Jonathan J. Foley

Activation energies of sigmatropic shifts in propene and acetone enolate from the anti-Hermitian contracted Schrödinger equation

The hydrogen [1,3]-sigmatropic shift in propene is predicted by the Woodward-Hoffman rules to occur by an antarafacial pathway, yet the lack of experimental evidence suggests that this pathway is not favorable. Two natural questions arise: (i) can the [1,3]-shift be made more favorable by a symmetry-forbidden multistep pathway, and (ii) can the energetics be influenced by a substituent on propene? As in many chemical reactions, describing the energetics of these reactions requires a balanced treatment of both single-reference and multireference electron correlations, and yet traditional wave function methods often excel in treating only one kind of correlation. An equitable description of correlation effects, however, can be achieved, at a cost similar to efficient single-reference methods, by computing the two-electron reduced density matrix (2-RDM) from the anti-Hermitian part of the contracted Schrödinger equation (ACSE) [D. A. Mazziotti, Phys. Rev. Lett. 97, 143002 (2006)]. As with the contracted Schrödinger equation, the indeterminacy of the ACSE is removed without the many-electron wave function by reconstructing the 3-RDM from the 2-RDM via cumulant theory [D. A. Mazziotti, Chem. Phys. Lett. 289, 419 (1998)]. In this paper we apply the ACSE to study sigmatropic shifts in both propene and acetone enolate while extending its formalism to treat doublet spin states. In the 6-311G(**) basis set the ACSE predicts the activation energy of the trimethylene-to-propene rearrangement to be 8.8 kcal/mol while multireference perturbation theory yields a smaller barrier of 2.2 kcal/mol and coupled cluster singles-doubles predicts a negative barrier. We further find that the [1,3]-shift in acetone enolate is more favorable by approximately 30 kcal/mol than the [1,3]-shift in propene, which is consistent with a prior theoretical investigation as well as experimental observations of these shifts in 2-butanone enolate.

When are surface plasmon polaritons excited in the Kretschmann-Raether configuration?

It is widely believed that the reflection minimum in a Kretschmann-Raether experiment results from direct coupling into surface plasmon polariton modes. Our experimental results provide a surprising discrepancy between the leakage radiation patterns of surface plasmon polaritons (SPPs) launched on a layered gold/germanium film compared to the K-R minimum, clearly challenging this belief. We provide definitive evidence that the reflectance dip in K-R experiments does not correlate with excitation of an SPP mode, but rather corresponds to a particular type of perfectly absorbing (PA) mode. Results from rigorous electrodynamics simulations show that the PA mode can only exist under external driving, whereas the SPP can exist in regions free from direct interaction with the driving field. These simulations show that it is possible to indirectly excite propagating SPPs guided by the reflectance minimum in a K-R experiment, but demonstrate the efficiency can be lower by more than a factor of 3. We find that optimal coupling into the SPP can be guided by the square magnitude of the Fresnel transmission amplitude.

Strongly correlated mechanisms of a photoexcited radical reaction from the anti-Hermitian contracted Schrödinger equation

Photoexcited radical reactions are critical to processes in both nature and materials, and yet they can be challenging for electronic structure methods due to the presence of strong electron correlation. Reduced-density-matrix (RDM) methods, based on solving the anti-Hermitian contracted Schrödinger equation (ACSE) for the two-electron RDM (2-RDM), are examined for studying the strongly correlated mechanisms of these reactions with application to the electrocyclic interconversion of allyl and cyclopropyl radicals. We combine recent extensions of the ACSE to excited states [G. Gidofalvi and D. A. Mazziotti, Phys. Rev. A 80, 022507 (2009)] and arbitrary spin states [A. E. Rothman, J. J. Foley IV, and D. A. Mazziotti, Phys. Rev. A 80, 052508 (2009)]. The ACSE predicts that the ground-state ring closure of the allyl radical has a high 52.5 kcal/mol activation energy that is consistent with experimental data, while the closure of an excited allyl radical can occur by disrotatory and conrotatory pathways whose transition states are essentially barrierless. Comparisons are made with multireference second- and third-order perturbation theories and multireference configuration interaction. While predicted energy differences do not vary greatly between methods, the ACSE appears to improve these differences when they involve a strongly and a weakly correlated radical by capturing a greater share of single-reference correlation that increases the stability of the weakly correlated radicals. For example, the ACSE predicts a -39.6 kcal/mol conversion of the excited allyl radical to the ground-state cyclopropyl radical in comparison to the -32.6 to -37.3 kcal/mol conversions predicted by multireference methods. In addition, the ACSE reduces the computational scaling with the number of strongly correlated orbitals from exponential (traditional multireference methods) to quadratic. Computed ground- and excited-state 2-RDMs are nearly N-representable.

Conical intersections in triplet excited states of methylene from the anti-Hermitian contracted Schrödinger equation

A conical intersection in triplet excited states of methylene is computed through the direct calculation of two-electron reduced density matrices (2-RDMs) from solutions of the anti-Hermitian contracted Schrodinger equation (ACSE). The study synthesizes recent extensions of the ACSE method for the treatment of excited states [G. Gidofalvi and D. A. Mazziotti, Phys. Rev. A 80, 022507 (2009)] and arbitrary-spin states [A. E. Rothman, J. J. Foley, and D. A. Mazziotti, Phys. Rev. A 80, 052508 (2009)]. We compute absolute energies of the 1 (3)B(1), 1 (3)A(2), and 2 (3)B(1) states of methylene (CH(2)) and the location of the conical intersection along the 1 (3)A(2)-2 (3)B(1) potential-energy surfaces. To treat multireference correlation, we seed the ACSE with an initial 2-RDM from a multiconfiguration self-consistent field (MCSCF) calculation. The ACSE produces energies that significantly improve upon those from MCSCF and second-order multireference many-body perturbation theory, and the 2-RDMs from the ACSE nearly satisfy necessary N-representability conditions. Comparison of the results from augmented double-zeta and triple-zeta basis sets demonstrates the importance of augmented (or diffuse) functions for determining the location of the conical intersection.

Cage versus Prism: Electronic Energies of the Water Hexamer

Recent experiments show that the cage isomer of the water hexamer is lower in energy than the prism isomer near 0 K, and yet state-of-the-art electronic structure calculations predict the prism to be lower in energy than the cage at 0 K. Here, we study the relative energies of the water hexamers from the parametric two-electron reduced density matrix (2-RDM) method in which the 2-RDM rather than the wave function is the basic variable of the calculations. In agreement with experiment and in contrast with traditional wave function methods, the 2-RDM calculations predict the cage to be more stable than the prism after vibrational zero-point correction. Multiple configurations from the hydrogen bonding are captured by the method. More generally, the results are consistent with our previous 2-RDM applications in that they reveal how multireference correlation in molecular systems is important for resolving small energy differences from hydrogen bonding as well as other types of intermolecular forces, even in systems that are not conventionally considered strongly correlated.

Reversible Modulation of Surface Plasmons in Gold Nanoparticles Enabled by Surface Redox Chemistry

Switchable surface redox chemistry is demonstrated in gold@iron/iron oxide core-shell nanoparticles with ambient oxidation and plasmon-mediated reduction to modulate the oxidation state of shell layers. The iron shell can be oxidized to iron oxide through ambient oxidation, leading to an enhancement and red-shift of the gold surface plasmon resonance (SPR). This enhanced gold SPR can drive reduction of the iron oxide shell under broadband illumination to reversibly blue-shift and significantly dampen gold SPR absorption. The observed phenomena provide a unique mechanism for controlling the plasmonic properties and surface chemistry of small metal nanoparticles.

Nano-optical imaging of WSe2 waveguide modes revealing light-exciton interactions

We report on a nano-optical imaging study of WSe2 thin flakes with scanning near-field optical microscopy (NSOM). The NSOM technique allows us to visualize in real space various waveguide photon modes inside WSe2. By tuning the excitation laser energy, we are able to map the entire dispersion of these waveguide modes both above and below the A exciton energy of WSe2. We found that all the modes interact strongly with WSe2 excitons. The outcome of the interaction is that the observed waveguide modes shift to higher momenta right below the A exciton energy. At higher energies, on the other hand, these modes are strongly damped due to adjacent B excitons or band-edge absorptions. Lastly, the mode-shifting phenomena are consistent with polariton formation in WSe2.

Design of emitter structures based on resonant perfect absorption for thermophotovoltaic applications.

We report a class of thermophotovoltaic emitter structures built upon planar films that support resonant modes, known as perfectly-absorbing modes, that facilitate an exceptional optical response for selective emission. These planar structures have several key advantages over previously-proposed designs for TPV applications: they are simple to fabricate, are stable across a range of temperatures and conditions, and are capable of achieving some of the highest spectral efficiencies reported of any class of emitter structure. Utilization of these emitters leads to exceptionally high device efficiencies under low operating temperature conditions, which should open new opportunities for waste heat management. We present a theoretical framework for understanding this performance, and show that this framework can be leveraged as a search algorithm for promising candidate structures. In addition to providing an efficient theoretical methodology for identifying high-performance emitter structures, our methodology provides new insight into underlying design principles and should pave way for future design of structures that are simple to fabricate, temperature stable, and possess exceptional optical properties.

Enhanced optical absorption in semiconductor nanoparticles enabled by nearfield dielectric scattering

The optical absorption of semiconducting AgBr nanocubes is significantly increased by up to 5 times in the measured spectral range when they are bonded to the surface of dielectric SiO2 nanospheres through electrostatic interaction. The absorption enhancement factor depends on the wavelength and the size of the SiO2 nanoparticles (NPs). Finite-difference time-domain calculations provide the nearfield intensity mapping of a heterostructure that is composed of a AgBr nanocube in close contact with a SiO2 nanosphere. The electric-field distributions indicate the field enhancement near the SiO2/AgBr interface due to light scattering and absorption enhancement in the AgBr nanocube, implying that the enhanced scattering nearfield increases the absorption cross section of the AgBr nanocube. The absorption cross-section spectra calculated using Mie theory agree with the experimental observations. This discovery sheds light on the utilization of dielectric spherical particles to increase the absorption in semiconductor NPs, thus improving the light-harvesting efficiency for solar-energy conversion.

Efficient geometry optimization by Hellmann–Feynman forces with the anti-Hermitian contracted Schrödinger equation

An efficient method for geometry optimization based on solving the anti-Hermitian contracted Schrödinger equation (ACSE) is presented. We formulate a reduced version of the Hellmann–Feynman theorem (HFT) in terms of the two-electron reduced Hamiltonian operator and the two-electron reduced density matrix (2-RDM). The HFT offers a considerable reduction in computational cost over methods which rely on numerical derivatives. While previous geometry optimizations with numerical gradients required 2M evaluations of the ACSE where M is the number of nuclear degrees of freedom, the HFT requires only a single ACSE calculation of the 2-RDM per gradient. Synthesizing geometry optimization techniques with recent extensions of the ACSE theory to arbitrary electronic and spin states provides an important suite of tools for accurately determining equilibrium and transition-state structures of ground- and excited-state molecules in closed- and open-shell configurations. The ability of the ACSE to balance single- and multi-reference correlation is particularly advantageous in the determination of excited-state geometries where the electronic configurations differ greatly from the ground-state reference. Applications are made to closed-shell molecules N2, CO, H2O, the open-shell molecules B2 and CH, and the excited state molecules N2, B2, and BH. We also study the HCN ↔ HNC isomerization and the geometry optimization of hydroxyurea, a molecule which has a significant role in the treatment of sickle-cell anaemia.