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With structural miniaturization down to the nanoscale, the detectable quantities of solid materials no longer remain constant but become tunable. For the II-VI semiconductors example, the band gap expands, the elastic modulus increases, the melting point drops, and the Raman optical phonons experience red shift associated with creation of low frequency Raman acoustic modes that undergo blue shift with decreasing the dimensional scale. In order to understand the common origin of the size dependency of these seemingly irrelevant properties, we formulated these quantities for CdS, ZnS, and CdSe semiconductors from the perspectives of bond order-length-strength correlation and the local bond averaging approach. Consistency between the theory predictions and the measured size dependence of these quantities clarified that the undercoordination-induced local strain and quantum entrapment and the varied fraction of undercoordinated atoms of the entire solid correlate these quantities and dominate their size effect., (This journal is © The Royal Society of Chemistry 2012)

Although the dielectric behavior of nanostructured semiconductors has been intensively investigated, the physics behind observations remains disputed with possible mechanisms such as quantum confinement and dangling bond polarization. Here we show that theoretical reproduction of the measured dielectric suppression of Ge nanocrystals asserts that the dielectric suppression originates from the shorter and stronger bonds at the skin-deep surface, the associated local densification and quantum entrapment of energy. Coordination-imperfection induced local quantum entrapment perturbs the Hamiltonian that determines the band gap and hence, the process of electron polarization consequently., (This journal is © The Royal Society of Chemistry 2012)

From the perspective of bond relaxation and bond vibration, we have formulated the Raman phonon relaxation of graphene, under the stimuli of the number-of-layers, the uni-axial strain, the pressure, and the temperature, in terms of the response of the length and strength of the representative bond of the entire specimen to the applied stimuli. Theoretical unification of the measurements clarifies that: (i) the opposite trends of the Raman shifts, which are due to the number-of-layers reduction, of the G-peak shift and arises from the vibration of a pair of atoms, while the D- and the 2D-peak shifts involve the z-neighbor of a specific atom; (ii) the tensile strain-induced phonon softening and phonon-band splitting arise from the asymmetric response of the C(3v) bond geometry to the C(2v) uni-axial bond elongation; (iii) the thermal softening of the phonons originates from bond expansion and weakening; and (iv) the pressure stiffening of the phonons results from bond compression and work hardening. Reproduction of the measurements has led to quantitative information about the referential frequencies from which the Raman frequencies shift as well as the length, energy, force constant, Debye temperature, compressibility and elastic modulus of the C-C bond in graphene, which is of instrumental importance in the understanding of the unusual behavior of graphene.

An edge-modified tight-binding (TB) approximation has been developed, enabling us to clarify the energetic origin of the width-dependent band gap (E(G)) expansion of the armchaired and the reconstructed zigzag-edged graphene nanoribbons with and without hydrogen termination. Consistency between the TB and the density-function theory calculations affirmed that: (i) the E(G) expansion originates from the Hamiltonian perturbation due to the shorter and stronger bonds between undercoordinated atoms, (ii) the combination of the edge-to-width ratio with a local bond strain up to 30% and the associated 152% potential well depression determines the width dependent E(G) change; and, (iii) hydrogen termination affects insignificantly the band gap width as the H-passivation minimizes the midgap impurity states.

Although they exist ubiquitously in human bodies and our surroundings, the impact of nonbonding lone electrons and lone electron pairs has long been underestimated. Recent progress demonstrates that: (i) in addition to the shorter and stronger bonds between under-coordinated atoms that initiate the size trends of the otherwise constant bulk properties when a substance turns into the nanoscale, the presence of lone electrons near to broken bonds generates fascinating phenomena that bulk materials do not demonstrate; (ii) the lone electron pairs and the lone pair-induced dipoles associated with C, N, O, and F tetrahedral coordination bonding form functional groups in biological, organic, and inorganic specimens. By taking examples of surface vacancy, atomic chain end and terrace edge states, catalytic enhancement, conducting-insulating transitions of metal clusters, defect magnetism, Coulomb repulsion at nanoscale contacts, Cu(3)C(2)H(2) and Cu(3)O(2) surface dipole formation, lone pair neutralized interface stress, etc, this article will focus on the development and applications of theory regarding the energetics and dynamics of nonbonding electrons, aiming to raise the awareness of their revolutionary impact to the society. Discussion will also extend to the prospective impacts of nonbonding electrons on mysteries such as catalytic enhancement and catalysts design, the density anomalies of ice and negative thermal expansion, high critical temperature superconductivity induced by B, C, N, O, and F, the molecular structures and functionalities of CF(4) in anti-coagulation of synthetic blood, NO signaling, and enzyme telomeres, etc. Meanwhile, an emphasis is placed on the necessity and effectiveness of understanding the properties of substances from the perspective of bond and nonbond formation, dissociation, relaxation and vibration, and the associated energetics and dynamics of charge repopulation, polarization, densification, and localization. Finding and grasping the factors controlling the nonbonding states and making them of use in functional materials design and identifying their limitations will form, in the near future, a subject area of "nonbonding electronics and energetics", which could be even more challenging, fascinating, promising, and rewarding than dealing with core or valence electrons alone.

Relativistic density functional theory calculations have been conducted to examine the effect of atomic under-coordination on the crystal structure, binding energy, and electron configuration of cuboctahedral and Marks decahedral gold clusters. Trend consistency between calculations and experimental observations confirmed the predictions made using BOLS correlation theory, suggesting that the shorter-and-stronger bonds between under-coordinated atoms induce local structure relaxation, potential well depression, and the associated local charge and energy densification, as well as the polarization of the otherwise conducting s-electrons (valence charge) by the densely- and tightly-trapped core electrons of which the binding energy shifts positively to deeper energies. Findings are in good agreement with scanning tunneling microscopy/spectroscopy results from monomers, dimers, chain ends, and nanostructures of gold and other metals.