Systematic reduction of sign errors in many-body calculations of atoms and molecules.

The self-healing diffusion Monte Carlo algorithm (SHDMC) is shown to be an accurate and robust method for calculating the ground state of atoms and molecules. By direct comparison with accurate configuration interaction results for the oxygen atom, we show that SHDMC converges systematically towards the ground-state wave function. We present results for the challenging N2 molecule, where the binding energies obtained via both energy minimization and SHDMC are near chemical accuracy (1 kcal/mol). Moreover, we demonstrate that SHDMC is robust enough to find the nodal surface for systems at least as large as C20 starting from random coefficients. SHDMC is a linear-scaling method, in the degrees of freedom of the nodes, that systematically reduces the fermion sign problem.

Algorithms for the electronic and vibrational properties of nanocrystals.

Solving the electronic structure problem for nanoscale systems remains a computationally challenging problem. The numerous degrees of freedom, both electronic and nuclear, make the problem impossible to solve without some effective approximations. Here we illustrate some advances in algorithm developments to solve the Kohn-Sham eigenvalue problem, i.e. we solve the electronic structure problem within density functional theory using pseudopotentials expressed in real space. Our algorithms are based on a nonlinear Chebyshev filtered subspace iteration method, which avoids computing explicit eigenvectors except at the first self-consistent-field iteration. Our method may be viewed as an approach to solve the original nonlinear Kohn-Sham equation by a nonlinear subspace iteration technique, without emphasizing the intermediate linearized Kohn-Sham eigenvalue problems. Replacing the standard iterative diagonalization at each self-consistent-field iteration by a Chebyshev subspace filtering step results in a significant speed-up, often an order of magnitude or more, over methods based on standard diagonalization. We illustrate this method by predicting the electronic and vibrational states for silicon nanocrystals.

Neutral and charged excitations in carbon fullerenes from first-principles many-body theories.

We investigate the accuracy of first-principles many-body theories at the nanoscale by comparing the low-energy excitations of the carbon fullerenes C(20), C(24), C(50), C(60), C(70), and C(80) with experiment. Properties are calculated via the GW-Bethe-Salpeter equation and diffusion quantum Monte Carlo methods. We critically compare these theories and assess their accuracy against available photoabsorption and photoelectron spectroscopy data. The first ionization potentials are consistently well reproduced and are similar for all the fullerenes and methods studied. The electron affinities and first triplet excitation energies show substantial method and geometry dependence. These results establish the validity of many-body theories as viable alternative to density-functional theory in describing electronic properties of confined carbon nanostructures. We find a correlation between energy gap and stability of fullerenes. We also find that the electron affinity of fullerenes is very high and size independent, which explains their tendency to form compounds with electron-donor cations.

Real space method for the electronic structure of one-dimensional periodic systems.

We present a real space pseudopotential method for calculating the electronic structure of one-dimensional periodic systems such as nanowires. As an application of this method, we examine H-passivated Si nanowires. The band structure and heat of formation of the Si nanowires are presented and compared to plane wave methods. Our method is able to offer the same accuracy as the traditional plane wave methods but offers a number of computational advantages such as faster convergence for heteropolar nanowires.

The "staple" motif: a key to stability of thiolate-protected gold nanoclusters.

Recently obtained single-crystal structure of a thiolate-protected gold cluster shows that all thiolate groups form "staple" motifs on the cluster surface. To find out the driving force for such a formation, we use first-principles density functional theory simulations to model formation of "staple" motifs on an Au38 cluster from zero to full coverage. By geometry optimization, molecular dynamics, and simulated annealing, we show that formation of "staples" is strongly preferred on a cluster surface and helps stabilize the cluster by pinning the surface Au atoms and increasing the HOMO-LUMO gap. We devise a method to generate initial structural models for thiolate-protected gold clusters by adding "staples" to the cluster surface. Using this method, we obtain a staple-covered, low-energy structure for Au38(SCH3)24, a much studied cluster whose structure is not yet known. Optical band-edge energy computed from time-dependent DFT for our Au38(SCH3)24 structure shows good agreement with experiment.

Size limits on doping phosphorus into silicon nanocrystals.

We studied the electronic properties of phosphorus-doped silicon nanocrystals using the real-space first-principles pseudopotential method. We simulated nanocrystals with a diameter of up to 6 nm and made a direct comparison with experimental measurement for the first time for these systems. Our calculated size dependence of hyperfine splitting was in excellent agreement with experimental data. We also found a critical nanocrystal size below which we predicted that the dopant will be ejected to the surface.

Ab initio calculation of temperature effects in the optical response of open-shell sodium clusters.

Many properties of atomic clusters have been found to be size dependent, e.g., the optical response. There are, however, factors other than size that can also play an important role in determining the properties of nanoscale systems. Temperature, in particular, has been shown to have a strong effect on the optical response of open-shell sodium clusters. We incorporate the temperature effect on the optical absorption spectra by combining pseudopotentials, Langevin molecular dynamics, and time-dependent density functional theory. We have done calculations for several open-shell sodium clusters, Na(4) (+), Na(7) (+), and Na(11) (+), for which experimental data are available for comparison. We find that the positions of the lower energy peaks of the calculated spectra correspond very well to the peaks in the experimental spectra, although the local density approximation tends to overestimate the gap of the smaller clusters by up to 0.2 eV and underestimate the gap of the largest cluster by 0.4 eV. We fit the width of the peaks in the lower-temperature calculations to the corresponding experimental result to obtain the instrumental linewidth. We then use this same width for the high-temperature calculations and find very good agreement with experiment. Finally, we analyze the transitions that contribute to the observed peaks in the absorption spectra and we plot the effective valence charge density for specific transitions for each cluster. We find that for the two smaller clusters the absorption spectra are dominated by transitions from the occupied levels to a few (three for Na(4) (+) and five for Na(7) (+)) empty levels, although the contribution from transitions to other empty levels can still be significant. In contrast, the absorption spectra for Na(11) (+) come from a greater mixture of transitions as evidenced in the analysis as well as in the plot of the effective valence charge density.

Shellwise Mackay transformation in iron nanoclusters.

Structure and magnetism of iron clusters with up to 641 atoms have been investigated by means of density functional theory calculations including full geometric optimizations. Body-centered cubic (bcc) isomers are found to be lowest in energy when the clusters contain more than about 100 atoms. In addition, another stable conformation has been identified for magic-number clusters, which lies well within the range of thermal energies as compared to the bcc isomers. Its structure is characterized by a close-packed particle core and an icosahedral surface, while intermediate shells are partially transformed along the Mackay path between icosahedral and cuboctahedral geometry. The gradual transformation results in a favorable bcc environment for the subsurface atoms. For Fe55, the shellwise Mackay-transformed morphology is a promising candidate for the ground state.

Evolution of magnetism in iron from the atom to the bulk.

The evolution of the magnetic moment in iron clusters containing 20-400 atoms is investigated using first-principles numerical calculations based on density-functional theory and real-space pseudopotentials. Three families of clusters are studied, characterized by the arrangement of atoms: icosahedral, body-centered cubic centered on an atom site, and body-centered cubic centered on the bridge between two neighboring atoms. We find an overall decrease of magnetic moment as the clusters grow in size towards the bulk limit. Clusters with faceted surfaces are predicted to have magnetic moment lower than other clusters with similar size. As a result, the magnetic moment is observed to decrease as function of size in a nonmonotonic manner, which explains measurements performed at low temperatures.

Excitonic effects and optical properties of passivated CdSe clusters.

We calculate the optical properties of a series of passivated nonstoichiometric CdSe clusters using two first-principles approaches: time-dependent density functional theory within the local-density approximation, and by solving the Bethe-Salpeter equation for optical excitations with the GW approximation for the self-energy. We analyze the character of optical excitations leading to the first low-energy peak in the absorption cross section of these clusters. Within time-dependent density functional theory, we find that the lowest-energy excitation is mostly a single-level to single-level transition. In contrast, many-body methods predict a strong mixture of several different transitions, which is a signature of excitonic effects. The majority of the clusters have a series of dark transitions before the first bright transition. This may explain the long radiative lifetimes observed experimentally.

Symmetry considerations in CdSe nanocrystals.

Semiconductor nanocrystals or quantum dots show a wide range of physical properties depending on their size or shape. In this paper, we show that symmetry is also an important characteristic that can lead to different electronic and optical properties. We use pseudopotential density-functional theory, within a real space approach, and address the sensitivity of electronic and optical properties with respect to the symmetry point groups associated to CdSe nanocrystals.

Parallel self-consistent-field calculations via Chebyshev-filtered subspace acceleration.

Solving the Kohn-Sham eigenvalue problem constitutes the most computationally expensive part in self-consistent density functional theory (DFT) calculations. In a previous paper, we have proposed a nonlinear Chebyshev-filtered subspace iteration method, which avoids computing explicit eigenvectors except at the first self-consistent-field (SCF) iteration. The method may be viewed as an approach to solve the original nonlinear Kohn-Sham equation by a nonlinear subspace iteration technique, without emphasizing the intermediate linearized Kohn-Sham eigenvalue problems. It reaches self-consistency within a similar number of SCF iterations as eigensolver-based approaches. However, replacing the standard diagonalization at each SCF iteration by a Chebyshev subspace filtering step results in a significant speedup over methods based on standard diagonalization. Here, we discuss an approach for implementing this method in multi-processor, parallel environment. Numerical results are presented to show that the method enables to perform a class of highly challenging DFT calculations that were not feasible before.

Photoisomerization of azobenzene from first-principles constrained density-functional calculations.

Despite considerable work in the field, the precise mechanism for the photoisomerization of azobenzene, C(12)H(10)N(2), is still an open issue. Early theoretical studies of the problem indicated that isomerization occurs through an in-plane inversion path, and this has been used to explain recent time-resolved UV-visible spectroscopy measurements. On the other hand, a number of recent theoretical studies have concluded that a torsion of the N-N bond ("rotation path") is probably the most favorable mechanism for photoisomerization involving the first excited state. We have performed first-principles calculations using constrained density-functional theory (DFT) and time-dependent DFT in the local-density approximation, with results that also favor the rotation path mechanism. Our results are compared with other analyses, primarily based on configuration interaction.