Parameters Influencing the Photochemical Cyclodehydrochlorination (CDHC) Reaction.

The photochemical cyclodehydrochlorination (CDHC) reaction has recently been used to prepare a wide variety of polycyclic aromatic hydrocarbons and graphene nanoribbons (GNRs). However, the parameters affecting the efficiency of this reaction have been scarcely studied. In this work, we investigated how the reaction conditions influence the outcome of the reaction. The effect of functional groups on the different phenyl rings of the o-terphenyl scaffold was also studied. The reaction kinetics follow the same trend as Hammett's constant when electron-donating and electron-withdrawing groups are present on the ring bearing the chlorine. The CDHC reaction can be successfully performed using less energetic 365 nm light in the presence of a triplet sensitizer. Computational results provide insight on the reaction mechanism, notably by identifying its three intermediate structures as well as its limiting step.

Density matrices of seniority-zero geminal wavefunctions.

Scalar products and density matrix elements of closed-shell pair geminal wavefunctions are evaluated directly in terms of the pair amplitudes, resulting in an analog of Wick's theorem for fermions or bosons. This expression is, in general, intractable, but it is shown how it becomes feasible in three distinct ways for Richardson-Gaudin (RG) states, the antisymmetrized geminal power, and the antisymmetrized product of strongly orthogonal geminals. Dissociation curves for hydrogen chains are computed with off-shell RG states and the antisymmetrized product of interacting geminals. Both are near exact, suggesting that the incorrect results observed with ground state RG states (a local maximum rather than smooth dissociation) may be fixable using a different RG state.

Near-exact treatment of seniority-zero ground and excited states with a Richardson-Gaudin mean-field.

Eigenvectors of the reduced Bardeen-Cooper-Schrieffer (BCS) Hamiltonian, Richardson-Gaudin (RG) states, are used as a variational wavefunction ansatz for strongly correlated electronic systems. These states are geminal products whose coefficients are solutions of non-linear equations. Previous results showed an un-physical apparent avoided crossing in ground state dissociation curves for hydrogen chains. In this paper, it is shown that each seniority-zero state of the molecular Coulomb Hamiltonian corresponds directly to an RG state. However, the seniority-zero ground state does not correspond to the ground state of a reduced BCS Hamiltonian. The difficulty is in choosing the correct RG state. The systems studied showed a clear choice, and we expect that it should always be possible to reason physically which state to choose.

Transition density matrices of Richardson-Gaudin states.

Recently, ground state eigenvectors of the reduced Bardeen-Cooper-Schrieffer (BCS) Hamiltonian, Richardson-Gaudin (RG) states, have been employed as a wavefunction ansatz for strong correlation. This wavefunction physically represents a mean-field of pairs of electrons (geminals) with a constant pairing strength. To move beyond the mean-field, one must develop the wavefunction on the basis of all the RG states. This requires both practical expressions for transition density matrices and an idea of which states are most important in the expansion. In this contribution, we present expressions for the transition density matrix elements and calculate them numerically for half-filled picket-fence models (reduced BCS models with constant energy spacing). There are no Slater-Condon rules for RG states, though an analog of the aufbau principle proves to be useful in choosing which states are important.

Fluorine effect in nucleophilic fluorination at C4 of 1,6-anhydro-2,3-dideoxy-2,3-difluoro-ß-D-hexopyranose.

In this work, we have developed a simple synthetic approach using Et3N·3HF as an alternative to the DAST reagent. We controlled the stereochemistry of the nucleophilic fluorination at C4 of 1,6-anhydro-2,3-dideoxy-2,3-difluoro-4-O-triflate-ß-ᴅ-talopyranose using Et3N·3HF or in situ generated Et3N·1HF. The influence of the fluorine atom at C2 on reactivity at C4 could contribute to a new fluorine effect in nucleophilic substitution. Finally, with the continuous objective of synthesizing novel multi-vicinal fluorosugars, we prepared one difluorinated and one trifluorinated alditol analogue.

Reduced density matrices of Richardson-Gaudin states in the Gaudin algebra basis.

Eigenvectors of the reduced Bardeen-Cooper-Schrieffer Hamiltonian have recently been employed as a variational wavefunction ansatz in quantum chemistry. This wavefunction is a mean-field of pairs of electrons (geminals). In this contribution, we report optimal expressions for their reduced density matrices in both the original physical basis and the basis of the Richardson-Gaudin pairs. Physical basis expressions were originally reported by Gorohovsky and Bettelheim [Phys. Rev. B 84, 224503 (2011)]. In each case, the expressions scale like O(N4), with the most expensive step being the solution of linear equations. Analytic gradients are also reported in the physical basis. These expressions are an important step toward practical mean-field methods to treat strongly correlated electrons.

Richardson-Gaudin mean-field for strong correlation in quantum chemistry.

Ground state eigenvectors of the reduced Bardeen-Cooper-Schrieffer Hamiltonian are employed as a wavefunction Ansatz to model strong electron correlation in quantum chemistry. This wavefunction is a product of weakly interacting pairs of electrons. While other geminal wavefunctions may only be employed in a projected Schrödinger equation, the present approach may be solved variationally with polynomial cost. The resulting wavefunctions are used to compute expectation values of Coulomb Hamiltonians, and we present results for atoms and dissociation curves that are in agreement with doubly occupied configuration interaction data. The present approach will serve as the starting point for a many-body theory of pairs, much as Hartree-Fock is the starting point for weakly correlated electrons.

Synthesis and Properties of Conjugated Polymers Based on a Ladderized Anthanthrene Unit.

Polycyclic aromatic hydrocarbons (PAHs) are interesting building blocks for the preparation of conjugated polymers due to their extended π surface and planar conformation. However, their use as comonomer in conjugated polymers often leads to nonplanar main chains as a consequence of high steric hindrance at the linking point. Herein, we report the synthesis of a ladderized anthanthrene unit using an sp3 carbon bridge. Three conjugated copolymers with fluorene, isoindigo, and bithiophene derivatives have been synthesized and characterized to study the effect of such ladderization on the electronic properties. The dihedral angle between the ladderized anthanthrene and adjacent units has been significantly reduced by the formation of the sp3 carbon bridge, thus eliminating the steric hindrance with the proton at the peri position of the anthanthrene unit and red-shifting the absorption spectrum by 25 nm.