Orbital minimal valence

The contracted basis in Figure 28.3 is called a minimal basis set because there is one contraction per occupied orbital. The valence region, and thus chemical bonding, could be described better if an additional primitive were added to each of the valence orbitals. This is almost always done using the even-tempered method. This method comes from the observation that energy-optimized exponents tend to nearly follow an exponential pattern given by... 

The number No of occupied valence SCF orbitals in a molecule is typically less than the total number Nmb of orbitals in the minimal valence basis sets of all atoms. The full valence MCSCF wavefunction is the optimal expansion in terms of all configurations that can be generated from N b molecular orbitals. Closely related is the full MCSCF wavefunction of all configurations that can be generated from Ne orbitals, where Nc is the number of valence electrons, i.e. each occupied valence orbital has a correlating orbital, as first postulated by Boys (48) and also presumed in perfect pairing models (49,50), We shall call these two types of frill spaces FORS 1 and FORS 2. In both, the inner shell remains closed. 

Fig. 4.26 The simple Huckel method normally uses only one basis function per heavy atom only one 2p orbital on each carbon, oxygen, nitrogen, etc., ignoring the hydrogens. The extended Huckel method uses for each carbon, oxygen, nitrogen, etc., a 2s and three 2p orbitals, and for each hydrogen a Is orbital. This is called a minimal valence basis 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. 

A minimal basis set is bigger than a minimal valence basis set by the inclusion of core atomic orbitals, e.g. a Is AO for carbon, and Is, 2s, and three 2p AOs for silicon. Including these in the electronic calculation probably should not lead to... 

The minimal valence basis set here consists of the hydrogen 1 orbital ( i)and the helium 1 orbital ( a)- The needed integrals are 5n = S22 and S 2 = 5ai, where... 

A more balanced description thus requires multiconfiguration self-consistent field (MCSCF)-based methods, where the orbitals are optimized for each particular state or optimized for a suitable average of the desired states (state-averaged MCSCF). In semiempirical methods, however, an MCSCF procedure is normally not required due to the limited flexibility of the minimal valence atomic orbital basis commonly used in these methods. Instead, a multireference Cl method including a limited number of suitably chosen configurations will be appropriate. 

At present, the electronic structure of crystals, for the most part, has been calculated using the density-functional theory in a plane-wave (PW) basis set. The one-electron Bloch functions (crystal orbitals) calculated in the PW basis set are delocalized over the crystal and do not allow one to calculate the local characteristics of the electronic structure. As a consequence, the functions of the minimal valence basis set for atoms in the crystal should be constructed from the aforementioned Bloch functions. There exist several approaches to this problem. The most consistent approach was considered above and is associated with the variational method for constructing the Wannier-type atomic orbitals (WTAO) localized at atoms with the use of the calculated Bloch functions. Another two approaches use the so-called projection technique to connect the calculated in PW basis Bloch states with the atomic-like orbitals of the minimal basis set. 

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. 

Chemists who have had some experience in these matters are likely to prefer thinking in terms of symmetry orbitals. Thus, in thinking of ammonia, they are likely to take as a minimal valence basis set the functions A2s, 2, ... 

A minimal basis in which the number of STO or GOTO orbitals is equal to the number of core and valence AOs in tlie atom. 

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