Self-assembled donor–acceptor chromophores have extensive applications in photofunctional devices owing to their unique charge transport properties. To explore the possibility of improving nonlinear optical (NLO) properties by self-assembly to multilayer complexes, we theoretically investigated the geometric and electronic structures, interlayer weak interactions, absorption spectra, charge transfer properties, polarizabilities (α), and first hyperpolarizabilities (β) of naphthalimide, -phenyl, and -naphthyl monomers, dimers, and trimers by increasing the layer number n (n = 1, 2, 3). Different stacking patterns of their dimers were also taken into account. These show that parallel stacking patterns are conducive to maximizing overlap with respect to antiparallel ones due to the concept of optimal π-orbital overlap is more vast than purely maximizing cofacial overlap to improve charge transport. The decreases in band gap for the di/trimeric versus monomeric naphthalimide, -phenyl, and -naphthyl monomers indicate the possibility of more favorable photoinduced electron transition in the aggregate when compared to the monomer. The linear and second-order NLO properties of these complexes are investigated in detail. The α values increase linearly as the increased number n of the layer (n = 1, 2, and 3), providing a new kind of tendency forecast method for the linear optical properties. Along with the increasing electron donating ability of the donor, the βtot values of monomers increased, revealing the general rule of designing NLO molecular materials. The dependence of βtot value on the layer number shows that the βtot value increased with the increased number of layer, which can be rationalized by considering the enhancement of interlayer electronic transition and two-dimensional NLO character with the two charge transfer axes. We hope this work may evoke one’s attention to design new, highly efficient second-order NLO materials with excellent building blocks: multilayer complexes.

•7-substituted coumarins can narrow the energy gap between the HOMO and LUMO.•The introductions of the transition metal caions have great effect on the second-order nonlinear optical response.•Absorption spectra and charge transfer were discussed by TDDFT calculations.•The bonding interaction of the O atoms and the metal cations has been explored using NBO and AIM.Most of the coumarins have been found useful as non-linear optical chromophores. The four novel water-soluble coumarin-based compounds (OC6, NC6, OC7, and NC7) and the metallic compounds of NC7 with different metal cations (Na+, K+, Mg2+, Ca2+, Fe2+, and Zn2+) have been investigated by carrying out density functional theory (DFT). Our DFT calculations revealed that the second-order nonlinear optical properties have a pronounced enhancement by means of the introduction of π-conjugatd electron donor (dimethylamino phenyl alkynyl) in 7-position of the coumarin ring and metal cations, especially for transition metals. The further investigations of the larger first hyperpolarizability (βtot) reveal that the NC7*Fe2+ and NC7*Zn2+ present the larger values as 1.151 × 10−27 and 1.083 × 10−27 esu owing to the lower transition energies and larger oscillator strengths of crucial electronic transitions. Moreover, time-dependent DFT results show that the large intramolecular charge transfers exist in the NC7*Fe2+ and NC7*Zn2+. In addition, the natural bond orbital analysis demonstrated that the second-order stabilization energies is from the lone pair (LP) orbital on O atom to the LP* orbital of metal cations interaction correlate with the O-Mn+ atomics distance. On the other hand, the atoms in molecules analysis showed that the O-Mn+ interactions can be characterized by the presence of a bond critical point (BCP) and the O-Fe2+ and O-Zn2+ interactions have partially ionic and partially covalent bonds rather than an electrostatic character for O-Mn+ (Na+, K+, Mg2+ and Ca2+). In addition, the delocalization indices of O-Mn+ bonds correlate reasonably well with electron density, kinetic and potential energy densities in these complexes. Thus, we hope this research will introduce a new relation between the structure and the property of chromophore nonlinear optical activity.Download high-res image (199KB)Download full-size image

•The βvec value can be efficiently tuned by the position of the Ru acetylide.•The differences on NLO properties are attributed to the more obvious charge transfer.•The enhancement of βvec value is due to decrease of the transition energy.•The βvec values of the open-ring complexes are larger than the closed-ring complexes.Ru metal acetylide electron donor-acceptor complexes have important applications in the field of nonlinear optics. Herein, in this work, a series of half-sandwich ruthenium-based Cp*(dpe)Ru ([Ru*]) metal complexes with the dihydroazulene/vinylheptafulvene (DHA/VHF) have been investigated by density functional theory (DFT) calculations. The results showed that the position of the [Ru*] acetylide functionality, either para or meta on the phenylene ring to the DHA/VHF core (1c/1o and 2c/2o), and additional a p-phenylene spacer (3c/3o) had a great influence on the second-order nonlinear optical (NLO) responses. The systems 1 and 3 can significantly increased second-order NLO responses compared with system 2. It was attributed to the more obvious charge transfer along y-axis, which is from [Ru*] acetylide functionality to DHA, accompanied by a significant decrease of the transition energy according electron density difference maps and time-dependent DFT calculations. The βvec values of the open-ring complexes were larger than the corresponding closed-ring complexes owing to the smaller HOMO−LUMO gap in the open-ring complexes. It was also because of the smaller BLA values in open-ring complexes, which had stronger π-conjugation. Especially, the change ratio of βvec value of system 2 was the largest due to the fact that their charge transfers degree varied greatly. In addition, the frequency-dependent NLO properties of the studied complexes were evaluated at 0.0239 a.u. and 0.0340 a.u. The calculation results demonstrated that the magnitude of the frequency-dependent first hyperpolarizability increased with the increasing frequency. We believe that our present work will be beneficial for further theoretical and experimental studies on large second-order NLO responses of metal complexes.The para-position of the Ru acetylide and additional a p-phenylene spacer greatly increase the second-order NLO responses.Download high-res image (250KB)Download full-size image

Spirooxazine, a photochromic material, can transform into metallic open-form merocyanine by molecular switching, giving rise to large contrasts in its second-order nonlinear optical (NLO) properties. The switching properties are particularly large when various metal ions (Li+, Na+, K+, Mg2+, Ca2+, Fe2+, Zn2+, and Ag+) are introduced, as evidenced by density functional theory calculations, which show that the spirooxazine undergoes a pronounced change in geometry accompanied by formation of a larger π-conjugated system. The resultant merocyanine derivatives have 10–21-fold higher static second-order NLO responses. Spirooxazine can therefore be used as a powerful and multi-use detection tool. The large first hyperpolarizability (βtot) is shown to rely on the alkaline earth metal, causing βtot values to increase nearly 21-fold, as evidenced by the larger charge distribution, lower transition energy, and separate distribution of first hyperpolarizability density. In contrast, variation of βtot in the Fe2+ derivative is not obvious, owing to stronger complexation, a larger amount of charge transferred from the napthoxazine moiety to the metal, and the reduction in N⋯O distance between the ligand heads. Therefore, spiropyran-to-merocyanine molecular switching can be used to distinguish alkaline earth metals and determine the efficiency of cation detection.

Confining excess electrons in a specific space is an effective strategy to design nonlinear optical (NLO) molecules. The complexants with excess electrons are usually organic compounds, but these compounds are thermally unstable and thus hardly meet the processing requirements of NLO materials. To obtain better thermostability and NLO response molecules, in this work, inorganic compounds of B20H26 isomers containing two cavities were proposed. With the two included cavities, B20H26 can be doped by one or two Li atoms to form electrides of Li@B20H26 and Li2@B20H26. These electrides show larger NLO responses, with respect to the corresponding undoped complexant of B20H26. Particularly, Li2@B20H26 has the largest β0 value of 108 846 a.u. (MP2/6-31+G(d) level) that is 850 times as large as that of corresponding B20H26. Moreover, the change of β0 values with excess electron number is remarkable for two of the isomers, and differences between the β0 values among those isomers are also significant owing to various B–B connection sites between the two cavities. Therefore, the present inorganic electrides have not only better performance due to the magnitude of their β0 values but also better behavior on the molecular-level modulation of NLO.

To reveal a new structure–property relationship regarding the nonlinear optical (NLO) properties of fullerenes that are associated with gamma (γ) density, fullerenes I (C40, C50, C60 and C70), whose heights range from 4.83 to 7.96 Å, and II (C24, C36, C48 and C72), whose widths range from 4.45 to 8.22 Å, have been the research objects. Calculation of their geometric and electronic structures, absorption spectra, and the second hyperpolarizability (γ) and the γ density analysis have been performed. It is found that the electronic spatial extent and the polarizability (α) value increase linearly as the fullerenes increase by every 12 carbon atoms. Similarly, the γ values are also proportional to the fullerene size. It is worth noting that the relative magnitude of γxxxx and γzzzz was exactly consistent with that of the width and height of fullerenes. The analysis of γ density provides the essential reason for this result, that is, the magnitude of the contribution to γ values associated with γ densities is proportional to the density amplitudes multiplied by the distance between them. Larger fullerenes possess larger density amplitudes and longer distances, resulting in larger γ values with respect to smaller fullerenes. This work presents a new structure–property interplay between the width and height of the fullerenes and their second hyperpolarizability γ. Moreover, the γ density analysis provides a new insight to explore the nature of the relationship between the structure and the NLO properties.

•The reduced centers should take place preferentially at the π-conjugated units.•The order of is in roughly consistent with anisotropy polarizability.•This open/close molecular motion allows efficient molecular switch.•The β enhancement is related to the intramolecular interlayer charge transfer.The control of rotational motion, using an external impulse (such as redox), has been intensively pursued as nonlinear optics switch. Four redox responsive ferrocene-based actuators with varied π-conjugated units have been systematically investigated by the density functional theory. The open structures of these complexes with antiparallel orientation of both π-conjugated units are due to the large charge repulsion effect, while the closed forms are stabilized by the intramolecular π–π stacking interactions.The rotational motion can be triggered by reduction process preferentially centered on the π-conjugated units. The polarizabilities and first hyperpolarizabilities of complexes [3]closed2+ and [4]closed2+ are significant enhanced, which are respectively related to the electronic spatial extent and intramolecular interlayer charge transfer occurred between two respective π-conjugated units. Overall, the present work shows that one can design the molecular nonlinear optical switches characterized by a large contrast varying from zero to a large value along the reversible transformations.

Sodium superoxide (NaO2) has attracted considerable attention as the main discharge product in Na–air batteries due to its specific energy, which exceeds that of the Li-ion battery. Pressure has become an irreplaceable tool to improve or alter the physical properties of a given material. By utilizing first-principles swarm structure-searching predictions, herein, we for the first time investigate the structures and electronic properties of NaO2 in the pressure range of 0–20 GPa. It is found that the orthorhombic Pnnm structure at ambient pressure transforms to another orthorhombic Immm structure at approximately 4.6 GPa, and subsequently to the tetragonal P4/mbm structure at 6.7 GPa. The pressure-induced structural transitions are mainly derived from the denser polyhedral packing and higher coordination number. It is interesting to find that the superoxide group (O2−) is maintained over the entire pressure range considered. Analysis of the electronic band structure and density of states shows that the structures found exhibit intriguing half-metallic magnetism. This study enables an opportunity to understand the structures and electronic properties of NaO2 at high pressures.

•N,N-Dimethylanilin can narrow the energy gap between the HOMO and LUMO.•The order of is in roughly consistent with anisotropy polarizability.•N,N-Dimethylanilin significantly increases the first hyperpolarizabilities (βtot).•The enhancement of βtot is related to the intramolecular electron transfer.The push-pull functionalized fullerenes consisting of multi-N,N-diethylamine donors covalently attached to N-methylpyrrolidine derivative of C60 have been designed and investigated. The structures and first hyperpolarizabilities of these fullerene derivatives were calculated using density functional theory. Furthermore, absorption spectra of the complexes along with electron density difference maps corresponding to the most intense electronic transitions were achieved by time-dependent density functional theory. It suggests that with the growing numbers of N,N-Dimethylanilin acting as electron-donating group, the polarizabilities, dipole moments and the first hyperpolarizabilits increase, however, transition energies of the crucial electronic transitions decrease and the absorption wavelength shows bathochromic effect. The excitation transitions have significant charge transfer character and, as a consequence, the novel complexes can behave as second-order nonlinear optical chromophores, in which the N,N-Dimethylanilin act as donors towards fullerenes.

•The βtot value can be efficiently tuned by the 2,2′-bipyridyl or I ion.•The differences on NLO properties are due to a change in charge transfer pattern.•The redox processes lead to different βtot values of 3 and 4, specifically.Carboranes are the chemist's toolbox, playing a crucial role in the development of the second-order nonlinear optical (NLO) materials. A series of 12-vertex ruthenacarborane half-sandwich complexes with the substituted 2,2′-bipyridyl and I ion ligands have been investigated by density functional theory (DFT). The calculated first hyperpolarizabilities (βtot) of the neutral complexes increase with replacing the –CO unite with electron donor 2,2′-bipyridyl and I ion. The redox processes of complex 3 significantly reduce βtot value. The oxidation process of complex 4 also reduce βtot value, while the reduced process enhance βtot value. Furthermore, the enhanced βtot values of the substituted systems are dominated by the intraligand charge transfer, ligand-to-metal charge transfer, metal-to-ligand charge transfer, and d–d transitions of Ru ion. Therefore, it can be concluded that different substituents and redox processes significantly influence the second-order NLO responses.A series of 12-vertex ruthenacarborane half-sandwich complexes with the substituted 2,2′-bipyridyl and I ion ligands have been investigated by density functional theory (DFT). It can be concluded that different substituents and redox processes significantly influence the second-order NLO responses.

•The different doping concentration and position change the electronic properties.•(Sr1−xMx)FeO2 (M = Ca, Ba; x = 0.25, 0.75) are semi-metallic property.•The different doping position for x = 0.5 has semi-metallic and semiconductor property.•The Ca-doped system has higher magnetic moment compare with the Ba-doped system.ABO2-type perovskite materials have been wide applied in solid oxide fuel cells and gas sensors. SrFeO2 with P4/mmm structure exhibiting an unparalleled FeO4 square-planar coordination structure. We have investigated the Sr-site substitution effect on the electronic conductivity of the perovskite-type structure of (Sr1−xCax)FeO2 and (Sr1−xBax)FeO2 (x = 0, 0.25, 0.5, 0.75) by using first-principle calculations. Six kinds of doping form have been considered for the Ca-site and Ba-site, respectively. The different doping concentration and position lead to change in crystal structure and electronic properties. When x = 0.5, α and β doping structures display Pmmm symmetry, while γ and δ doping structures show P4/mmm symmetry. The band structure and density of states reveal that different doping concentration and position can make the electronic conductivity change from semiconductor to semi-metallic. When x = 0.25, 0.75, 0.5 for γ and δ doping, the doped system were semi-metallic properties. Whereas, when x = 0.5 for α and β doping, the doped system were semiconductor properties. Further, doping can lead to an increase of the magnetic moments. It is worth noting that the Ca-doped system has higher growth in the magnetic moments compare with the Ba-doped system. This work provides a new route for the potential application in electrochemistry devices.

Zwitterionic complexes have been the subject of great interest in the past several decades due to their multifunctional application in supramolecular chemistry. Herein, a series of internally stable charge-compensated carboranylated square-planar Pt(II) zwitterionic complexes have been explored by density functional theory aim to assessing their structures, the first hyperpolarizabilities, first hyperpolarizability densities, and electronic absorption spectra. It is found that the first hyperpolarizabilities of two-dimensional (2D) structure complexes are much larger with respect to the one-dimensional complex. It is ascribed to the lower transition energy and more obvious charge transfer, which can be further illustrated by their large amplitude and separate distribution of first hyperpolarizability density. In addition, the first hyperpolarizabilities of 2D complexes can be further significantly modified by introducing electron-donating/withdrawing groups on the carborane cage. As a consequence, we believe that these 2D zwitterionic complexes can behave as novel second-order nonlinear optical chromophore with a promising future.

•The interaction formed in ion–buckybowl complexes is weak ion–π interaction.•Cl− ion has marked influence on the NLO responses as compared to Na+.•The difference on NLO property is due to a change in the charge transfer pattern.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.Ion–π weak interaction has been formed between the ions and buckybowls. And the first hyperpolarizabilities (βtot) of Cl−-buckybowl complexes are all larger as compared to that of Na+–buckybowl complexes, which is attributed to the large charge-transfer from Cl− to buckybowl.

•The βtot value can be tuned by introducing substituent groups.•Substituent effect on the NLO response is different for closed/open-ring forms.•The difference on NLO response is due to the change in charge transfer pattern.•Carborane has little contribution to the NLO responses for closed-ring forms.Carborane has been the subject of great interest over the last decades due to its high structural, chemical, biological stability and diverse applications. In the present work, carboranyl-substituted indole/indoline compounds and their functionalized derivatives have been systematically investigated by density functional theory (DFT) method with the view of assessing their electronic structures and first hyperpolarizabilities. Significantly, the first hyperpolarizabilities can be obviously enhanced by the introduction of a strong electron-withdrawing group for closed-ring forms, while the strong electron-donating group is beneficial for large first hyperpolarizabilities for open-ring forms. It indicates that the NLO properties of these compounds can be enhanced by controlling their relative substituent groups. Furthermore, the time-dependent DFT calculation illustrates that the enhancement of the first hyperpolarizabilities are found due to the obvious charge transfer (CT) transition, and closed-ring forms have a significant difference on the CT patterns versus open-ring ones. Investigation of the structure–property relationship and substituent effects at the molecular level can benefit for further exploration of carboranyl-substituted indole/indoline derivatives with versatile and fascinating NLO properties.

The size-selective formation of eight molecular recognition pairs between the host corannulene and fullerene guest of various size have been studied by taking advantage of concave–convex π–π interactions. Herein, the structures, binding interactions, electronic absorption spectra, and first hyperpolarizabilities have been explored using density functional theory calculations. It is found that with the aim to maximize the concave–convex shape complementarity, the base of fullerene can be modified at certain angles with the central ring plane of C20H10 (0° for complexes 1–4 and 46°, 34°, 19°, and 5° for complexes 5–8, respectively). The interaction energies depend linearly on the convex surface area and the size of the fullerene sphere. Further, the results of first hyperpolarizabilities show that the shape of the fullerene is the dominant factor for complexes 1–4 because of the intramolecular charge transfer (CT) within fullerene cage. Among them, complex 4 presents the largest βtot value as 5.64 × 10–30 esu because of the more obvious intramolecular CT from the upper part to the bottom part of the C70 cage, derived from the larger height of the cage. On the other hand, low-lying CT character accounts for a large part of the first hyperpolarizability. The achieved understanding provides the prospect of size-selective strategy for enhancing the concave–convex interaction and second order nonlinear optical response in the recognition of fullerenes.

The electron donor–acceptor complexes, which undergo intramolecular charge transfer under external stimulus, are an emerging class of materials showing important application in nonlinear optics. Synthesizing ferrocene/fullerene complexes through face-to-face fusion would enjoy the merits of both ferrocene and fullerene due to their strong donor–acceptor interactions. Four ferrocene/fullerene hybrid complexes with the gradual extension of fullerene cage size, including CpFe(C60H5), CpFe(C66H5), CpFe(C70H5), and CpFe(C80H5) (Cp is cyclopentadienyl), have been investigated by density functional theory. These hybrid molecules give eclipsed and staggered isomers. The main reason that the eclipsed isomer is stable is that the eclipsed structure possesses large CpFe⋯fullerene bonding energy. The CpFe⋯fullerene interaction is smaller than that of Cp⋯Fefullerene, which must come from two different interfaces. The presence of covalent bond character between CpFe and fullerene is supported by the localized orbital locator, deformation of electron density distribution and energy decomposition analysis. Significantly, the absorption bands and first hyperpolarizabilities of these hybrid complexes are strongly sensitive to the fullerene cage size, which is ascribed to a change in the charge transfer pattern, especially for CpFe(C80H5), which displays reverse π → π* charge transfer from bottom to top cage, leading to notable hyperpolarizability. Investigation of the structure–property relationship at the molecular level can benefit the design and preparation of such hybrid complexes in chemistry and materials science.

A class of D1–A–D2–A–D1-type small molecule (SM) donors (2–5) was engineered via modifying or replacing the core donor moiety in three building blocks based on the reported DTS(PTTh2)2 (1) to screen suitable donor materials for organic photovoltaics (OPV). Density functional theory calculation was performed to investigate the electronic structures, open circuit voltage (Voc) and key parameters closely relevant to the short-circuit current density (Jsc), including (i) absorption spectrum, (ii) electron–hole coherence, (iii) energy driving force, (iv) charge transfer dynamics, and (v) carrier transport efficiency. The results manifest that the designed 2–5 show good performance with large Voc, stable charge transfer and effective charge transport. Surprisingly, the ratios kinter-CT/kinter-CR of 2/PCBM, 3/PCBM, and 5/PCBM heterojunctions present over 104 times higher than that of 1/PCBM. Our conclusions indicate that designed PT-based SMs can better the performance of OPVs, which will provide theoretical guideline for the design and synthesis of new organic SM donors.

Buckybowls involving π–π interactions offer exciting future opportunities in terms of designing novel smart nonlinear optical (NLO) materials. Dimeric species of corannulene (C20H10), the smallest buckybowl, was considered as a model for the host–guest assemblies, which exhibited the convex–concave stacking of curved conjugated carbon surfaces. Different stacking motifs (concave–convex and convex–convex dimers) of C20H10 dimers that affect the NLO properties are the focus of our study. We performed density functional theory calculations on the structure, binding interactions, electronic absorption spectra and second hyperpolarizabilities of π-stacking dimers of C20H10 and its Li-doped derivative. It was found that the concave–convex dimers exhibit stronger binding interactions because of larger electrostatic interactions and thus are more stable with respect to the convex–convex dimers. The doping of Li ion significantly enhances the orbital interaction between the monomers but slightly affects the spectra and the second hyperpolarizabilities of the dimers. The convex–convex dimers exhibit larger polarizabilities and second hyperpolarizabilities (γzzzz) as a result of enhanced interlayer charge transfer properties. There is an increasing linear relationship between the electronic coupling and γzzzz values. The results presented in this article provide important evidence for the convex–convex stacking motif that enhances the NLO properties of the π-stacking dimers. Thus, controlling molecular stacking is an important way in terms of designing novel smart NLO materials.

Alkali metal peroxides have a wide range of industrial applications (e.g., energy storage and oxygen source). It is well known that pressure can cause profound structural and electronic changes, leading to the fundamental modification of the physical properties. Here, we reported the structural phase transition, lattice dynamics, and electronic properties of alkali metal (Li, Na, K, and Rb) peroxides by using the unbiased structure searching techniques and first-principles density functional calculations in the pressure range of 0–100 GPa. The predicted first-order phase transitions pressures in Li2O2, Na2O2, K2O2 and Rb2O2 occur at ∼84, 28, 7 and 6 GPa, respectively, which closely correlates with the electronegativity of alkali metals. Different phase transition mechanisms and complex phase transition structures have been observed for these alkali metal peroxide compounds. These predicated high-pressure phases are thermodynamically stable against decomposition into alkali metal oxides plus O2 or alkali metals plus O2. Interestingly, the character of the peroxide group (O22−) is maintained under the considered pressure range. Phonon calculations using the quasi harmonic approximation confirm that these structures are dynamically stable. The band gaps for the studied alkali metal peroxides increase with increasing pressure. This work provides an opportunity for understanding the structures and electron properties of alkali metal peroxides at high pressures.

Much effort has been devoted to investigating the molecular geometries, electronic structures, redox properties and nonlinear optical (NLO) properties of Ir complexes involving o-, m- or p-carborane groups by density functional theory (DFT) methods. Switchable second-order NLO properties were induced by redox processes involving these complexes, and it was found that mainly the coordination bonds of Ir complexes changed during the oxidation process. Our calculations revealed that oxidation reactions have a significant influence on the second-order NLO response owing to the change in charge transfer pattern. The βtot values of oxidized species are at least ∼9 times larger for set I and ∼5 times larger for set II than those of the corresponding parent complexes. Introduction of carborane groups into ppy (phenylpyridine) ligands can enhance the second-order NLO response by 1.2– 1.6 times by a metal-to-ligand charge transfer (MLCT) transition between the Ir atom and carborane. The βtot of complex 2 [(ppy)2Ir(phen)]+ (phen = phenanthroline) is 3.3 times larger than that of complex 1 (ppy)2Ir(acce) (acce = acetylacetonate), which is caused by ligand-to-ligand charge transfer (LLCT) between ppy ligands and the ancillary ligand. Therefore, it can be concluded that the second-order NLO response can be effectively enhanced by oxidation reactions.

•The structures of the π dimers at fully staggered position are the most stable.•The strong binding interactions are beneficial for the stabilities of the dimers.•Red shift in electronic spectrum is dependent on the interlayer charge-transfer.•The low transition energies are the key factors to determine γyyyy values.Hexathiophenalenylium (HTPLY) has gained increasing attention for its interesting and potentially useful optical properties as a result of the enhancement in spin delocalization and charge-transfer of phenalenyl radicals, occasioned by the attachment of successive three disulfide linkages. Herein, we performed density functional theory to calculate the binding interactions, electronic absorption spectra and the second hyperpolarizabilities of cation and radical dimers of HTPLY and its nitro derivatives. It is found that the equilibrium structures of the π dimers at fully staggered position are most stable. Among these π dimers, radical dimers exhibit stronger binding interactions with respect to cation dimers. In addition, obvious red shifts in electronic spectra of radical dimers are dependent on the large interlayer charge-transfers. More importantly, radical dimers [4]dim3 and [5]dim1 exhibit a significant increase in the second hyperpolarizabilities as compared to cation dimers, which is due to lower excitation energies and larger interlayer charge-transfers. We believe that the results presented in this article shall provide important evidence for the large interlayer charge-transfers in enhancing the NLO properties of the π dimers.Increasing nonlinear optical response: Density functional theory calculation shows that the radical dimers exhibit considerable enhancement of the second hyperpolarizabilities (γyyyy) with respect to the cation dimers. The enhancement is due to the lower transition energy and larger interlayer charge-transfer.

A charge transfer (CT) complex was formed between C20H10 and Li+@C60 in the ground state by the concave–convex π–π CT interaction. Herein, the structures, binding interactions, electronic absorption spectra, and first hyperpolarizabilities of a series of Li+ and Li atom in contact with C60 have been explored with density functional theory methods. It is found that independent of the doping position, doping Li atom can significantly narrow the wide gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) (Egap = 2.82 eV) of the pure C20H10/C60 in the range of 0.86–0.99 eV. Among them, the Li-doped outer isomer C20H10/LiC60 can exhibit the intriguing n-type characteristic, where a high energy level containing the excess electron is introduced as the new HOMO orbital in the original gap of C20H10/C60. Furthermore, the diffuse excess electron also brings C20H10/C60 the considerable first hyperpolarizability, which is 3.53 × 10–29 esu. When Li+ and Li were encapsulated into the C60 cage, inner complexes C20H10/Li+@C60 and C20H10/Li@C60 of enhanced static first hyperpolarizabilities (5.39 and 2.13 × 10–29 esu, respectively) are also delivered due to that encapsulated Li+@C60 and Li@C60 show enhanced electron acceptability as compared to pristine C60, leading to more obvious intermolecular CT transitions. From a certain point of view, such systems can be considered as high-performance NLO materials that combine the basic characteristics of a classical donor–acceptor superstructure and systems with cations and easily polarizable excess electrons.

The rotary motion based on metallacarboranes around a molecular axis can be controlled by simple electron transfer processes, which provides a basis for the structure–property relationship for the nonlinear optical (NLO) switching. However, this phenomenon has not been previously reported in the development of NLO properties of metallacarboranes. In this work, the metallacarboranes [NiIII/IV(C2B9H11)2]−/0 and their C-,B-functionalized derivatives are studied by the density functional theory (DFT) method. By calculating relative energies, we obtained the stable states before and after rotation controlled by simple electron transfer. Then, the static and frequency-dependent second-order NLO properties were calculated by several DFT functionals. According to the TDDFT results, the large NLO responses of the studied compounds are mainly caused by substituent group-to-carborane cage charge transfer (L′LCT) and substituent group-to-metal charge transfer (L′MCT) processes. The order of first hyperpolarizabilities (β values) illustrates that the NLO response can be enhanced by introducing a strong electron-donating group. Significantly, the geometric interconversions resulting from the redox reaction of 1C/1T–6C/6T allow the NLO responses to be switched “ON” or “OFF”. The B(9,9′)-methoxyphenyl-functionalized derivative of nickelacarborane, having low energetic cost and large different NLO responses between two states (from 0 to 20998 a.u.), can be an excellent switchable NLO material.

The studies of geometrical structures, thermal stabilities, redox properties, nonlinear responses and optoelectronic properties have been carried out on a series of novel ferrocenyl (Fc) chromophores with the view of assessing their switchable and tailorable second order nonlinear optics (NLO). The use of a constant Fc donor and a 4,4′-bipyridinium acceptor and varied conjugated bridges makes it possible to systematically determine the contribution of organic connectors to chromophore nonlinear optical activities. The structures reveal that both the reduction reactions and organic connectors have a significant influence on 4,4′-bipyridinium. The potential energy surface maps along with plots of reduced density gradient mirror the thermal stabilities of the Fc-based chromophores. The first and second reductions take place preferentially at the 4,4′-bipyridinium moieties. Significantly, the reduction processes result in the molecular switches with large NLO contrast varying from zero or very small to a large value. Moreover, time-dependent density functional theory results indicate that the absorption peaks are mainly attributed to Fc to 4,4′-bipyridinium charge transfer and the mixture of intramolecular charge transfer within the two respective 4,4′-bipyridinium moieties coupled with interlayer charge transfer between the two 4,4′-bipyridinium moieties. This provides us with comprehensive information on the effect of organic connectors on the NLO properties.

•The NLO responses are tuned by photoisomerization, redox, and protonation.•Three pathways change the structural and the charge transfer pattern.•The oxidization and protonation processes slightly affect NLO coefficient.•The photoisomerization stimulus is the best way.In this paper, the switchable second-order nonlinear optical (NLO) responses of Ru dithienylperfluorocyclopentene (DTE) complexes controlled by photoisomerization, oxidation and protonation have been systematically investigated by the density functional theory. Theoretical results reveal some important structural changes upon these three pathways. It can also be found that the protonation and oxidation processes have some infuence on the charge transfer (CT) pattern but slightly affect the first hyperpolarizability (βvec). In striking contrast, in the photoisomerization process, the difference on the βvec values between 2o and 2c is the largest with respect to the protonation and oxidation processes with a βvec(2c)/βvec(2o) = 52.7 ratio. Time-dependent density functional theory calculation predicts that the DTE intramolecular π–π* charge transfer is helpful for the large NLO response. It confirms that the photoirradiation evokes the photoisomerization character to display dramatic difference in βvec values, which paves the way for the applications of switchable NLO materials.The switching of the second-order nonlinear optical (NLO) properties for Ru-coordinated DTE complexes have been investigated by density functional theory. The second-order polarizabilities are sensitive to photoisomerization, redox, and protonation processes. Photoisomerization manipulation is the best pathway for switching the second-order NLO responses of the Ru-coordinated DTE complexes.

•A significant enhancement of βtot value is observed.•System 3 possesses the largest βtot value (18640 a.u.) at the MP2/6-31+G(d) level.•The enhanced βtot value is well explained by large fΔμ/ΔE3 value.•A guideline for an effective molecular design of NLO material is provided.The structures with all real frequencies and static first hyperpolarizabilities (βtot) of a series of Lin@indeno[1,2-b]fluorene (n = 1–6) salts have been calculated by the second-order Møller–Plesset (MP2) theory. The results show that the Li-substituted effect can significantly enhance the βtot values of Lin@indeno[1,2-b]fluorene compared with that of non-substituted molecule indeno[1,2-b]fluorene. Especially, the βtot value (18640 a.u.) for Li3@indeno[1,2-b]fluorene is the largest among all systems. According to the two-level model, the calculated fΔμ/ΔE3 values further explain the large second-order nonlinear optical (NLO) responses of Lin@indeno[1,2-b]fluorene. In addition, the investigations on frequency-dependent first hyperpolarizabilities (β(ω)) show that the dispersion has less influence on the β(ω) values at low frequency area of all studied systems. It is our expectation that this work will be beneficial for further theoretical and experimental studies on the NLO properties of the lithium salts.Graphical abstractIn this work, we have designed a series of Li-substituted salts Lin@indeno[1,2-b]fluorene (n = 1–6) of substituted H atom(s) by Li atom(s) in indeno[1,2-b]fluorene. The studied systems are constructed by getting their global minimum energy. The second-order nonlinear optical responses of the studied systems are dominated by the number and the location of Li atoms. System 3 (Li atoms at 2, 3 and 4 positions) possesses the largest βtot value (18640 a.u.) at the MP2/6-31+G(d) level.

Recently, the N-connecting pattern of the BN-segment has been shown as a suitable strategy to enhance the static first hyperpolarizability (β0) of carbon–boron–nitride heterojunction nanotubes (J. Phys. Chem. C 2013, 117, 10039–10044). In this work, we report a quantum chemical investigation on the lithiation effect to further reveal the mechanism of modification. Interestingly, the lithiation effect is significantly dependent on the activating segment of the heterojunction nanotubes. For lithiation on the BN-segment, the β0 (3.22 × 104 au) of Li5–BN-1a is larger than that (1.42 × 104 au) of Li5–BN-2a, which shows that the N-connecting pattern of the BN-segment linking to the C-segment is an efficient way to enhance the β0 of heterojunction nanotubes. However, for lithiation on the C-segment, the β0 (6.03 × 104 au) of Li5–BN-1b is even slightly smaller than that (6.97 × 104 au) of Li5–BN-2b. Besides, results show that activating the C-segment is a more effective strategy than activating the BN-segment for enhancing the β0 of carbon–boron–nitride heterojunction nanotubes by lithiation. The new knowledge about heterojunction nanotubes might provide important information for designing nonlinear optical molecules by rationally introducing lithium atoms on carbon–boron–nitride heterojunction nanotubes.

Unusual long, multicenter dimers bearing a large electron donor and acceptor have been the subject of great interest over the last decades due to their better conducting, superconducting, magnetic, or other physical properties. Two-electron, multicenter bonding between two interplanar fragments has been recently recognized as a novel and important bonding interaction. Herein, the [TTF][TCNE], [TTF][TCNQ], [TTF][TCNP], and [TTF][TCNB] dimeric species have been studied by quantum mechanics methods with the view of assessing their interactions and first hyperpolarizabilities. It is found that the stabilities of the dimers primarily originate from the electrostatic bonding component. Although to a lesser extent, long, multicenter interactions due to the overlap of the molecular orbitals of the monomers are important also in the stability of these systems. Significantly, a severe hyperpolarizability decrease with changing the acceptor monomers of the dimeric species is qualitatively explained in terms of change in their charge transfer patterns. It indicates that the first hyperpolarizabilities of these dimers can be optimized by controlling their relative acceptor monomers. We believe that these results shall provide important information for further exploration of long, multicenter dimers with versatile and fascinating nonlinear optical properties.

A series of redox-active complexes 1–3 (1,1′-diquadrannulenylferrocene, 1,1′-dicorannulenylferrocene, 1,1′-disumanenylferrocene) and their corresponding conformational isomers that are composed of ferrocene donor and various acceptors of different buckybowl (open bowl-shaped polyaromatic hydrocarbon) subunits have been investigated by density functional theory. The nature of the redox property makes it possible to develop novel examples of chromophores that are amenable to molecular switches, which can therefore be used in optical devices. The complexes 1–3, with high thermal and chemical stabilities, show π–π stacking interaction between two buckybowl subunits, and support for the presence of significant donor–acceptor interaction was obtained from the employment of the natural bond orbital charge and charge decomposition analysis. Both one-electron oxidation and one- and two-electron reduction have been considered. The results show some important electronic structure changes upon oxidation/reduction that are accompanied by significant differences in the corresponding absorption spectra and second-order nonlinear optical properties. These differences are due to a change in the charge transfer pattern. The redox switch ability suggests that these ferrocene–buckybowl complexes can be viewed as redox-triggered nonlinear optical switches with one of the complexes having an on/off ratio of 100.2 for the hyperpolarizability values. Thus, our work has helped to establish ferrocene–buckybowl complexes as versatile and fascinating nonlinear optical switching compounds with a promising future.

•The electron density is bounded by the Li atom and its neighboring B atoms.•The Li-doped effect on the first hyperpolarizability is dramatic.•There are clearly dependencies of βtot values on the transition energies.•Charge transfer from BNNC to Li atom becomes more pronounced.•The frequency-dependent effect on the first hyperpolarizability is weak.The unusual properties of Li-doped boron nitride nanomaterials have been paid further attention due to their wide applications in many promising fields. Here, density functional theory (DFT) calculations have been carried out to investigate the second-order nonlinear optical (NLO) properties of boron nitride nanocone (BNNC) and its Li-doped BNNC derivatives. The natural bond orbital charge, electron location function, localized orbital locator and frontier molecular orbital analysis offer further insights into the electron density of the Li-doped BNNC derivatives. The electron density is effectively bounded by the Li atom and its neighboring B atoms. The Li-doped BNNC molecules exhibit large static first hyperpolarizabilities (βtot) up to 1.19 × 103 a.u. for Li@2N-BNNC, 5.05 × 103 a.u. for Li@2B-BNNC, and 1.08 × 103 a.u. for Li@BN-BNNC, which are significantly larger than that of the non-doped BNNC (1.07 × 102 a.u.). The further investigations show that there are clearly dependencies of the first hyperpolarizabilities on the transition energies and oscillator strengths. Moreover, time-dependent DFT results show that the charge transfer from BNNC to Li atom becomes more pronounced as doping the Li atom to BNNC. It is also found that the frequency-dependent effect on the first hyperpolarizabilities is weak, which may be beneficial to experimentalists for designing Li-doped BNNC molecules with large NLO responses.Increasing response: Density functional theory shows that doping Li atom into boron nitride nanocone (BNNC) (see picture) can lead to a substantial increase of the first hyperpolarizability. The enhancement of the first hyperpolarizability is due to the large electron transfer from BNNC moiety to Li atom and the small difference in transition energies between the ground and the crucial excited states.

The third-order nonlinear optical (NLO) properties of aromatic diimide molecules have been studied for the first time using density functional theory (DFT) with a finite field (FF). This study shows that the size of the aromatic core can affect the static second hyperpolarizability (γ). Increasing the number of benzenes along the longitudinal axis can effectively improve the γ values because the degree of charge transfer along the longitudinal direction increases, whereas an increase in the number of benzenes along the perpendicular axis does not enhance the γ values. Furthermore, the NLO responses of the reduced form radical anions 1−, 5− and 6−, which were obtained by a reversible redox process, are discussed. The results show that the γ values of the radical anions are changed by the redox process. For the reduced form radical anion 6−, the γ value is −1906.71 × 10−36 esu, and its absolute value is ∼7.3 times larger than that of its neutral parent. An analysis of the BLA values demonstrates that the γ value is closely related to the conjugation of the aromatic core used in the redox process.Graphical abstractRedox effect on the static third-order nonlinear optical (NLO) properties of aromatic diimides systems with different aromatic core have been investigated with density functional theory (DFT). The results show that the studied system, especially the large aromatic core system, exhibit larger alteration of the second hyperpolarizability in reduced process and is promising to become redox-switchable NLO molecular materials.Highlights► The size of aromatic core can affect the γ values. ► Increasing benzenes along z axis can effectively improve the γ values. ► The reduced process causes an efficient third-order NLO switching for system 6. ► The γ values are closely related to BLA values of aromatic core for redox systems.

The second-order nonlinear optical (NLO) properties of a series of Pt(II) dithienylethene (DTE) complexes possessing the reversible photochromic behavior have been investigated by density functional theory (DFT) combined with the analytic derivatives method. The results show that the calculated static first hyperpolarizabilities (βtot) of the open-ring and closed-ring systems significantly increase in the range of 2.1–4.5 times through strengthening of the electron-withdrawing ability of the substituent R (R = H, CF3, NO2) and an increase of the number of thiophene rings. Moreover, there is a large enhancement of the βtot values from the open-ring systems to the corresponding closed-ring systems. This efficient enhancement is attributed to the better delocalization of the π-electron system, the more obvious degree of charge transfer, and the larger fos/Egm3 (fos is the oscillator strength, and Egm is the transition energy between the ground and the excited states) values in the closed forms according to the bond length alternation (BLA) and time-dependent density functional theory (TDDFT) calculations. In addition, the dispersion has less influence on the frequency-dependent first hyperpolarizabilities (βtot(ω)) of the studied systems at the low-frequency area ω (0.000–0.040 au). Our present work would be beneficial for further theoretical and experimental studies on large second-order NLO responses of metal complexes.

We report a theoretical study based on density functional theory (DFT) on the geometric and electronic structure, linear optical and second-order nonlinear optical properties of a series of new inorganic–organic hybrid hexamolybdate–organoimido–(car)boranes. By the incorporation of borane/carborane at the end of the phenyl ring of the organoimido segment, the studied systems show excellent nonlinear optical (NLO) response than the organoimido-substituted hexamolybdate. The computed static first hyperpolarizability βvec value of [Mo6O18(NC8H8)(B12H11)]4− (II) is largest, −167.2 × 10−30 esu, and a higher βvec value of [Mo6O18(NC8H8)(C2B10H11)]2− (III-2p) is 58.6 × 10−30 esu. Moreover, the time-dependent (TD)DFT calculation illustrates that the maximum absorption, which is helpful for the large NLO responses, is mainly assigned to the charge transfer (CT) from (car)borane and organoimido segment to the hexamolybdate cluster. The density of density (DOS) calculations further illustrate the excitation from valence orbitals of boron atoms to that of Mo and O atoms in hexamolybdate can be responsible for larger NLO responses. The linear and nonlinear optical properties of species III both vary with the position of the vertex on the carborane. Furthermore, the order of the βvec values is consistent with the bathochromic shift of the maximum absorption for our studied systems, and the studied systems show a wider transparency range extending into the entire visible and infrared (IR) region.

Donor substituted heteroleptic bis-tridentate Ru(II) complexes with different deprotonated forms exhibit larger alterations of the first hyperpolarizabilities in oxidized process and are promising to become redox-switchable nonlinear optical (NLO) molecular materials. For systems with diprotonated form, the βvec value of the two-electron-oxidized system 132+ is 5.3 and 178.6 times as large as those of the reduced parent 3 and the one-electron-oxidized system 3+ according to the DFT–FF results. For systems with mono-protonated form, the oxidization of the deprotonated benzimidazole anion is more helpful to enhance the βvec value because of the increasing βx component. For systems with fully deprotonated form, the largest ratio of |βvec((1″)+)/βvec(1″)| of the system without substituent is about 13.2 due to the dominant off-diagonal tensor βzxx. And the time-dependent density functional theory (TDDFT) results indicate that the charge transfer transition of the first excited state displays an indispensable role for larger off-diagonal tensor. Finally, the calculated frequency-dependent β results exhibit a small dispersion effect at the low-frequency region.Graphical abstractRedox effect on the static second-order nonlinear optical (NLO) properties of donor substituted complexes [(H2pbbzim)Ru(tpy-X)]2+ (X = H, Ph-NMe2 and monopyrrolo-TTF) with different deprotonated forms has been investigated with density functional theory (DFT). The results show that the studied systems, especially the diprotonated system with TTF unit, exhibit larger alterations of the first hyperpolarizabilities in oxidized process and are promising to become redox-switchable NLO molecular materials.Highlights► Redox affects βvec value and causes an efficient second-order NLO switching. ► βvec value changes in various degrees due to the different oxidized center. ► Oxidation of donor causes larger βz while that of deprotonated ion causes larger βx. ► Frequency-dependent βvec suggests the efficient redox-switchable NLO responses.

The static second-order nonlinear optical (NLO) properties on a series of the two-dimensional (2D) pincer Ru(II) complexes with the substituted Tpy and H2SCS tridentate ligands (Tpy = 2,2′:6′,2″-terpyridyl and H2SCS = 2,6-bis(benzylaminothiocarbonyl)phenyl) have been investigated by density functional theory (DFT). Introducing different donor/acceptor substituents to two ligands has an influence on the static first hyperpolarizabilities (βtot) of the 2D systems. Compared to the reference system 1 [Ru(H2SCS)(Tpy)]+, introducing the branches with strong electron acceptor group (p-NO2-phenylethynyl) to the Tpy ligand or the branches with strong electron donor group (p-NH2-phenylethynyl) to the H2SCS ligand can effectively improve the βtot values. Time-dependent DFT (TDDFT) calculations indicate that the enhanced βtot values of the substituted systems are dominated by the intraligand charge transfer (ILCT), metal-to-ligand charge transfer (MLCT) and ligand-to-metal charge transfer (LMCT) transitions. Furthermore, the proton abstraction plays an important role in tuning the second-order NLO response. Particularly, for system 5 bearing the branches with NO2 groups on H2SCS ligand, there is a dramatic enhancement in the βtot values for its deprotonated forms. The βtot values of the monodeprotonated system 5-H and the dideprotonated system 5-2H (58.712 × 10–30 and 761.803 × 10–30 esu) are about 7.58 times and 36.4 times larger than their diprotonated system 5, respectively. The second-order NLO responses based on substituent effect and proton abstraction switch are two-dimensional in characteristic with the large off-diagonal tensor values.

The redox-switchable second-order nonlinear optical (NLO) properties of a series of Rh(I) complexes have been studied based on density functional theory (DFT) calculations. The analysis of the electronic structure shows that the Rh(I) ion acts as the oxidation center in a one-electron-oxidized process, while both the Rh(I) ion and the 9,10-phenanthrenediimine (phdi) ligand act as reduction centers in a one-electron-reduced process. Different redox centers lead to different charge-transfer (CT) features, which alter the static first hyperpolarizabilities of the neutral complexes. Our DFT calculations indicated that these complexes show large second-order NLO responses and that the redox process can significantly enhance these NLO responses. For complexes 2 and 3, the βtot values of the one-electron-reduced species 2− and the one-electron-oxidized species 3+ are ∼10.0 and ∼8.5 times larger, respectively, than those of the corresponding neutral complexes. Therefore, complexes 2 and 3 are promising candidates for redox-switchable NLO molecular materials. The large NLO responses of the oxidized species are mainly related to ligand-to-ligand charge-transfer (LLCT) transitions when combined with intraligand charge-transfer (ILCT) transitions, while the results for the reduced species are strongly associated with metal-to-ligand charge-transfer (MLCT) transitions.Graphical abstractThe static first hyperpolarizabilities of complexes 2, 2−, 3 and 3+.Highlights► The –NH2 substituted 3 displays desirable NLO properties. ► Oxidized or reduced center is different in redox process. ► Complexes 2 and 3 are promising candidates for redox-switchable NLO materials.

In this work, density functional theory (DFT) combined with the finite field (FF) method has been adopted to analyze the second-order nonlinear optical (NLO) properties of the triarylborane (TAB) derivatives obtained by introducing different inductive electron groups into the phenylene ring of the TAB (RTAB, where R=2-C6H5-C2B10H10(1), R=F(2), R=Me(3), R=NO2(4), R=NH2(5)). The static first hyperpolarizabilities (βtot) of the RTAB molecules can be switched by binding one F− to the boron center (RTAB′) or one-electron reduction (RTAB″). The DFT-FF calculations show that the βtot values of 2′, 3′ and 5′ decrease while those of 1′ and 4′ increase compared with the values of their neutral molecules, which was attributed to the fact that the charge transfers of 3 and 5 become smaller and those of 1 and 4 become larger by binding one F− ion to the boron center, according to time-domain DFT (TD-DFT) analysis. However, the incorporation of one electron enhances the second-order NLO properties of the RTAB molecules remarkably, especially for system 1. It is notable that the βtot value of reduced form 1″ is 508.69×10−30 esu, i.e. abou 578 times larger than that of system 1. Frontier molecular orbital (FMO) and natural bond orbital (NBO) analyses suggest that the reversal of the charge distribution between the neutral molecules and their reduced forms leads to low HOMO-LUMO energy gaps (E0) and thus large βtot values for the reduced forms.

A second-order nonlinear optical (NLO) molecular switching with redox has been investigated in the present paper. The static first hyperpolarizabilities of 5-(BMes2)-5′-(NPh2)-2,2′-bipyridine (BNbpy) containing three-coordinate organoboron, Pt(II) chelate complex Pt(BNbpy)Ph2, and their reduced forms have been calculated by density functional theory (DFT) combined with the analytic derivatives method. There is an enhancement of static first hyperpolarizabilities in the reduced form according to the calculations. That is, the βvec value of one-electron-reduced form is ∼7 times as large as that of neutral form BNbpy; the βvec values of one- and two-electron-reduced forms are ∼3 and ∼4 times as large as that of neutral form Pt(BNbpy)Ph2, respectively. In particular, the βvec value of two-electron-reduced form 3Pt(BNbpy)Ph22– is 1349 × 10–30 esu, ∼286 times larger than its neutral form. Moreover, the component βz value of the metal chelate complex Pt(BNbpy)Ph2 is 25 × 10–30 esu, which is ∼14 times as large as that of ligand BNbpy; the corresponding F–/CN– compounds show a decrease in βx values compared with the case of the ligand and Pt(II) complex. Analyses of geometries, density of states (DOS), and time-dependent DFT (TDDFT) calculations reveal that the one-electron reduction promotes the molecular conjugation in the x-axis and intensifies the interaction between the metal Pt(II) and ligand and then results in an enhancement of the static first hyperpolarizability, whereas the binding of F–/CN– to the B atom turns off the pπ–π* conjugation and has no effect on the conjugation of bipyridine, which leads to a decreasing β value in the x-axis.

The polarizabilities and hyperpolarizabilities of the tetrahydropyrrole diradical in different electronic states have been investigated using ab initio and density functional theory (DFT) methods combined with the finite field (FF) approach. The polarizability average value αs is a maximum for the singlet state, while that for the closed-shell is a minimum. The trend in second hyperpolarizability average value γ is in good agreement with that for αs. The γ values of the singlet and triplet states are, respectively, about 3 and 2 times larger than that of the closed-shell. The order of the first hyperpolarizability total effective value βtot is βtot (closed-shell) > βtot (singlet) > βtot (triplet). The αs, βtot, and γ values of different electronic states obtained using the B3LYP and MP4SDQ methods are close to those obtained using the reliable CCSD method. The nonlinear optical (NLO) properties of two systems isoelectronic with the tetrahydropyrrole diradical — cyclopentane and tetrahydrofuran diradicals — show that the polarizabilities and hyperpolarizabilities of these systems are all smaller than those of the tetrahydropyrrole diradical in the three electronic states.

DFT B3LYP/LANL2DZ method was employed to calculate electron properties and the second-order nonlinear optical (NLO) respond of platinum (II) complexes which have been synthesized by Weinstein group. 4,7-diphenyl-1,10-phenanthroline shows the ability to push electron in these complexes. Metal Pt plays a balancing charge role. Comparing complex 1b–6b with complex a, the βvec value of complex 1b–5b is larger than one of complex a, while the βvec value of complex 6b is smaller than one of complex a. In these seven complexes, the βvec values of complexes increase with decreasing of the energy difference between HOMO and LUMO. Moreover, the electron transfers from deeper layer occupied orbitals to empty orbitals have a distinct contribution to second-order NLO coefficient.

Three novel polymers, {[Cd(m-bdc)(L)]·H2O}n (1), [Co(m-bdc)(L)0.5(H2O)]n (2) and [Zn5(L)2(p-bdc)5(H2O)]n (3) based on 1,1′-bis(pyridin-3-ylmethyl)-2,2′-biimidazole (L) ligand and benzenedicarboxylate isomers, have been prepared and structurally characterized. Compound 1 exhibits a 2D architecture with (42·6)(42·67·8) topology, which is synthesized by L and 1,3-benzenedicarboxylate (m-bdc) ligands. Compound 2 is constructed from 1D chains that are linked by L ligands extending a 2D (4,4) grid. Compound 3 is a 3D framework with (43)(46·618·84) topology, which is composed of trinuclear clusters and five-coordinated metal centers joined through 1,4-benzenedicarboxylate (p-bdc) and L ligands. Moreover, the fluorescent properties of L ligand, compounds 1 and 3 are also determined.Three unprecedented complexes have been constructed from a new semirigid ligand 1,1′-bis(pyridin-3-ylmethyl)-2,2′-biimidazole (L) combined with benzenedicarboxylate isomers and different metal ions under hydrothermal conditions, which exhibit novel topologies. Luminescent properties of L ligand, compounds 1 and 3 are also determined.

Density functional theory (DFT) B3LYP method was employed to calculate electron properties and the second-order nonlinear optical (NLO) responses of the derivatives which were formed by (C5H5)Co(C2B4H6) and CHCHC6H4NO2, CHCHC6H4NH2. The results show: when H atom of (C5H5)Co(C2B4H6) is substituted by CHCHC6H4NO2, the βtot values of isomers are all slightly smaller than that of ferrocene (Fc) derivative (FcCHCHC6H4NO2). However, when H atom of (C5H5)Co(C2B4H6) is substituted by CHCHC6H4NH2, the βtot values of isomers are close to that of ferrocene (Fc) derivative (FcCHCHC6H4NH2). It indicates that (C5H5)Co(C2B4H6) can be either a donator or an acceptor.

Density functional theory (DFT) B3LYP at 6-31G* level is employed to optimize the structures of the molecules bridged through n-vertex bis-substituted carborane (n=5, 6, 7) and combined with finite field (FF) formalism to calculate the second-order NLO properties. The results indicate that the structures of n-vertex bis-substituted carborane (n=5, 6, 7) are changed due to bridged donor and acceptor moieties. The distances between two C atoms are becoming longer. And the stability and dipole moment are influenced by changing substituted positions of C atoms. The isomers with the substituents connecting with C atoms of lower coordination number have better stability and larger values of polarizability. One-dimensional structure of the molecules bridged through n-vertex bis-substituted carborane (n=5, 6, 7) is in favor of intramolecular charge-transfer. Meanwhile, the isomer with a larger change of dipole moment has larger value of second-order NLO properties during the charge-transfer process.

For designing three-dimensional cobalt(II) metal complexes and Schiff base ligands, the geometry was taken from the starting structures based on the crystallographic data. The density functional theory (DFT) B3LYP/6-31g(d)-FF method was used to calculate the second-order nonlinear optical (NLO) properties of open-shell cobalt(II) metal complexes. The key findings revealed that when compared with the Schiff base ligands, the second-order NLO properties of the metal complexes did not change obviously. The reason is that the NLO responses of cobalt(II) metal complexes are strongly related to intraligand charge transfer processes. According to the frontier molecular orbitals, the less contributions of Co2+ in determining the NLO responses of metal complexes arise from the action of bridging moiety in the charge transfer (CT) processes.

The rotary motion based on metallacarboranes around a molecular axis can be controlled by simple electron transfer processes, which provides a basis for the structure–property relationship for the nonlinear optical (NLO) switching. However, this phenomenon has not been previously reported in the development of NLO properties of metallacarboranes. In this work, the metallacarboranes [NiIII/IV(C2B9H11)2]−/0 and their C-,B-functionalized derivatives are studied by the density functional theory (DFT) method. By calculating relative energies, we obtained the stable states before and after rotation controlled by simple electron transfer. Then, the static and frequency-dependent second-order NLO properties were calculated by several DFT functionals. According to the TDDFT results, the large NLO responses of the studied compounds are mainly caused by substituent group-to-carborane cage charge transfer (L′LCT) and substituent group-to-metal charge transfer (L′MCT) processes. The order of first hyperpolarizabilities (β values) illustrates that the NLO response can be enhanced by introducing a strong electron-donating group. Significantly, the geometric interconversions resulting from the redox reaction of 1C/1T–6C/6T allow the NLO responses to be switched “ON” or “OFF”. The B(9,9′)-methoxyphenyl-functionalized derivative of nickelacarborane, having low energetic cost and large different NLO responses between two states (from 0 to 20998 a.u.), can be an excellent switchable NLO material.

Confining excess electrons in a specific space is an effective strategy to design nonlinear optical (NLO) molecules. The complexants with excess electrons are usually organic compounds, but these compounds are thermally unstable and thus hardly meet the processing requirements of NLO materials. To obtain better thermostability and NLO response molecules, in this work, inorganic compounds of B20H26 isomers containing two cavities were proposed. With the two included cavities, B20H26 can be doped by one or two Li atoms to form electrides of Li@B20H26 and Li2@B20H26. These electrides show larger NLO responses, with respect to the corresponding undoped complexant of B20H26. Particularly, Li2@B20H26 has the largest β0 value of 108846 a.u. (MP2/6-31+G(d) level) that is 850 times as large as that of corresponding B20H26. Moreover, the change of β0 values with excess electron number is remarkable for two of the isomers, and differences between the β0 values among those isomers are also significant owing to various B–B connection sites between the two cavities. Therefore, the present inorganic electrides have not only better performance due to the magnitude of their β0 values but also better behavior on the molecular-level modulation of NLO.

The studies of geometrical structures, thermal stabilities, redox properties, nonlinear responses and optoelectronic properties have been carried out on a series of novel ferrocenyl (Fc) chromophores with the view of assessing their switchable and tailorable second order nonlinear optics (NLO). The use of a constant Fc donor and a 4,4′-bipyridinium acceptor and varied conjugated bridges makes it possible to systematically determine the contribution of organic connectors to chromophore nonlinear optical activities. The structures reveal that both the reduction reactions and organic connectors have a significant influence on 4,4′-bipyridinium. The potential energy surface maps along with plots of reduced density gradient mirror the thermal stabilities of the Fc-based chromophores. The first and second reductions take place preferentially at the 4,4′-bipyridinium moieties. Significantly, the reduction processes result in the molecular switches with large NLO contrast varying from zero or very small to a large value. Moreover, time-dependent density functional theory results indicate that the absorption peaks are mainly attributed to Fc to 4,4′-bipyridinium charge transfer and the mixture of intramolecular charge transfer within the two respective 4,4′-bipyridinium moieties coupled with interlayer charge transfer between the two 4,4′-bipyridinium moieties. This provides us with comprehensive information on the effect of organic connectors on the NLO properties.

We report a theoretical study based on density functional theory (DFT) on the geometric and electronic structure, linear optical and second-order nonlinear optical properties of a series of new inorganic–organic hybrid hexamolybdate–organoimido–(car)boranes. By the incorporation of borane/carborane at the end of the phenyl ring of the organoimido segment, the studied systems show excellent nonlinear optical (NLO) response than the organoimido-substituted hexamolybdate. The computed static first hyperpolarizability βvec value of [Mo6O18(NC8H8)(B12H11)]4− (II) is largest, −167.2 × 10−30 esu, and a higher βvec value of [Mo6O18(NC8H8)(C2B10H11)]2− (III-2p) is 58.6 × 10−30 esu. Moreover, the time-dependent (TD)DFT calculation illustrates that the maximum absorption, which is helpful for the large NLO responses, is mainly assigned to the charge transfer (CT) from (car)borane and organoimido segment to the hexamolybdate cluster. The density of density (DOS) calculations further illustrate the excitation from valence orbitals of boron atoms to that of Mo and O atoms in hexamolybdate can be responsible for larger NLO responses. The linear and nonlinear optical properties of species III both vary with the position of the vertex on the carborane. Furthermore, the order of the βvec values is consistent with the bathochromic shift of the maximum absorption for our studied systems, and the studied systems show a wider transparency range extending into the entire visible and infrared (IR) region.

To reveal a new structure–property relationship regarding the nonlinear optical (NLO) properties of fullerenes that are associated with gamma (γ) density, fullerenes I (C40, C50, C60 and C70), whose heights range from 4.83 to 7.96 Å, and II (C24, C36, C48 and C72), whose widths range from 4.45 to 8.22 Å, have been the research objects. Calculation of their geometric and electronic structures, absorption spectra, and the second hyperpolarizability (γ) and the γ density analysis have been performed. It is found that the electronic spatial extent and the polarizability (α) value increase linearly as the fullerenes increase by every 12 carbon atoms. Similarly, the γ values are also proportional to the fullerene size. It is worth noting that the relative magnitude of γxxxx and γzzzz was exactly consistent with that of the width and height of fullerenes. The analysis of γ density provides the essential reason for this result, that is, the magnitude of the contribution to γ values associated with γ densities is proportional to the density amplitudes multiplied by the distance between them. Larger fullerenes possess larger density amplitudes and longer distances, resulting in larger γ values with respect to smaller fullerenes. This work presents a new structure–property interplay between the width and height of the fullerenes and their second hyperpolarizability γ. Moreover, the γ density analysis provides a new insight to explore the nature of the relationship between the structure and the NLO properties.

The electron donor–acceptor complexes, which undergo intramolecular charge transfer under external stimulus, are an emerging class of materials showing important application in nonlinear optics. Synthesizing ferrocene/fullerene complexes through face-to-face fusion would enjoy the merits of both ferrocene and fullerene due to their strong donor–acceptor interactions. Four ferrocene/fullerene hybrid complexes with the gradual extension of fullerene cage size, including CpFe(C60H5), CpFe(C66H5), CpFe(C70H5), and CpFe(C80H5) (Cp is cyclopentadienyl), have been investigated by density functional theory. These hybrid molecules give eclipsed and staggered isomers. The main reason that the eclipsed isomer is stable is that the eclipsed structure possesses large CpFe⋯fullerene bonding energy. The CpFe⋯fullerene interaction is smaller than that of Cp⋯Fefullerene, which must come from two different interfaces. The presence of covalent bond character between CpFe and fullerene is supported by the localized orbital locator, deformation of electron density distribution and energy decomposition analysis. Significantly, the absorption bands and first hyperpolarizabilities of these hybrid complexes are strongly sensitive to the fullerene cage size, which is ascribed to a change in the charge transfer pattern, especially for CpFe(C80H5), which displays reverse π → π* charge transfer from bottom to top cage, leading to notable hyperpolarizability. Investigation of the structure–property relationship at the molecular level can benefit the design and preparation of such hybrid complexes in chemistry and materials science.