The First and Second Static Electronic Hyperpolarizabilities of Zigzag Boron Nitride Nanotubes. An ab Initio Approach through the Coupled Perturbed Kohn–Sham Scheme

Theoretical Study on the Correlation between Open-Shell Electronic Structures and Third-Order Nonlinear Optical Properties in One-Dimensional Chains of π-Radicals

This paper theoretically investigated the correlation between the open-shell electronic structure and third-order nonlinear optical (NLO) properties of one-dimensional (1D) stacked chains of π-radicals. By employing the finite N-mer models consisting of methyl or phenalenyl radicals with different stacking distances, we evaluated the average and standard deviation of diradical characters yi for N-mer models of π-radicals (yav and ySD). Then, we estimated these diradical characters at the limit of N → ∞. These y-based indices were helpful in discussing the correlation between the open-shell electronic structures and the second hyperpolarizability per dimer at the limit N → ∞, γ∞ for the 1D chains with stacking distance alternation (SDA). The calculated γ∞ values and the polymer/dimer ratio γ∞/γ(N = 2) were enhanced significantly when both the stacking distance and SDA are small. We also found that the spin-unrestricted long-range-corrected (LC-)UBLYP method with the range-separating parameter μ = 0.47 bohr-1 well reproduced the trend of γ∞ of this type of 1D chain estimated at the spin-unrestricted coupled-cluster levels. The present study is expected to contribute to establishing the design guidelines for future high-performance open-shell molecular NLO materials.

Geometrical Stability and Nonlinear Optical Properties of Crystallogen and Pnictogen Fullerene Analogues

The linear and nonlinear optical (NLO) properties of fullerene and fullerene-like structures, including crystallogen and pnictogen elements, are computed quantum mechanically. The tensors of optical polarizability, α, and second hyperpolarizability, γ, for a series of buckyball fullerene analogues, namely, Si₆₀, Ge₆₀, Sn₆₀, Pb₆₀, P₆₀, As₆₀, Sb₆₀, and Bi₆₀, are reported and analyzed. The eight considered nanocages are here classified into four categories: nanocages stabilized in the X₆₀ form, including C₆₀, As₆₀, Sb₆₀, and Bi₆₀; nanocages that are not stabilized in the X₆₀ form but are found to be stable in a distorted buckled b-X₆₀ form, with X = Si and Ge; nanocages stabilized only in an exohedral decorated X₆₀-Y₆₀ form, X = Sn, Y = H or F; and finally nanocages that are not stable in either distorted or decorated form; however, their corresponding tabular nanotubes are found to be stable; such group includes P and Pb elements. A suggested nomenclature for the above-mentioned fullerenes is given for the first time, where many geometrical, energetic, and optical parameters are discussed extensively. These systems are energetically stable. The cohesive energies of Bi₆₀ and Sn₆₀-F₆₀ range from -1.2 to -4.8 eV/atom and can be compared to -2.4 and -3.3 eV/atom from the corresponding 2D bismuthene and stanene monolayers, respectively. While bismuthellene, Bi₆₀, shows vigorous optical responses compared to standard fullerene, the (9, 0) phosphorus nanotube gives not only enhanced polarizability and second hyperpolarizability but also an inducing first hyperpolarizability, β, which was null by symmetry in the case of spherical fullerenes. The proposed models are expected to be promising materials for optoelectronic and NLO applications.

A generalized few-state model for the first hyperpolarizability

The properties of molecules depend on their chemical structure, and thus, structure-property relations help design molecules with desired properties. Few-state models are often used to interpret experimental observations of non-linear optical properties. Not only the magnitude but also the relative orientation of the transition dipole moment vectors is needed for few-state models of the non-linear optical properties. The effect of the relative orientation of the transition dipole moment vectors is called dipole alignment, and this effect has previously been studied for multiphoton absorption properties. However, so far, no such studies are reported for the first hyperpolarizability. Here, we present a generalized few-state model for the static and dynamic first hyperpolarizability β, accounting for the effect of dipole alignment. The formulas derived in this work are general in the sense that they can be used for any few-state model, i.e., a two-state model, a three-state model, or, in general, an n-state model. Based on the formulas, we formulate minimization and maximization criteria for the alignment of transition dipole moment vectors. We demonstrate the importance of dipole alignment by applying the formulas to the static first hyperpolarizability of ortho-, meta-, and para-nitroaniline. The formulas and the analysis provide new ways to understand the structure-property relationship for β and can hence be used to fine-tune the magnitude of β in a molecule.

The unique Raman fingerprint of boron nitride substitution patterns in graphene

Boron nitride-substituted graphene (BNsG) two-dimensional structures are new materials of wide technological interest due to the rich variety of electronic structures and properties they can exploit. The ability to accurately characterize them is key to their future success. Here we show, by means of ab initio simulations, that the vibrational Raman spectra of such compounds are extremely sensitive to substitution motifs and concentration, and that each structure has unique and distinct features. This result can be useful as a guide for the optimization of production processes.

Tuning the inter-molecular charge transfer, second-order nonlinear optical and absorption spectra properties of a π-dimer under an external electric field

Different strengths of external electric fields enhance the stability, control the inter-molecular charge transfer and strengthen the nonlinear optical responses of a π-dimer.

Effect of alkaline earth metal at the single wall CNT mouth on the electronic structure and second hyperpolarizability

In the present work, electronic structure and second hyperpolarizability of a number of alkaline earth metals (M [Formula: see text] Be, Mg and Ca) complexes with carbon nanotube (CNT) has been studied by using different DFT functional. The complexes have sufficient thermal stability. Significant amount of charge transfer from metal to CNT results in stronger ground state polarization. The second hyperpolarizability obtained at different DFT functional (BHHLYP, CAM-B3LYP, B2PLYP, [Formula: see text]B97XD) showed a consistent trend. The magnitude of second hyperpolarizability of M@CNT[3,0] complexes enhances rather appreciably when a second metal atom is introduced into other mouth position. The longitudinal component of second hyperpolarizability of M@CNT[3,0]@M complexes increases with increasing size of metal atom. The magnitude of second hyperpolarizability of Ca@CNT[3,0]@Ca complex is comparable with Fe([Formula: see text]-C[Formula: see text]B[Formula: see text]. However, widening/lengthening of CNT markedly reduces the cubic responses. The two state model can qualitatively explain the variation of second hyperpolarizability.

Connecting effect on the first hyperpolarizability of armchair carbon-boron-nitride heteronanotubes: pattern versus proportion

Carbon-boron-nitride heteronanotubes (BNCNT) have attracted a lot of attention because of their adjustable properties and potential applications in many fields. In this work, a series of CA, PA and HA armchair BNCNT models were designed to explore their nonlinear optical (NLO) properties and provide physical insight into the structure-property relationships; CA, PA and HA represent the models that are obtained by doping the carbon segment into pristine boron nitride nanotube (BNNT) fragments circularly around the tube axis, parallel to the tube axis and helically to the tube axis, respectively. Results show that the first hyperpolarizability (β0) of an armchair BNCNT model is dramatically dependent on the connecting patterns of carbon with the boron nitride fragment. Significantly, the β0 value of PA-6 is 2.00 × 10(4) au, which is almost two orders of magnitude larger than those (6.07 × 10(2) and 1.55 × 10(2) au) of HA-6 and CA-6. In addition, the β0 values of PA and CA models increase with the increase in carbon proportion, whereas those of HA models show a different tendency. Further investigations on transition properties show that the curved charge transfer from N-connecting carbon atoms to B-connecting carbon atoms of PA models is essentially the origin of the big difference among these models. This new knowledge about armchair BNCNTs may provide important information for the design and preparation of advanced NLO nano-materials.

Structural, electronic and energetic properties of giant icosahedral fullerenes up to C6000: insights from an ab initio hybrid DFT study

An accurate and detailed electronic structure study of giant carbon fullerenes, benefitting from improved symmetry exploitation in the CRYSTAL14 code.

Optical second-harmonic generation from two-dimensional hexagonal crystals with broken space inversion symmetry

We propose a microscopic theory of the optical second-harmonic generation (SHG) from π electrons in two-dimensional (2D) honeycomb lattice structures with broken space inversion symmetry, such as graphene epitaxially grown on a SiC substrate and boronitrene (a single sheet of hexagonal boron nitride (h-BN)). The approach developed is based on a simple two-band π-electron tight-binding model combined with the original Genkin-Mednis formalism of the second-order nonlinear optical response theory, detailed in our recent paper (2010 Phys. Rev. B 82 235426). Within the framework of the approach, we derive an explicit expression for the SHG susceptibility χ2(SHG(ω), which involves two distinct contributions originating from a mixture of interband and intraband motion of π electrons. Both the contributions, and, hence, the χ2(SHG(ω) on the whole, are found to tend to zero when the π-electron energy bands involved are treated at the simplest level of approximation, neglecting the effect of their trigonal warping around the corners of the Brillouin zone of the 2D hexagonal lattice. Through numerical calculations, it is shown that this effect, though rather small, leads to a fairly large magnitude of the SHG susceptibility, reaching the order of 10(-4) esu for the graphene/SiC overlayer system and 10(-7) esu for monolayer h-BN, when the pump photon energy ħω approaches half the bandgap energy Eg of those structures. These theoretical findings suggest that SHG can be used as a sensitive optical probe of the electronic structure of the examined 2D hexagonal crystals and simultaneously demonstrate that those crystals may be an appropriate material for practical uses in future optoelectronic nano-devices.