The Structure and C=C Vibrational Frequencies of the all- trans Polyenes C2nH2n+2(n=2-15), C2nH2n(Me)2(n=2-13), and C2nH2n(tert-Butyl)2(n=2-5): Computational Results

Carbon-carbon bond lengths and C=C vibrational frequencies are reported for the linear, all-trans unsubstituted C2nH2n+2 (n=2-15), methyl capped C2nH2nMe2 (n=2-13), and tert-butyl capped C2nH2n(tert-butyl)2 (n=2-5) polyenes (C2h) calculated at the B3LYP/6-311++G(d,p) level. The C=C/C-C bond length alternation remains evident at this level for the unsubstituted and methyl capped polyenes as the chain length increases; the center-most difference in the length of the C-C/C=C bonds is ~0.06 Å for C30H32 and C26H26Me2. The Ag, in-phase, harmonic C=C Raman frequency for the unsubstituted polyenes decreases from 1699.2 cm-1 (n = 2) to 1528.9 cm-1 (n=15); the anharmonic frequency decreases from 1651.5 cm-1 (n = 2) to 1547.7 cm-1 (n = 8). The harmonic C=C frequency for the methyl capped polyenes decreases from 1717.9 cm-1 (n = 2) to 1539.6 cm- 1 (n= 13), and the anharmonic C=C frequency decreases from 1675.0 cm-1 (n = 2) to 1562.8 cm-1 (n = 7)

Multireference Correlation in Long Molecules with the Quadratic Scaling Density Matrix Renormalization Group

We have devised and implemented a local ab initio Density Matrix Renormalization Group (DMRG) algorithm to describe multireference nondynamic correlations in large systems. For long molecules that are extended in one of their spatial dimensions, this method allows us to obtain an exact characterisation of correlation, in the given basis, with a cost that scales only quadratically with the size of the system. The reduced scaling is achieved solely through integral screening and without the construction of correlation domains. We demonstrate the scaling, convergence, and robustness of the algorithm in polyenes and hydrogen chains. We converge to exact correlation energies (with 1-10 microhartree precision) in all cases and correlate up to 100 electrons in 100 active orbitals. We further use our algorithm to obtain exact energies for the metal-insulator transition in hydrogen chains and compare and contrast our results with those from conventional quantum chemical methods.Comment: 14 pages, 12 figures, tciLaTeX, aip-BibTeX styl

Excited state geometry optimization with the density matrix renormalization group as applied to polyenes

We describe and extend the formalism of state-specific analytic density matrix renormalization group (DMRG) energy gradients, first used by Liu et al (J. Chem. Theor.Comput. 9, 4462 (2013)). We introduce a DMRG wavefunction maximum overlap following technique to facilitate state-specific DMRG excited state optimization. Using DMRG configuration interaction (DMRG-CI) gradients we relax the low-lying singlet states of a series of trans-polyenes up to C20H22. Using the relaxed excited state geometries as well as correlation functions, we elucidate the exciton, soliton, and bimagnon ("single-fission") character of the excited states, and find evidence for a planar conical intersection

Subgap Two-Photon States in Polycyclic Aromatic Hydrocarbons: Evidence for Strong Electron Correlations

Strong electron correlation effects in the photophysics of quasi-one-dimensional $\pi$-conjugated organic systems such as polyenes, polyacetylenes, polydiacetylenes, etc., have been extensively studied. Far less is known on correlation effects in two-dimensional $\pi$-conjugated systems. Here we present theoretical and experimental evidence for moderate repulsive electron-electron interactions in a number of finite polycyclic aromatic hydrocarbon molecules with $D_{6h}$ symmetry. We show that the excited state orderings in these molecules are reversed relative to that expected within one-electron and mean-field theories. Our results reflect similarities as well as differences in the role and magnitude of electron correlation effects in these two-dimensional molecules compared to those in polyenes.Comment: 11 pages, 5 figures, 2 table

Orbital Optimization in the Density Matrix Renormalization Group, with applications to polyenes and \beta-carotene

In previous work we have shown that the Density Matrix Renormalization Group (DMRG) enables near-exact calculations in active spaces much larger than are possible with traditional Complete Active Space algorithms. Here, we implement orbital optimisation with the Density Matrix Renormalization Group to further allow the self-consistent improvement of the active orbitals, as is done in the Complete Active Space Self-Consistent Field (CASSCF) method. We use our resulting DMRGCASSCF method to study the low-lying excited states of the all-trans polyenes up to C24H26 as well as \beta-carotene, correlating with near-exact accuracy the optimised complete \pi-valence space with up to 24 active electrons and orbitals, and analyse our results in the light of the recent discovery from Resonance Raman experiments of new optically dark states in the spectrum.Comment: 16 pages, 8 figure