scholarly journals Does the Presence of a Bond Path Really Mean Interatomic Stabilization? The Case of the Ng@Superphane (Ng = He, Ne, Ar, and Kr) Endohedral Complexes

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2241
Author(s):  
Mirosław Jabłoński
Keyword(s):  
Noble Gas ◽  
Molecular Graph ◽  
Basis Set ◽  
Chemical Bonds ◽  
Bond Orders ◽  
Endohedral Complexes ◽  
Bond Path ◽  
Endohedral Complex ◽  
Computational Methodology ◽  
Complex Features

Using a fairly structurally flexible and, therefore, very suitable for this type of research, superphane molecule, we demonstrate that the inclusion of a noble gas atom (Ng = He, Ne, Ar, and Kr) inside it and, thus, the formation of the Ng@superphane endohedral complex, leads to its ‘swelling’. Positive values of both the binding and strain energies prove that encapsulation and in turn ‘swelling’ of the superphane molecule is energetically unfavorable and that the Ng⋯C interactions in the interior of the cage are destabilizing, i.e., repulsive. Additionally, negative Mayer Bond Orders indicate the antibonding nature of Ng⋯C contacts. This result in combination with the observed Ng⋯C bond paths shows that the presence of a bond path in the molecular graph does not necessarily prove interatomic stabilization. It is shown that the obtained conclusions do not depend on the computational methodology, i.e., the method and the basis set used. However, on the contrary, the number of bond paths may depend on the methodology. This is yet another disadvantageous finding that does not favor the treatment of bond paths on molecular graphs as indicators of chemical bonds. The Kr@superphane endohedral complex features one of the longest C–C bonds ever reported (1.753 Å).

From Atomic Orbitals to Molecular Orbitals and Chemical Bonds

2020 ◽  
pp. 150-187
Author(s):  
Jochen Autschbach
Keyword(s):  
Hydrogen Molecule ◽  
Atomic Orbital ◽  
Plane Waves ◽  
Basis Set ◽  
Orbital Method ◽  
Chemical Bonds ◽  
Atomic Orbitals ◽  
Hartree Fock ◽  
Generalized Matrix

It is shown how an aufbau principle for atoms arises from the Hartree-Fock (HF) treatment with increasing numbers of electrons. The Slater screening rules are introduced. The HF equations for general molecules are not separable in the spatial variables. This requires another approximation, such as the linear combination of atomic orbitals (LCAO) molecular orbital method. The orbitals of molecules are represented in a basis set of known functions, for example atomic orbital (AO)-like functions or plane waves. The HF equation then becomes a generalized matrix pseudo-eigenvalue problem. Solutions are obtained for the hydrogen molecule ion and H2 with a minimal AO basis. The Slater rule for 1s shells is rationalized via the optimal exponent in a minimal 1s basis. The nature of the chemical bond, and specifically the role of the kinetic energy in covalent bonding, are discussed in details with the example of the hydrogen molecule ion.

Bond order-bond length relationships in conjugated hydrocarbons - the microwave spectrum and structure of 3,4-dimethylenecyclobutene

1983 ◽  
Vol 36 (4) ◽  
pp. 639 ◽  
Author(s):  
RD Brown ◽  
PD Godfry ◽  
BT Hart ◽  
AL Ottrey ◽  
M Onda ◽  
...  
Keyword(s):  
Dipole Moment ◽  
Ab Initio ◽  
Bond Length ◽  
Bond Order ◽  
Microwave Spectrum ◽  
Basis Set ◽  
Molecular Orbital Calculations ◽  
Bond Orders ◽  
Bond Lengths ◽  
Typical Error

The microwave spectrum of the benzene isomer 3,4-dimethylenecyclobutene including spectra of all possible single 13C-substituted and sufficient singly and doubly D-substituted species to give a complete r5 geometry, have been measured and analysed. An estimate of the re geometry has also been derived. The additional precise CC bond lengths obtained for an unsubstituted, conjugated hydrocarbon enable us to examine bond order-bond length relationships more thoroughly than has previously been possible. The CC bond lengths exhibit a noticeably better correlation with SCFMO bond orders than with simple H�ckel bond orders. Further confirmatory measurements of the dipole moment of dimethylenecyclobutene have been made. Ab initio molecular orbital calculations using a 6-31G basis set give an optimized geometry with CC bond lengths within 2 pm of the r5 values. The computed dipole moment agrees almost exactly with experiment but a corresponding calculation on fulvene is discrepant with experiment by 0.16 D, which is probably a more typical error.

Noble Gas Endohedral Complexes of C60Buckminsterfullerene

1997 ◽  
Vol 101 (38) ◽  
pp. 7141-7144 ◽  
Author(s):  
Richard B. Darzynkiewicz ◽  
Gustavo E. Scuseria
Keyword(s):  
Noble Gas ◽  
Endohedral Complexes

scholarly journals Computation of General Zagreb Index of Nanotubes Covered by C5 and C7

2020 ◽  
Vol 11 (1) ◽  
pp. 8001-8008
Keyword(s):  
Carbon Nanotubes ◽  
Connected Graph ◽  
Molecular Graph ◽  
Topological Indices ◽  
Topological Descriptors ◽  
Chemical Bonds ◽  
Graph Invariant ◽  
Zagreb Index ◽  
Physical And Chemical ◽  
Simple Connected Graph

A molecular graph is hydrogen deleted simple connected graph in which vertices and edges are represented by atoms and chemical bonds, respectively. Topological indices are numerical parameters of a molecular graph which characterize its topology and are usually graph invariant. In Mathematical chemistry, topological descriptors play an important role in modeling different physical and chemical activities of molecules. In this study, the generalized Zagreb index for three types of carbon nanotubes is computed. By putting some particular values to the parameters, some important degree-based topological indices are also derived.

scholarly journals Noble Gas Endohedral Complexes of C60Buckminsterfullerene

1998 ◽  
Vol 102 (19) ◽  
pp. 3458-3458 ◽  
Author(s):  
Richard B. Darzynkiewicz ◽  
Gustavo E. Scuseria
Keyword(s):  
Noble Gas ◽  
Endohedral Complexes

SEMIEMPIRICAL SCF CALCULATIONS ON AZULENE AND ITS SINGLY CHARGED IONS

1965 ◽  
Vol 43 (11) ◽  
pp. 3026-3038 ◽  
Author(s):  
J. E. Bloor
Keyword(s):  
Dipole Moment ◽  
Excited States ◽  
Ground State ◽  
Basis Set ◽  
Bond Orders ◽  
Electron Charge Density ◽  
Charge Densities ◽  
Bond Lengths ◽  
Set Agreement ◽  
Singly Charged

SCF MOs for azulene have been obtained by the semiempirical Pariser, Parr, Pople procedure using the Nishimoto–Mataga method of calculating repulsion integrals and the assumption that nearest neighbor resonance integrals are independent of interatomic distance. Excited states calculated from these MOs by a CI calculation are in very good agreement with experiment. Ground state charge densities, bond orders, and the dipole moment are similar to other SCFMO calculations and reveal no disadvantage in adopting a constant resonance integral for all bonds. It is shown that estimates of the π-electron charge density by n.m.r. methods are not compatible with direct dipole moment measurements and it is suggested that the interpretation of the n.m.r. measurements suffers from inaccuracies in estimating ring currents. Doubt is also thrown on the use of simple relationships between calculated π-bond orders and bond lengths obtained by X-ray crystallographic measurements on the solid state, particularly since all the bond lengths in azulene are predicted to be longer than in benzene whereas experiment shows some to be shorter. Calculations on spin densities and charge densities of the singly charged azulene anion and cation have been performed by a restricted Hartree–Fock perturbation method in which the matrix elements for the interaction between singly excited states and the ground state are calculated using the closed shell SCFMOs of azulene as the basis set. Agreement with experiment for the anion is fairly good. For the cation our results are in severe disagreement with recent VB calculations, but there are no experimental results available to decide between the two methods.

scholarly journals Noble gas cluster ions

2018 ◽  
Vol 174 ◽  
pp. 06003
Author(s):  
Yunus Kaya ◽  
Yalçin Kalkan ◽  
Rob Veenhof
Keyword(s):  
Density Functional ◽  
Noble Gas ◽  
Kinetic Studies ◽  
Basis Set ◽  
Cluster Ions ◽  
Functional Theory ◽  
B3lyp Method ◽  
Xenon Cluster ◽  
The Density Functional Theory ◽  
Potential Basis

In this work, a reaction mechanism of formation of noble gas (Ng) cluster ions has been theoretically investigated in detail. The kinetic studies of formation of Xe+Xe cluster in Xe, Ar+Ar cluster ions in Ar, and Ne+Ne cluster ions in Ne have been made as theoretically. The optimized structures in the ground state were calculated using the density functional theory (DFT) by the B3LYP method combined with the Stuttgart/Dresden effective core potential basis set (SDD). In addition, we calculated the rate constants of all cluster formations. The results are 1.15 × 10−31, 3.58 × 10−31, 0.23 × 10−31cm6/s, respectively for Neon, Argon, Xenon cluster ions.

scholarly journals Texture-like representation of objects in human visual cortex

2022 ◽  
Author(s):  
Akshay Vivek Jagadeesh ◽  
Justin Gardner
Keyword(s):  
Visual Cortex ◽  
Human Performance ◽  
Object Perception ◽  
Image Synthesis ◽  
Spatial Arrangement ◽  
Basis Set ◽  
Visual Features ◽  
Deep Convolutional Neural Networks ◽  
Natural Feature ◽  
Complex Features

The human visual ability to recognize objects and scenes is widely thought to rely on representations in category-selective regions of visual cortex. These representations could support object vision by specifically representing objects, or, more simply, by representing complex visual features regardless of the particular spatial arrangement needed to constitute real world objects. That is, by representing visual textures. To discriminate between these hypotheses, we leveraged an image synthesis approach that, unlike previous methods, provides independent control over the complexity and spatial arrangement of visual features. We found that human observers could easily detect a natural object among synthetic images with similar complex features that were spatially scrambled. However, observer models built from BOLD responses from category-selective regions, as well as a model of macaque inferotemporal cortex and Imagenet-trained deep convolutional neural networks, were all unable to identify the real object. This inability was not due to a lack of signal-to-noise, as all of these observer models could predict human performance in image categorization tasks. How then might these texture-like representations in category-selective regions support object perception? An image-specific readout from category-selective cortex yielded a representation that was more selective for natural feature arrangement, showing that the information necessary for object discrimination is available. Thus, our results suggest that the role of human category-selective visual cortex is not to explicitly encode objects but rather to provide a basis set of texture-like features that can be infinitely reconfigured to flexibly learn and identify new object categories.

Sign in / Sign up

Export Citation Format

Share Document