Size dependences of the diradical character and the second hyperpolarizabilities in dicyclopenta-fused acenes: relationships with their aromaticity/antiaromaticity.

Using long-range corrected density functional theory, the relationships between the electronic, magnetic, and nonlinear optical properties are drawn for two families of organic compounds, the dicyclopenta-fused acenes (DPAs) and the polyacenes (PAs), containing up to N = 12 fused rings. First, the longitudinal second hyperpolarizability (γ) of singlet DPAs is significantly enhanced with increasing system size, in comparison to PAs. This behavior is associated with an increase in the longitudinal spin polarization between the terminal five-membered rings of DPAs and is consistent with previous studies where γ is maximized for intermediate diradical character. The size dependence of the diradical character is also found to cause a hump in the γ/N evolution for singlet DPAs around N = 8. In fact, in the case of singlet PAs, the diradical characters y(0) and y(1), the various magnetic properties and the γ/N values vary monotonically with N, whereas for singlet DPAs, the shielding, the magnetizability, and the γ/N values exhibit extrema near N = 8 due to the appearance of transversal spin polarization in the middle six-membered rings in addition to the longitudinal spin polarization between the terminal five-membered rings. Moreover, it is shown that for singlet DPAs the longitudinal spin polarization (characterized by y(0)) is associated with the antiaromaticity (N ≤ 3) and the slight- or non-aromaticity (N ≥ 4) of the terminal five-membered rings, whereas the appearance of transversal spin-polarization (characterized by y(1)) is associated with the decrease in the aromaticity in the inner six-membered rings as shown for large PAs. Therefore, the exceptional behaviors in singlet DPAs for small N (N < 9) are caused by the increase in diradical character y(0) correlated with the anti-aromaticity or the slight-/non-aromaticity of terminal rings and the corresponding emergence of a global aromatic character. Such a relationship between the aromaticity/antiaromaticity and the diradical character is useful for designing real open-shell NLO molecules through the control of their diradical characters.

[1]  Patrick W. Fowler,et al.  Localisation and reversal of paratropic ring currents in molecules with formal anti-aromatic electron countsPresented at the ESF Exploratory Workshop: New Perspectives on Aromaticity, Exeter, UK, July 5?9, 2003. , 2004 .

[2]  Paul von Ragué Schleyer,et al.  Nucleus-Independent Chemical Shifts:  A Simple and Efficient Aromaticity Probe. , 1996, Journal of the American Chemical Society.

[3]  M. Nakano,et al.  Theoretical study of third-order nonlinear optical properties in square nanographenes with open-shell singlet ground states , 2008 .

[4]  A. Soncini,et al.  Ring Currents and Magnetic Properties of s-Indacene, an Archetypal Paratropic, Non-Antiaromatic Molecule , 2002 .

[5]  Trygve Helgaker,et al.  Hartree-Fock limit magnetizabilities from London orbitals , 1993 .

[6]  Ernest R. Davidson,et al.  Distribution of effectively unpaired electrons , 2000 .

[7]  M. Nakano,et al.  EHF theory of chemical reactions Part 4. UNO CASSCF, UNO CASPT2 and R(U)HF coupled-cluster (CC) wavefunctions , 1994 .

[8]  M. Nakano,et al.  Third-order nonlinear optical properties of trigonal, rhombic and bow-tie graphene nanoflakes with strong structural dependence of diradical character , 2009 .

[9]  J. Aihara,et al.  Local aromaticities in large polyacene molecules. , 2005, The journal of physical chemistry. A.

[10]  R. Zanasi.  Coupled Hartree–Fock calculations of molecular magnetic properties annihilating the transverse paramagnetic current density , 1996 .

[11]  Martin Head-Gordon,et al.  Characterizing unpaired electrons from the one-particle density matrix , 2003 .

[12]  A. Rajca,et al.  Isolation of the triplet ground state aminyl diradical. , 2010, Angewandte Chemie.

[13]  Roland H. Hertwig,et al.  s‐Indacene: A Delocalized, Formally Antiaromatic 12 π Electron System , 1994 .

[14]  Kazuo Takatsuka,et al.  Distribution of odd electrons in ground-state molecules , 1978 .

[15]  M. Nakano,et al.  Synthesis and characterization of teranthene: a singlet biradical polycyclic aromatic hydrocarbon having Kekulé structures. , 2010, Journal of the American Chemical Society.

[16]  M. Nakano,et al.  Second hyperpolarizabilities of polycyclic aromatic hydrocarbons involving phenalenyl radical units , 2006 .

[17]  M. Nakano,et al.  Strong two-photon absorption of singlet diradical hydrocarbons. , 2007, Angewandte Chemie.

[18]  Benoît Champagne,et al.  Second Hyperpolarizability (γ) of Singlet Diradical System: Dependence of γ on the Diradical Character , 2005 .

[19]  J. Aihara,et al.  Aromaticity and magnetotropicity of dicyclopenta-fused polyacenes. , 2008, Physical chemistry chemical physics : PCCP.

[20]  M. Nakano,et al.  Long-range corrected density functional theory study on static second hyperpolarizabilities of singlet diradical systems. , 2010, The Journal of chemical physics.

[21]  Paolo Lazzeretti.  Assessment of aromaticity via molecular response properties , 2004 .

[22]  E. Ortí,et al.  Quinoidal oligothiophenes: towards biradical ground-state species. , 2010, Chemistry.

[23]  F. Guinea,et al.  The electronic properties of graphene , 2007, Reviews of Modern Physics.

[24]  H. Bettinger,et al.  Photogeneration of octacene and nonacene. , 2010, Angewandte Chemie.

[25]  Klaus Müllen,et al.  A bottom-up approach from molecular nanographenes to unconventional carbon materials , 2008 .

[26]  M. Kertész,et al.  Conjugated polymers and aromaticity. , 2005, Chemical reviews.

[27]  Zhendong Zhu,et al.  Pentalene: Formation, Electronic, and Vibrational Structure , 1997 .

[28]  G. Trinquier,et al.  Theoretical design of high-spin polycyclic hydrocarbons. , 2010, Chemistry.

[29]  M. Nakano,et al.  Signature of multiradical character in second hyperpolarizabilities of rectangular graphene nanoflakes , 2010 .

[30]  M. Itkis,et al.  Resonating valence bond and sigma-charge density wave phases in a benzannulated phenalenyl radical. , 2010, Journal of the American Chemical Society.

[31]  Koji Ohta,et al.  Relationship between third-order nonlinear optical properties and magnetic interactions in open-shell systems: a new paradigm for nonlinear optics. , 2007, Physical review letters.

[32]  E. Canesi,et al.  Biradicaloid and Polyenic Character of Quinoidal Oligothiophenes Revealed by the Presence of a Low-Lying Double-Exciton State , 2010 .

[33]  C. Roothaan,et al.  Electric Dipole Polarizability of Atoms by the Hartree—Fock Method. I. Theory for Closed‐Shell Systems , 1965 .

[34]  B. Champagne,et al.  Ring Current Model and Anisotropic Magnetic Response of Cyclopropane. , 2010, Journal of chemical theory and computation.

[35]  Mark A Ratner,et al.  Singlet fission for dye-sensitized solar cells: can a suitable sensitizer be found? , 2006, Journal of the American Chemical Society.

[36]  Andre K. Geim,et al.  Electric Field Effect in Atomically Thin Carbon Films , 2004, Science.

[37]  Clémence Corminboeuf,et al.  Nucleus-independent chemical shifts (NICS) as an aromaticity criterion. , 2005, Chemical reviews.

[38]  K. Houk,et al.  Oligoacenes: theoretical prediction of open-shell singlet diradical ground states. , 2004, Journal of the American Chemical Society.

[39]  Garnet Kin-Lic Chan,et al.  The radical character of the acenes: a density matrix renormalization group study. , 2007, The Journal of chemical physics.

[40]  Yong Tian,et al.  Is there a lower limit to the CC bonding distances in neutral radical pi-dimers? The case of phenalenyl derivatives. , 2010, Journal of the American Chemical Society.

[41]  K. Hirao,et al.  A long-range correction scheme for generalized-gradient-approximation exchange functionals , 2001 .

[42]  Swapan K. Pati,et al.  Novel properties of graphene nanoribbons: a review , 2010 .

[43]  M. Nakano,et al.  Theoretical study on third-order nonlinear optical properties in hexagonal graphene nanoflakes: Edge shape effect , 2009 .

[44]  H. Okamoto,et al.  Resonance balance shift in stacks of delocalized singlet biradicals. , 2009, Angewandte Chemie.

[45]  Haijun Jiao,et al.  What is aromaticity? , 1996, J. Chem. Inf. Comput. Sci..

[46]  E. F. Hayes,et al.  Electronic structure of the open forms of three-membered rings , 1971 .

[47]  M. Nakano,et al.  Origin of the enhancement of the second hyperpolarizability of singlet diradical systems with intermediate diradical character. , 2006, The Journal of chemical physics.