Chemical bonding basis sets

Basis sets can be further improved by adding new functions, provided that the new functions represent some element of the physics of the actual wave function. Chemical bonds are not centered exactly on nuclei, so polarized functions are added to the basis set leading to an improved basis denoted p, d, or f in such sets as 6-31G(d), etc. Electrons do not have a very high probability density far from the nuclei in a molecule, but the little probability that they do have is important in chemical bonding, hence dijfuse functions, denoted - - as in 6-311 - - G(d), are added in some very high-level basis sets. 

Likewise, a basis set can be improved by uncontracting some of the outer basis function primitives (individual GTO orbitals). This will always lower the total energy slightly. It will improve the accuracy of chemical predictions if the primitives being uncontracted are those describing the wave function in the middle of a chemical bond. The distance from the nucleus at which a basis function has the most significant effect on the wave function is the distance at which there is a peak in the radial distribution function for that GTO primitive. The formula for a normalized radial GTO primitive in atomic units is... 

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... 

J Chem. Phys., 52, 431 (1970)] is a relatively inexpensive one and can be used for calculations on quite large molecules. It is minimal in the sense of having the smallest number of functions per atom required to describe the occupied atomic orbitals of that atom. This is not exactly true, since one usually considers Is, 2s, and 2p, i.e., five functions, to construct a minimal basis set for Li and Be, for example, even though the 2p orbital is not occupied in these atoms. The 2sp (2s and 2p), 3sp, 4sp, 3d,. .., etc. orbitals are always lumped together as a shell , however. The minimal basis set thus consists of 1 function for H and He, 5 functions for Li to Ne, 9 functions for Na to Ar, 13 functions for Kand Ca, 18 functions for Sc to Kr,. .., etc. Because the minimal basis set is so small, it generally can not lead to quantitatively accurate results. It does, however, contain the essentials of chemical bonding and many useful qualitative results can be obtained. 

The chemical bonding occurs between valence orbitals. Doubling the 1 s-functions in for example carbon allows for a better description of the 1 s-electrons. However, the Is-orbital is essentially independent of the chemical environment, being very close to the atomic case. A variation of the DZ type basis only doubles the number of valence orbitals, producing a split valence basis. In actual calculations a doubling of tire core orbitals would rarely be considered, and the term DZ basis is also used for split valence basis sets (or sometimes VDZ, for valence double zeta). 

The substituent effects on the H-bonding in an adenine-uracil (A-U) base pair were studied for a series of common functional groups [99JPC(A)8516]. Substitutions in the 5 position of uracil are of particular importance because they are located toward the major groove and can easily be introduced by several chemical methods. Based on DFT calculation with a basis set including diffuse functions, variations of about 1 kcal/mol were found for the two H-bonds. The solvent effects on three different Watson-Crick A-U base pairs (Scheme 100) have been modeled by seven water molecules creating the first solvation shell [98JPC(A)6167]. 

As an example of the interest to scrutinise the UHF solution, one may quote the Bea problem [19]. The bond is weak but it takes plaee at short interatomic distance and is definitely not the dispersion well which one might expect from two closed shell atoms (and which occurs in Mga and heavier eompounds). Quantum chemical calculations only reproduce this bond when using large basis sets and extensive Cl calculations [20]. It is amazing to notice that the UHF solution gives a qualitatively correct behaviour, and suggests a physical interpretation of this bond since in... 

CS INDO [10] (as well as the parent C INDO [9]) shares the same basic idea as the PCILO scheme [29,30] to exploit the conceptual and computational advantages of using a basis set of hybrid atomic orbitals (AOs) directed along, or nearly, the chemical bonds. 

Figure 3.12. Optimized structure of the free triplet state (a) and the triplet of the carbonyl H-bond complex (b) calculated from the DPT calculations using the UB3LYP method with a 6-311G basis set. (Reprinted with permission from reference [42]. Copyright (2005) American Chemical Society.)...

Figure 5. The INDO/S transition densities for four conformers of Si2QH<2 (G = gauche, T = trans) in terms of the hybrid orbital basis set (contributions from Si-H bonds are negligible). Coefficient sign (bar color) and magnitude (bar length) are shown for each Si atom (circle). (Reproduced from Ref. 19. Copyright 1986 American Chemical Society.)...

The natural localized orbitals introduced in Section 1.5 provide a useful alternative to the canonical delocalized MOs (CMOs) that are usually employed to analyze chemical bonding. The NAO and NBO basis sets may be regarded as intermediates in a succession of basis transformations that lead from starting AOs /, to the final canonical MOs , ... 

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