Minimal valence basis set

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. 

What would be the advantages and disadvantages of using the general MNDO/ AMI parameterization procedure, but employing a minimal basis set instead of a minimal valence basis set ... 

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... 

Topiol, S. and Osman, R., On the use of minimal valence basis sets with the coreless Hartree-Fock effective potential, J. Chem. Phys. 73, 5191-5196 (1980). 

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... 

The present section essentially discusses the attempts to build effective valence-only Hamiltonians spanned by a valence minimal basis set, which has been the subject of several tens of papers by Freed et al. (reviewed in Ref. 78 see also Westhaus and Mukherjee ). One should notice first that the purpose of such attempts is two-fold elimination of the core electrons from the explicit treatment and reduction of the basis set for the treatment of the valence states of the molecule to a minimal valence basis set. The effective Hamiltonian should reproduce the energetic results of a calculation including the core electrons, their exclusion, polarization and correlation effects, and performed in a large basis set (for both the concentrated core distribution and the more diffuse valence cioud). 

From a basic point of view, the two purposes are different and should be distinguished one may be tempted to eliminate the core electrons while keeping a non-minimal valence basis set, as occurs in pseudopotential techniques, on the one hand, while on the other hand, one may try to treat a coreless problem such as a cluster of hydrogen atoms in a minimal basis set, or... 

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. 

In Table 9.19 we compare the local characteristics of the electronic structure determined for the Ti02 crystal with the use of the projection technique and those obtained in an earlier study [623], in which the Wannier-type atomic frmctions of the minimal valence basis set of titanium and oxygen atoms were constructed by the variational method. In [623], the Bloch functions were calculated by the DFT method... 

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, ... 

Since there are two carbon atoms per unit cell and four valence AOs per carbon, we have eight basis functions per unit cell for a minimal valence basis set calculation. Therefore, we expect eight bands. Since the system is planar we can distinguish two n AOs and six a AOs. We know that these two symmetry types will not interact for any k, so we can predict or interpret the a and n band behaviors independently. 

Calculation of the cluster with a minimal valence basis set ... 

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