Origin of the Enhancement of the Second Hyperpolarizabilities in Open-Shell Singlet Transition-Metal Systems with Metal–Metal Multiple Bonds

Using the spin-unrestricted coupled-cluster method, we explore the origin of the second hyperpolarizabilities (γ) of singlet dichromium(II) and dimolybdenum(II) model systems with various bond lengths as a function of the diradical characters of the dσ, dπ, and dδ orbitals. Both systems exhibit enhanced γ values in the intermediate diradical character region, but by using a partitioning scheme, the dσ electrons are shown to play the essential role in contrast with the π-electrons of conventional organic π-conjugated systems. Then, in the equilibrium bond length region, the γ values are still governed by dσ electrons in the dichromium(II) system, although by dδ/dπ electrons in the dimolybdenum(II) system

Halide Ion Complexes of Decaborane (B₁₀H₁₄) and Their Derivatives: Noncovalent Charge Transfer Effect on Second-Order Nonlinear Optical Properties

Quantum molecular engineering has been performed to determine the second-order nonlinear optical (NLO) properties in different halo complexes of decaborane (B₁₀H₁₄) and their derivatives using the density functional theory (DFT) method. These decaborane halo complexes of X^–@B₁₀H₁₄ (X = F, Cl, Br, and I) are found to possess noncovalent charge transfer interactions. The static polarizability (α₀) and first hyperpolarizability (β₀) among these complexes increase by moving down the group from F to I, partly due to the increase in size of their anionic radii and the decrease in their electron affinities. A two-level approximation has been employed to investigate the origin of β₀ values in these halo complexes, which show very consistent results with those by the finite-field method. Furthermore, in the same line, two experimentally existing complexes, I^–@B₁₀H₁₄ and I^–@2,4-I₂B₁₀H₁₂, are found to have considerably large β₀ values of 2859 and 3092 a.u., respectively, which are about three times larger than a prototypical second-order NLO molecule of <i>p</i>-nitroaniline, as reported by Soscun et al. [<i>Int. J. Quantum Chem.</i> <b>2006</b>, <i>106</i>, 1130–1137]. Besides this, the special effects of solvent, counterion, and bottom substitutions have also been investigated. Interestingly, 2,4-alkali metal-substituted decaborane iodide complexes show remarkably large second-order NLO response with β₀ amplitude as large as 62436 a.u. for I^–@2,4-K₂B₁₀H₁₂ complex, which are explained in terms of their transition energies, frontier molecular orbitals and electron density difference plots. Thus, the present investigation provides several new comparative insights into the second-order NLO properties of halo complexes of decaborane, which possess not only large first hyperpolarizabilities, but also high tunability to get a robustly large second-order NLO response by alkali metal substitution effects

Enhancement of the Third-Order Nonlinear Optical Properties in Open-Shell Singlet Transition-Metal Dinuclear Systems: Effects of the Group, of the Period, and of the Charge of the Metal Atom

Metal–metal multiply bonded complexes in their singlet state have been predicted to form a novel class of “σ-dominant” third-order nonlinear optical compounds based on the results of dichromium­(II) and dimolybdenum­(II) systems (H. Fukui et al. <i>J. Phys. Chem. Lett.</i> <b>2011</b>, <i>2</i>, 2063) whose second hyperpolarizabilities (γ) are enhanced by the contribution of the dσ electrons with an intermediate diradical character. In this study, using the spin-unrestricted coupled-cluster method with singles and doubles as well as with perturbative triples, we investigate the dependences of γ on the group and on the period of the transition metals as well as on their atomic charges in several open-shell singlet dimetallic systems. A significant enhancement of γ is observed in those dimetallic systems composed of (i) transition metals with a small group number, (ii) transition metals with a large periodic number, and (iii) transition metals with a small positive charge. From the decomposition of the γ values into the contributions of dσ, dπ, and dδ electrons, the γ enhancements are shown to originate from the dσ contribution, because it corresponds to the intermediate diradical character region. Furthermore, the amplitude of dσ contribution turns out to be related to the size of the d_<i>z</i>² atomic orbital of the transition metal, which accounts for the dependence of γ on the group, on the period, and on the charge of the metal atoms. These dependences provide a guideline for an effective molecular design of highly efficient third-order nonlinear optical (NLO) systems based on the metal–metal bonded systems

Open-Shell Character and Second Hyperpolarizabilities of One-Dimensional Chromium(II) Chains: Size Dependence and Bond-Length Alternation Effect

Using the long-range corrected spin-unrestricted density functional theory (LC-UBLYP) method, we have investigated the longitudinal third-order nonlinear optical (NLO) properties, i.e., the second hyperpolarizabilities γ of open-shell singlet one-dimensional (1D) extended metal atom chain (EMAC) systems, chromium­(II) chains Cr^II_2<i>n</i> (<i>n</i> = 1–4), with different metal–metal bond lengths from the viewpoint of the open-shell character dependences of each d orbital contribution (dσ, dπ, dδ) to γ and of the chain-length dependence of γ. It turns out that the chain length dependences of the open-shell characters of dπ and dδ orbitals at any metal–metal bond length are negligible, while the dσ open-shell character decreases as a function of chain length. The systems display bell-shaped behaviors of γ as a function of the metal–metal bond length, in which the γ values attain maxima for intermediate dσ open-shell character. The maximum γ value (γ_max) exhibits remarkable enhancement as a function of chain length. It is also found that the bond length alternation (BLA) significantly affects the γ values and their chain-length dependences. The present results provide the guiding principles for designing transition-metal complexes with open-shell singlet 1D metallic chains exhibiting large third-order optical nonlinearity