Three-propeller-blade-shaped electride: remarkable alkali-metal-doped effect on the first hyperpolarizability

Endohedral metallofullerene electrides of Ca12O12 with remarkable nonlinear optical response

Herein, the structural, electronic, thermodynamic, linear and nonlinear optical properties of inorganic electrides, generated by alkali metal doping in group II–VI Ca₁₂O₁₂ fullerene, are studied. Endohedral doping of alkali metal leads to the formation of electrides whereas no such phenomenon is seen for exohedral doping. The electride nature of the endohedral fullerenes is confirmed through the analysis of frontier molecular orbitals. The results show that doping of alkali metal atoms leads to a reduction of the HOMO–LUMO gap and increase of the dipole moment, polarizability and hyperpolarizability of nanocages. Doping causes shifting of electrons from alkali metal atoms towards the Ca₁₂O₁₂ nanocage, which serve as excess electrons. Furthermore, the participation of excess electrons for enhancing the NLO response of these nanocages has been confirmed through the calculation of hyperpolarizability (β_o). For exploring the controlling factors of hyperpolarizability, a two level model has been employed and the direct relation of hyperpolarizability with Δμ & f_o, while an inverse relation of hyperpolarizability with ΔE has been studied. The electrides possess remarkable nonlinear response where the highest hyperpolarizability can reach up to 1.0 × 10⁶ a.u. for endo-K@Ca₁₂O₁₂. This electride has the lowest ΔE of 0.63 eV among all compounds studied here. These intriguing results will be expedient for promoting the potential applications of the Ca₁₂O₁₂-based nano systems in high-performance nonlinear optical (NLO) materials.

Electride formation by alkali metal doping with a drastic increase in hyperpolarizability

Assessing the structure and first hyperpolarizability of Li@B10H14 in solution: a sequential QM/MM study using the ASEC-FEG method

The structure and electronic properties of the lithium decahydroborate (Li@B₁₀H₁₄) complex in chloroform and water in normal thermodynamic conditions have been investigated using sequential QM/MM calculations by means of the average solvent electrostatic configuration (ASEC) and the Free Energy Gradient (FEG) methods. To obtain the structure of the Li@B₁₀H₁₄ complex in each of the solvents considered, we have performed geometry optimizations in solution using the ASEC-FEG method. The results show, for the first time with a realistic model of the molecular environment, that this alkali-metal-borane cluster is stable in chloroform but unstable in water. We have also explored the role of the electronic polarization of the solute due to solvent in the static first hyperpolarizability. The results show that, despite the reduction due to the effect of electrostatic polarization in chloroform, the Li@B₁₀H₁₄ complex still exhibits a large electronic first hyperpolarizability, with potential for application as a second-order nonlinear optical (NLO) material. In water, in contrast, the contribution of the excess electron for NLO responses is significantly affected by the electrostatic polarization effects. Therefore our results reveal that the influence of the environment must be considered in the design of new stable NLO materials.

Density-functional description of alkalides: introducing the alkalide state

Alkalides are crystalline salts in which the anion is a negatively charged alkali metal. A systematic investigation of the electronic structure of thirteen alkalides, with known crystal structures, is conducted using density-functional theory. For each alkalide, a high-lying valence state is identified that is localised on the alkali anions and is consistent with the low band gap and strong reducing power characteristic of these materials. This 'alkalide state' is compared to a similar state in the related class of electride materials, where the alkali anions are replaced by crystal voids occupied by localised, interstitial electrons. Finally, a thermodynamic cycle is constructed to examine the energy differences between the alkalides and electrides, revealing that the alkali-metal anion significantly stabilises the crystal.

Electronic and Vibrational Hyperpolarizabilities of Lithium Substituted (Aza)benzenes and (Aza)naphthalenes

In this article we report results for the electronic and vibrational hyperpolarizabilities of ten molecules: Li@benzene, Li@pyridine, Li@pyrimidine, and Li@pyrazine; Li@naphthalene, Li@quinoline, Li@isoquinoline, Li@cinnolin, Li@quinazoline, and Li@quinoxaline. An electron correlation study shows that second-order many-body perturbation theory and density functional theory with CAM-B3LYP and M05-2X functionals give results for the electronic hyperpolarizabilities in good agreement with coupled cluster with single and doubles reference values. Static and dynamic vibrational corrections were computed through the perturbation theoretical method of Bishop and Kirtman and using a variational approach. In general, we obtained notable discrepancies between the results obtained by the two methods for the pure vibrational corrections because of the deficiency of the perturbation method to properly treat low-frequency normal modes present in the investigated systems. However, both methods give results similar to the zero-point vibrational average corrections.

Static second hyperpolarizability of inverse sandwich compounds (M1-C5H5-M2) of alkali (M1 = Li, Na, K) and alkaline earth metals (M2 = Be, Mg, Ca)

In the investigated inverse sandwich complexes, charge transfer from alkali metal (M1) led to aromatically stabilized Cp ring, which prevented further charge transfer from the alkaline earth metal (M2). This electron push effect resulted in diffusion of electron density from the outermost "ns" subshell of alkaline earth metal. The alkaline earth metal is weakly bound to the alkali metal-C5H5 complex. The vertical ionization energy of the chosen M1-Cp-M2 complexes was smaller than that of the corresponding alkaline earth metals. Large second hyperpolarizability (106-108 a.u.) was obtained for the studied molecules. The correction due to the basis set superposition error (BSSE) in the calculated second hyperpolarizability was found to be small for larger systems, while it was rather significant for small systems. The MP4SDQ and CCSD results were in fair agreement, which indicates the necessity of higher order electron correlation treatment in the accurate description of second hyperpolarizability. Calculated dynamic second hyperpolarizabilities at 1064 nm were found to increase considerably for most of the chosen metal complexes.

Successive lithiation of acetylene, ethylene and benzene: a comprehensive computational study of large static second hyperpolarizability

This work is a revisit of the study of the electron correlation effect of lithium substitution on the second hyperpolarizability (10⁶ a.u.) of acetylene, ethylene and benzene. The large quenching of mean second hyperpolarizability has been addressed by CCSD calculations. The inclusion of triple excitation in the MP4 method generally overestimates second hyperpolarizability in comparison to the MP4SDQ method. The present CCSD γ_av value of C₆Li₆: 405 × 10⁴ a.u. obtained with a relatively larger basis set established the earlier prediction of Sadlej et al. [Phys. Chem. Phys. Chem., 2000, 2, 3393-3399] where degenerate non-dipolar transitions in low lying excited states play the crucial role. The successive lithiation results in gradual red shifting of transition energy leading to significant enhancement of second hyperpolarizability. Most of the chosen DFT functionals predict the correct qualitative trend of second hyperpolarizability. The quantitatively different results may be attributed to the case when the ground state wave function cannot be approximated by a single SD.

Thermodynamic cycles of the alkali metal–ligand complexes central to electride formation

Alkali metal–ligand complexes are the building blocks of the exotic organic alkalide and electride materials.

The explicit examination of the magnetic states of electrides

Electrides are a unique class of ionic solids in which the anions are stoichiometrically replaced by electrons localised within the crystal voids. We present the first all electron magnetic state calculations for electrides and show the magnetic properties of these materials come from the localised electrons.

Constructing a mixed π-conjugated bridge to effectively enhance the nonlinear optical response in the Möbius cyclacene-based systems

Using density functional theory computations, employing the concept of a mixed π-conjugated bridge can effectively improve the first hyperpolarizability (β0) of Möbius cyclacene (MC)-based systems with a D-π-A framework. This mixed π-conjugated bridge is constructed by applying a -(CH=CH)x-NH2 or -(CH=CH)x-NO2 chain to modify [8]MC, which can lead to a considerable β0 value (e.g. [8]MC-(CH=CH)12-NO2 (9.87 × 10(5) au) with only a certain chain length), much larger than the sole [8]MC (261 au) and the corresponding NH2/NO2-modified polyethylene chain with the same π-conjugated length. It is revealed that the substituent sites and the chain length can play a crucial role in improving β0 values of these MC-chain systems, where the β0 value can monotonically increase with increasing -(CH=CH)x- length, and the substituent electron-withdrawing -(CH=CH)x-NO2 chain is superior to the parallel electron-donating -(CH=CH)x-NH2. These appealing findings can provide valuable insights into the design of novel NLO materials based on MC.

Role of Excess Electrons in Nonlinear Optical Response

The excess electron is a kind of special anion with dispersivity, loosely bounding and with other fascinating features, which plays a pivotal role (promote to about 10(6) times in (H2O)3{e}) in the large first hyperpolarizabilities (β0) of dipole-bound electron clusters. This discovery opens a new perspective on the design of novel nonlinear optical (NLO) molecular materials for electro-optic device application. Significantly, doping alkali metal atoms in suitable complexants was proposed as an effective approach to obtain electride and alkalide molecules with excess electron and large NLO responses. The first hyperpolarizability is related to the characteristics of complexants and the excess electron binding states. Subsequently, a series of new strategies for enhancing NLO response and electronic stability of electride and alkalide molecules are exhibited by using various complexants. These strategies include not only the behaviors of pushed and pulled electron, size, shape, and number of coordination sites of complexants but also the number and spin state of excess electrons in these unusual NLO molecules.

One lithium atom binding with P-nitroaniline: lithium salts or lithium electrides?

Recently, both lithium (Li) salts and Li electrides formed by one Li atom interacting with ligand complexes, have been widely investigated. An interesting question emerges: is the configuration of one Li atom interacting with ligand complexes a Li salt or electride? In the present work, four configurations n-Li-PNA (n = 1-4) were obtained by binding one Li atom with the p-nitroaniline (PNA) at different positions to explore this question. The results show that 1-Li-PNA and 2-Li-PNA are typical Li salts, and 4-Li-PNA is a typical Li electride. Significantly, 3-Li-PNA possesses both characteristics of Li salt and electride. At the same time, 3-Li-PNA has the largest first hyperpolarizability (2.9 × 10(6) au) by ROMP2 method compared with the other three configurations. Furthermore, the first hyperpolarizability of 3-Li-PNA is about 2600 times larger than that of PNA. Further, the vertical ionization potential (VIP) and interaction energy (E int) indicate that 3-Li-PNA is less stable than 1-Li-PNA and 2-Li-PNA (Li salts), but is more stable than 4-Li-PNA (Li electrides).

Third-order NLO property of beryllium-pyridyne complexes

Six pyridyne isomers and their complexes with beryllium have been considered for the theoretical study of the third-order polarizability. The NLO properties are calculated by employing the DFT functionals BLYP, B3LYP, BHHLYP, B3PW91, BP86 and B2PLYP for the 6-311++G(d,p) basis set. The C - Be bond length in the complexes varies within 1.644 Å–1.771 Å indicating covalent interactions between the metal and pyridynes. The present investigation reveals that the magnitude of second-hyperpolarizability of pyridynes strongly enhances upon complex formation with beryllium. The maximum hyperpolarizability has been predicted for the 2,5-diberyllium pyridine complex. The lowest value of hyperpolarizability is obtained for the 2,3- and 3,4-diberyllium pyridine complexes. The chosen DFT methods predict almost identical pattern of variation of NLO property. The variation of second-hyperpolarizability has been satisfactorily explained by the excitation energy and transition dipole moment associated with the most dominant excited state.

Beryllium-cyclobutadiene multidecker inverse sandwiches: electronic structure and second-hyperpolarizability

Beryllium forms stable sandwich and inverse sandwich complexes with the cyclobutadiene molecule. Two types of multidecker complexes are designed. Multidecker inverse sandwiches are found to be thermally more stable than the corresponding sandwich complexes. The average distance between two consecutive metals and the two consecutive cyclobutadiene rings increase gradually on increasing size of the chosen inverse sandwich complexes. The density functional theory functionals B3LYP, BHHLYP, BLYP, M06, CAM-B3LYP, and B2PLYP in conjunction with the 6-311++G (d, p) basis set have been employed for calculating the third-order electric response properties of the chosen beryllium-cyclobutadiene complexes and the results obtained for each functional are found to have a consistent trend. Compared to the normal sandwich compounds the second-hyperpolarizability of inverse sandwiches is predicated to be larger, which fairly correlates with the extent of ground-state polarization. The significant enhancement of cubic polarizability of higher-order multidecker inverse sandwiches arises from the strong coupling between the ground and the low lying charge transfer excited states. The rather strong enhancement of second-hyperpolarizability on increasing size of the beryllium-multidecker inverse sandwiches may provide a new route to design efficient nonlinear optical materials.

INTERACTION OF BERYLLIUM WITH ACCEPTOR HYDROCARBONS: ELECTRONIC STRUCTURE AND SECOND HYPERPOLARIZABILITY

Some selected acceptor-Be hydrocarbon complexes have been considered for evaluation of second hyperpolarizability at different DFT functional. All the complexes have been found thermally stable and there is a significant increase of second hyperpolarizability compared to the ligands. Second hyperpolarizability has been explained in terms of charge transfer interaction. Co-operative interaction is required for maximization of second hyperpolarizability. Localized charge transfer in the vicinity of metal alone cannot increase second hyperpolarizability while charge delocalization over entire molecule is mandatory. Substitution by more electropositive metals e.g. Mg , Ca have greater enhancement in longitudinal component of γ. Basis set 6-311++G** is reasonable with respect to computational cost at aug-cc-pVnZ's (n = D, T, Q) for evaluation of second hyperpolarizability for the present complexes.

An effective method for accurate prediction of the first hyperpolarizability of alkalides

The proper theoretical calculation method for nonlinear optical (NLO) properties is a key factor to design the excellent NLO materials. Yet it is a difficult task to obatin the accurate NLO property of large scale molecule. In present work, an effective intelligent computing method, as called extreme learning machine-neural network (ELM-NN), is proposed to predict accurately the first hyperpolarizability (β(0)) of alkalides from low-accuracy first hyperpolarizability. Compared with neural network (NN) and genetic algorithm neural network (GANN), the root-mean-square deviations of the predicted values obtained by ELM-NN, GANN, and NN with their MP2 counterpart are 0.02, 0.08, and 0.17 a.u., respectively. It suggests that the predicted values obtained by ELM-NN are more accurate than those calculated by NN and GANN methods. Another excellent point of ELM-NN is the ability to obtain the high accuracy level calculated values with less computing cost. Experimental results show that the computing time of MP2 is 2.4-4 times of the computing time of ELM-NN. Thus, the proposed method is a potentially powerful tool in computational chemistry, and it may predict β(0) of the large scale molecules, which is difficult to obtain by high-accuracy theoretical method due to dramatic increasing computational cost.