Orbital Contour Plots Research Articles

Interactions in coinage-metal/ligand complexes, CM–L, and their cations (CM = Cu, Ag, Au; L = CO, N2 and H2)

The CM–L and CM+–L complexes for the three coinage metals, CM = Cu, Ag and Au interacting with three key ligands, L = CO, N2 and H2, are investigated. Calculations are undertaken using various quantum chemical methods to ascertain the equilibrium geometries and interaction energies; the latter are calculated at the coupled-cluster level of theory, and extrapolated to the basis set limit. Some of the neutral species are found to be particularly challenging, and significant disparity is found in some cases for the geometry and/or harmonic vibrational wavenumbers. In addition, molecular orbital diagrams, atomic charges, and orbital contour plots are presented, in order to gain insight into the interactions occurring in these complexes.

Graphical Representation of Hydrogenic Orbitals: Incorporating Both Radial and Angular Parts of the Wave Function

There exist several two- and three-dimensional graphical representations of hydrogen-like orbitals. Despite this, connecting the mathematical form of the atomic orbital, a function of both radial and angular variables, to its actual shape is often challenging for students. Here, we present a new graphical representation using bubble plots to show the combined contribution of the radial and angular parts of the wave function to its shape. This representation can be demonstrated on the blackboard, as well as easily plotted by students. Additionally, it is one step away from contour plots of orbitals, which are commonly used in their depiction.

A Surprisingly Simple Electrostatic Model Explains Bent Versus Linear Structures in M(+)-RG2 Species (M = Group 1 Metal, Li-Fr; RG = Rare Gas, He-Rn).

It is found that a simple electrostatic model involving competition between the attractive dispersive interaction and induced-dipole repulsion between the two RG atoms performs extremely well in rationalizing the M(+)-RG2 geometries, where M = group 1 metal and RG = rare gas. The Li(+)-RG2 and Na(+)-RG2 complexes have previously been found to exhibit quasilinear or linear minimum-energy geometries, with the Na(+)-RG2 complexes having an additional bent local minimum [A. Andrejeva, A. M. Gardner, J. B. Graneek, R. J. Plowright, W. H. Breckenridge, T. G. Wright, J. Phys. Chem. A, 2013, 117, 13578]. In the present work, the geometries for M = K-Fr are found to be bent. A simple electrostatic model explains these conclusions and is able to account almost quantitatively for the binding energy of the second RG atom, as well as the form of the angular potential, for all 36 titular species. Additionally, results of population analyses are presented together with orbital contour plots; combined with the success of the electrostatic model, the expectation that these complexes are all physically bound is confirmed.

The comparative investigation on the optical properties and electronic structures of the alkoxy-tuned 1,3,4-oxadiazole derivatives

The optical properties and electronic structures of three series of 1,3,4-oxadiazole derivatives, 1,4-bis[(4-methylphenyl)-1,3,4-oxadiazolyl]phenylene (OXD1), 1,4-bis[(4-alkoxyphenyl)-1,3,4-oxadiazolyl]phenylene (OXD3– n+1 ) and 5,5′-di-(4-methyl)-2,2′-p-(2,5-bisalkoxyphenylene)-bis-1,3,4-oxadiazole (OXD2– n+1 ) were investigated theoretically by quantum calculation theory method as well as experimentally by UV/vis absorption, photoluminescence (PL), excitation spectra and differential pulse polarograph (DPP). The maximum absorption and emission for these oxadiazole derivatives were increasingly red-shifted with the electron-donating abilities of the different position substituents, which was in accordance with the results from time-dependent density functional theory (TD-DFT) calculations. The excitation spectra for these oxadiazole derivatives in CH 2Cl 2 solution were extended in wide region from 250 nm to 420 nm, and the broad excitation band was attributed to the increasing effect of alkoxy group. The HOMO level, the LUMO level and energy gap (Eg, LUMO–HOMO) for these oxadiazole derivatives were determined by the experimental method and by DFT method, and the results showed that only HOMO had been evidently influenced by changing the different position substituents. We used the DFT methods to generate the optimized structures of their model compounds, OXD1, OXD3-1 and OXD2-1. It was found that the slight difference in bond length and dihedral angle for the model compounds was generated. This strongly localized character of the electron density was illustrated by the frontier orbital contour plots as the effect of alkoxy substituents. The calculated results showed that LUMO mainly localized on the central benzene ring and two oxadiazole rings and HOMO delocalized along the whole conjugated chain except for OXD2-1. It suggested that the spectral properties of these oxadiazole derivatives were determined by the electronic structures with the different effect of alkoxy substituents on the HOMO.

Computational modeling of environmental plutonyl mono-, di- and tricarbonate complexes with Ca counterions: Structures and spectra: [formula omitted], PuO 2(CO 3) 2Ca, and PuO 2(CO 3) 3Ca 3

We have computed the structures, and select vibrational spectra, electron density and molecular orbital contour plots of plutonium(VI) complexes of environmental importance such as [PuO 2(CO 3) 2] 2− and [PuO 2(CO 3) 3] 4−. We show that Ca 2+ is efficacious in gas-phase modeling of electronic and spectroscopic properties of multiply charged plutonyl di and tricarbonate anions through complexes such as PuO 2(CO 3) 2Ca and [PuO 2(CO 3) 3Ca 3] 2+.

Electronic structure of exohedral interactions between C 60 and transition metals

The electron distribution and orbital interactions of C 60 with metals coordinated at different sites on the outside of the fullerene are evaluated. These sites include the position of a metal atom directly above a carbon atom (η 1 site), the metal atom centered above two carbons of a pentagon or above two carbons between two pentagons (both η 2 sites), the metal atom centered above a pentagon (η 5 site), and the metal atom centered above a hexagon (η 6 site). The frontier orbitals of C 60 are illustrated first with three-dimensional orbital contour plots. A palladium atom is then used to probe the bonding at the different sites on the C 60 surface. The results with Pd 0 are compared to our earlier study with the harder Ag + ion in order to examine the effects of metal electron richness and size. In addition, these results are compared with the bonding to more traditional ligands that represent the hapticity of these sites, such as methyl (η 1), ethylene (η 2), cyclopentadienyl (η 5), and benzene (η 6). The strength of the metal-C 60 interaction and the amount of charge delocalized from the metal to C 60 is sensitive to the site of coordination, the electron richness of the metal, and distortions in the geometry of C 60. As discussed in our previous work, the frontier orbitals of C 60 are well-suited for synergistic bonding of a metal atom to a carbon-carbon pair in an alkene-like fashion, in which the HOMO of C 60 donates carbon-carbon π bonding electron density to the metal, and the LUMO of C 60 accepts electron density from the metal into a carbon-carbon π* antibonding orbital. Although the HOMO and LUMO of C 60 describe the basic interaction, many frontier orbitals are involved. The site above the CC bond between two pentagons is favored over the site above the CC bond within a pentagon, and the interaction above the other sites is indicated to be net repulsive by these calculations. The differentiation between these sites increases with the electron richness of the metal center. The bonding of the metal to C 60 is generally weaker than to the small ligands, except for very electron rich metal centers where the bonding to the η 2 site between pentagons apparently becomes stronger than the bonding to ethylene.

ChemInform Abstract: A THEORETICAL POTENTIAL ENERGY SURFACE STUDY OF SEVERAL STATES OF THE METHOXY RADICAL

Several low‐lying potential energy surfaces of the methoxy radical have been studied at C3v conformations using ab initio quantum chemical techniques. A double‐zeta quality basis set augmented with polarization and diffuse functions has been used throughout. Eight doublet and quartet states have been characterized as a function of C–O distance. The equilibrium conformation of the 2E ground state is found (RCO = 1.405 A, RCH = 1.112 A, ϑHCO = 111.3°), and the harmonic vibrational frequencies of the three a1 modes are calculated (3118, 1330, and 1017 cm−1). The ? 2A1←? 2E vertical excitation energy has been estimated to be 4.01 eV. The wave functions for the ? and ? states have been analyzed in terms of their dipole moments, population analyses, and orbital contour plots.

A theoretical potential energy surface study of several states of the methoxy radical

Several low-lying potential energy surfaces of the methoxy radical have been studied at C3v conformations using ab initio quantum chemical techniques. A double-zeta quality basis set augmented with polarization and diffuse functions has been used throughout. Eight doublet and quartet states have been characterized as a function of C–O distance. The equilibrium conformation of the 2E ground state is found (RCO = 1.405 Å, RCH = 1.112 Å, ϑHCO = 111.3°), and the harmonic vibrational frequencies of the three a1 modes are calculated (3118, 1330, and 1017 cm−1). The ? 2A1←? 2E vertical excitation energy has been estimated to be 4.01 eV. The wave functions for the ? and ? states have been analyzed in terms of their dipole moments, population analyses, and orbital contour plots.

Binding and energy-level shifts of carbon monoxide adsorbed on nickel: Model studies

Hartree-Fock calculations on linear NiCO and ${\mathrm{Ni}}_{2}$CO clusters have been used to model the local binding of CO upon adsorption on Ni. The Ni-CO bond is determined by a mixing of the $\mathrm{CO}(5\ensuremath{\sigma})$ and $\mathrm{Ni}(3d)$ orbitals; the $\mathrm{Ni}(4s)$ electrons are not directly involved in the bond as can be seen from orbital contour plots. A knowledge of the absolute and relative shifts of molecular ionization potentials from their free-molecule values is important for the interpretation of the photoelectron spectra of chemisorbed species. For our model clusters, we have made a detailed analysis of the origins of the shifts for CO on Ni. The different contributions to the energy-level shifts of the CO-like orbitals show a grouping into core, nonbonding valence, and bonding valence levels. Chemical shifts due to the changed environment of the adsorbed molecule are seen to be important for the initial-state shifts of the nonbonding orbitals. A bonding shift appears to be important only for the CO $5\ensuremath{\sigma}$ level. The relaxation shifts are different among the different groups of levels. Analysis of the calculated and observed shifts gives support to the assignment that the order of the $5\ensuremath{\sigma}$ and $1\ensuremath{\pi}$ levels for CO adsorbed on Ni is the same as for free CO; $5\ensuremath{\sigma}$ less strongly bound than $1\ensuremath{\pi}$. The $\mathrm{O}(1s)$ and $\mathrm{C}(1s)$ core-level shifts indicate that the CO bond is stretched only slightly upon adsorption. The multiplet splitting of the final ionic states is considered and found to be small.

Ab initio calculations on 1,6-dioxa-2,5-diaza-6-thia-pentalene

Ab initio MO-LCAO-SCF calculations have been carried out for 1,6-dioxa-2,5-diaza-6a-thiapentalene with a double-zeta basis set. Liunited geometry variation indicates that the molecular configuration corresponding to the minimum energy belongs to the C 2v group. Charge distribution and bonding are discussed on the basis of valence orbital contour plots and population analysis. Calculated core ionization potentials show reasonable agreement with ESCA measurements. A contour map of the electrostatic potential around the molecule reveals negative regions near the oxygen and nitrogen atoms.

Theory of lone pairs. II. A moment analysis of localized molecular orbitals in ten‐electron hydrides

AbstractAb initio double‐zeta quality molecular orbital calculations have been carried out on an extensive series of ten‐electron hydrides. The Edmiston–Ruedenberg energy‐localized molecular orbitals were calculated and the total molecular and localized orbital densities analyzed in terms of dipole moments, contour plots, and a simplified model for the orbital density involving analysis of the first and second moments. The simplified moment analysis model may be easily visualized in terms of threedimensional geometric objects, spheres, and ellipsoids. The model summarizes the information on the effective functional distribution inherent in the more detailed orbital contour plots in a clear and concise manner.