How does it become possible to treat delocalized and/or open-shell systems in fragmentation-based linear-scaling electronic structure calculations? The case of the divide-and-conquer method

The authors have developed a fragmentation-based linear-scaling electronic structure calculation strategy named the divide-and-conquer (DC) method, which has been implemented into the Gamess program package. Although there are many sorts of fragmentation-based linear-scaling schemes, most of them require the charge and spin multiplicity of each fragment a priori. Therefore, their applications to delocalized and/or open-shell systems have been limited. However, the DC method is a notable exception because the distribution of electrons in the entire system is automatically determined by the universal Fermi level. In this perspective, the authors have summarized the performance of the linear-scaling self-consistent field (SCF) and post-SCF calculations of delocalized and/or open-shell systems based on the DC method. Furthermore, some future prospects of the method have been discussed.     

Linear scaling calculation of band edge states and doped semiconductors

Linear scaling methods provide total energy, but no energy levels and canonical wave functions. From the density matrix computed through the density matrix purification methods, we propose an order-N [O(N)] method for calculating both the energies and wave functions of band edge states, which are important for optical properties and chemical reactions. In addition, we also develop an O(N) algorithm to deal with doped semiconductors based on the O(N) method for band edge states calculation. We illustrate the O(N) behavior of the new method by applying it to boron nitride (BN) nanotubes and BN nanotubes with an adsorbed hydrogen atom. The band gap of various BN nanotubes are investigated systematically and the acceptor levels of BN nanotubes with an isolated adsorbed H atom are computed. Our methods are simple, robust, and especially suited for the application in self-consistent field electronic structure theory.     

Linear-scaling divide-and-conquer second-order M?ller�CPlesset perturbation calculation for open-shell systems: implementation and application

We have developed the spin-unrestricted divide-and-conquer (DC)-based linear-scaling self-consistent field method for treating open-shell systems (Kobayashi et al. in Chem Phys Lett 500:172, 2010). Because the method does not require the position of excess spins or charges, it made the treatment of large spin-delocalized systems tractable. The present study extends the DC-based unrestricted open-shell scheme to the correlated second-order M?ller?CPlesset perturbation (MP2) theory. Numerical applications to polyene cations demonstrate that the present method gives highly accurate results with less computational costs even for spin-delocalized systems.     

(Hyper)polarizability density analysis for open-shell molecular systems based on natural orbitals and occupation numbers

We have developed a method for analyzing the (hyper)polarizabilities of open-shell molecular systems. This method employs the (hyper)polarizability densities based on the natural orbitals and occupation numbers, which enables us to analyze the contributions of odd electrons having various open-shell (diradical) characters. Within broken-symmetry, i.e., spin-unrestricted, single-determinant molecular orbital and density functional theory approaches, we can also remove the spin contamination effects on these quantities through spin projection. To do that, an approximate spin projected method has been elaborated and applied to the analysis of the (hyper)polarizability of multi-radical systems. As examples, typical open-shell singlet systems, 1,3-dipoles and rectangular graphene nanoflakes, are examined.     

A direct method for locating minimum-energy crossing points (MECPs) in spin-forbidden transitions and nonadiabatic reactions

An efficient computational method for locating minimum-energy crossing points (MECPs) between potential-energy surfaces in spin-crossover transitions and nonadiabatic spin-forbidden (bio)chemical reactions is introduced. The method has been tested on the phenyl cation and the computed MECP associated with its radiationless singlet-triplet spin crossover is in good agreement with available data. However, the convergence behavior of the present method is significantly more efficient than some alternative methods which allows us to study nonadiabatic processes in larger systems such as spin crossover in metal-containing compounds. The convergence rate of the method obeys a fast logarithmic law which has been verified on the phenyl cation. As an application of this new methodology, the MECPs of the ferrous complex [Fe(ptz)(6)](BF(4))(2), which exhibits light-induced excited spin state trapping, have been computed to identify their geometric and energetic parameters during spin crossover. Our calculations, in conjunction with spin-unrestricted density-functional calculations, show that the transition from the singlet ground state to a triplet intermediate and to the quintet metastable state of [Fe(ptz)(6)](BF(4))(2) is accompanied by unusually large bond-length elongations of the axial ligands ( approximately 0.26 and 0.23 A, respectively). Our results are consistent with crystallographic data available for the metastable quintet but also predict new structural and energetic information about the triplet intermediate and at the MECPs which is currently not available from experiment.     

多组态含时自旋非限制HartreeFock理论

基于自旋非限制HartreeFock理论,发展了自旋非限制多组态含时HartreeFock理论方法来研究激光场中的多电子相关动力学．自旋向上和自旋向下的自旋轨道分别在他们各自的子空间内传播;并通过约化密度矩阵和平均场算符相互作用．分别利用了自旋限制和非限制的多组态含时HartreeFock方法虚时和实时传播计算氦原子基态能量和电离几率．自旋非限制的计算结果与其他报道相吻合．     

First-principles study of interaction between H2 molecules and BN nanotubes with BN divacancies

The interaction between H(2) molecules and boron nitride (BN) single-walled nanotubes with BN divacancies is investigated with density-functional theory. Our calculations reveal that H(2) molecules adsorb physically outside defective BN nanotubes, and cannot enter into BN nanotubes through bare BN divacancies because the energy barrier is as high as 4.62 eV. After the defects are saturated by hydrogen atoms, the physisorption behavior of H(2) molecules is not changed, but the energy barrier of H(2) molecules entering into BN nanotubes through the defects is reduced to 0.58 eV. This phenomenon is ascribed to hydrogen saturation induced reduction of electrostatic potential around the defects.     

Linear-scaling computation of excited states in time-domain

The applicability of quantum mechanical methods is severely limited by their poor scaling.To circumvent the problem,linearscaling methods for quantum mechanical calculations had been developed.The physical basis of linear-scaling methods is the locality in quantum mechanics where the properties or observables of a system are weakly influenced by factors spatially far apart.Besides the substantial efforts spent on devising linear-scaling methods for ground state,there is also a growing interest in the development of linear-scaling methods for excited states.This review gives an overview of linear-scaling approaches for excited states solved in real time-domain.     

Linear-scaling multipole-accelerated Gaussian and finite-element Coulomb method

A linear-scaling implementation of the Gaussian and finite-element Coulomb (GFC) method is presented for the rapid computation of the electronic Coulomb potential. The current work utilizes the fast multipole method (FMM) for the evaluation of the Poisson equation boundary condition. The FMM affords significant savings for small- and medium-sized systems and overcomes the bottleneck in the GFC method for very large systems. Compared to an exact analytical treatment of the boundary, more than 100-fold speedups are observed for systems with more than 1000 basis functions without any significant loss of accuracy. We present CPU times to demonstrate the effectiveness of the linear-scaling GFC method for both one-dimensional polyalanine chains and the challenging case of three-dimensional diamond fragments.     

Purification of pulsed laser synthesized single wall carbon nanotubes by magnetic filtration

Great effort has been expended in the development of methods to purify raw nanotubes by chemical treatment, washing, mechanical filtration, or heat treatment in a vacuum or oxidative environment. These techniques are limited by incomplete removal of catalyst nanoparticles and by the damage to the nanotubes that often results. We have applied a new purification method using filtration in a magnetic field and oxidation and investigated the efficacy using magnetic filtration alone, or combined with chemical-based or annealing-based oxidative treatments. By applying magnetic filtration only, we reduce catalyst content from 11.7 to 3.7 wt %, which is a superior result to oxidation and/or chemical treated samples. By combining chemical and magnetic purification, metal catalyst content is reduced to as much as 0.3 wt %, which is the best result ever for SWNTs synthesized by the laser method. In addition to the reduction of catalyst content, the new purification method increased sample quality, confirmed by Raman spectroscopy and near-infrared absorption. Magnetic filtration is found to be very effective in removing metal catalysts, producing material with high quality and yields.     

Potential magnetic properties of nanotubes (n, 0) with Klein and Fujita edges

Analytical solutions for localized states of zigzag-type nanotube (NT) fragments with various combinations of Klein and Fujita borders are considered using the Hückel approach. It is shown that the equations for determining molecular orbitals (MOs) in systems with two Klein edges are similar to equations for systems with two Fujita edges. An analytical formula for the energies of all ?? MOs is obtained for systems that have a Klein edge on one side and a Fujita edge on the other. It is established that these systems have n orbitals with energy ?? that are localized on the Fujita and Klein edges in dependence on the MO symmetry. The degeneracy of edge orbitals indicates that there is a tendency toward single occupancy of them and to the appearance of spin (magnetic) properties. In addition, the energies of the states of different multiplicity for NT fragments (8, 0) are calculated using the CASSCF approach. It is shown that the ground state has a multiplicity of 9, as was also indicated by estimates obtained using the density functional method (B3LYP). It is concluded that zigzag-type NTs with asymmetric edges have a tendency to exhibit spin properties. It is noted that the construction of nanoscale magnetic materials based on them is very promising.     

Electronic and magnetic properties of substituted BN sheets: a density functional theory study

Using density functional calculations, we investigate the geometries, electronic structures and magnetic properties of hexagonal BN sheets with 3d transition metal (TM) and nonmetal atoms embedded in three types of vacancies: V(B), V(N), and V(B+N). We show that some embedded configurations, except TM atoms in V(N) vacancy, are stable in BN sheets and yield interesting phenomena. For instance, the band gaps and magnetic moments of BN sheets can be tuned depending on the embedded dopant species and vacancy type. In particular, embedment such as Cr in V(B+N), Co in V(B), and Ni in V(B) leads to half-metallic BN sheets interesting for spin filter applications. From the investigation of Mn-chain (C(Mn)) embedments, a regular 1D structure can be formed in BN sheets as an electron waveguide, a metal nanometre wire with a single atom thickness.     

Adsorption of transition-metal atoms on boron nitride nanotube: a density-functional study

Adsorption of transition atoms on a (8,0) zigzag single-walled boron nitride (BN) nanotube has been investigated using density-functional theory methods. Main focuses have been placed on configurations corresponding to the located minima of the adsorbates, the corresponding binding energies, and the modified electronic properties of the BN nanotubes due to the adsorbates. We have systemically studied a series of metal adsorbates including all 3d transition-metal elements (Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, and Zn) and two group-VIIIA transition-metal elements (Pd and Pt). We found that many transition-metal atoms can be chemically adsorbed on the outer surface of the BN nanotubes and that the adsorption process is typically exothermic. Upon adsorption, the binding energies of the Sc, Ti, Ni, Pd, and Pt atoms are relatively high (>1.0 eV), while those of V, Fe, and Co atoms are modest, ranging from 0.62 to 0.92 eV. Mn atom forms a weak bond with the BN nanotube, while Zn atom cannot be chemically adsorbed on the BN nanotube. In most cases, the adsorption of transition-metal atoms can induce certain impurity states within the band gap of the pristine BN nanotube, thereby reducing the band gap. Most metal-adsorbed BN nanotubes exhibit nonzero magnetic moments, contributed largely by the transition-metal atoms.     

氮化硼纳米管的研究进展

氮化硼纳米管的研究进展;结构;制备;性能;储氢;综述     

Linear-scaling implementation of molecular electronic self-consistent field theory

A linear-scaling implementation of Hartree-Fock and Kohn-Sham self-consistent field (SCF) theories is presented and illustrated with applications to molecules consisting of more than 1000 atoms. The diagonalization bottleneck of traditional SCF methods is avoided by carrying out a minimization of the Roothaan-Hall (RH) energy function and solving the Newton equations using the preconditioned conjugate-gradient (PCG) method. For rapid PCG convergence, the Lowdin orthogonal atomic orbital basis is used. The resulting linear-scaling trust-region Roothaan-Hall (LS-TRRH) method works by the introduction of a level-shift parameter in the RH Newton equations. A great advantage of the LS-TRRH method is that the optimal level shift can be determined at no extra cost, ensuring fast and robust convergence of both the SCF iterations and the level-shifted Newton equations. For density averaging, the authors use the trust-region density-subspace minimization (TRDSM) method, which, unlike the traditional direct inversion in the iterative subspace (DIIS) scheme, is firmly based on the principle of energy minimization. When combined with a linear-scaling evaluation of the Fock/Kohn-Sham matrix (including a boxed fitting of the electron density), LS-TRRH and TRDSM methods constitute the linear-scaling trust-region SCF (LS-TRSCF) method. The LS-TRSCF method compares favorably with the traditional SCF/DIIS scheme, converging smoothly and reliably in cases where the latter method fails. In one case where the LS-TRSCF method converges smoothly to a minimum, the SCF/DIIS method converges to a saddle point.     

Orbital-corrected orbital-free density functional theory

A new implementation of density functional theory (DFT), namely orbital-corrected orbital-free (OO) DFT, has been developed. With at most two non-self-consistent iterations, OO-DFT accomplishes the accuracy comparable to fully self-consistent Kohn-Sham DFT as demonstrated by its application on the cubic-diamond Si and the face-centered-cubic Ag systems. Our work provides a new impetus to further improve orbital-free DFT method and presents a robust means to significantly lower the cost associated with general applications of linear-scaling Kohn-Sham DFT methods on large systems of thousands of atoms within different chemical bonding environment.     

Spin-spin and spin-orbit interactions in nanographene fragments: a quantum chemistry approach

The relativistic behavior of graphene structures, starting from the fundamental building blocks--the poly-aromatic hydrocarbons (PAHs) along with other PAH nanographenes--is studied to quantify any associated intrinsic magnetism in the triplet (T) state and subsequently in the ground singlet (S) state with account of possible S-T mixture induced by spin-orbit coupling (SOC). We employ a first principle quantum chemical-based approach and density functional theory (DFT) for a systematic treatment of the spin-Hamiltonian by considering both the spin-orbit and spin-spin interactions as dependent on different numbers of benzene rings. We assess these relativistic spin-coupling phenomena in terms of splitting parameters which cause magnetic anisotropy in absence of external perturbations. Possible routes for changes in the couplings in terms of doping and defects are also simulated and discussed. Accounting for the artificial character of the broken-symmetry solutions for strong spin polarization of the so-called "singlet open-shell" ground state in zigzag graphene nanoribbons predicted by spin-unrestricted DFT approaches, we interpolate results from more sophisticated methods for the S-T gaps and spin-orbit coupling (SOC) integrals and find that these spin interactions become weak as function of size and increasing decoupling of electrons at the edges. This leads to reduced electron spin-spin interaction and hence almost negligible intrinsic magnetism in the carbon-based PAHs and carbon nanographene fragments. Our results are in agreement with the fact that direct experimental evidence of edge magnetism in pristine graphene has been reported so far. We support the notion that magnetism in graphene only can be ascribed to structural defects or impurities.     

Linear-scaling localized-density-matrix method for the ground and excited states of one-dimensional molecular systems

A linear-scaling localized-density-matrix (LDM) method is developed to evaluate the ground-state reduced single-electron density matrices of one-dimensional molecular systems. The new method may be combined with the existing linear-scaling LDM method for the excited states (Yokojima and Chen, Chem. Phys. Lett. 292 (1998) 379), and thus leads to a linear-scaling calculation method for the properties of both the ground and excited states. The combined method is applied to the polyacetylene oligomers and the linear-scaling of the total computational time is clearly demonstrated.     

True nanocable assemblies with insulating BN nanotube sheaths and conducting Cu nanowire cores

Nanocable models comprised of BN nanotubes filled with close-packed Cu nanowires were investigated by gradient-corrected density functional theory (DFT) computations. The optimal distance between the sidewall of BN nanotubes and the atoms in a copper nanowire is about 0.35 nm, with a weak insertion energy (ca. -0.04 eV per Cu atom). Hence, such nanocables are assembled by weaker van der Waals (vdW) forces, rather than by chemical bonding interactions. The electronic band structures of the BN/Cu hybrid systems are superposition of those of the separate components, the BN nanotubes, and the Cu nanowires. Since charge density analyses show that the conduction electrons are distributed only on the copper atoms, charge transport will occur only in these inner nanowires, which are effectively insulated by the outer BN nanotubes. On the basis of these computational results, BN/Cu hybrid structures should be ideal nanocables.     

Effects of the covalent linker groups on the spin transport properties of single nickelocene molecules attached to single-walled carbon nanotubes

The understanding of how the spin moment of a magnetic molecule transfers to a carbon nanotube, when the molecule is attached to it, is crucial for designing novel supramolecular spin devices. Here we explore such an issue by modeling the spin transport of a single-walled carbon nanotube grafted with one nickelocene molecule. In particular we investigate how the electron transport becomes spin-polarized depending on the specific linking group bonding nickelocene to the nanotube. We consider as linkers both aziridine and pyrrolidine rings and the amide group. Our calculations show that, at variance with aziridine, both pyrrolidine and amide, do alter the sp(2) character of the binding site of the nanotube and thus affect the transmission around the Fermi level. However, only aziridine allows transferring the spin polarization of the nickelocene to the nanotube, whose conductance at the Fermi level becomes spin-polarized. This suggests the superiority of aziridine as a linker for grafting magnetic molecules onto carbon nanotubes with efficient spin filtering functionality.