Higher‐order response theory based on the quasienergy derivatives: The derivation of the frequency‐dependent polarizabilities and hyperpolarizabilities

Qualitative and quantitative analysis of electrons donated by pollutants in electron transfer-based oxidation system: Electrochemical measurement and theoretical calculations

In order to gain a profound understanding of the fate of pollutants in advanced oxidation processes (AOPs), this study analyzed the electron contribution of pollutants qualitatively and quantitatively which rarely reported before. The rich electron transfer system was constructed by mesoporous carbon nitride (MCN) coupling with persulfate (PS) driven by visible light and the sulfanilamide antibiotics (SULs) were used as target contaminants. Firstly, the qualitative analysis of electron transfer in the system was confirmed systematically. The electron flow direction tested by i-t curves indicated that PS absorbed electrons, while SULs released electrons. The flow rate of electrons was also accelerated after the addition of SULs. The fitting curve between the kinetics and the peak potential difference tested by CV curve showed that the larger potential difference, the slower rate of oxidative degradation. Secondly, the quantification of electron transfer was achieved through theoretical calculations to simulate the interactions of the 'catalyst-oxidant-antibiotic' system. After the addition of SULs, the adsorption energy of the 'catalyst-oxidant-antibiotic' system was enhanced and the bond length of the peroxide bond was stretched. Notably, the electron transfer analysis results showed that the charge of SULs was around 0.032-0.056e, indicating that SULs pollutants played the role of electron contributors in the system. The oxidative degradation pathway included the direct cracking of S-N bond, shedding of marginal groups, ring-opening and hydroxyl addition reaction. This study clarified the electronic contribution of SULs in the oxidation system, providing necessary theoretical supplement for the analysis of the transformation of pollutants in AOPs.

Intramolecular boron-locking strategy induced remarkable first hyperpolarizability: role of torsion angles between donor and acceptor units

In conventional strategies to design donor-acceptor (D-A) organic molecules with a large electronic contribution to the first hyperpolarizability (β), the effects of the torsion angles (θ1 and θ2) between donor and acceptor moieties are barely considered. To address this issue, in this work, a promising and novel intramolecular boron-locking strategy combined with the different locking groups of different acceptors to control θ1 and θ2, has been proposed to make D-A organic molecules with large β values. Intriguingly, reducing the torsion angles will make the β value of the pyridiny thiophene triphenylamine unit (Py-Th-TPA) dramatically increase up to 94%, which is mainly ascribed to the smaller θ1 and θ2 leading to lower excited energy of the crucial excited state, and enhanced charge transfer (CT) from TPA to Py-Th moieties, and finally greatly increase the donor and acceptor part contributions to β. Correlation between the difference, |θ1 - θ2| and β, provides a large coefficient of determination, R2 = 0.78, which demonstrates that |θ1 - θ2| can be regarded as a potential descriptor for designing nonlinear optics (NLO) materials with D-A architecture. Clearly, we uncovered that θ1 and θ2 play a crucial role in the performance of NLO materials with D-A fragments.

Electro-Induced Phase Transformation of a Conductive Metal-Organic Framework Film for Nonlinear Optical Switching

Achieving metal-organic frameworks (MOFs) with nonlinear optical (NLO) switching is profoundly important. Herein, the conductive MOFs Cu-TCNQ phase I (Ph-I) and phase II (Ph-II) films were prepared using the liquid-phase-epitaxial layer-by-layer spin-coating method and steam heating method, respectively. Electronic experiments showed that the Ph-II film could be changed into the Ph-I film under an applied electric field. The third-order NLO results revealed that the Ph-I film had a third-order nonlinear reverse saturation absorption (RSA) response and the Ph-II film displayed a third-order nonlinear saturation absorption (SA) response. With increases in the heating time and applied voltage, the third-order NLO response realized the reversible transition between SA and RSA. The theoretical calculations indicated that Ph-I possessed more interlayer charge transfer, resulting in a third-order nonlinear RSA response that was stronger than that of Ph-II. This work applies phase-transformed MOFs to third-order NLO switching and provides new insights into the nonlinear photoelectric applications of MOFs.

Tuning optical properties of π-conjugated double nanohoops under external electric field stimuli-responsiveness

Carbon nanorings have attracted substantial interest from synthetic chemists due to their unique topological structures and distinct physical properties. An intriguing π-conjugated double-nanoring structure, denoted as [8]CPP-[10]cyclacene, was constructed via the integration of [8]cycloparaphenylene ([8]CPP) into [10]cyclacene. Using the external electric field stimuli-responsiveness of [8]CPP-[10]cyclacene, directional charge transfer can be induced, resulting in the emergence of intriguing properties. The effects of the external electric field in three specific directions were explored, vertically in the [8]CPP unit (Fy), vertically in the [10]cyclacene unit (Fz), and horizontally along the double nanorings diameter (Fx). Interestingly, the external electric field vertically to the [10]cyclacene unit significantly enhanced the first hyperpolarizability (βtot) compared to that vertically to the [8]CPP unit. Notably, [8]CPP-[10]cyclacene under Fx exhibited significantly larger the βtot values (1.48 × 105 a.u.) than those of vertical Fy and Fz. This work opens up a wide range of nonlinear optics, making it a compelling area to explore in the field of carbon nanomaterials.

Formulation and Implementation of Frequency-Dependent Linear Response Properties with Relativistic Coupled Cluster Theory for GPU-Accelerated Computer Architectures

We present the development and implementation of relativistic coupled cluster linear response theory (CC-LR), which allows the determination of molecular properties arising from time-dependent or time-independent electric, magnetic, or mixed electric-magnetic perturbations (within a common gauge origin for the magnetic properties) as well as taking into account the finite lifetime of excited states in the framework of damped response theory. We showcase our implementation, which is capable to offload the computationally intensive tensor contractions characteristic of coupled cluster theory onto graphical processing units, in the calculation of (a) frequency-(in)dependent dipole-dipole polarizabilities of IIB atoms and selected diatomic molecules, with a particular emphasis on the calculation of valence absorption cross sections for the I2 molecule; (b) indirect spin-spin coupling constants for benchmark systems such as the hydrogen halides (HX, X = F-I) as well the H2Se-H2O dimer as a prototypical system containing hydrogen bonds; and (c) optical rotations at the sodium D line for hydrogen peroxide analogues (H2Y2, Y = O, S, Se, Te). Thanks to this implementation, we are able to show the similarities in performance, but often the significant discrepancies, between CC-LR and approximate methods such as density functional theory. Comparing standard CC response theory with the flavor based upon the equation of motion formalism, we find that for valence properties such as polarizabilities, the two frameworks yield very similar results across the periodic table as found elsewhere in the literature; for properties that probe the core region, such as spin-spin couplings, on the other hand, we show a progressive differentiation between the two as relativistic effects become more important. Our results also suggest that as one goes down the periodic table, it may become increasingly difficult to measure pure optical rotation at the sodium D line due to the appearance of absorbing states.

Second-order nonlinear optical properties of X-shaped pyrazine derivatives

This work reports an investigation of the second-order NLO properties of two isomer series of X-shaped pyrazine derivatives, by means of HRS measurements and DFT calculations. The systems differ in the relative position of the donor and acceptor substituents with respect to the axis formed by the nitrogen atoms of the central pyrazine ring. Although the magnitude of the second harmonic signal is similar, HRS measurements revealed that the anisotropy of the NLO response strongly differs in the two chromophore series, the one of the 2,3-isomers being strikingly dipolar, while the one of the 2,6-isomers is mostly octupolar. The experimental observations are well supported by DFT calculations. In particular, the sum-over-states approach allows us to rationalize the different NLO anisotropies observed in the two isomer series through a detailed analysis of the symmetry of the low-lying excited states.

Designed metal-organic π-clusters combining the aromaticity of the metal cluster and ligands for a third-order nonlinear optical response

The pivotal role of clusters and aromaticity in chemistry is undeniable, but there remains a gap in systematically understanding the aromaticity of metal-organic clusters. Herein, this article presents a novel metal-organic π-cluster, melding both metal-organic chemistry and aromaticity, to guide the construction of structurally stable Os-organic π-clusters. An in-depth analysis of these clusters reveals their bonding attributes, π-electronic composition, and origins of aromaticity, thereby confirming their unique metal-organic π-cluster properties. Furthermore, the Os5 cluster exhibits a promising third-order nonlinear optical (NLO) response, attributable to its narrow band gap and uniform electron/hole distribution, suggesting its potential as an optical switching material. This research introduces a fresh perspective on clusters, centered on delocalization, and broadens the domain of aromaticity studies. It also presents a novel method for designing efficient third-order NLO materials through consideration of the structure-activity relationship.

Quantum Simulation of Molecular Response Properties in the NISQ Era

Accurate modeling of the response of molecular systems to an external electromagnetic field is challenging on classical computers, especially in the regime of strong electronic correlation. In this article, we develop a quantum linear response (qLR) theory to calculate molecular response properties on near-term quantum computers. Inspired by the recently developed variants of the quantum counterpart of equation of motion (qEOM) theory, the qLR formalism employs "killer condition" satisfying excitation operator manifolds that offer a number of theoretical advantages along with reduced quantum resource requirements. We also used the qEOM framework in this work to calculate the state-specific response properties. Further, through noiseless quantum simulations, we show that response properties calculated using the qLR approach are more accurate than the ones obtained from the classical coupled-cluster-based linear response models due to the improved quality of the ground-state wave function obtained using the ADAPT-VQE algorithm.

Theoretical study on porphyrin arch-tapes of carbonyl-inserted seven-membered rings with high nonlinear optical properties

Porphyrin tapes have attracted extensive attention because their fully conjugated π-networks act as nonlinear optical (NLO) materials. A family of Ni(II) and Zn(II) porphyrin arch-tapes that are connected by varying bridge (B) ligands (meso-meso β-β doubly linked dimer 1, meso-meso β-β β-β triply linked dimer 3, methylene-inserted dimer 2 and trimer 5, carbonyl-inserted dimer 4, trimer 6, and Zn(II) trimer 7) have been synthesized by a density functional theory (DFT) method. The results show that carbonyl-inserted arch-tapes significantly enhance second hyperpolarizability (γ), indicating that the remarkably contorted structure incorporated seven-membered ring(s) directly affect their NLO properties of our focus. Moreover, the electronic absorption spectra calculated for all studied complexes with time-dependent DFT theory (TDDFT) predict that carbonyl-inserted complex 4 contributes to a red-shift of the Q-band (160 nm) for the meso-meso β-β doubly linked complex 1. The third-order NLO responses and the electron transition properties strongly depend on the nature of the bridge (B) ligand, which means that an active involvement of the carbonyl group presents an advantage for its application in NLO materials.

A quantum chemical investigation of the second hyperpolarizability of p-nitroaniline

Recent measurements of the third harmonic scattering responses of molecules have given a new impetus for computing molecular second hyperpolarizabilities (γ) and for deducing structure-property relationships. This paper has employed a variety of wavefunction and density functional theory methods to evaluate the second hyperpolarizability of the p-nitroaniline prototypical push-pull π-conjugated molecule, addressing also numerical aspects, such as the selection of an integration grid and the impact of the order of differentiation vs the achievable accuracy by using the Romberg quadrature. The reliability of the different methods has been assessed by comparison to reference Coupled-Cluster Singles and Doubles with perturbative treatment of the Triples results. On the one hand, among wavefunction methods, the MP2 scheme offers the best accuracy/cost ratio for computing the static γ. On the other hand, using density functional theory, γ remains a challenging property to compute because all conventional, global hybrid or range-separated hybrid, exchange-correlation functionals underestimate static γ values by at least 15%. Even tuning the range-separating parameter to minimize the delocalization errors does not enable to improve the γ values. Nevertheless, the original double-hybrid B2-PLYP functional, which benefits from 27% of PT2 correlation and 53% Hartree-Fock exchange, provides accurate estimates of static γ values. Unfortunately, the best performing exchange-correlation functionals for γ are not necessarily reliable for the first hyperpolarizability, β, and vice versa. In fact, the β of p-nitroaniline (pNA) could be predicted, with a good accuracy, with several hybrid exchange-correlation functionals (including by tuning the range-separating parameter), but these systematically underestimate γ. As for γ, the MP2 wavefunction method remains the best compromise to evaluate the first hyperpolarizability of pNA at low computational cost.

Torsion Angles between Donor and Acceptor Moieties as a Descriptor for Designing Nonlinear Optics and Thermally Activated Delayed Fluorescence Materials

The performances of nonlinear optics (NLO) and thermally activated delayed fluorescence (TADF) materials are strongly related to the torsion angles (θ) between donor (D) and acceptor (A) moieties in D-A architecture molecules. However, the underlying relationships connecting θ to the performances of NLO/TADF materials remain unclear. Herein, we present a comprehensive theoretical study on NLO/TADF materials composed of a series of D-A backbone molecules (TPAAP/TPAAQ series and AQ-DMAC/AQ-MeFAC series) to shed light on these relationships. It is found that changing θ via the intramolecular locking strategy can greatly influence values of the first hyperpolarizability (β) and singlet-triplet energy gap (ΔEST), further leading to better/worse performances of NLO/TADF materials, respectively. Intriguingly, a more detailed analysis indicates that the variation trends between θ and β/ΔEST are changeable in low θ regions, exhibiting volcano-like relationships. The large coefficients of determination (R2, ranging from 0.76 to 0.93) suggest that this experimentally measurable parameter (θ) can be used as a promising descriptor to evaluate the performances of related materials. Following the revealed θ-β/θ-ΔEST correlations, the optimal/worst torsion angles for different materials are identified. These findings highlight the importance of the intrinsic structure-performance relationships, thus providing novel design strategies for high-performance NLO/TADF materials.

Physical Mechanism of Spectra in Carbon Nanobelts under Quantum Size Effect

Since the successful synthesis of [6,6]carbon nanobelt (CNB), [8,8]CNB and [12,12]CNB have been synthesized successively. CNBs with different sizes ([2N,2N]CNB; N = 2, 3, 4, 5, 6, 7, and 8) have quantum size effects and exhibit completely different optical properties. In this work, the linear and nonlinear optical properties and spectral changes of [2N,2N]CNB are studied based on density functional theory (DFT). The molecular volume, pore volume, and stability of [2N,2N]CNB are investigated. The electron transition mechanism of the one-photon absorption (OPA) and two-photon absorption (TPA) spectra of [2N,2N]CNB is explained, and the extrapolation formula between the wavelength of the absorption peak and the absorption coefficient (ε) and size is given. The infrared (IR) and Raman spectra of [2N,2N]CNB are calculated, and the vibrational modes of characteristic peaks are provided. Finally, the nonlinear optical properties of [2N,2N]CNB are studied, which reflect the anisotropy of molecular polarization. The extrapolation formulas for the polarizability (α) and second hyperpolarizability (γ) of [2N,2N]CNB under different external fields are given. The extrapolation formulas given in this work will help to predict the linear and nonlinear optical properties of arbitrary [2N,2N]CNB beyond computational power, laying the foundation for the practical application of [2N,2N]CNB's theoretical basis.

An intramolecular-locked strategy for designing nonlinear optical materials with remarkable first hyperpolarizability

To meet the expanding demands of high performance nonlinear optical (NLO) materials, an unprecedented intramolecular-locked strategy is proposed to design NLO materials with remarkable static first hyperpolarizability (β₀). This strategy means that importing a large steric hindrance group diphenylmethane (DPM) decreases the torsion angles (θ) between the donor {triphenylamine (TPA)} and acceptor {9-H-thioxanthen-9-one-10,10-dioxide (TXO)} units, as well as between the donor (TPA) and π-bridge (benzene) fragments. The decrease of θ can accelerate the intramolecular charge transfer and enhance the contributions of the TPA, TXO and quinoxaline-6,7-dicarbo-nitrile (QCN) fragments to the axial component of the β₀ value, and then the β₀ values of TPA-TXO (β₀ = 10 762 au) and TPA-QCN (β₀ = 22 495 au) are increased by 14.9% and 34.4%, respectively. Overall, the intramolecular-locked strategy is very effective for designing high performance NLO materials.

Control and Modulation of Photoinduced Charge Transfer in a Rigid Donor-Bridge-Acceptor System by Electric Fields

This article theoretically studies the photoinduced charge transfer (CT) of rigid D-B-A molecules in two-photon absorption (TPA) adjusted by the external electric fields. Using a visualization method, the dynamic changes of light-induced CT in different channels of TPA are presented through a two-dimensional (2D) transition density matrix and a three-dimensional (3D) charge different density. Here, we prove the controllability of TPA on CT under the induction of a strong electric field. Adjusting the field direction and intensity significantly affects the position of the strong absorption peak in the TPA spectra, thereby further changing the electron-hole coherence length and the degree of dispersion. Our results can promote the recognition of the optical properties of the D-B-A system in synthetic molecules and provide an idea for increasing the proportion of excited states for CT in the molecule.

Second-Order Nonlinear Optics Response of the Boron-Dipyrromethenes-Based Mislinked Expanded Porphyrins: Revealing the Role of the -BF2 Group

Here, the mislinked expanded porphyrins singly (labeled A) and doubly (labeled B) neo-confused [22]smaragdyrin, the boron-dipyrromethenes-based mislinked expanded porphyrins singly (labeled C) and doubly (labeled D) neo-confused [22]smaragdyrin, where both C and D include a -BF₂ group, are chosen to serve as the study objects, and theoretical calculations are carried out to study the role of the -BF₂ group in the second-order nonlinear optics (NLO) behaviors. Results highlighted that the -BF₂ group plays an important role for the second-order behaviors in mislinked expanded porphyrins; namely, embedding the -BF₂ group well enhanced the hyper-Rayleigh scattering (HRS) value {β_HRS(0;0,0)}, C{βHRS(0;0,0)}A{βHRS(0;0,0)} = 2.0 and D{βHRS(0;0,0)}B{βHRS(0;0,0)} = 2.9, main owning to the fact that installing -BF₂ increases the electron delocalization degree and decreases the excited energy of the crucial excited state.

Third-order nonlinear optical property contrast as self-assembly recognition for nanorings⊃C60

High third-order NLO contrasts tuned by self-assembly can be applied for the recognition of host–guest nanorings⊃C60.

Local-Field Effects in Linear Response Properties within a Polarizable Frozen Density Embedding Method

In this work, we present a polarizable frozen density embedding (FDE) method for calculating polarizabilities of coupled subsystems. The method (FDE-pol) combines a FDE method with an explicit polarization model such that the expensive freeze/thaw cycles can be bypassed, and approximate nonadditive kinetic potentials are avoided by enforcing external orthogonality between the subsystems. To describe the polarization of the frozen environment, we introduce a Hirshfeld partition-based density-dependent method for calculating the atomic polarizabilities of atoms in molecules, which alleviates the need to fit the atomic parameters to a specific system of interest or to a larger general set of molecules. We show that the Hirshfeld partition-based method predicts molecular polarizabilities close to the basis set limit, and thus, a single basis set-dependent scaling parameter can be introduced to improve the agreement against the reference polarizability data. To test the model, we characterized the uncoupled and coupled response of small interacting molecular complexes. Here, the coupled response properties include the perturbation of the frozen system due to the external perturbation which is ignored in the uncoupled response. We show that FDE-pol can accurately reproduce both the exact uncoupled polarizability and the coupled polarizabilities of the supermolecular systems. Using damped response theory, we also demonstrate that the coupled frequency-dependent polarizability can be described by including local field effects. The results emphasize the necessity of including local-field effects for describing the response properties of coupled subsystems, as well as the importance of accurate atomic polarizability models.

Tin Metal Cluster Compounds as New Third-Order Nonlinear Optical Materials by Computational Study

It is quite appealing but challenging to predict and synthesize new nonlinear optical (NLO) materials with exceptional performance. Herein, the different Sn₄ cluster core structures and third-order NLO properties are studied through electronic structure, excited hole-electron, bonding character, and aromaticity analysis. As a result, Sn₄ clusters with ring core structure (Sn₄-R) not only have the smallest E_gap, the largest UV-vis response intensity, but also the strongest third-order NLO response in our work. As proved by natural bond orbitals' (NBO) analysis, electron localization function (ELF), and adaptive natural density partitioning (AdNDP), the Sn₄⁴⁺ has two in-plane four center-two electron (4c-2e) Sn-Sn σ-bonds, resulting in a good delocalization. For the first time, delocalization of metal cluster cores in tin clusters that is beneficial to the third-order NLO response is proposed, which provides a new guidance to design and prepare third-order NLO materials.

Interpretation of Coupled-Cluster Many-Electron Dynamics in Terms of Stationary States

We demonstrate theoretically and numerically that laser-driven many-electron dynamics, as described by bivariational time-dependent coupled-cluster (CC) theory, may be analyzed in terms of stationary-state populations. Projectors heuristically defined from linear response theory and equation-of-motion CC theory are proposed for the calculation of stationary-state populations during interaction with laser pulses or other external forces, and conservation laws of the populations are discussed. Numerical tests of the proposed projectors, involving both linear and nonlinear optical processes for He and Be atoms and for LiH, CH+, and LiF molecules show that the laser-driven evolution of the stationary-state populations at the coupled-cluster singles-and-doubles (CCSD) level is very close to that obtained by full configuration interaction (FCI) theory, provided that all stationary states actively participating in the dynamics are sufficiently well approximated. When double-excited states are important for the dynamics, the quality of the CCSD results deteriorates. Observing that populations computed from the linear response projector may show spurious small-amplitude, high-frequency oscillations, the equation-of-motion projector emerges as the most promising approach to stationary-state populations.

Simplified Ab Initio Molecular Dynamics-Based Raman Spectral Simulations

We describe a simplified approach to simulating Raman spectra from ab initio molecular dynamics (AIMD) calculations. The protocol relies on on-the-fly calculations of approximate molecular polarizabilities using the well-known sum over orbitals (as opposed to states) method. This approach bypasses the more accurate but computationally expensive approach to calculating molecular polarizabilities along AIMD trajectories, i.e., solving the coupled perturbed Hartree-Fock/Kohn-Sham equations. We demonstrate the advantages and limitations of our method through a few case studies targeting molecular systems of interest to surface- and/or tip-enhanced Raman spectroscopy practitioners.

Photoinduced charge transfer in quasi-one-dimensional polymers in two-photon absorption

In this work, we theoretically investigate the structure and the transition characteristics of one- (OPA) and two-photon absorption (TPA) spectra of different length neutral and charged thiophene polymers. The effects and regulation of different charges on photoinduced charge transfer are discovered and their physical mechanisms are explained. We find that both the OPA and TPA spectra undergo a sizeable redshift after the charge is injected into the polymer, and the redshift after the positive charge injection is excellent. The alternating charge transfer that occurs in a two-photon transition of a charged system is derived from the alternating distribution of charge (dipole moment) in the dynamics of the system. To study the gradual behavior of infinite polymers, we also theoretically calculated the optical properties and electronic structures of infinitely long thiophene polymers under different electrical charge injections by a one-dimensional periodic model. The redshift of the OPA and TPA spectra is found to be due to orbital energy level movement.

A mononuclear cobalt(II) salophen-type complex: Synthesis, theoretical and experimental electronic absorption and infrared spectra, crystal structure, and predicting of second- and third-order nonlinear optical properties

A tetradentate Schiff base ligand, (4-nitro-N,N'-o-phenylene-bis(5-methoxysalicylideneimine)) (H₂L), and its cobalt(II) complex (CoL•DMF) were synthesized. Elemental analysis, and FT-IR and ¹H NMR spectra were used to confirm the molecular structure of H₂L ligand. In addition, elemental analysis, molar conductance measurement, infrared and electronic absorption spectroscopies as well as single crystal X-ray diffraction were employed to distinguish the molecular structure of the complex that has a slightly distorted square-planar geometry around the cobalt(II) ion. The geometries of H₂L and CoL were optimized by means of the DFT/(U)PBE0/Def2-TZVP level of theory. Good agreement of the optimized geometric parameters of the complex with the corresponding experimental ones and successfully reproduction of the FT-IR spectra of the ligand and complex validated the applied method. Based on the optimized structure of CoL, its electronic absorption spectrum was reproduced by using time-dependent density functional theory (TDDFT) at the same level. Its analysis was carried out to assign the observed electronic transitions and determine their characters. The computed nonlinear optical (NLO) parameters (β, γ and < γ > values) of H₂L and CoL by using TDDFT at the same level combined with the sum-over-states (SOS) method are considerable larger values than reference compound i.e. urea. The ligand and the complex in the absence of nitro and methoxy moieties referred to as H₂L' and CoL' respectively were optimized to elucidate the effect of these moieties on hyperpolarizabilities values.

A nonlinear optical switch induced by an external electric field: inorganic alkaline–earth alkalide

Exploring a new type of nonlinear optical switch molecule with excess electron character is extremely important for promoting the application of excess electron compounds in the nonlinear optical (NLO) field. Here, we report external electric field (EEF) induced second-order NLO switch molecules of inorganic alkaline–earth alkalides, M(NH₃)₆Na₂ (M = Mg or Ca). The centrosymmetric structure of M(NH₃)₆Na₂ is destroyed in the presence of an EEF, and then a long-range charge transfer process occurs. It has been found that excess electrons are gradually transferred from one Na atom to the other Na atom through the inorganic metal cluster M(NH₃)₆. Finally, the excess electrons are completely located on one of the two Na atoms. In particular, the electronic contribution of the static first hyperpolarizability (β^e₀) for M(NH₃)₆Na₂ exhibits a large significant difference when the EEF is switched on. The β^e₀ value of M(NH₃)₆Na₂ is 0 when EEF = 0, while the peak β^e₀ values are 5.95 × 10⁶ (a.u.) for Mg(NH₃)₆Na₂ (EEF = 58 × 10⁻⁴ (a.u.)) and 1.83 × 10⁷ (a.u.) for Ca(NH₃)₆Na₂ (EEF = 53 × 10⁻⁴ (a.u.)). This work demonstrates that the compounds M(NH₃)₆Na₂ can serve as potential candidates for NLO switches.

The inorganic alkaline–earth alkalide M(NH₃)₆Na₂ (M = Mg or Ca) can serve as a potential candidate for a nonlinear optical switch.

A quantum-mechanical perspective on linear response theory within polarizable embedding

We present a derivation of linear response theory within polarizable embedding starting from a rigorous quantum-mechanical treatment of a composite system. To this aim, two different subsystem decompositions (symmetric and nonsymmetric) of the linear response function are introduced and the pole structures as well as residues of the individual terms are discussed. In addition to providing a thorough justification for the descriptions used in polarizable embedding models, this theoretical analysis clarifies which form of the response function to use and highlights complications in separating out subsystem contributions to molecular properties. The basic features of the presented expressions and various approximate forms are illustrated by their application to a composite model system.

First hyperpolarizabilities of Pt(4-ethynylbenzo-15-crown-5)2(bpy) derivatives with the complexation of mono-cations (Li+, Na+, K+) and di-cations (Mg2+, Ca2+): development of a cation detector

The coordination of mono-cations and di-cations onto the crown merits the design of the NLO-based cation detector.

Inner salt-shaped small molecular photosensitizer with extremely enhanced two-photon absorption for mitochondrial-targeted photodynamic therapy

An inner salt-shaped small-molecular photosensitizer with unprecedentedly strong two-photon absorption was developed for highly efficient two-photon photodynamic therapyviaa mitochondrial apoptosis pathway.

The multilevel CC3 coupled cluster model

We present an efficient implementation of the closed shell multilevel coupled cluster method where coupled cluster singles and doubles (CCSD) is used for the inactive orbital space and CCSD with perturbative triples (CC3) is employed for the smaller active orbital space. Using Cholesky orbitals, the active space can be spatially localized and the computational cost is greatly reduced compared to full CC3 while retaining the accuracy of CC3 excitation energies. For the small organic molecules considered we achieve up to two orders of magnitude reduction in the computational requirements.

Variational first hyperpolarizabilities of 2,3-naphtho-15-crown-5 ether derivatives with cation-complexing: a potential and selective cation detector

When the crown ether and its cation derivatives display obvious contrasts in NLO properties, the NLO-based detection of cations is achieved.

Open-ended response theory with polarizable embedding: multiphoton absorption in biomolecular systems

We present the theory and implementation of an open-ended framework for electric response properties that includes effects from the molecular environment modeled by the polarizable embedding model.