Chemical natural orbitals

Almlof, J., Taylor, P.R. Atomic natural orbital (ANO) basis-sets for quantum-chemical calculations. Adv. Quantum Chem. 1991, 22, 301-73. 

General relationships between AOM and crystal field parameters are shown in Table 23. Using the AOM one can easily compute the electronic energy levels, inclusive of spin-orbit coupling, without any symmetry assumption or perturbation procedure, and it is also easy to account for the different chemical natures of the ligands and for differences in bond distances. It is also possible to handle anisotropic n interactions, which can be expected to occur with pyridine or pyridine iV-oxide ligands.366,367 General review articles on the AOM and its applications have already appeared.364,368-371... 

It can be necessary and/or desirable to impose symmetry and equivalence restrictions on quantum chemical calculations or results beyond the single-configuration SCF level. For instance, most Cl programs generate natural orbitals (NOs) after computing the Cl wave function, by forming and diagonalizing the first-order reduced density matrix or 1-matrix p in... 

But if the chemical nature of a substrate atom can change the observed STM image, then also the chemical nature of the tip apex can have a decisive role. This effect changed the focus in STM theory somewhat from the discussion about single tip-orbitals (most theoretical work previously assumed that the representation of a tip by one orbital would be sufficient), to the chemistry of the STM tip. This is still a very lively topic today, not least because subtle effects are more and more dominant in experimental practice. 

One can argue that for the application of 1) and 2) only trends in orbital nature and orbital populations matter so that any quantum chemical method (HF or DFT) or any way of calculating charges (Mulliken or natural orbital populations) suffices for this purpose as long as it is applied in a consistent way. One can further argue that the silylium cation character of a given silyl ion has only to be determined for the gas phase. Once this has been done, other molecular properties of the ion in question can be calculated and compared with the corresponding measured values for either gas or solution phase. In this way, a purely theoretical definition of the silylium ion character could be adjusted and extended to measurable quantities. 

Even though computers were an essential tool in quantum chemical calculations, the main challenge was the further development of methods and concepts to describe even more facets of chemistry and with higher accuracy. Methods that account for electron correlation were extended to be able to describe energy surfaces more reliably. Several variants of the CEPA Ansatz (CEPA-1, CEPA-2) were developed as well as the method of self-consistent electron pairs (SCEP). Formulations using canonical or localized orbitals (e.g., pair natural orbitals, PNO, as a kind of optimized virtual orbitals) were put forth. These methods were extensively used for two decades, primarily in Germany, until coupled cluster formulations became more popular. ... 

Consideration of the chemical nature of zero-valent lanthanide metals raises some intriguing questions. The stability of zero oxidation state transition metal complexes depends in large part on the capacity of the metal to transfer its excess electron density back to the ligands via backbonding. Given the limited radial extension of the 4/orbitals (8, 9),... 

In the past ten years, many investigations and theoretical calculations have been made with regard to the chemical nature of the bent bond. In contrast with molecular orbital theory, classical theory considers the bent bond to be connected only with the localized bond or the bond orbital. The Foster-Bogs method has been employed for the indirect generation of the localized orbitals and the resulting orbitals have subsequently been analyzed from the aspect of the bent bond. ... 

Mechanistic and Theoretical Studies of Phosphonium Ylides and the Wittig Reaction. - The physico-chemical nature of the P-C bond in phosphonium ylides is complex and, despite intensive research over many years, remains the subject of dispute Numerous theoretical studies of this problem have appeared in the scientific literature. A recent contribution to this area by Mitrasinovic uses sharing indices and sharing amplitudes to study P-C bonds in a number of tri-and penta-valent phosphorus species. Sharing indices and amplitudes are quantitative, orbital dependent, measurements of the degree to which an electron, as a wave, is shared between two spatial points in a many electron system. Ylides studied using this method include (1), (2) and (3). ... 

The standard potentials f/R,oo, which hold for Oox = red in Eq. (21) or y = 1/2 in Eq. (22), depend directly on the chemical nature of the compound. Consequently, they are linked to the corresponding electronic energy levels derived from the molecular orbital (MO) theory. A linear dependency between [/r,oo and the corresponding eigenvalue coefficients for the lowest unoccupied molecular orbital (LUMO) or highest occupied molecular orbital (HOMO) energy levels was found... 

The stereochemical insensitivity of tricoordinate phosphorus to the chemical nature of its substituents may be ascribed to the fact that, in contrast to nitrogen, it shows no tendency to form multiple bonds in which its pn orbitals are involved. 

As proposed by Marzari and Vanderbilt [219], an intuitive solution to the problem of the non-uniqueness of the unitary transformed orbitals is to require that the total spread of the localized function should be minimal. The Marzari-Vanderbilt scheme is based on recent advances in the formulation of a theory of electronic polarization [220, 221]. By analyzing quantities such as changes in the spread (second moment) or the location of the center of charge of the MLWFs, it is possible to learn about the chemical nature of a given system. In particular the charge centers of the MLWFs are of interest, as they provide a classical correspondence to the location of an electron or electron pair. 

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