculation, 545-550 Forward peak scattering, electron nuclear... 

The naive concept that a fixed set of valence AOs suffices for all charge states and bonding environments is equivalent to the use of a minimum basis set (e.g., STO-3G), which is known to be quite inadequate for quantitative purposes. Nevertheless, if the AOs are properly allowed to adjust dynamically in the molecular environment, one recovers a minimal-basis description that is surprisingly accurate the natural minimal basis. In the NBO framework the effective natural atomic orbitals are continually optimized in the molecular environment, and the number of important NAOs therefore remains close to minimal, greatly simplifying the description of bonding. 

A minimum basis set of Slater-type orbitals (STO) is used. 

As in the recent QCCD study by Head-Gordon et al. (28, 128), we tested the ECCSD, LECCSD, and QECCSD methods, based on eqs (52)-(59), using the minimum basis set STO-3G (145) model of N2. In all correlated calculations, the lowest two core orbitals were kept frozen. As in the earlier section, our discussion of the results focuses on the bond breaking region, where the standard CCSD approach displays, using a phrase borrowed from ref 128, a colossal failure (see Table II and Figure 2). 

In minimal basis sets, each atom is represented by a single orbital of each type. For example, oxygen is represented by Is, 2s, 2p, 2py, and 2p orbitals only. In double zeta basis sets, twice the functions in the minimum basis sets are used. Extended basis sets generally refer to sets that make use of functions that are more than the minimum basis set. 

Semiempirical methods, on the other hand, utilize minimum basis sets to speed up computations, and the loss in rigor is compensated by the use of experimental data to reproduce important chemical properties, such as the heats of formation, molecular geometries, dipole moments, and ionization potentials (Dewar, 1976 Stewart, 1989a). As a result of their computational simplicity and their chemically useful accuracy, semiempirical methods are widely used, especially when large molecules are involved (see, for example, Stewart, 1989b Dewar et al., 1985 Dewar, 1975). 

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