We present a combined experimental and computational study that probes the thermoelectric and electrical transport properties of molecular junctions. Experiments were performed on junctions created by trapping aromatic molecules between gold electrodes. The end groups (-SH, -NC) of the aromatic molecules were systematically varied to study the effect of contact coupling strength and contact chemistry. When the coupling of the molecule with one of the electrodes was reduced by switching the terminal chemistry from -SH to -H, the electrical conductance of molecular junctions decreased by an order of magnitude, whereas the thermopower varied by only a few percent. This has been predicted computationally in the past and is experimentally demonstrated for the first time. Further, our experiments and computational modeling indicate the prospect of tuning thermoelectric properties at the molecular scale. In particular, the thiol-terminated aromatic molecular junctions revealed a positive thermopower that increased linearly with length. This positive thermopower is associated with charge transport primarily through the highest occupied molecular orbital, as shown by our computational results. In contrast, a negative thermopower was observed for a corresponding molecular junction terminated by an isocyanide group due to charge transport primarily through the lowest unoccupied molecular orbital.

state energy, subject to a fixed number of elements in the finite-element mesh. To this end, we first develop an estimate for the finite-element discretization error in the Kohn-Sham ground-state energy as a function of the characteristic mesh-size distribution, h(r), and the exact ground-state electronic fields comprising of wavefunctions and electrostatic potential. We subsequently determine the optimal mesh distribution for the chosen representative solution by determining the h(r) that minimizes the discretization error. The resulting expressions for the optimal mesh distribution are in terms of the degree of the interpolating polynomial and the exact solution fields of the Kohn-Sham DFT problem. Since the exact solution fields are a priori unknown, we use the asymptotic behavior of the atomic wavefunctions [38] away from the nuclei to determine the coarse-graining rates for the finite-element meshes used in our numerical study. Though the resulting finite-element meshes are not necessarily optimal near the vicinity of the nuclei, the mesh coarsening rate away from the nuclei provides an efficient way of resolving the vacuum in non-periodic calculations.We next implement an efficient solution strategy for solving the finite-element discretized eigenvalue problem, which is crucial before assessing the computational efficiency of the basis. We note that the non-orthogonality of the finite-element basis results in a discrete generalized eigenvalue problem, which is computationally more expensive than the standard eigenvalue problem that results from using an orthogonal basis like planewaves. We address this issue by employing a spectral finite-element discretization and Gauss-Lobatto quadrature rules to evaluate the integrals which results in a diagonal overlap matrix, and allows for a trivial transformation to a standard eigenvalue problem. Further, we use the Chebyshev acceleration technique for standard eigenvalue problems to efficiently compute the occupied eigenspace (cf. e.g. [39] in the context of electronic structure calculations). Our investigations suggest that the use of spectral finite-elements and Gauss-Lobatto rules in conjunction with Chebyshev acceleration techniques to compute the eigenspace gives a 10 − 20 fold computational advantage, even for modest materials system sizes, in comparison to traditional methods of solving the standard eigenvalue problem where the eigenvectors are computed explicitly. Further, the proposed approach has been observed to provide a staggering 100 − 200 fold computational advantage over the solution of a generalized eigenvalue problem that does not take advantage of the spectral finite-element discretization and Gauss-Lobatto quadrature rules. In our implementation, we use a self-consistent field (SCF) iteration with Anderson mixing [40], and employ the finite-temperature Fermi-Dirac smearing [3] to suppress the charge sloshing associated with degenerate or close to degenerate eigenstates around the Fermi energy.We next study various numerical aspects of the finite-...

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GÀconvergence a b s t r a c tWe present a real-space, non-periodic, finite-element formulation for Kohn-Sham density functional theory (KS-DFT). We transform the original variational problem into a local saddle-point problem, and show its well-posedness by proving the existence of minimizers. Further, we prove the convergence of finite-element approximations including numerical quadratures. Based on domain decomposition, we develop a parallel finite-element implementation of this formulation capable of performing both all-electron and pseudopotential calculations. We assess the accuracy of the formulation through selected test cases and demonstrate good agreement with the literature. We also evaluate the numerical performance of the implementation with regard to its scalability and convergence rates. We view this work as a step towards developing a method that can accurately study defects like vacancies, dislocations and crack tips using density functional theory (DFT) at reasonable computational cost by retaining electronic resolution where it is necessary and seamlessly coarse-graining far away.

Hot-carriers in plasmonic nanostructures, generated via plasmon decay, play key roles in applications like photocatalysis and in photodetectors that circumvent band-gap limitations. However, direct experimental quantification of steady-state energy distributions of hot-carriers in nanostructures has so far been lacking. We present transport measurements from single-molecule junctions, created by trapping suitably chosen single molecules between an ultra-thin gold film supporting surface plasmon polaritons and a scanning probe tip, that can provide quantification of plasmonic hot-carrier distributions. Our results show that Landau damping is the dominant physical mechanism of hot-carrier generation in nanoscale systems with strong confinement. The technique developed in this work will enable quantification of plasmonic hot-carrier distributions in nanophotonic and plasmonic devices.

We present an accurate, efficient and massively parallel finite-element code, DFT-FE, for largescale ab-initio calculations (reaching ∼ 100, 000 electrons) using Kohn-Sham density functional theory (DFT). DFT-FE is based on a local real-space variational formulation of the Kohn-Sham DFT energy functional that is discretized using a higher-order adaptive spectral finite-element (FE) basis, and treats pseudopotential and all-electron calculations in the same framework, while accommodating non-periodic, semi-periodic and periodic boundary conditions. We discuss the main aspects of the code, which include, the various strategies of adaptive FE basis generation, and the different approaches employed in the numerical implementation of the solution of the discrete Kohn-Sham problem that are focused on significantly reducing the floating point operations, communication costs and latency. We demonstrate the accuracy of DFT-FE by comparing the energies, ionic forces and periodic cell stresses on a wide range of problems with popularly used DFT codes. Further, we demonstrate that DFT-FE significantly outperforms widely used planewave codes-both in CPU-times and wall-times, and on both non-periodic and periodic systems-at systems sizes beyond a few thousand electrons, with over 5 − 10 fold speedups in systems with more than 10,000 electrons. The benchmark studies also highlight the excellent parallel scalability of DFT-FE, with strong scaling demonstrated on up to 192,000 MPI tasks.

The quest for accurate exchange-correlation functionals has long remained a grand challenge in density functional theory (DFT), as it describes the many-electron quantum mechanical behavior through a computationally tractable quantity—the electron density—without resorting to multi-electron wave functions. The inverse DFT problem of mapping the ground-state density to its exchange-correlation potential is instrumental in aiding functional development in DFT. However, the lack of an accurate and systematically convergent approach has left the problem unresolved, heretofore. This work presents a numerically robust and accurate scheme to evaluate the exact exchange-correlation potentials from correlated ab-initio densities. We cast the inverse DFT problem as a constrained optimization problem and employ a finite-element basis—a systematically convergent and complete basis—to discretize the problem. We demonstrate the accuracy and efficacy of our approach for both weakly and strongly correlated molecular systems, including up to 58 electrons, showing relevance to realistic polyatomic molecules.

We propose an approach to perform orbital-free density functional theory calculations in a non-periodic setting using the finite-element method. We consider this a step towards constructing a seamless multi-scale approach for studying defects like vacancies, dislocations and cracks that require quantum mechanical resolution at the core and are sensitive to long range continuum stresses. In this paper, we describe a local real space variational formulation for orbital-free density functional theory, including the electrostatic terms and prove existence results. We prove the convergence of the finite-element approximation including numerical quadratures for our variational formulation. Finally, we demonstrate our method using examples.