Doping-enhanced hyperpolarizabilities of silicon clusters: A global ab initio and density functional theory study of Si10 (Li, Na, K)n (n = 1, 2) clusters

First-principles evaluation of the second harmonic generation response of reference organic and inorganic crystals

Using the CRYSTAL17 package at the coupled-perturbed Kohn-Sham (CPKS) level, periodic boundary conditions first-principles calculations are enacted to predict the second harmonic generation second-order nonlinear optical (NLO) susceptibility, χ⁽²⁾, values of six historical NLO crystals. This selection allowed the comparison between state-of-the-art calculations and experiment. Several computational aspects are tackled to define conditions where the results are converged with respect to the range of lattice summations, to the number of k-points in the first Brillouin zone, to the order of the multipole expansions for evaluating the long-range part of the electrostatic interactions, as well as to the atomic basis set size. A valence triple zeta basis set supplemented with polarization functions has been selected. Then, χ⁽²⁾ calculations have been performed using a range of exchange-correlation functionals (XCFs). Results show the large impact of the amount of Hartree-Fock (HF) exchange on the amplitude but also on the sign on the χ⁽²⁾ tensor components. To a given extent, these amplitude effects are consistent with results on molecules, but the sign reversal effects and the non-monotonic behavior of the χ⁽²⁾ tensor components as a function of the amount of HF exchange are scarcely found for molecules. Then, using the recommended range-separated hybrid XCFs, the CPKS scheme leads to good agreement with experimental data for potassium dihydrogenophosphate, urea, and χ_ZXX ⁽²⁾ of LiNbO₃. The agreement is more questionable for χ_ZZZ ⁽²⁾ of LiNbO₃ whereas it remains poor for ammonium dihydrogenophosphate and 2-methyl-4-nitroaniline, with large underestimations by about a factor of 3, opening a path to further fine-tuning of the ranges of inclusion of HF exchange.

Structural and Electronic Properties of LaSin-/0 (n = 2-6) Clusters: Anion Photoelectron Spectroscopy and Density Functional Calculations

The structures and electronic properties of LaSi_n^- (n = 2-6) anions and their neutral counterparts were investigated by anion photoelectron spectroscopy and theoretical calculations. The vertical detachment energies of the most stable structures of LaSi_n^- (n = 2-6) were measured to be 1.28, 1.58, 2.30, 2.05, and 2.91 eV, respectively. The lowest-energy isomer of LaSi₂^- is an isosceles triangle with a C_2v symmetry. For LaSi_3-6^- clusters, the most stable isomers are polyhedrons with La atom face-capping the Si_n frameworks. The lowest-energy structures of neutral LaSi_2,4,5 clusters are similar to their anionic counterparts. The most stable isomer of neutral LaSi₃ is a planar structure with C_2v symmetry, which is different from the triangular pyramid structure of LaSi₃^- anion. The lowest-energy isomer of LaSi₆^- is a C_5v symmetric pentagonal bipyramid structure, while for neutral LaSi₆ cluster, the C_5v structure is not the most stable one. The natural population analysis showed that there is electron transfer from La atoms to Si atoms in LaSi_n^-/0 (n = 2-6). The ZZ tensor component in isochemical shielding surfaces and the anisotropy of the induced current density analyses indicate that the most stable isomer of LaSi₆^- has aromaticity.

Applicability of DFT functionals for evaluating the first hyperpolarizability of phenol blue in solution

The first electronic hyperpolarizability (β) of phenol blue (PB) in several solvents in a wide range of dielectric constants is investigated using the density functional theory (DFT). The reliability of various exchange-correlation functionals is assessed by a comparison to reference Møller-Plesset second-order perturbation theory (MP2) calculations. The equilibrium geometry of PB in each solvent is obtained by using the average solvent electrostatic configuration/free energy gradient method, which performs optimizations on the free energy hyper-surface by employing iteratively the sequential quantum mechanics/molecular mechanics methodology. The dependence of β on the bond length alternation (BLA) coordinate is rationalized by means of the two-level model. Within the employed exchange-correlation functionals, the LC-BLYP functional shows the best performance for describing the static and dynamic MP2 results of β, which increases as the BLA diminishes, reaching a maximum in an intermediate value of BLA. The results also illustrate the role played by the difference between the ground- and excited-state dipole moments (Δμ) in determining the hyperpolarizability behavior in solution. Particularly, in the aqueous solution case, Δμ goes to around zero when BLA is near zero, leading to an abrupt decline in the β value. The DFT results of this study, therefore, indicate a clear relationship between the first hyperpolarizability and the BLA coordinate for the PB in solution, in agreement with experiment.

Structural diradical character

A reliable first-principles description of singlet diradical character is essential for predicting nonlinear optical and magnetic properties of molecules. As diradical and closed-shell electronic structures differ in their distribution of single, double, triple, and aromatic bonds, modeling electronic diradical character requires accurate bond-length patterns, in addition to accurate absolute bond lengths. We therefore introduce structural diradical character, which we suggest as an additional measure for comparing first-principles calculations with experimental data. We employ this measure to identify suitable exchange-correlation functionals for predicting the bond length patterns and electronic diradical character of a biscobaltocene with the potential for photoswitchable nonlinear optical activity. Out of four popular approximate exchange-correlation functionals with different exact-exchange admixtures (BP86, TPSS, B3LYP, TPSSh), the two hybrid functionals TPSSh and B3LYP perform best for diradical bond length patterns, with TPSSh being best for the organometallic validation systems and B3LYP for the organic ones (for which the D3 dispersion correction was included). Still, none of the functionals is suitable for correctly describing relative bond lengths across the range of molecules studied, so that none can be recommended for predictive studies of (potential) diradicals without reservation. © 2018 Wiley Periodicals, Inc.

Stability and Reactivity of Silicon Magic Numbers Doped with Aluminum and Phosphorus Atoms

The progressive scaling down of the silicon-based electronics has allowed to develop devices at nanometer scale, requiring new engineering techniques guided by fundamental chemical and physical concepts. Particularly, the nanostructured cluster systems are promising materials since their physical-chemical properties are sensitive to its shape, size, and chemical components, such that completely different materials can be produced by the simple addition or removal of a single atom. These size-tunable properties can open a new area in materials science and engineering. In the present work, quantum chemical methods were used to study the chemical substitution effects caused by subvalent (aluminum) and supervalent (phosphorus) atoms in the physical-chemical properties of some small silicon clusters, which demonstrate high stability, called magic numbers. The changes in the electronic structure and chemical acceptance to the dopants were evaluated with respect to ionization potential, electronic excitation energy, stability, and reactivity parameters. Taken together, these results enable to identify the most stable silicon-doped clusters. Regarding electrophilic reactions, Si₁₀P is the most favorable system, while for nucleophilic reactions, none of the doped clusters resulted in higher stability.

A comparative theoretical study on the electrical and nonlinear optical properties of Li atom adsorbed on AlN and BN single-walled nanotubes

The geometrical structures, electrical properties, and nonlinear optical (NLO) properties of AlNNT-Li and BNNT-Li nanotube systems were investigated by means of the density functional theory (DFT) method. Frontier molecular orbitals and density of states analyses show that adsorption of the Li atom can significantly narrow the wide HOMO-LUMO gaps of pure AlNNT and BNNT. The results reveal that AlNNT-Li and BNNT-Li systems containing diffuse excess electrons can be regarded as inorganic electrides. The formation of diffuse excess electrons leads to a decrease in transition energies, thereby increasing the first hyperpolarizabilities (β ₀) of AlNNT-Li and BNNT-Li. This work may contribute to the development of potential high-performance NLO materials. Graphical abstract The structural characteristics and nonlinear optical properties of the AlNNT-Li and BNNT-Li systems were studied by means of density functional theory. Introduction of Li atoms greatly enhances the static first hyperpolarizabilities of AlNNT-Li and BNNT-Li.

Effect of Alkali Metal Atoms Doping on Structural and Nonlinear Optical Properties of the Gold-Germanium Bimetallic Clusters

A new series of alkali-based complexes, AM@Ge_nAu (AM = Li, Na, and K), have been theoretically designed and investigated by means of the density functional theory calculations. The geometric structures and electronic properties of the species are systematically analyzed. The adsorption of alkali metals maintains the structural framework of the gold-germanium bimetallic clusters, and the alkali metals prefer energetically to be attached on clusters’ surfaces or edges. The high chemical stability of Li@Ge₁₂Au is revealed by the spherical aromaticity, the hybridization between the Ge atoms and Au-4d states, and delocalized multi-center bonds, as well as large binding energies. The static first hyperpolarizability (β_tot) is related to the cluster size and geometric structure, and the AM@Ge_nAu (AM = Na and K) clusters exhibit the much larger β_tot values up to 13050 a.u., which are considerable to establish their strong nonlinear optical (NLO) behaviors. We hope that this study will promote further application of alkali metals-adsorbed germanium-based semiconductor materials, serving for the design of remarkable and tunable NLO materials.

The nature of structure and bonding between transition metal and mixed Si-Ge tetramers: A 20-electron superatom system

A novel superatom species with 20-electron system, Six Gey M(+) (x + y = 4; M = Nb, Ta), was properly proposed. The trigonal bipyramid structures for the studied systems were identified as the putative global minimum by means of the density functional theory calculations. The high chemical stability can be explained by the strong p-d hybridization between transition metal and mixed Si-Ge tetramers, and closed-shell valence electron configuration [1S(2) 1P(6) 2S(2) 1D(10) ]. Meanwhile, the chemical bondings between metal atom and the tetramers can be recognized by three localized two-center two-electron (2c-2e) and delocalized 3c-2e σ-bonds. For all the doped structures studied here, it was found that the π- and σ-electrons satisfy the 2(N + 1)(2) counting rule, and thus these clusters possess spherically double (π and σ) aromaticity, which is also confirmed by the negative nucleus-independent chemical shifts values. Consequently, all the calculated results provide a further understanding for structural stabilities and electronic properties of transition metal-doped semiconductor clusters. © 2016 Wiley Periodicals, Inc.

Ion-π interaction in impacting the nonlinear optical properties of ion-buckybowl complexes

Ion-buckybowl complexes have received considerable attention in modern chemical research due to its fundamental and practical importance. Herein, we performed density functional theory (DFT) to calculate the geometical structure, binding interactions, dipole moments and the first hyperpolarizabilities (βtot) of ion-buckybowl complexes (ions are Cl(-) and Na(+), buckybowls are quadrannulene, corannulene and sumanene). It is found that the stabilities of ion-buckybowl compounds primarily originate from the interaction energy, which was proved by a new isomerization energy decomposition analysis approach. Plots of reduced density gradient mirror the ion-π weak interaction has been formed between the ions and buckybowls. Significantly, the buckybowl subunits cannot effectively impact the nonlinear optical (NLO), but the kind of ion has marked influence on the second-order NLO responses. The βtot values of Cl(-)-buckybowl complexes are all larger as compared to that of Na(+)-buckybowl complexes, which is attributed to the large charge-transfer (CT) from Cl(-) to buckybowl. Our present work will be beneficial for further theoretical and experimental studies on the NLO properties of ion-buckybowl compounds.

The effect of heterocyclic π bridges on second order nonlinear optical properties of compounds formed between ferrocenyl and corannulenyl

Among D–π–A type compounds, when imidazole acts as a π bridge (endo/exo-3), the β_tot values are almost 2 times as large as when the phenyl acts as a π bridge (endo/exo-2).

Solvent effects on static polarizability, static first hyperpolarizability and one- and two-photon absorption properties of functionalized triply twisted Möbius annulenes: a DFT study

Solvent effects on the polarizability (α), static first hyperpolarizability (β) and one- and two-photon absorption (OPA and TPA) properties of triply twisted Möbius annulenes.

Vibrational corrections to the second hyperpolarizabilities of Al(n)P(n) clusters

In this work, we report results of vibrational corrections to the second hyperpolarizabilities of Al2P2, Al3P3, Al4P4, Al6P6, and Al9P9 clusters. The vibrational corrections were calculated through the perturbation theoretic method of Bishop and Kirtman and also using a variational methodology at the second order Møller-Plesset perturbation theory level with the aug-cc-pVDZ basis set. Results show that the vibrational corrections are important, accounting for more than half of the corresponding electronic second hyperpolarizabilities at the static limit. Comparisons between results obtained through both methods show very good agreements for the terms [α(2)] and [μβ] but significant differences for the term [μ(2)α]. Dynamic vibrational corrections to the second hyperpolarizabilities related to the dc-second harmonic generation, intensity dependent refractive index, and dc-Kerr nonlinear optical processes are also reported.

SCC-DFTB calculation of the static first hyperpolarizability: from gas phase molecules to functionalized surfaces

The performance of the self-consistent charge density functional tight binding (SCC-DFTB) method for calculating the first hyperpolarizability of π-conjugated compounds has been assessed with respect to results obtained with high-level ab initio methods and density functional theory (DFT). The SCC-DFTB method performs similarly or better than DFT with the PBE XC functional. Thus, if for small π-conjugated linkers SCC-DFTB can reproduce trends, for longer chains the first hyperpolarizabilities are overestimated. In the case of push-pull thiophenes, the β values are strongly overestimated, as it is also the case with the B3LYP and PBE XC functionals. On the other hand, the SCC-DFTB method closely reproduces the evolution of β in p-disubstituted benzenes as a function of the donor and acceptor groups, as estimated at the MP2 level. The reliability of SCC-DFTB to determine the bond length alternation and the dihedral angles between the aromatic rings has also been tackled, demonstrating that both are underestimated. Overall, the SCC-DFTB calculations are of the same quality as those performed with the conventional PBE XC functional on which the method was parameterized but the SCC-DFTB calculations are computationally very little demanding, and it can therefore be adopted for very large systems for screening nonlinear optical materials as well as for assessing structure-property relationships. This is illustrated with an application on the first hyperpolarizability of an indolino-oxazolidine molecular switch grafted on a SiO2 surface. This has enabled to pinpoint (i) the effect of the surface on the donor/acceptor character of the linking substituent, (ii) the impact of molecular orientation, (iii) the role of a spacer between the π-conjugated switch and the surface, (iv) the global effect of the surface on the β contrast, and also (v) the fact that the molecular switches can maintain this contrast when adsorbed.

New acceptor-bridge-donor strategy for enhancing NLO response with long-range excess electron transfer from the NH2...M/M3O donor (M = Li, Na, K) to inside the electron hole cage C20F19 acceptor through the unusual σ chain bridge (CH2)4

Using the strong electron hole cage C20F19 acceptor, the NH2...M/M3O (M = Li, Na, and K) complicated donors with excess electron, and the unusual σ chain (CH2)4 bridge, we construct a new kind of electride molecular salt e(-)@C20F19-(CH2)4-NH2...M(+)/M3O(+) (M = Li, Na, and K) with excess electron anion inside the hole cage (to be encapsulated excess electron-hole pair) serving as a new A-B-D strategy for enhancing nonlinear optical (NLO) response. An interesting push-pull mechanism of excess electron generation and its long-range transfer is exhibited. The excess electron is pushed out from the (super)alkali atom M/M3O by the lone pair of NH2 in the donor and further pulled inside the hole cage C20F19 acceptor through the efficient long σ chain (CH2)4 bridge. Owing to the long-range electron transfer, the new designed electride molecular salts with the excess electron-hole pair exhibit large NLO response. For the e(-)@C20F19-(CH2)4-NH2...Na(+), its large first hyperpolarizability (β0) reaches up to 9.5 × 10(6) au, which is about 2.4 × 10(4) times the 400 au for the relative e(-)@C20F20...Na(+) without the extended chain (CH2)4-NH2. It is shown that the new strategy is considerably efficient in enhancing the NLO response for the salts. In addition, the effects of different bridges and alkali atomic number on β0 are also exhibited. Further, three modulating factors are found for enhancing NLO response. They are the σ chain bridge, bridge-end group with lone pair, and (super)alkali atom. The new knowledge may be significant for designing new NLO materials and electronic devices with electrons inside the cages. They may also be the basis of establishing potential organic chemistry with electron-hole pair.

Ionization enhancement in silicon clusters and germanium atoms in the presence of zirconium

Molecules/clusters have been shown to undergo an enhancement in ionization under ultrafast laser pulses. This enhancement results in the lowering of the laser intensity required to observe ion signal from higher atomic charge states resulting from Coulomb explosion of clusters. Here, we explore the effect of using an early-group transition metal as an electron source in the formation of small silicon clusters on the observed enhancement in ionization. Intensity selective scanning is used to measure the onset of ion signal for the atomic charge states of silicon, germanium, zirconium, and oxygen. Additionally, the kinetic energy released values for the resulting high charge states of silicon are measured and compared to those previously observed using a copper electron source. A significant increase in ionization enhancement is observed upon using zirconium metal, despite a decrease in cluster size. Germanium metal with zirconium is studied for comparison and shows a larger enhancement in ion signal than silicon, indicating that atomic mass may be significant.