Long-range corrected density functional theory study on static second hyperpolarizabilities of singlet diradical systems.

Within the spin-unrestricted density functional theory (DFT) the long-range correction (LC) scheme combined with the Becke-Lee-Yang-Parr exchange-correlation functional, referred to as LC-UBLYP method, has been applied to the calculation of the second hyperpolarizability (gamma) of open-shell singlet diradical systems of increasing complexity and has demonstrated good performance: (i) for the simplest H(2) dissociation model, the gamma values calculated by the LC-UBLYP method significantly overshoot the full configuration interaction result but reproduce qualitatively the evolution of gamma as a function of the diradical character, (ii) for small singlet diradical 1,3-dipole systems, the diradical character dependence of gamma determined by the UCCSD and UCCSD(T) reference methods is reproduced semiquantitatively by the LC-UBLYP method except in the small diradical character region, where the spin-unrestricted solutions coincide with spin-restricted solutions, (iii) the LC-UBLYP method also closely reproduces the UCCSD(T) results on the diradical character dependence of gamma of the p-quinodimethane model system, particularly in the intermediate and large diradical character regions, whereas it shows an abrupt change for a diradical character (y) close to 0.2 originating from the triplet instability, (iv) the reliability of LC-UBLYP to reproduce reference coupled cluster results on open-shell singlet systems with intermediate and large diradical characters has also been substantiated in the case of gamma of 1,4-bis-(imidazol-2-ylidene)-cyclohexa-2,5-diene (BI2Y), then (v), for real systems built from a pair of phenalenyl radicals separated by a conjugated linker, the LC-UBLYP results have been found to closely match the UBHandHLYP values-which, for small systems are in good agreement with those obtained using correlated molecular orbital methods-whereas the UB3LYP results can be much different. These results are not only important from the viewpoint of an efficient determination of the nonlinear optical properties of open-shell singlet systems, but also from the viewpoint of defining new challenges for elaborating improved exchange-correlation functionals.

Calculation of electric dipole (hyper)polarizabilities by long-range-correction scheme in density functional theory: a systematic assessment for polydiacetylene and polybutatriene oligomers.

The long-range correction (LC) for treating electron exchange in density functional theory, combined with the Becke-Lee-Yang-Parr (BLYP) exchange-correlation functional, was used to determine (hyper)polarizabilities of polydiacetylene/polybutatriene oligomers. In comparison with coupled-cluster calculations including single and double excitations as well as a perturbative treatment of triple excitations, our values indicate that the tendency of conventional functionals to result in a catastrophic overshoot for these properties is alleviated but not eliminated. No clear-cut preference for LC-BLYP over Hartree-Fock values is obtained. This analysis is consistent with the calculations of Sekino et al. [J. Chem. Phys. 126, 014107 (2007)] on polyacetylene and molecular hydrogen oligomers. Thus, the performance of LC-BLYP with regard to (hyper)polarizabilities of quasilinear conjugated systems is now well characterized.

Density functional theory investigation of the polarizability and second hyperpolarizability of polydiacetylene and polybutatriene chains: treatment of exact exchange and role of correlation.

The static polarizability and second hyperpolarizability of increasingly large polydiacetylene and polybutatriene (PBT) chains have been evaluated using the optimized effective potential for exact exchange (OEP-EXX) method developed by Yang and Wu [Phys. Rev. Lett. 89, 143002 (2002)], where the unknown part of the effective potential is expressed as a linear combination of Gaussian functions. Various conventional atomic orbital basis sets were employed for the exchange potential (X basis) as well as for the Kohn-Sham orbitals [molecular orbital (MO) basis]. Our results were compared to coupled-perturbed Hartree-Fock (CPHF) calculations and to ab initio correlated values obtained at various levels of approximation. It turns out that (a) small conventional basis sets are, in general, unsatisfactory for the X basis; (b) the performance of a given X basis depends on the MO basis and is generally improved when using a larger MO basis; (c) these effects are exaggerated for the second hyperpolarizability compared to the polarizability; (d) except for the second hyperpolarizability of PBT chains, using 6-311++G** for the X basis gives reasonable agreement with the CPHF results for all MO basis sets; (e) our results suggest that in the limit of a complete X basis the OEP-EXX values may approach the CPHF data; and (f) in general, the quality of a given conventional X basis degrades with the length of the oligomer, which correlates with the fact that the number of X basis functions becomes a smaller fraction of the number required to reproduce exactly the finite-basis-set Hartree-Fock energies. Linear and especially nonlinear electric field responses constitute a very stringent test for assessing the quality of functionals and potentials; appropriately tailored basis sets are needed to describe the latter. Finally, this study further highlights the importance of electron correlation effects on linear and nonlinear responses, for which correlated functionals with OEP are required.

Simulation of photoelectron spectra with anharmonicity fully included: Application to the X 2A2<--X 1A1 band of furan.

Using a new unconventional procedure for calculating Franck-Condon factors with anharmonicity fully included the X 2A2<--X 1A1 band in the photoelectron spectrum of furan (and deuterated furan) was simulated at the second-order perturbation theory level. All 21 vibrational modes were considered but, in the end, only 4 are required to accurately reproduce the spectrum. Except for our own recent work on ethylene such calculations have been previously limited to tri- or tetraatomic molecules. Most of the effect of anharmonicity is accounted for in first order, although second-order corrections to the vibrational frequencies are important. Based on these simulations we were able to improve upon and extend previous assignments as well as suggest further measurements.