AO Populations Research Articles

Relativistic Effects on the Properties of Lr: A Periodic DFT Study of the Adsorption of Lr on Surfaces of Ta in Comparison with Lu and Tl.

With the aim of finding out whether the predicted 7s27p1/2 ground-state electron configuration of Lr will have an effect on its reactivity, calculations of the adsorption properties of Lr(7s27p), its homologue Lu(6s25d), and the related p element Tl(6s26p) on the surface of Ta were performed using the relativistic periodic ADF BAND suite. The obtained adsorption energies, Eads(M), are in excellent agreement with the measured adsorption enthalpies of Lu and Tl, showing that Lr adsorbs on the surface of Ta similarly to Lu and much differently (215 kJ/mol more strongly) from Tl. An AO population analysis reveals that Lr interacts with the Ta surface preferentially via the 7s AO, with some participation of the 6d as well as 7p1/2 and 7p3/2 AOs. In contrast, Eads(Tl) is governed mainly by the 6p(Tl) AOs. Thus, the present investigations show that Lr should behave like Lu but not like the p element Tl on transition-metal surfaces.

Unique positive definite extension of Mulliken's charge populations of non-orthogonal atomic basis functions

Although Mulliken's charge population concept is widely used in literature, it suffers from the main conceptual disadvantage of not describing a probability distribution of the electron on the constituent atoms; small negative population values can occur as well. This fact prohibits some practical applications, too. Mulliken's AO population can be written as the expectation value of a self-adjoint operator P̂μ, corresponding to each atomic orbital |μ〉. Using the algebra generated by P̂μ, we will give in this paper a positive definite extension of Mulliken's expressions which can be written as the expectation value of a proper self-adjoint operator; it is local in the sense of Mulliken's definition; and it remains in the framework of the usual LCAO techniques (i.e. only the atomic overlap matrix is required for calculations). It is shown that only non-physical populations change significantly, realistic values remain close to Mulliken ones. From computational point of view, the extra work required to calculate this positive definite distribution is practically negligible.

Electronic structure of fluoroborates activated by rare-earth elements

By means of a spin-polarized discrete variation method, electronic structure calculations have been performed for the optically active centers of rare-earth elements in the fluoroborates Mg{sub 3}BO{sub 3}F{sub 3}, Mg{sub 2}BO{sub 3}F, and Mg{sub 5}(BO{sub 3}){sub 3}F, which differ in fluorine content and crystal structure. Large fragments of the crystals, including a lanthanide atom, one or several fluorine centers, and three to five complete borate ions, have been examined. The transformation of AO populations and effective charges on the atoms in various systems have been investigated. Chemical bonding in the fluoroborates has been analyzed on the basis of overlap populations of orbitals of neighboring atoms. Excitation energies have been estimated for the matrices and impurity centers, and the influence of crystal structure on the spectral properties of these systems has been investigated.

29Si NMR: A new approach to the analysis of chemical shift variations

A new approach to the analysis of the U-shaped dependence of 29Si NMR chemical shifts on the sum of group electronegativities of ligands, based on a proper account of the presence of the silicon core AO of the same symmetry as the silicon valence 3p AO is presented. A new dependence between λ Si=〈 r −3〉 3p and the valence AO populations has been established. 29Si NMR chemical shift calculations for organosilicon compounds using the FPT INDO-CS method are in good agreement with experimental data.

Test of an integral approximation scheme based on semiorthogonalized orbitals in LCAO SCF MO CI calculations of naphthalene

AbstractAb initio LCAO SCF MO CI calculations of naphthalene are carried out with a minimal basis set to test an integral approximation scheme proposed in a previous paper. When 71.3 and 53.0% of the two‐electron integrals are neglected, the errors in the SCF total energy are only −0.0534 and −0.0006 a.u., respectively. In the latter case, the maximum absolute errors of the orbital energy and the gross AO population are 0.007 a.u. and 0.001, respectively. Even in the former case the errors of the excitation energies are less than 0.0004 a.u. Errors of oscillator strengths are also examined and are found to be tolerably small.

Approximate-additive variation of the AO populations and effective atomic charges in isovalently substituted series of molecules according to MO LCAO SCF calculations

Approximate-additive variation of the AO populations and effective atomic charges in isovalently substituted series of molecules according to MO LCAO SCF calculations

An MO-Theoretical Study of the Decomposition of Hydroperoxides by Sulfonium Compounds and Some Nucleophiles

Abstract The decomposition reactions of hydroperoxides (ROOH) by sulfonium compounds or some nucleophiles (sulfides, phosphites, and transition metal ions) were treated by the extended Hückel method, augmented by the use of d-orbitals. We obtained serveral findings. First, ROOH was more reactive to nucleophiles and was energetically more stable than (ROOH)2. Second, the order of the ability for the ROOH decomposition, sulfonium compounds>>sulfides>phosphites\gtrsimthiophene, was in good agreement with that of the AO populations of the nonbonding lone pair orbitals of the above compounds. Third, the distinguished ability of the sulfonium compound may be attributed to the contribution of the partially-occupied sulfur d-orbitals, in particular, the lowest unoccupied dz2-orbital; in the ROOH decomposition, these orbitals interact with the lowest unoccupied antibonding pσ-orbital of the O–O in ROOH at the Oβ atom in the direction of the O–O axis. Finally, it was concluded that the sulfur d-orbitals contribute to the long-range interaction (S–Oβ>3.0 Å) between ROOH and sulfonium compounds.

A MO-theoretical Study of the Catalytic Activity of Onium Compounds in the Liquid-phase Oxidation

Abstract A theoretical study with the extended Hückel method augmented by d-orbitals was undertaken in order to elucidate the relation between the electronic structures of various onium compounds and their catalytic activities in the liquid-phase oxidation of hydrocarbons. There were several findings. Firstly, the differences in the catalytic activities of the carbonium, ammonium, and oxonium compounds are ascribed to those in the AO populations of the pz-orbitals on their central atoms. Secondly, the distinguished activities of sulfonium and phosphonium compounds were well explained by the partially-occupied sulfur or phosphorus 3d-orbitals, in which the dxz (or dyz) orbital is utilized most effectively for the interaction with the (1πg)z orbital of O2. Finally, the relatively low activities of arsonium and telluronium compounds are ascribed to the vacant and diffused 4d or 5d orbitals, while the appreciable activity of the selenonium compound is caused by the partial electron-occupancy of the 4dxz (or 4dyz) orbital of the central selenium.

Molecular orbital study of the catalytic activity of onium compounds in liquid-phase oxidation

A theoretical study involving ASMO-SCF and extended Huckel methods including d-orbitals has been undertaken in an attempt to correlate the electronic properties of various onium compounds and their catalytic activities in the liquid-phase oxidation of hydrocarbons. First, the stable geometries of trimethylonium compounds (carbonium, oxonium, sulphonium, selenonium, and telluronium) were found to involve planar cations; whilst ammonium, phosphonium, and arsonium cations assume tetrahedral configurations. Secondly, the differences in the catalytic activities of second-row onium compounds may be ascribed to the differences in the AO populations of the pz- orbital on their central atoms. Thirdly, the distinctive activities of sulphonium and phosphonium compounds are reasonably well explained by the contribution of the partially occupied sulphur or phosphorous 3d-orbitals, to the catalytic activity. Among 3d-orbitals, the dxz(or dyz)-orbital is most effective for interaction with the (1πg)z-orbital of molecular oxygen. Finally, the relatively low activities of arsonium, selenonium, and telluronium compounds are due to the vacant and diffuse 4d and 5d orbitals of the central atoms. The order of activity, arsonium ≃ telluronium < selenonium, is in reasonable accord with the AO populations of 4d or 5d orbitals of the central arsenic, selenium, or tellurium.

Calculation of the ao populations and effective atomic charges within the zero-differential-overlap approximation

Calculation of the ao populations and effective atomic charges within the zero-differential-overlap approximation

A Mo-theoretical treatment of the decomposition of hydroperoxides by nucleophiles and electrophiles

The mechanism of the decomposition of hydroperoxides (ROOH) by some nucleophiles (sulfides, phosphites, thiophene, sulfonium compounds, and transition metal ions) and electrophiles (transition metal ions) has been investigated using the extended Hückel method including d-orbitals, and the following results were obtained. ROOH is more stable energetically than (ROOH) 2. The reactivity of ROOH to nucleophiles and electrophiles has been explained by the partial AO population of the OO pσ at the LU MO( 1 2 N pσ LU) and that of the nonbonding O β 2p at the HO MO( 1 2 N nbo HO), respectively. Except for transition metal ions, the order of the ability of necleophiles to decompose ROOH is in good agreement with that of 1 2 N nbo HO of the nonbonding orbital of the central atom, while the ability of transition metal ions is reflected in the ionization potentials of their d-orbitals. The process of decomposition is discussed giving regard to the electron-migrations between reactants: and the intramolecular reaction of RO radicals formed is treated by the extended Hückel method.

Role of &lt;i&gt;d&lt;/i&gt;-Orbitals in the Catalytic Activation of Molecular Oxygen in the Liquid-Phase Oxidation

The catalytic activation of molecular oxygen by various onium compounds were interpreted theoretically with particular attention to the role of d-orbitals. We made several findings. First, there exists a parallelism between the catalytic activities of onium compounds and the AO population on the nonbonding p-orbital or the partially occupied d-orbitals of their central atoms. Second, the preferred mode of the interaction between onium compounds and molecular oxygen was expressed by the parallel form (see Fig. 2). Third, the above interaction was confirmed by the red shift of the band near 200mμ of the transition, nonbonding 2p AO→3d AO on the central sulfur of sulfonium compounds, in an oxygen atmosphere. Finally, the process of the hydrogen abstraction of molecular oxygen activated by onium compounds from a hydrocarbon was discussed.

Some Remarks on the Extended Hückel Approximation in the Independent-Electron MO Theory

Abstract The sum of one-electron energies in the extended Hückel MO theory has been related to the total energy in the LCAO SCF MO theory including electron repulsion and nuclear repulsion terms. The sum of one-electron energies in the extended Hückel MO theory can be divided into the two parts; one almost independent of nuclear configuration and one highly sensitive to the configurational change. Of these the latter is found to be responsible for the stabilization energy due to the bond formation. The role of the highest occupied MO and the lowest unoccupied MO toward chemical reaction has been also discussed in the framework of the extended Hückel calculations. The partial AO population in these particular MO’s is shown to be almost valence-inactive one, being ready to be mobilized in case of chemical interaction with other systems.

Electronic Population Analysis on LCAO-MO Molecular Wave Functions. III. Effects of Hybridization on Overlap and Gross AO Populations

The effects of AO hybridization on gross AO and overlap populations for LCAO-MO electron configurations are discussed in terms of some simple examples, using equations and graphs. The validity of ``gross AO populations'' as true measures of the population in various AOs is critically discussed. It is shown that the degree of hybridization in the AOs of an LCAO MO does not in general give the true amount of s or p character in the MO; this is given instead by the gross s or p population in the MO. Nevertheless, ``forced hybridization'' among the AOs, although not contributing to gross AO populations, leads to important negative contributions to overlap populations, hence to bond energies. For example, forced 2s—2p hybridization has the result that the total overlap population for two pairs of electrons occupying bonding σ LCAO MOs built from 2s and 2pσ AOs in a homopolar diatomic molecule is actually less than the sum of the overlap populations which one would have if one pair could be in an MO built from pure 2s AOs and the other in an MO built from pure 2pσ AOs. This sort of forced hybridization with resultant loss of bond strength may explain why double bonds seldom if ever consist of two σ bonds.