A projected approximation to strongly contracted N-electron valence perturbation theory for DMRG wavefunctions.

A novel approach to strongly contracted N-electron valence perturbation theory (SC-NEVPT2) as a means of describing dynamic electron correlation for quantum chemical density matrix renormalization group (DMRG) calculations is presented. In this approach the strongly contracted perturber functions are projected onto a renormalized Hilbert space. Compared to a straightforward implementation of SC-NEVPT2 with DMRG wavefunctions, the computational scaling and storage requirements are reduced. This favorable scaling opens up the possibility of calculations with larger active spaces. A specially designed renormalization scheme ensures that both the electronic ground state and the perturber functions are well represented in the renormalized Hilbert space. Test calculations on the N2 and [Cu2O2(en)2](2+) demonstrate some key properties of the method and indicate its capabilities.

Fast Emulation of Fermionic Circuits with Matrix Product States.

We describe a matrix product state (MPS) extension for the Fermionic Quantum Emulator (FQE) software library. We discuss the theory behind symmetry-adapted MPSs for approximating many-body wave functions of spin-1/2 Fermions, and we present an open-source, MPS-enabled implementation of the FQE interface (MPS-FQE). The software uses the open-source pyblock3 and block2 libraries for most elementary tensor operations, and it can largely be used as a drop-in replacement for FQE that allows for more efficient but approximate emulation of larger Fermionic circuits. Finally, we show several applications relevant to both near-term and fault-tolerant quantum algorithms where approximate emulation of larger systems is expected to be useful: characterization of state preparation strategies for quantum phase estimation, the testing of different variational quantum eigensolver ansätze, the numerical evaluation of Trotter errors, and the simulation of general quantum dynamics problems. In all these examples, approximate emulation with MPS-FQE allows us to treat systems that are significantly larger than those accessible with a full statevector emulator.

Optimization of orbital-specific virtuals in local Møller-Plesset perturbation theory.

We present an orbital-optimized version of our orbital-specific-virtuals second-order Møller-Plesset perturbation theory (OSV-MP2). The OSV model is a local correlation ansatz with a small basis of virtual functions for each occupied orbital. It is related to the Pulay-Saebø approach, in which domains of virtual orbitals are drawn from a single set of projected atomic orbitals; but here the virtual functions associated with a particular occupied orbital are specifically tailored to the correlation effects in which that orbital participates. In this study, the shapes of the OSVs are optimized simultaneously with the OSV-MP2 amplitudes by minimizing the Hylleraas functional or approximations to it. It is found that optimized OSVs are considerably more accurate than the OSVs obtained through singular value decomposition of diagonal blocks of MP2 amplitudes, as used in our earlier work. Orbital-optimized OSV-MP2 recovers smooth potential energy surfaces regardless of the number of virtuals. Full optimization is still computationally demanding, but orbital optimization in a diagonal or Kapuy-type MP2 approximation provides an attractive scheme for determining accurate OSVs.

On-chip Rayleigh imaging and spectroscopy of carbon nanotubes.

We report a novel on-chip Rayleigh imaging technique using wide-field laser illumination to measure optical scattering from individual single-walled carbon nanotubes (SWNTs) on a solid substrate with high spatial and spectral resolution. This method in conjunction with calibrated AFM measurements accurately measures the resonance energies and diameters for a large number of SWNTs in parallel. We apply this technique for fast mapping of key SWNT parameters, including the electronic-types and chiral indices for individual SWNTs, position and frequency of chirality-changing events, and intertube interactions in both bundled and distant SWNTs.

Tensor factorizations of local second-order Møller-Plesset theory.

Efficient electronic structure methods can be built around efficient tensor representations of the wavefunction. Here we first describe a general view of tensor factorization for the compact representation of electronic wavefunctions. Next, we use this language to construct a low-complexity representation of the doubles amplitudes in local second-order Møller-Plesset perturbation theory. We introduce two approximations--the direct orbital-specific virtual approximation and the full orbital-specific virtual approximation. In these approximations, each occupied orbital is associated with a small set of correlating virtual orbitals. Conceptually, the representation lies between the projected atomic orbital representation in Pulay-Saebø local correlation theories and pair natural orbital correlation theories. We have tested the orbital-specific virtual approximations on a variety of systems and properties including total energies, reaction energies, and potential energy curves. Compared to the Pulay-Saebø ansatz, we find that these approximations exhibit favorable accuracy and computational times while yielding smooth potential energy curves.

A Practical Guide to Density Matrix Embedding Theory in Quantum Chemistry.

Density matrix embedding theory (DMET) (Knizia, G.; Chan, G. K.-L. Phys. Rev. Lett. 2012, 109, 186404) provides a theoretical framework to treat finite fragments in the presence of a surrounding molecular or bulk environment, even when there is significant correlation or entanglement between the two. In this work, we give a practically oriented and explicit description of the numerical and theoretical formulation of DMET. We also describe in detail how to perform self-consistent DMET optimizations. We explore different embedding strategies with and without a self-consistency condition in hydrogen rings, beryllium rings, and a sample SN2 reaction. The source code for the calculations in this work can be obtained from https://github.com/sebwouters/qc-dmet .

Single-walled carbon nanotubes as excitonic optical wires.

Although metallic nanostructures are useful for nanoscale optics, all of their key optical properties are determined by their geometry. This makes it difficult to adjust these properties independently, and can restrict applications. Here we use the absolute intensity of Rayleigh scattering to show that single-walled carbon nanotubes can form ideal optical wires. The spatial distribution of the radiation scattered by the nanotubes is determined by their shape, but the intensity and spectrum of the scattered radiation are determined by exciton dynamics, quantum-dot-like optical resonances and other intrinsic properties. Moreover, the nanotubes display a uniform peak optical conductivity of approximately 8 e(2)/h, which we derive using an exciton model, suggesting universal behaviour similar to that observed in nanotube conductance. We further demonstrate a radiative coupling between two distant nanotubes, with potential applications in metamaterials and optical antennas.

Single-molecule conductance of pyridine-terminated dithienylethene switch molecules.

We have investigated the conductance of individual optically switchable dithienylethene molecules in both their conducting closed configuration and nonconducting open configuration, using the technique of repeatedly formed break-junctions. We employed pyridine groups to link the molecules to gold electrodes in order to achieve relatively well-defined molecular contacts and stable conductance. For the closed form of each molecule, we observed a peak in the conductance histogram constructed without any data selection, allowing us to determine the conductance of the fully stretched molecules. For two different dithienylethene derivatives, these closed-configuration conductances were (3.3 ± 0.5) × 10(-5)G(0) and (1.5 ± 0.5) × 10(-6)G(0), where G(0) is the conductance quantum. For the open configuration of the molecules, the existence of electrical conduction via the molecule was evident in traces of conductance versus junction displacement, but the conductance of the fully stretched molecules was less than the noise floor of our measurement. We can set a lower limit of 30 for the on/off ratio for the simplest dithienylethene derivative we have investigated. Density functional theory calculations predict an on/off ratio consistent with this result.