Slater-type orbitals minimal valence

The complete neglect of differential overlap (CNDO) method is the simplest of the neglect of differential overlap (NDO) methods. This method models valence orbitals only using a minimal basis set of Slater type orbitals. The CNDO method has proven useful for some hydrocarbon results but little else. CNDO is still sometimes used to generate the initial guess for ah initio calculations on hydrocarbons. 

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. 

MNDO [37], a modified NDDO (Section 6.2.5) method, was reported in 1977 [38]. MNDO is conveniently explained by reference to CNDO (Section 6.2.3). MNDO is a general geometry method with a minimal valence basis set of Slater-type orbitals. The Fock matrix elements are calculated using Eq. 6.1=5.82. We discuss the core and two-electron integrals in the same order as for CNDO. 

The HF method represents a point of departure in electronic structure theory. One direction involves improvement of the accuracy by including electron correlation (see Section n.B.3.). Semiempirical methods, however, try to provide moderate accuracy, but at much lower cost than that of ab initio methods. Therefore, only valence electrons are treated explicitly and core electrons are replaced by an effective core (covering nucleus plus core electrons) and a minimal basis of orthogonal Slater-type orbitals (usually only s and p types) is chosen to describe the valence electrons. 

For SCF calculations on diatomic molecules, one can use Slater-type orbitals [Eq. (11.14)] centered on the various atoms of the molecule as the basis functions. (For an alternative choice, see Section 15.4.) The procedure used to find the coefficients Cj, of the basis functions in each SCF MO is discussed in Section 14.3. To have a complete set of AO basis functions, an infinite number of Slater orbitals are needed, but the true molecular Hartree-Fock wave function can be closely approximated with a reasonably small number of carefully chosen Slater orbitals. A minimal basis set for a molecular SCF calculation consists of a single basis function for each inner-sheU AO and each valence-shell AO of each atom. An extended basis set is a set that is larger than a minimal set. Minimal-basis-set SCF calculations are easier than extended-basis-set calculations, but the latter are much more accurate. 

The simplest level of the nonempirical (ab initio) and semiempirical all-valence calculations is the use of a minimal basis set of AO s where each AO in the expansion of Eq. (2.3) is represented by one function, for example, by a Slater-type orbital (STO) ... 

A second example is the minimal-basis-set (MBS) Hartree-Fock wave function for the diatomic molecule hydrogen fluoride, HF (Ransil 1960). The basis orbitals are six Slater-type (i.e., single exponential) functions, one for each inner and valence shell orbital of the two atoms. They are the Is function on the hydrogen atom, and the Is, 2s, 2per, and two 2pn functions on the fluorine atom. The 2sF function is an exponential function to which a term is added that introduces the radial node, and ensures orthogonality with the Is function on fluorine. To indicate the orthogonality, it is labeled 2s F. The orbital is described by... 

The STO basis set of the DZ type ean be approximated by split polynomials of the Gaussian-type functions M-NP G. Each inner AO is replaced by M GTO orbitals, the valence 2s orbital—by AT, while the p orbital—by P GTO functions. For example, the 4-31 G basis set describes every inner (Is) orbital by four GTO s, every valence 2s AO by three GTO s and every valence p AO by one GTO. It is important to point out that whereas in the case of the minimal basis set of the NG type the accuracy level of the minimal STO basis set cannot be attained even at great values of N, the use of the split-valence GTO M-NPG basis sets allows the Slater basis set level to be exceeded. 

At the semiempirical level, explicit treatment is given to valence shell electrons only, and a minimal basis set of Slater-type s and p orbitals is assigned to each atom. The combined set of atomic basis functions (xi. Xz. . Ywl S used to... 

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