Approximate Spin-Projected Density-Based Romberg Differentiation Procedure to Evaluate the Second-Hyperpolarizability of p-Quinodimethane and Twisted Ethylene and Their Diradical Character Dependence.

The evaluation of the static second hyperpolarizability (γ) of diradical species is a challenging task due to the use of spin-unrestricted methods, which may suffer from spin contamination. Here, we present the methodological aspect of a density-based differentiation procedure to evaluate static polarizability and hyperpolarizabilities. The finite-field calculations are done on the spin-projected electron density to remove the spin contamination, and the automatized Romberg’s differentiation procedure is used to improve the numerical accuracy in the finite-field method. This implementation is tested in the present report for the challenging case of the evaluation of the second hyperpolarizability of the singlet ground state of p-quinodimethane (PQM) for the equilibrium geometry as well as for a stretched geometry where the diradical character of PQM is increased, and for twisted ethylene models where the diradical character changes with the dihedral angle. The application of the approximate spin-projected...

[1]  M. Nakano,et al.  Challenging compounds for calculating molecular second hyperpolarizabilities: the triplet state of the trimethylenemethane diradical and two derivatives. , 2016, Physical chemistry chemical physics : PCCP.

[2]  B. Champagne,et al.  QTAIM-Based Scheme for Describing the Linear and Nonlinear Optical Susceptibilities of Molecular Crystals Composed of Molecules with Complex Shapes , 2016 .

[3]  P. Nandi,et al.  Static second hyperpolarizability of twisted ethylene: A comprehensive computational study , 2015 .

[4]  B. Champagne,et al.  Evaluation of the molecular static and dynamic first hyperpolarizabilities , 2014 .

[5]  Lewis E Johnson,et al.  Optimizing calculations of electronic excitations and relative hyperpolarizabilities of electrooptic chromophores. , 2014, Accounts of chemical research.

[6]  B. Champagne,et al.  Design and characterization of molecular nonlinear optical switches. , 2013, Accounts of chemical research.

[7]  Kotaro Fukuda,et al.  Challenging compounds for calculating hyperpolarizabilities: p-quinodimethane derivatives. , 2013, The journal of physical chemistry. A.

[8]  Jean-Paul Malrieu,et al.  A recipe for geometry optimization of diradicalar singlet states from broken-symmetry calculations. , 2012, The journal of physical chemistry. A.

[9]  Liuxia Liu,et al.  Local and nonlocal contributions to molecular first-order hyperpolarizability: a Hirshfeld partitioning analysis. , 2012, The Journal of chemical physics.

[10]  Y. Shigeta,et al.  Approximate spin-projected spin-unrestricted density functional theory method: Application to the diradical character dependences of the (hyper)polarizabilities in p-quinodimethane models , 2010 .

[11]  Benoît Champagne,et al.  Theoretical investigation on the second hyperpolarizabilities of open-shell singlet systems by spin-unrestricted density functional theory with long-range correction: Range separating parameter dependence , 2010 .

[12]  Yasuyuki Nakanishi,et al.  Spin contamination error in optimized geometry of singlet carbene ((1)A1) by broken-symmetry method. , 2009, The journal of physical chemistry. A.

[13]  Jerzy Leszczynski,et al.  Non-Linear Optical Properties of Matter , 2006 .

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

[15]  M. Nakano,et al.  Theoretical study on second hyperpolarizabilities of phenylacetylene dendrimer: toward an understanding of structure-property relation in NLO responses of fractal antenna dendrimers. , 2002, Journal of the American Chemical Society.

[16]  Benoît Champagne,et al.  Theoretical approach to the design of organic molecular and polymeric nonlinear optical materials , 2001 .

[17]  S. Yamada,et al.  ELECTRON CORRELATION AND STRUCTURE DEPENDENCIES OF THE SECOND HYPERPOLARIZABILITY OF ETHYLENE , 1999 .

[18]  Masayoshi Nakano,et al.  Static second hyperpolarizabilities γ of nitroxide radical and formaldehyde: evaluation of spatial contributions to γ by a hyperpolarizability density analysis , 1996 .

[19]  S. Yamada,et al.  Dynamic (hyper)polarizability density analysis based on virtual excitation processes: visualization of the dynamic electron fluctuatability of systems under time-dependent external electric fields , 1996 .

[20]  B. Champagne,et al.  Static vibrational polarizability of all-trans polyethylene and polysilane , 1995 .

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

[22]  M. Nakano,et al.  Coupled-Hartree—Fock calculations of the third-order hyperpolarizabilities of substituted polydiacetylenes , 1991 .

[23]  H. F. King,et al.  Ab initio calculations of polarizabilities and second hyperpolarizabilities in organic molecules with extended .pi.-electron conjugation , 1989 .

[24]  K. Yamaguchi.  The electronic structures of biradicals in the unrestricted Hartree-Fock approximation , 1975 .