Molecular orbitals basis set

Del Bene J, Pople JA (1973) Theory of molecular interactions. III. A comparison of studies of H20 polymers using different molecular orbital basis sets. J Chem Phys 58 3605 -3608... 

Piepho has responded to the criticisms of the PKS model by developing an improved version, the MO vibronic coupling model for mixed-valence complexes (32). Multicenter vibrations are now considered and a molecular orbital basis set (as with the three-site model) is used. This model was used to calculate band shape and g values for the Cretuz-Taube ion (33). The MO vibronic coupling model is admittedly more empirical than the three-site model but it has the advantage in being applicable to all mixed-valence complexes. 

Clearly, it is desirable to make the length of the expansion in (15) as short as possible. The number of Slater determinants needed to obtain a given accuracy depends on the molecular orbital basis set used to construct the Slater determinants. There have been several proposals in the recent literature for suitable molecular orbital basis sets.81,88-90 It is generally agreed that the virtual Hartree-Fock orbitals (i.e. those Hartree-Fock orbitals which result from solving the standard Hartree-Fock orbital equations, but which are not used in the Hartree-Fock determinant) are a poor basis for expanding the wavefunction. A very important concept in connection with both the... 

Abstract This work reports the formulation of Shannon entropy indices in terms of seniority numbers of the Slater determinants expanding an A-electron wave fimc-tion. Numerical determinations of those indices prove that they provide a suitable quantitative procedure to evaluate compactness of wave functions and to describe their configurational structures. An analysis of the results, calculated for full configuration interaction wave functions in selected atomic and molecular systems, allows one to compare and to discuss the behavior of several types of molecular orbital basis sets in order to achieve more compact wave... 

Keywords Compactness of wave functions Seniority number Shannon enttopy indices Optimization of molecular orbital basis sets... 

We have determined expansions of wave functions of several atomic and molecular systems in their ground states, at FCI level. These wave functions have been expressed in the three mentioned molecular basis sets CMO, NO, and in order to study their compacmess in different molecular orbital basis sets. Our aim is to analyze the structure and compactness of those expansions by means of the entropic indices proposed in Eqs. (5), (7), and (8) according to the seniority numbers. We have mainly chosen the systems of... 

The results reported in Table 1 also allow one to compare, in terms of the values of the indices ( and lyy, the expansions of the wave fnnctions of these systems according to the molecular orbital basis sets in which they are expressed. As can be seen from that table, the values of both indices are considerably lower in the NO and basis sets than in their CMO counterparts (except for the Be atom in the STO-3G basis set) the Be atom recovers the improvement in the and NO molecular basis sets when the larger cc-pVDZ basis set is used. These results again confirm that the NO and molecular basis sets lead to more compact wave functions, as has been reported in Refs. [6, 9, 11]. These valnes also point out that the Ic and % indices constitute suitable devices to describe quantitatively the compactness of a wave function. The high values found for the indices in the Be and Mg atoms in the three molecular basis sets can be interpreted in terms of the strong correlation exhibited by those systems. The appropriate ground-state wave functions for these atoms reqnire several dominant Slater determinants. The values reported in Table 2 reflect that seniority levels with very low contribution to the wave functions can present a broad determinantal distribution, i.e., the Li2 molecule exhibits 7 2=4 > 5 values because its W =4 = 10 " weight is expanded on 7560 Slater determinants in the STO-3G basis set [6]. Moreover, the Ia=o index values reported in that table indicate that aU systems possess a narrower... 

Even though we explained, in Sect. 2.1, why the simple band structure cannot be immediately related to transport characteristics in organic semiconductors, it is important to analyze the microscopic origin of the difference between the electronic structures of the polymorphs. The main advantage of using a molecular orbital basis set in the computation of the band structure is that the result can be discussed in... 

Each of these tools has advantages and limitations. Ab initio methods involve intensive computation and therefore tend to be limited, for practical reasons of computer time, to smaller atoms, molecules, radicals, and ions. Their CPU time needs usually vary with basis set size (M) as at least M correlated methods require time proportional to at least M because they involve transformation of the atomic-orbital-based two-electron integrals to the molecular orbital basis. As computers continue to advance in power and memory size, and as theoretical methods and algorithms continue to improve, ab initio techniques will be applied to larger and more complex species. When dealing with systems in which qualitatively new electronic environments and/or new bonding types arise, or excited electronic states that are unusual, ab initio methods are essential. Semi-empirical or empirical methods would be of little use on systems whose electronic properties have not been included in the data base used to construct the parameters of such models. 

The first kind of simplification exclusively concerns the size of the basis set used in the linear combination of one center orbitals. Variational principle is still fulfilled by this type of "ab initio SCF calculation, but the number of functions applied is not as large as necessary to come close to the H. F. limit of the total energy. Most calculations of medium-sized structures consisting for example of some hydrogens and a few second row atoms, are characterized by this deficiency. Although these calculations belong to the class of "ab initio" investigations of molecular structure, basis set effects were shown to be important 54> and unfortunately the number of artificial results due to a limited basis is not too small. 

CCSDTQ (CC singles, doubles, triples, and quadruples) (75-75), CCSDTQP (CC singles, doubles, triples, quadruples, and pentuples) (7P), etc. approaches are far too expensive for routine applications. For example, the full CCSDTQ method requires iterative steps that scale as ( g(/i )is the number of occupied (unoccupied) orbitals in the molecular orbital basis). This scaling restricts the applicability of the CCSDTQ approach to very small systems, consisting of 2 - 3 light atoms described by small basis sets. For comparison, CCSD(T) is an nln procedure in the iterative CCSD steps and an nl procedure in the non-iterative part related to the calculation of the triples (T) correction. In consequence, it is nowadays possible to perform the CCSD(T) calculations for systems with 10-20 atoms. The application of the local correlation formalism (80-82) enabled SchOtz and Werner to extend the applicability of the CCSD(T) approach to systems with 100 atoms (53, 83, 84). 

In order to analyze the performance of this purification procedure and to compare it with those reported in the previous section, the same atomic and molecular systems in their ground state were selected as test systems. Again, the basis sets used were formed by Hartree-Eock molecular orbitals built out of minimal Slater orbital basis sets and the initial data were chosen to be the approximate 2-RDMs built by application of the independent pair model within the framework of the SRH theory. 

In general, a molecular-centered basis set is not suitable for constructing a function which does not approach spherical symmetry and have most of its structure close to the origin. For example, an extensive linear combination of molecule-centered atomiclike orbitals would be needed to construct the nodes in a b2g molecular orbital of benzene. Also, because the interference effects are specifically characteristic of the interplay between electron wavelength and the set of internuclear spacings, a molecule-centered basis set will not adequately describe interference effects. 

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