Two-electron/24-center (2e/24c) bonding in novel diradical π-dimers.

A series of diradical π-dimers 2 with interesting pancake-shaped 2e/24c π-π bonding character were designed and investigated based on the famous phenalenyl (PLY) π-dimer with 2e/12c π-π bonding character. The position of stronger interaction between two layers of radicals was found by the Wiberg bond index (WBI) maximum component. Further, the different contributions of the interaction energy were analyzed quantitatively by energy decomposition analysis (EDA). Among these new diradical π-dimers, 2180 has the smallest layer distance and the largest interaction between two layers of radicals. The unusual PLY analogues can provide new insights into the unique features of two-electron/multicenter (2e/mc) π-π bonding.

Modulating the charge transfer of D-S-A molecules: structures and NLO properties.

Very recently, the investigation of an Li atom doped effect on the "through-space" electronic interaction (S) of a donor-S-acceptor (D-S-A, 1) shows that the Li-doping effect can modulate the first hyperpolarizability of 1 ( Dyes Pigm. 2014 , 106 , 7 - 13 ). Can we further enhance the first hyperpolarizability (ßtot) of 1 by modulating the charge transfer of D-S-A molecules? The present work indicates that the ßtot value can be successfully modulated by replacing the sp(2)-hybridized CH═CH moiety connected with substituted para-cyclophane (PCP). On the other hand, the NO2 contributes more than NH2 to the ßtot value. The results of time-dependent density functional theory (TD-DFT) provide a good explanation for the variation in the ßtot value. Interestingly, the ßtot value of 3 (4.09 × 10(3) au) is larger than 1.52 × 10(3) au of 4, while the difference between the dipole moments (Δµ) of the ground state and the crucial excited state of 3 (2.93 D) is smaller than that of 4 (7.79 D). Further, the charge-transfer excitation length (D(CT)) of 3 (1.41 Å) is smaller than that of 4 (2.89 Å). Therefore, D(CT) is the major factor in determining the Δµ value.

Influence of spiral framework on nonlinear optical materials.

A series of spiral donor-π-acceptor frameworks (i.e. 2-2, 3-3, 4-4, and 5-5) based on 4-nitrophenyldiphenylamine with π-conjugated linear acenes (naphthalenes, anthracenes, tetracenes, and pentacenes) serving as the electron donor and nitro (NO2 ) groups serving as the electron acceptor were designed to investigate the relationships between the nonlinear optical (NLO) responses and the spirality in the frameworks. A parameter denoted as D was defined to describe the extent of the spiral framework. The D value reached its maximum if the number of NO2 groups was equal to the number of fused benzene rings contained in the linear acene. A longer 4-nitrophenyldiphenylamine chain led to a larger D value and, further, to a larger first hyperpolarizability. Different from traditional NLO materials with charge transfer occurring in the one-dimensional direction, charge transfer in 2-2, 3-3, 4-4, and 5-5 occur in three-dimensional directions due to the attractive spiral frameworks, and this is of great importance in the design of NLO materials. The origin of such an enhancement in the NLO properties of these spiral frameworks was explained with the aid of molecular orbital analysis.

Redox control of ferrocene-based complexes with systematically extended π-conjugated connectors: switchable and tailorable second order nonlinear optics.

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.

An accurate and efficient method to predict the electronic excitation energies of BODIPY fluorescent dyes.

Recently, the extreme learning machine neural network (ELMNN) as a valid computing method has been proposed to predict the nonlinear optical property successfully (Wang et al., J. Comput. Chem. 2012, 33, 231). In this work, first, we follow this line of work to predict the electronic excitation energies using the ELMNN method. Significantly, the root mean square deviation of the predicted electronic excitation energies of 90 4,4-difluoro-4-bora-3a,4a-diaza-s-indacene (BODIPY) derivatives between the predicted and experimental values has been reduced to 0.13 eV. Second, four groups of molecule descriptors are considered when building the computing models. The results show that the quantum chemical descriptions have the closest intrinsic relation with the electronic excitation energy values. Finally, a user-friendly web server (EEEBPre: Prediction of electronic excitation energies for BODIPY dyes), which is freely accessible to public at the web site: http://202.198.129.218, has been built for prediction. This web server can return the predicted electronic excitation energy values of BODIPY dyes that are high consistent with the experimental values. We hope that this web server would be helpful to theoretical and experimental chemists in related research.

After the electronic field: structure, bonding, and the first hyperpolarizability of HArF.

In this work, we add different strength of external electric field (E(ext)) along molecule axis (Z-axis) to investigate the electric field induced effect on HArF structure. The H-Ar bond is the shortest at E(ext) = -189 × 10(-4) and the Ar-F bond show shortest value at E(ext) = 185 × 10(-4) au. Furthermore, the wiberg bond index analyses show that with the variation of HArF structure, the covalent bond H-Ar shows downtrend (ranging from 0.79 to 0.69) and ionic bond Ar-F shows uptrend (ranging from 0.04 to 0.17). Interestingly, the natural bond orbital analyses show that the charges of F atom range from -0.961 to -0.771 and the charges of H atoms range from 0.402 to 0.246. Due to weakened charge transfer, the first hyperpolarizability (ß(tot)) can be modulated from 4078 to 1087 au. On the other hand, make our results more useful to experimentalists, the frequency-dependent first hyperpolarizabilities were investigated by the coupled perturbed Hartree-Fork method. We hope that this work may offer a new idea for application of noble-gas hydrides.

Strategy for enhancing second-order nonlinear optical properties of the Pt(II) dithienylethene complexes: substituent effect, π-conjugated influence, and photoisomerization switch.

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 (ßtot) 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 ßtot 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 f(os)/E(gm)(3) (f(os) is the oscillator strength, and E(gm) 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 (ßtot(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.

Theoretical investigation on the 2e/12c bond and second hyperpolarizability of azaphenalenyl radical dimers: strength and effect of dimerization.

An increasing number of chemists have focused on the investigations of two-electron/multicenter bond (2e/mc) that was first introduced to describe the structure of radical dimers. In this work, the dimerization of two isoelectronic radicals, triazaphenalenyl (TAP) and hexaazaphenalenyl (HAP) has been investigated in theory. Results show TAP2 is a stable dimer with stronger 2e/12c bond and larger interaction energy, while HAP2 is a less stable dimer with larger diradical character. Interestingly, the ultraviolet-visible absorption spectra suggest that the dimerization induces a longer wavelength absorption in visible area, which is dependent on the strength of dimerization. Significantly, the amplitude of second hyperpolarizability (γ(yyyy)) of HAP2 is 1.36 × 10(6) a.u. that is larger than 7.79 × 10(4) a.u. of TAP2 because of the larger diradical character of HAP2. Therefore, the results indicate that the strength of radical dimerization can be effectively detected by comparing the magnitude of third order non-linear optical response, which is beneficial for further theoretical and experimental studies on the properties of complexes formed by radical dimerization.

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 (ß(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 ß(0) of the large scale molecules, which is difficult to obtain by high-accuracy theoretical method due to dramatic increasing computational cost.

The excess electron in a boron nitride nanotube: pyramidal NBO charge distribution and remarkable first hyperpolarizability.

The unusual properties of species with excess electrons have attracted a lot of interest in recent years due to their wide applications in many promising fields. In this work, we find that the excess electron could be effectively bound by the B atoms of boron nitride nanotube (BNNT), which is inverted pyramidally distributed from B-rich edge to N-rich edge. Further, Li@B-BNNT and Li@N-BNNT are designed by doping the Li atom to the two edges of BNNT, respectively. Because of the interaction between the Li atom and BNNT, the 2s valence electron of Li becomes a loosely bound excess electron. Interestingly, the distribution of the excess electron in Li@N-BNNT is more diffuse and pyramidal from B-rich edge to N-rich edge, which is fascinating compared with Li@B-BNNT. Correspondingly, the transition energy of Li@N-BNNT is 0.99 eV, which is obviously smaller than 2.65 eV of Li@B-BNNT. As a result, the first hyperpolarizability (3.40×10(4) a.u.) of Li@N-BNNT is dramatically larger (25 times) than 1.35×10(3) a.u. of Li@B-BNNT. Significantly, we find that the pyramidal distribution of the excess electron is the key factor to determine the first hyperpolarizability, which reveals useful information for scientists to develop new electro-optic applications of BNNTs.

Spiral intramolecular charge transfer and large first hyperpolarizability in Möbius cyclacenes: new insight into the localized π electrons.

Much effort has been devoted to investigating the unusual properties of the π electrons in Möbius cyclacenes, which are localized in a special region. However, the localized π electrons are a disadvantage for applications in optoelectronics, because intramolecular charge transfer is limited. This raises the question of how the intramolecular charge transfer of a Möbius cyclacene with clearly localized π electrons can be enhanced. To this end, [8]Möbius cyclacene ([8]MC) is used as a conjugated bridge in a donor-π-conjugated bridge-acceptor (D-π-A) system, and NH(2)-6-[8]MC-10-NO(2) exhibits a fascinating spiral charge-transfer transition character that results in a significant difference in dipole moments Δµ between the ground state and the crucial excited state. The Δµ value of 6.832 D for NH(2)-6-[8]MC-10-NO(2) is clearly larger than that of 0.209 D for [8]MC. Correspondingly, the first hyperpolarizability of NH(2)-6-[8]MC-10-NO(2) of 12,467 a.u. is dramatically larger than that of 261 a.u. for [8]MC. Thus, constructing a D-π-A framework is an effective strategy to induce greater spiral intramolecular charge transfer in MC although the π electrons are localized in a special region. This new insight into the properties of π electrons in Möbius cyclacenes may provide valuable information for their applications in optoelectronics.

Modulation of the second-order nonlinear optical properties of the two-dimensional pincer Ru(II) complexes: substituent effect and proton abstraction switch.

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 H(2)SCS tridentate ligands (Tpy = 2,2':6',2″-terpyridyl and H(2)SCS = 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 (ß(tot)) of the 2D systems. Compared to the reference system 1 [Ru(H(2)SCS)(Tpy)](+), introducing the branches with strong electron acceptor group (p-NO(2)-phenylethynyl) to the Tpy ligand or the branches with strong electron donor group (p-NH(2)-phenylethynyl) to the H(2)SCS ligand can effectively improve the ß(tot) values. Time-dependent DFT (TDDFT) calculations indicate that the enhanced ß(tot) 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 NO(2) groups on H(2)SCS ligand, there is a dramatic enhancement in the ß(tot) values for its deprotonated forms. The ß(tot) 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.

Quantum chemical research on structures, linear and nonlinear optical properties of the Li@n-acenes salt (n = 1, 2, 3, and 4).

On the basis of the n-acenes (n = 1, 2, 3 and 4), the α-Li@n-acenes and ß-Li@n-acenes salts were selected to investigate how increasing the number n of conjugated benzenoid rings affects the linear and nonlinear optical responses. The α-Li@n-acenes and ß-Li@n-acenes salts are obtained by a lithium atom substituting the α-H and ß-H, respectively. In the present work, both ab initio (HF and MP2) and DFT (B3LYP, BhandHLYP, M05-2X, and CAM-B3LYP) methods are adopted to calculate the polarizability (α(0)) and first hyperpolarizability (ß(tot)) of the α-Li@n-acenes and ß-Li@n-acenes salts. MP2 results show that the α(0) values of both classes of lithium salts increase with increasing number n of conjugated benzenoid rings. Interestingly, we found that the ß(tot) values of α-Li@n-acenes and ß-Li@n-acenes salts take on opposite trends: the ß(tot) values of α-Li@n-acenes are decreasing slowly (2187 for α-Li@benzene > 1978 for α-Li@naphthalene > 1898 for α-Li@anthrecene > 1830 au for α-Li@tetracene) and inceasing remarkably (2738 for ß-Li@naphthalene < 3186 for ß-Li@anthrecene < 3314 au for ß-Li@tetracene) for ß-Li@n-acenes. Furthermore, we found that the ß(tot) values (2738-3314 au) of the ß-Li@n-acenes are larger than those of the α-Li@n-acenes (1830-2187 au). On the other hand, comparing the results of different methods, the ß(tot) values obtained by the M05-2X and CAM-B3LYP methods reproduce the polarizability and first hyperpolarizability of the α-Li@n-acenes and ß-Li@n-acenes salts well, which test and verify the results of the MP2 method. Our present work may be beneficial to development of high-performance organic NLO optical materials.

Quantum chemical study of redox-switchable second-order nonlinear optical responses of D-π-A system BNbpy and metal Pt(II) chelate complex.

A second-order nonlinear optical (NLO) molecular switching with redox has been investigated in the present paper. The static first hyperpolarizabilities of 5-(BMes(2))-5'-(NPh(2))-2,2'-bipyridine (BNbpy) containing three-coordinate organoboron, Pt(II) chelate complex Pt(BNbpy)Ph(2), 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 ß(vec) value of one-electron-reduced form is ~7 times as large as that of neutral form BNbpy; the ß(vec) values of one- and two-electron-reduced forms are ~3 and ~4 times as large as that of neutral form Pt(BNbpy)Ph(2), respectively. In particular, the ß(vec) value of two-electron-reduced form (3)Pt(BNbpy)Ph(2)(2-) is 1349 × 10(-30) esu, ~286 times larger than its neutral form. Moreover, the component ß(z) value of the metal chelate complex Pt(BNbpy)Ph(2) 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 ß(x) 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 p(π)-π* conjugation and has no effect on the conjugation of bipyridine, which leads to a decreasing ß value in the x-axis.

An accurate density functional theory calculation for electronic excitation energies: the least-squares support vector machine.

Support vector machines (SVMs), as a novel type of learning machine, has been very successful in pattern recognition and function estimation problems. In this paper we introduce least-squares (LS) SVMs to improve the calculation accuracy of density functional theory. As a demonstration, this combined quantum mechanical calculation with LS-SVM correction approach has been applied to evaluate the electronic excitation energies of 160 organic molecules. The newly introduced LS-SVM approach reduces the root-mean-square deviation of the calculated electronic excitation energies of 160 organic molecules from 0.32 to 0.11 eV for the B3LYP/6-31G(d) calculation. Thus, the LS-SVM correction on top of B3LYP/6-31G(d) is a better method to correct electronic excitation energies and can be used as the approximation of experimental results which are impossible to obtain experimentally.

Superalkali atoms bonding to the phenalenyl radical: structures, intermolecular interaction and nonlinear optical properties.

Due to unpaired electrons, both radicals and superalkali are investigated widely. In this work, two interesting complexes (Li3O-PLY and Li3-PLY) were constructed by phenalenyl radical and superalkali atoms. Why are they interesting? Firstly, for Li3O-PLY and Li3-PLY, although the charge transfer between superalkali atoms and PLY is similar, the sandwich-like charge distribution for Li3O-PLY causes a smaller dipole moment than that of Li3-PLY. Secondly, their UV-vis absorption show that the maximum wavelengths for Li3O-PLY and Li3-PLY display a bathochromic shift compared to PLY. Moreover, Li3-PLY has two new peaks at 482 and 633 nm. Significantly, the ß 0 values of Li3-PLY (4943-5691 a.u.) are much larger than that of Li3O-PLY (225-347 a.u.). Further, the ß HRS values of Li3O-PLY decrease slightly while ß HRS of Li3-PLY increase dramatically with increasing frequency. It is our expectation that these results might provide beneficial information for theoretical and experimental studies on complexes with superalkali and PLY radicals. Graphical Abstract Two interesting complexes (Li3O-PLY and Li3-PLY) were constructed by phenalenyl radical and superalkali atoms. We explore their structures, Wiberg bond indices, interaction energies and the static first hyperpolarizabilities (ß 0). The ß 0 values of Li3-PLY (4943-5691 a.u.) were much larger than those of Li3O-PLY (225-347 a.u.).

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).

Charge transfer and first hyperpolarizability: cage-like radicals C59X and lithium encapsulated Li@C59X (X=B, N).

Very recently, two new cage-like radicals (C59B and C59N) formed by a boron or nitrogen atom substituting one carbon atom of C60 were synthesized and characterized. In order to explore the structure-property relationships of combination the cage-like radical and alkali metal, the endohedral Li@C59B and Li@C59N are designed by lithium (Li) atom encapsulated into the cage-like radicals C59B and C59N. Further, the structures, natural bond orbital (NBO) charges, and nonlinear optical (NLO) responses of C59B, C59N, Li@C59B, and Li@C59N were investigated by quantum chemical method. Three density functional methods (BHandHLYP, CAM-B3LYP, and M05-2X) were employed to estimate their first hyperpolarizabilities (ß tot) and obtained the same trend in the ß tot value. The ß tot values by BHandHLYP functional of the pure cage-like radicals C59B (1.30 × 10(3) au) and C59N (1.70 × 10(3) au) are close to each other. Interestingly, when one Li atom encapsulated into the electron-rich radical C59N, the ß tot value of the Li@C59N increases to 2.46 × 10(3) au. However, when one Li atom encapsulated into the electron-deficient radical C59B, the ß tot value of the Li@C59B sharply decreases to 1.54 × 10(2) au. The natural bond orbital analysis indicates that the encapsulated Li atom leads to an obvious charge transfer and valence electrons distribution plays a significant role in the ß tot value. Further, frontier molecular orbital explains that the interesting charge transfer between the encapsulated Li atom and cage-like radicals (C59B and C59N) leads to differences in the ß tot value. It is our expectation that this work will provide useful information for the design of high-performance NLO materials.

"Dancing inside the ball": the structures and nonlinear optical properties of three Sc2S@C3v(8)-C82 isomers.

Recently, the crystal structures and electrochemical properties of the isomers (Sc2S "trapped" in C82) have been reported, in which the Sc2S is located inside the different positions of the C82 cage. In the present work, three isomers of endohedral metallofullerenes Sc2S@C3v(8)-C82 (A, B, and C) have been designed to explore the effect of the position of Sc2S on their interaction energies and nonlinear optical properties. Among three isomers, the Sc2S is located in different positions of the C82 cage: the angles of Sc-S-Sc in A, B, and C are 104.9, 114.8, and 115.7°, respectively. Furthermore, the analysis of natural bond orbital (NBO) charge indicates that the electron-transfer is from the Sc2S to the adjacent carbon atoms of the C82 cage. The interaction energy of B is the smallest among three isomers which is -226.2 kcal mol(-1). It was worth mentioning that their first hyperpolarizabilities (ß tot) were studied, we found that their ß tot values were related to the positions of Sc2S: C (2100) > B (1191) > A (947 au). We hope that the present work can provide a new strategy to promote the nonlinear optical properties of endohedral metallofullerenes by changing the positions of the encapsulated molecular. Graphical abstract Three isomers of endohedral metallofullerenes Sc2S@C3v(8)-C82 (A, B, and C) have been designed to explore the position effect of Sc2S on the interaction energies and nonlinear optical properties. Among three isomers, the Sc2S in B has the most stable position. Significantly, the first hyperpolarizability is related to the position of Sc2S inside the C82 cage, which provides a novel strategy to enhance the first hyperpolarizability by the Sc2S revolving inside the C82 cage.

Structures and electro-optical properties of Möbius [n]Cyclacenes[13-18]: a theoretical study.

Due to the unusual properties of the Möbius cyclacenes (MC) such as π electrons, MC has drawn the extensive attention of scientists. In the present work, six [n]MC (n = 13-18, n is the number of benzenoid rings) were systematically investigated to explore the size-dependent effects on structures, electro-optical properties, and frontier molecule orbits (FMO). According to the dihedral angles (C-C-C-C), the un-twisted area and twisted area are defined, respectively. The twisted area mainly distributes on seven or eight benzenoid rings for [n]MC (n = 13-18). Further, the polarizability (α0) and first hyperpolarizability (ß0) of [n]MC (n = 13-18) were calculated with three density functional methods (BHandHLYP, Cam-B3LYP, and M06-2X). Results show that the α0 values increase linearly with increasing the number (n) of benzenoid rings. Significantly, the ß0 values are increased to zigzag with increasing the number (n) of benzenoid rings. Interestingly, when n is even (14, 16, and 18), the electron transfer is from the twisted area to the un-twisted area, but the electron transfer is from the un-twisted area to the twisted area when n is odd (13, 15, and 17).