Spectral moments of polymer graphs

Spectral Moments of the Edge Adjacency Matrix in Molecular Graphs. 3. Molecules Containing Cycles

“…The study of the spectral moments of the vertex adjacency matrix of molecular graphs has received great attention in the chemical literature. , The relationships between such moments and the energy in the Hückel theory was the first incentive for its study since the pioneering work of Hall and Marcus − The other alternative of the use of spectral moments of graph theoretical matrices is what we are using in the present work: as structural descriptors to be used in QSPR and QSAR studies. Some reports of the use of spectral moments of the vertex adjacency matrix of molecular graphs to the desrciption of physical properties of molecules have also been given in the literature.…”

Tenth Spectral Moment for Molecular Graphs of Phenylenes

“…The applications of the spectral moments of the same matrix in theoretical chemistry of conjugated molecules are too numerous to be outlined here in due detail. [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42] In a series of papers, moments were used for the estimation of HMO total π-electron energy and the examination of its dependence on molecular struc- ture. [23][24][25][26][27][28][29][30][31][32][33]35,39,40 A treatment based on the energy partitioning via spectral moments was proposed for dealing with the aromaticity of conjugated systems.…”

“…The spectral moments of the A matrix have found noteworthy applications in solid-state physical chemistry. − Namely, using a continued fraction technique, the normalized moments were used to obtain the HMO density of states and other useful properties of the solids. The applications of the spectral moments of the same matrix in theoretical chemistry of conjugated molecules are too numerous to be outlined here in due detail. − In a series of papers, moments were used for the estimation of HMO total π-electron energy and the examination of its dependence on molecular structure. − ,,, A treatment based on the energy partitioning via spectral moments was proposed for dealing with the aromaticity of conjugated systems. , In all applications of spectral moments, it is necessary to understand how they depend on the molecular structure. For this purpose, explicit expressions, in terms of counts of simple structural features, were designed for the first few spectral moments of various classes of molecular graphs.…”

Spectral Moments of the Edge Adjacency Matrix in Molecular Graphs. Benzenoid Hydrocarbons

“…[15][16][17] When a continued fraction technique was used, the normalized moments were used to obtain the Huckel molecular orbital (HMO) density of states and other useful properties of solids. The applications of spectral moments of the same matrix in theoretical chemistry of conjugated molecules [5][6][7][8][9][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32] are too numerous to be outlined here in due detail. In a series of papers moments were used for the estimation of HMO total π-electron energy and examination of its dependence on molecular structure.…”

“…The spectral moments of the A matrix have found noteworthy applications in the solid state physical chemistry. − When a continued fraction technique was used, the normalized moments were used to obtain the Huckel molecular orbital (HMO) density of states and other useful properties of solids. The applications of spectral moments of the same matrix in theoretical chemistry of conjugated molecules − ,− are too numerous to be outlined here in due detail. In a series of papers moments were used for the estimation of HMO total π-electron energy and examination of its dependence on molecular structure. − ,− A treatment based on the energy partitioning via spectral moments was proposed for dealing with aromaticity of conjugated systems. , Explicit expressions, in terms of counts of simple structural features, were designed for the first few spectral moments of various classes of molecular graphs.…”