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It remains a great challenge in condensed matter physics to develop a method to treat strongly correlated many-body systems with balanced accuracy and efficiency. We introduce an extended Gutzwiller (EG) method incorporating a manifold technique, which builds an effective manifold of the many-body Hilbert space, to describe the ground-state (GS) and excited-state (ES) properties of strongly correlated electrons. We systematically apply an EG projector onto the GS and ES of a non-interacting system. Diagonalization of the true Hamiltonian within the manifold formed by the resulting EG wavefunctions gives the approximate GS and ES of the correlated system. To validate this technique, we implement it on even-numbered fermionic Hubbard rings at half-filling with periodic boundary conditions, and compare the results with the exact diagonalization (ED) method. The EG method is capable of generating high-quality GS and low-lying ES wavefunctions, as evidenced by the high overlaps of wavefunctions between the EG and ED methods. Favorable comparisons are also achieved for other quantities including the total energy, the double occupancy, the total spin and the staggered magnetization. With the capability of accessing the ESs, the EG method can capture the essential features of the one-electron removal spectral function that contains contributions from states deep in the excited spectrum. Finally, we provide an outlook on the application of this method on large extended systems.

We introduce a rotationally invariant approach combined with the Gutzwiller conjugate gradient minimization method to study correlated electron systems. In the approach, the Gutzwiller projector is parametrized based on the number of electrons occupying the onsite orbitals instead of the onsite configurations. The approach efficiently groups the onsite orbitals according to their symmetry and greatly reduces the computational complexity, which yields a speedup of 20 ∼ 50 × in the minimal basis energy calculation of dimers. The computationally efficient approach promotes more accurate calculations beyond the minimal basis that is inapplicable in the original approach. A large-basis energy calculation of F2 demonstrates favorable agreements with standard quantum-chemical calculations Bytautas et al (2007 J. Chem. Phys. 127 164317)

We review our recent work on the Gutzwiller conjugate gradient minimization method, an ab initio approach developed for correlated electron systems. The complete formalism has been outlined that allows for a systematic understanding of the method, followed by a discussion of benchmark studies of dimers, one- and two-dimensional single-band Hubbard models. In the end, we present some preliminary results of multi-band Hubbard models and large-basis calculations of F2 to illustrate our efforts to further reduce the computational complexity.

Molecular dynamics simulations were performed to study the effects of Si solute on the glass formation and crystallization of Pd liquid. Pure Pd sample prepared by quenching process with cooling rate of $10^{13}$ K/s can be in an amorphous state but the structural analysis indicates there is nearly no glass-forming motif in the sample. However, doping a small amount Si (Si concentration ~ 4%) the sample can be vitrified at a cooling rate of $10^{12}$ K/s. The glass-forming motifs such as Pd-centered Z13, Si-centered Z9-like and Mixed-ICO-Cube clusters with 5-fold local symmetry are found to be the dominant short-range orders in the glassy samples. With the increasing of the Si-doping concentration, these glass-forming motifs tend to aggregate and connect with each other forming a network structure. Our calculated results revealed that Si solutes in liquid Pd can significantly enhance the glass-forming ability.

The thermal conductivity of anatase TiO2 nanotubes was investigated using equilibrium molecular dynamics simulations based on Green-Kubo formalism. The calculated thermal conductivity of [Formula: see text] for anatase crystal at room temperature agrees well with experimental value of ~8.5 W K-1 · m-1, demonstrating that the method used in our calculation can provide a good description for the thermal transport of TiO2. The dependence of the thermal conductivity of TiO2 nanotubes with temperature, tube size and chirality were studied in detail. The relationship between the thermal conductivity and the vibrational density-of-states of the nanotubes was also investigated.

An interatomic potential for carbon is developed that is based on an empirical tight-binding approach. The model reproduces accurately the energy-versus-volume diagram of carbon polytypes and gives a good description of the phonons and elastic constants for carbon in the diamond and graphite structures. To test the transferability of the model to different environments further, the authors performed molecular-dynamics simulations to study the liquid phase and the properties of small carbon microclusters. The results obtained are in good agreement with those obtained from ab initio calculations.

We have performed molecular dynamics simulations on a typical Al-based alloy Al90Sm10. The short-range and medium-range correlations of the system are reliably produced by ab initio calculations, whereas the long-range correlations are obtained with the assistance of a semi-empirical potential well-fitted to ab initio data. Our calculations show that a prepeak in the structure factor of this system emerges well above the melting temperature, and the intensity of the prepeak increases with increasing undercooling of the liquid. These results are in agreement with x-ray diffraction experiments. The interplay between the short-range order of the system originating from the large affinity between Al and Sm atoms, and the intrinsic repulsion between Sm atoms gives rise to a stronger correlation in the second peak than the first peak in the Sm-Sm partial pair correlation function (PPCF), which in turn produces the prepeak in the structure factor.

As a distinct class of ultra-hard materials, transition metal borides are found to have superior mechanical properties that challenge the traditional materials. In this work, we explored new stable structures for rhenium borides with different stoichiometries using genetic algorithm in combination with first-principles calculations. Based on theoretical calculations, ReB in a P-3m1 structure is found to be stable against decomposition reactions below 10 GPa and ReB3 in a P-6m2 structure is stable above 22 GPa. Two new phases of Re(2)B are predicted to be thermodynamically stable at pressures higher than 55 GPa and 80 GPa respectively. We also show that a C2/m structure discovered for ReB(4) has energy lower than that of the R-3m structure reported earlier (Wang et al 2013 J. Alloys Compd. 573 20). Elastic and vibrational properties from first-principles calculations indicate that the low-energy structures obtained in our search are mechanically and dynamically stable and are promising targets as new ultra-hard materials.

Atomic structure transitions of liquid niobium during solidification, at different temperatures from 3200 to 1500 K, were studied by using ab initio molecular dynamics simulations. The local atomic structure variations with temperature are investigated by using the pair-correlation function, the structure factor, the bond-angle distribution function, the Honeycutt-Anderson index, Voronoi tessellation and the cluster alignment methods. Our results clearly show that, upon quenching, the icosahedral short-range order dominates in the stable liquid and supercooled liquid states before the system transforms to crystalline body-center cubic phase at a temperature of about 1830 K.

We have characterized the (010) surface of Gd5Ge4 using scanning tunneling microscopy (STM) and x-ray photoelectron spectroscopy. Data from different samples have the following features in common: (1) the surface composition equals the bulk composition to within 5 at.%, both after ion etching and after annealing at temperatures of 400-1200 K; and (2) the surface exhibits terraces of two types. The height of the steps between similar terraces corresponds well to the separation between equivalent layers along the010direction in the bulk structure. Density functional theory (DFT) shows that the surface energy of the (0001) plane of hexagonal close-packed Gd is lower than that of the (111) plane of diamond-type Ge, suggesting that surfaces of Gd5Ge4 (for comparable density) should be rich in Gd. Indeed, DFT shows that among the bulk terminations of Gd5Ge4, a pure Ge termination is not favored. Each of the three remaining terminations (two pure Gd and one mixed, Gd-Ge) has its minimum surface energy in a different range of the possible Gd chemical potentials, indicating that different terminations may be stable under different conditions. DFT shows that the heights of the steps between dissimilar terraces, measured in STM, are consistent with the two pure Gd terminations.

Binary C(7)Si(n) (n = 1-7) clusters are studied using density functional calculations at the level of B3LYP/6-311G(d). Lowest-energy structures have been determined theoretically and their properties such as binding energies, second differences in energy and highest-occupied and lowest-unoccupied molecular orbital gaps have been analyzed. It is found that the lowest-energy structures of the C(7)Si(n) (n = 1-7) clusters change from linear to planar when n ≥ 3, and in the planar structures C atoms prefer to form five- and six-membered rings surrounded by extra Si atoms in the form of the C(2)Si units.

Neutral lead clusters Pb(n) (n = 21-30) were studied using a genetic algorithm (GA)/tight-binding (TB) search combined with density functional theory (DFT)-Perdew-Burke-Ernzerhof (PBE) calculations. The calculated results show that the Pb(n) (22 ≤ n ≤ 30) clusters favor endohedral cage structures with two (Pb(22 - 26)) or three (Pb(27 - 30)) endohedral atoms. The binding energies, stabilities, and highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) gaps of the Pb(n) clusters were also discussed. The results from our calculations also indicate that Pb(24) and Pb(28) are especially stable clusters compared with their neighbors.