Evaluation of the Nonlinear Optical Properties for Annulenes with Hückel and Möbius Topologies

Recently, much attention has been focused on the design and synthesis of molecules with aromatic Möbius topology. One of the most promising applications is the manufacture of Hückel-to-Möbius topological optical switches with high nonlinear optical properties. In this work, we evaluate the electronic and vibrational contributions to static and dynamic nonlinear optical properties of the <i>C</i>_S Hückel and <i>C</i>₂ Möbius topologies synthesized by Herges and co-workers (Ajami, D. et al.<i> Nature</i> <b>2003</b>, <i>426</i>, 819). Calculations are performed at the HF, B3LYP, BHandHLYP, BMK, M052X, CAM-B3LYP, and MP2 levels with the 6-31+G(d) basis set. Our results conclude that the BHandHLYP, M052X, and CAM-B3LYP methods correctly reproduce the X-ray crystal structure and provide similar nonlinear optical properties

Comparison of Property-Oriented Basis Sets for the Computation of Electronic and Nuclear Relaxation Hyperpolarizabilities

In the present work, we perform an assessment of several property-oriented atomic basis sets in computing (hyper)­polarizabilities with a focus on the vibrational contributions. Our analysis encompasses the Pol and LPol-ds basis sets of Sadlej and co-workers, the def2-SVPD and def2-TZVPD basis sets of Rappoport and Furche, and the ORP basis set of Baranowska-Łączkowska and Łączkowski. Additionally, we use the d-<i>aug</i>-cc-pVQZ and <i>aug</i>-cc-pVTZ basis sets of Dunning and co-workers to determine the reference estimates of the investigated electric properties for small- and medium-sized molecules, respectively. We combine these basis sets with <i>ab initio</i> post-Hartree–Fock quantum-chemistry approaches (including the coupled cluster method) to calculate electronic and nuclear relaxation (hyper)­polarizabilities of carbon dioxide, formaldehyde, <i>cis</i>-diazene, and a medium-sized Schiff base. The primary finding of our study is that, among all studied property-oriented basis sets, only the def2-TZVPD and ORP basis sets yield nuclear relaxation (hyper)­polarizabilities of small molecules with average absolute errors less than 5.5%. A similar accuracy for the nuclear relaxation (hyper)­polarizabilites of the studied systems can also be reached using the <i>aug</i>-cc-pVDZ basis set (5.3%), although for more accurate calculations of vibrational contributions, i.e., average absolute errors less than 1%, the <i>aug</i>-cc-pVTZ basis set is recommended. It was also demonstrated that anharmonic contributions to first and second hyperpolarizabilities of a medium-sized Schiff base are particularly difficult to accurately predict at the correlated level using property-oriented basis sets. For instance, the value of the nuclear relaxation first hyperpolarizability computed at the MP2/def2-TZVPD level of theory is roughly 3 times larger than that determined using the <i>aug</i>-cc-pVTZ basis set. We link the failure of the def2-TZVPD basis set with the difficulties in predicting the first-order field-induced coordinates. On the other hand, the <i>aug</i>-cc-pVDZ and ORP basis sets overestimate the property in question only by roughly 30%. In this study, we also propose a low-cost composite treatment of anharmonicity that relies on the combination of two basis sets, i.e., a large-sized basis set is employed to determine lowest-order derivatives with respect to the field-induced coordinates, and a medium-sized basis set is used to compute the higher-order derivatives. The results of calculations performed at the MP2 level of theory demonstrate that this approximate scheme is very successful at predicting nuclear relaxation hyperpolarizabilities

Electronic and Vibrational Nonlinear Optical Properties of Five Representative Electrides

The electrides have a very special electronic structure with diffuse excess electrons not localized on any specific atom. Such systems are known to have huge electronic nonlinear optical (NLO) properties. Here, we determine and analyze the vibrational, as compared to the electronic, NLO properties for a representative set of electrides: Li@Calix, Na@Calix, Li@B₁₀H₁₄, Li₂^•+TCNQ^•–, and Na₂^•+TCNQ^•–. The static and dynamic vibrational (hyper)­polarizabilities are computed by the nuclear relaxation method (with field-induced coordinates and the infinite optical frequency approximation) at the UB3LYP level using a hybrid Pople basis set. In general, the static vibrational β_vec and γ_∥ exceed the corresponding static electronic property values by up to an order of magnitude. The same comparison for dynamic vibrational hyperpolarizabilities shows a smaller ratio. For the intensity-dependent refractive index (IDRI) and dc-Kerr processes, the ratio is on the order of unity or somewhat larger; it is less for the dc-Pockels and the electric field induced second harmonic (EFISH) effects (as well as the static α̅) but still important. The role of anharmonicity, motion of the alkali atoms, and substitution of Na for Li is discussed along with specific aspects of the charge distribution associated with the excess electron

Computational Insight into the Mechanism of Alkane Hydroxylation by Non-heme Fe(PyTACN) Iron Complexes. Effects of the Substrate and Solvent

The reaction mechanisms for alkane hydroxylation catalyzed by non-heme Fe^VO complexes presented in the literature vary from rebound stepwise to concerted highly asynchronous processes. The origin of these important differences is still not completely understood. Herein, in order to clarify this apparent inconsistency, the hydroxylation of a series of alkanes (methane and substrates bearing primary, secondary, and tertiary C–H bonds) through a Fe^VO species, [Fe^V(O)­(OH)­(PyTACN)]²⁺ (PyTACN = 1-(2′-pyridylmethyl)-4,7-dimethyl-1,4,7-triazacyclononane), has been computationally examined at the gas phase and in acetonitrile solution. The initial breaking of the C–H bond can occur via hydrogen atom transfer (HAT), leading to an intermediate where there is an interaction between the radical substrate and [Fe^IV(OH)₂(PyTACN)]²⁺, or through hydride transfer to form a cationic substrate interacting with the [Fe^III(OH)₂(PyTACN)]⁺ species. Our calculations show the following: (i) except for methane in the rest of the alkanes studied, the intermediate formed by R⁺ and [Fe^III(OH)₂(PyTACN)]⁺ is more stable than that involving the alkyl radical and the [Fe^IV(OH)₂(PyTACN)]²⁺ complex; (ii) in spite of (i), the first step of the reaction mechanism for all substrates is a HAT instead of hydride abstraction; (iii) the HAT is the rate-determining step for all analyzed cases; and (iv) the barrier for the HAT decreases along methane → primary → secondary → tertiary carbon. The second part of the reaction mechanism corresponds to the rebound process. Therefore, the stereospecific hydroxylation of alkane C–H bonds by non-heme Fe^V(O) species occurs through a rebound stepwise mechanism that resembles that taking place at heme analogues. Finally, our study also shows that, to properly describe alkane hydroxylation processes mediated by Fe^VO species, it is essential to consider the solvent effects during geometry optimizations. The use of gas-phase geometries explains the variety of mechanisms for the hydroxylation of alkanes reported in the literature

Resonant and Nonresonant Hyperpolarizabilities of Spatially Confined Molecules: A Case Study of Cyanoacetylene

In this theoretical study we report on resonant and nonresonant electric-dipole (hyper)­polarizabilities of cyanoacetylene molecule confined by repulsive potentials of cylindrical symmetry mimicking a topology of nanotubelike carbon cages. The set of investigated electronic properties encompasses dipole moment, polarizability, first and second hyperpolarizability as well as the two-photon transition matrix elements. The effect of external potential on vibrational contributions to electric-dipole properties is also included in our treatment. The computations are performed at several levels of theoretical approximation including state-of-the-art coupled-cluster (CCSD­(T)) and multireference configuration interaction methods (MRCISD­(Q)). The results of calculations presented herein indicate that the decrease in dipole moment observed experimentally for the HCCCN molecule solvated in helium nanodroplets may be partially attributed to the confinement effects. The external confining potential causes a substantial drop of the isotropic average electronic polarizability and second hyperpolarizability. In contrast, the vector component of the electronic first hyperpolarizability substantially increases. Nuclear relaxation contributions to all studied electric-dipole properties are found to diminish upon confinement. Our calculations also indicate that the most intense ¹Σ⁺ ← <i>X̃</i> one-photon transition is slightly blue-shifted whereas the corresponding oscillator strength is virtually unaffected upon confinement. Interestingly, the absolute magnitude of the diagonal component of the second-order transition moment for the bright state (<i>S</i>_<i>zz</i>^0→¹∑⁺) increases with the strength of external potential. The effect of structural relaxation on the electric-dipole properties, arising from the presence of the external potential, is also investigated in the present work

A Full Dimensionality Approach to Evaluate the Nonlinear Optical Properties of Molecules with Large Amplitude Anharmonic Tunneling Motions

Previously, a reduced dimensionality approach was used to determine the vibrational contribution to nonlinear optical properties for molecules with large amplitude anharmonic modes that takes into account tunneling between potential wells (Luis, J. M.; Reis, H.; Papadopoulos, M. G.; Kirtman, B. <i>J. Chem. Phys.</i> <b>2009</b>, <i>131</i>, 034116). Here, the treatment is extended, again using ammonia as an example, to include the remaining modes at several approximate levels. It is shown that this extension is essential to obtaining the correct results. Our new approach fully accounts for tunneling and avoids possible convergence problems associated with the normal coordinate expansion of the potential energy surface in a single-well treatment. For accurate numerical values, a good treatment of electron correlation is required along with a flexible basis set including diffuse functions

The Frozen Cage Model: A Computationally Low-Cost Tool for Predicting the Exohedral Regioselectivity of Cycloaddition Reactions Involving Endohedral Metallofullerenes

Functionalization of endohedral metallofullerenes (EMFs) is an active line of research that is important for obtaining nanomaterials with unique properties that might be used in a variety of fields, ranging from molecular electronics to biomedical applications. Such functionalization is commonly achieved by means of cycloaddition reactions. The scarcity of both experimental and theoretical studies analyzing the exohedral regioselectivity of cycloaddition reactions involving EMFs translates into a poor understanding of the EMF reactivity. From a theoretical point of view, the main obstacle is the high computational cost associated with this kind of studies. To alleviate the situation, we propose an approach named the frozen cage model (FCM) based on single point energy calculations at the optimized geometries of the empty cage products. The FCM represents a fast and computationally inexpensive way to perform accurate qualitative predictions of the exohedral regioselectivity of cycloaddition reactions in EMFs. Analysis of the Dimroth approximation, the activation strain or distortion/interaction model, and the noncluster energies in the Diels–Alder cycloaddition of <i>s-cis</i>-1,3-butadiene to X@<i>D</i>_3<i>h</i>-C₇₈ (X = Ti₂C₂, Sc₃N, and Y₃N) EMFs provides a justification of the method

Carboxylate-Assisted Formation of Aryl-Co(III) Masked-Carbenes in Cobalt-Catalyzed C–H Functionalization with Diazo Esters

Herein we describe the synthesis of a family of aryl-Co­(III)-carboxylate complexes and their reactivity with ethyl diazoacetate. Crystallographic, full spectroscopic characterization, and theoretical evidence of unique C-metalated aryl-Co­(III) enolate intermediates is provided, unraveling a carboxylate-assisted formation of aryl-Co­(III) <i>masked-carbenes</i>. Moreover, additional evidence for an unprecedented Co­(III)-mediated intramolecular S_N2-type C–C bond formation in which the carboxylate moiety acts as a relay is disclosed. This novel strategy is key to tame the hot reactivity of a metastable Co­(III)-carbene and elicit C–C coupling products in a productive manner

Carboxylate-Assisted Formation of Aryl-Co(III) Masked-Carbenes in Cobalt-Catalyzed C–H Functionalization with Diazo Esters

Herein we describe the synthesis of a family of aryl-Co­(III)-carboxylate complexes and their reactivity with ethyl diazoacetate. Crystallographic, full spectroscopic characterization, and theoretical evidence of unique C-metalated aryl-Co­(III) enolate intermediates is provided, unraveling a carboxylate-assisted formation of aryl-Co­(III) <i>masked-carbenes</i>. Moreover, additional evidence for an unprecedented Co­(III)-mediated intramolecular S_N2-type C–C bond formation in which the carboxylate moiety acts as a relay is disclosed. This novel strategy is key to tame the hot reactivity of a metastable Co­(III)-carbene and elicit C–C coupling products in a productive manner

Carboxylate-Assisted Formation of Aryl-Co(III) Masked-Carbenes in Cobalt-Catalyzed C–H Functionalization with Diazo Esters

Herein we describe the synthesis of a family of aryl-Co­(III)-carboxylate complexes and their reactivity with ethyl diazoacetate. Crystallographic, full spectroscopic characterization, and theoretical evidence of unique C-metalated aryl-Co­(III) enolate intermediates is provided, unraveling a carboxylate-assisted formation of aryl-Co­(III) <i>masked-carbenes</i>. Moreover, additional evidence for an unprecedented Co­(III)-mediated intramolecular S_N2-type C–C bond formation in which the carboxylate moiety acts as a relay is disclosed. This novel strategy is key to tame the hot reactivity of a metastable Co­(III)-carbene and elicit C–C coupling products in a productive manner