A multilevel circulant is defined as a graph whose adjacency matrix has a certain block decomposition into circulant matrices. A general algebraic method for finding the eigenvectors and the eigenvalues of multilevel circulants is given. Several classes of graphs, including regular poly-hedra, suns, and cylinders can be analyzed using this scheme.
The paper reports computations on endohedral fullerene systems, combining the treatments of quantum chemistry and statistical mechanics. Relative concentrations of five isomers of Ca@C72 are presented as an illustration, using the Gibbs energy based on density-functional theory computations. Anharmonicity effects are probed on a simple model system of C6.… (More)
The mechanism of aryl propargyl ether Claisen rearrangement in gas and solvent phase was investigated using DFT methods. Solvent phase calculations are carried out using N,N-diethylaniline as a solvent in the PCM model. The most favorable pathways involve a [3,3]-sigmatropic reaction followed by proton transfer in the first two steps and then deprotonation… (More)
Density functional theory (DFT) and Fourth-order Möller-Plesset (MP4) perturbation theory calculations are performed to examine the possibility of hydrogen storage in V-capped VC(3)H(3) complex. Stability of bare and H(2) molecules adsorbed V-capped VC(3)H(3) complex is verified using DFT and MP4 method. Thermo-chemistry calculations are carried out to… (More)
This report briefly describes the development and applications of net-sign graph theory. The current work enunciates the graph (molecule) signature of non-alternant non-benzenoid hydrocarbons with odd member of rings (non-bipartite molecular graphs) based on chemical signed graph theory. Experimental evidences and Hückel spectrum reveal that structure… (More)
The paper reports computations for Al@C 82 , Sc@C 82 , Y@C 82 and La@C 82 based on encapsulation into the IPR (isolated pentagon rule) C 2υ C 82 cage and also on Mg@C 74 , Ca@C 74 , Sr@C 74 and Ba@C 74 based on encapsulation into the only C 74 IPR cage. Their structural and energetic characteristics are used for evaluations of the relative production… (More)
Li@C(60) and Li@C(70) can be prepared and thus, their calculations at higher levels of theory are also of interest. In the report, the computations are carried out on Li@C(60), Li(2)@C(60) and Li(3)@C(60) with the B3LYP density-functional theory treatment in the standard 3-21G and 6-31G* basis sets. The computed energetics suggests that Li(x) @C(60) species… (More)
The first and second hyperpolarizability beta and gamma are obtained for formaldehyde oligomers (H2CO)n (n = 1-7) using computational methods. We have used the finite field (FF) approach and hyperpolarizability density analysis (HDA) to predict the microscopic first and second nonlinear hyperpolarizability of the formaldehyde oligomers. The spatial… (More)