Parallel implementation of a divide and conquer semiempirical algorithm

We have implemented a parallel version of the semiempirical divide and conquer program DivCon previously developed in our laboratory. By utilizing a parallel machine we are able to leverage the linear scaling of the divide and conquer algorithm itself to perform semiempirical calculations on large bio-molecules. The utility of the implementation is demonstrated with a partial geometry optimization of hen egg white lysozyme in the gas phase. Received: 5 December 1997 / Accepted: 13 February 1998 / Published online: 17 June 1998     

Simulation of liquid water using semiempirical Hamiltonians and the divide and conquer approach

This work examines the ability of semiempirical methods to describe the structure of liquid water. Particularly, the standard AM1 and PM3 methods together with recently developed PM3-PIF and PM3-MAIS parametrizations have been considered. We perform molecular dynamics simulations for a system consisting of 64 or 216 water molecules in a periodic cubic box. The whole system is described quantum mechanically. Calculations with 64 molecules have been carried out using standard SCF techniques whereas calculations with 216 molecules have been done using the divide and conquer approach. This method has also been used in one simulation case with 64 molecules for test purposes. Within this scope, the molecular dynamics program ROAR have been coupled with a linear scaling semiempirical code (DivCon) implemented in a parallel MPI version. The predicted liquid water structure using either AM1 or PM3 is shown to be very poor due to well-known limitations of these methods describing hydrogen bonds. In contrast, PM3-PIF and PM3-MAIS calculations lead to results in reasonably good agreement with experimental data. The best results for the heat of vaporization are obtained with the PM3-PIF method. The average induced dipole moment of the water molecule in the liquid is underestimated by all semiempirical techniques, which seems to be related to the NDDO approximation and to the use of minimal basis sets. A brief discussion on charge-transfer effects in liquid water is also presented.     

A divide and conquer real-space approach for all-electron molecular electrostatic potentials and interaction energies

A computational scheme to perform accurate numerical calculations of electrostatic potentials and interaction energies for molecular systems has been developed and implemented. Molecular electron and energy densities are divided into overlapping atom-centered atomic contributions and a three-dimensional molecular remainder. The steep nuclear cusps are included in the atom-centered functions making the three-dimensional remainder smooth enough to be accurately represented with a tractable amount of grid points. The one-dimensional radial functions of the atom-centered contributions as well as the three-dimensional remainder are expanded using finite element functions. The electrostatic potential is calculated by integrating the Coulomb potential for each separate density contribution, using our tensorial finite element method for the three-dimensional remainder. We also provide algorithms to compute accurate electron-electron and electron-nuclear interactions numerically using the proposed partitioning. The methods have been tested on all-electron densities of 18 reasonable large molecules containing elements up to Zn. The accuracy of the calculated Coulomb interaction energies is in the range of 10(-3) to 10(-6) E(h) when using an equidistant grid with a step length of 0.05 a(0).     

A finite temperature linear tetrahedron method for electronic structure calculations of periodic systems

A finite-temperature linear tetrahedron method for electronic structure calculations of periodic systems is developed. When compared to widely used simple temperature broadening, the number of k points necessary for accurate integration at finite temperatures is reduced. The utility of the method is demonstrated with benchmark calculations on 1D, 2D, and 3D systems.     

Exact dynamics of dissipative electronic systems and quantum transport: Hierarchical equations of motion approach

A generalized quantum master equation theory that governs the exact, nonperturbative quantum dissipation and quantum transport is formulated in terms of hierarchically coupled equations of motion for an arbitrary electronic system in contact with electrodes under either a stationary or a nonstationary electrochemical potential bias. The theoretical construction starts with the influence functional in path integral, in which the electron creation and annihilation operators are Grassmann variables. Time derivatives on the influence functionals are then performed in a hierarchical manner. Both the multiple-frequency dispersion and the non-Markovian reservoir parametrization schemes are considered for the desired hierarchy construction. The resulting hierarchical equations of motion formalism is in principle exact and applicable to arbitrary electronic systems, including Coulomb interactions, under the influence of arbitrary time-dependent applied bias voltage and external fields. Both the conventional quantum master equation and the real-time diagrammatic formalism of Schon and co-workers can be readily obtained at well defined limits of the present theory. We also show that for a noninteracting electron system, the present hierarchical equations of motion formalism terminates at the second tier exactly, and the Landuer-Buttiker transport current expression is recovered. The present theory renders an exact and numerically tractable tool to evaluate various transient and stationary quantum transport properties of many-electron systems, together with the involving nonperturbative dissipative dynamics.     

Electron-molecule scattering calculations in a 3D finite element R-matrix approach

We have implemented a three-dimensional finite element approach, based on tricubic polynomials in spherical coordinates, which solves the Schrodinger equation for scattering of a low energy electron from a molecule, approximating the electron exchange as a local potential. The potential is treated as a sum of three terms: electrostatic, exchange, and polarization. The electrostatic term can be extracted directly from ab initio codes (GAUSSIAN 98 in the work described here), while the exchange term is approximated using different local density functionals. A local polarization potential approximately describes the long range attraction to the molecular target induced by the scattering electron.     

Nitrogen vacancy and ferromagnetism in Cr-doped GaN: First-principles calculations

Nitrogen defects and their effect on the ferromagnetism (FM) in Cr-doped GaN have been systematically investigated by first-principles. Four considered configurations including one N vacancy (V_N), single substitutional Cr, double substitutional Cr, and complex of Cr-V_N are all ferromagnetic. The lowest energy arrangements for double Cr-doped (or Cr-V_N) GaN occur at the nearest Cr-Cr (or Cr-V_N) distance. One Cr contributes 84.3% of the total magnetic moment (2.533 μ_B), while one Cr-Cr pair leads to 5.998 μ_B moment (more than twice moment of one Cr) by the strong d-d spin coupling, which is mediated by two Cr 3d states antiferromagnetically coupling with the “commonly shared” N 2p states, and driven by a double exchange mechanism. The V_N can enhance the FM by adding about 1 μ_B to the Cr moment but reduce the FM spin exchange interaction between the nearest Cr-Cr pairs, so experimentally, high-performance samples may be synthesized by controlling N pressure.     

A new algorithm to handle finite nuclear mass effects in electronic calculations: the ISOTOPE program

We report the development of a simple algorithm to modify quantum chemistry codes based on the LCAO procedure, to account for the isotope problem in electronic structure calculations. No extra computations are required compared to standard Born-Oppenheimer calculations. An upgrade of the Gamess package called ISOTOPE is presented, and its applicability is demonstrated in some examples.     

Sources of error in electronic structure calculations on small chemical systems

The sources of error in electronic structure calculations arising from the truncation of the one-particle and n-particle expansions are examined with very large correlation consistent basis sets, in some cases up through valence 10-zeta quality, and coupled cluster methods, up through connected quadruple excitations. A limited number of full configuration interaction corrections are also considered. For cases where full configuration interaction calculations were unavailable or prohibitively expensive, a continued fraction approximation was used. In addition, errors arising from corevalence and relativistic corrections are also probed for a number of small chemical systems. The accuracies of several formulas for estimating total energies and atomization energies in the complete basis set limit are compared in light of the present large basis set findings. In agreement with previous work, the CCSD(T) method is found to provide results that are closer to the CCSDTQ and full configuration-interaction results than the less approximate CCSDT method.     

Dynamic hyperpolarizability calculations of large systems: the linear-scaling divide-and-conquer approach

We report a linear-scaling computation method for evaluating the dynamic first hyperpolarizability β based on the divide-and-conquer (DC) method. In the present scheme, we utilized the quasi-density-matrix expression derived from Wigner's (2n + 1) rule for β, where the quasi-density matrices are constructed from the solution obtained via the DC time-dependent self-consistent field (TD-SCF) method [T. Touma, M. Kobayashi, and H. Nakai, Chem. Phys. Lett. 485, 247 (2010)]. Numerical evaluation of π-conjugated and saturated organic chain systems verified that the present scheme considerably reduces the computational time for the β evaluation with a slight loss of accuracy, even around the singular frequency appearing at the electronic excitation energy. This evaluation indicates that the present linear-scaling TD-SCF scheme can also be used to estimate the molecular excitation energy. Furthermore, we succeeded in accurately evaluating the macroscopic second-harmonic generation coefficient of the polyvinylidene fluoride from the molecular (hyper)polarizabilities.     

Studying electronic transport in polyazulene-ionic liquid systems using infrared vibrational spectroscopy

This paper presents an in situ spectroelectrochemical characterization of polyazulene (PAz) and PAz-C(60) composite films using Fourier Transform Infrared Attenuated Total Reflection (FTIR-ATR) spectroscopy. In situ FTIR-ATR spectra were recorded simultaneously as the films were charged and discharged electrochemically. The aim was to clarify how the use of ILs and the addition of C(60) affected the electronic transport and structural changes occurring in PAz during electrochemical charging. We found that electrosynthesis of PAz in an IL lowered the oxidation potential of the film and improved its electroactivity. The FTIR-ATR data also suggest that PAz with a longer effective conjugation length is obtained during electrosynthesis when using ILs. With in situ FTIR-ATR it is possible to quite accurately determine the onset potential for oxidation/reduction. These values are important since they determine the suitability of the polymer for a specific application. Our experiments indicate that two types of charge carriers are formed during electrochemical oxidation of PAz in an IL. Furthermore, their formation is strongly affected by the addition of C(60) into the film. The type of charge carrier formed affects the electronic and possibly also ionic transport within the film. The inclusion of C(60) into PAz influenced the optical and structural properties considerably. In situ FTIR-ATR is also an extremely useful method for studying the potential stability of an IL during electrochemical cycling. We showed that cathodic decomposition of N,N-butyl-methyl-pyrrolidinium bis(trifluoromethylsulfonyl)imide ([BMP][Tf(2)N]) occurs at less negative potentials than those determined electrochemically.     

First-principles calculations on the curvature evolution and cross-linkage in carbon nitride

First-principles calculations were utilized to study the formation mechanisms and structural features of fullerene-like carbon nitride (FL CN_x). Cohesive energy comparisons reveal the energy cost for different defects arising from substitution of C for N as a function of the nitrogen concentration. In FL CN_x, combinations of pentagons and heptagons compete in causing graphene sheet curvature during the addition of CN-precursors and single species. Also, cross-linkage between graphene layers in FL CN_x can be explained by the bond rotation due to incorporated N atoms. The computational results agree with recent experimental observations from the growth of FL CN_x thin films.     

Derivation of the electronic nonadiabatic coupling field in molecular systems: an algebraic-vectorial approach

In this Communication it is suggested that various elements of the nonadiabatic coupling matrix, tau(jk)(s) are created by the singular nonadiabatic coupling terms of the system. Moreover, given the spatial distribution of these coupling terms in the close vicinity of their singularity points yields, according to this approach, the integrated intensity of the field at every point in the region of interest. To support these statements we consider the conical intersections of the three lower states of the H+H(2) system: From an ab initio treatment we obtain the nonadiabatic coupling terms around each conical intersection separately (at its close vicinity) and having those, create the field at every desired point employing vector-algebra. This approach is also used to calculate the intensity of the Curl of those matrix elements that lack their own sources [tau(13)(s) in the present case]. The final results are compared with relevant ab initio calculations.     

Symmetry and equivalence restrictions in electronic structure calculations

A simple method for obtaining MCSCF orbitals and CI natural orbitals adapted to degenerate point groups, with full symmetry and equivalence restrictions, is described. Among several advantages accruing from this method are the ability to perform atomic SCF calculations on states for which the SCF energy expression cannot be written in terms of Coulomb and exchange integrals over real orbitals, and the generation of symmetry-adapted atomic natural orbitals for use in a recently proposed method for basis set contraction.     

First-principles calculations of migration energy of lithium ions in halides and chalcogenides

Migration of Li+ ions via the vacancy mechanism in LiX (X = F, Cl, Br, and I) with the rocksalt and hypothetical zinc blende structures and Li2X (X = O, S, Se, and Te) with the antifluorite structure has been investigated using first-principles projector augmented wave calculations with the generalized gradient approximation. The migration paths and energies, determined by the nudged-elastic-band method, are discussed on the basis of two idealized models: the rigid-sphere and charged-sphere models. The trajectories and energy profiles of the migration in these lithium compounds vary between these two models, depending on the anion species and crystal structure. The migration energies in LiX with both the rocksalt and hypothetical zinc blende structures show a tendency to decrease with increasing periodic number of the anion species in the periodic table. This is consistent with the widely accepted view that anion species with large ionic radii and high polarizabilities are favorable for good ionic conduction. In contrast, Li2O exhibits the lowest migration energy among Li2X compounds, although O is the smallest among the chalcogens, indicating that electrostatic attractive interactions play the dominant role in the inter-ion interactions in Li2O and, therefore, in the ion migration.     

Molecular structure and electronic spectrum of taspine: Semiempirical calculations

AM1 calculations show that taspine has the three energy-minima along the rotation-like nuclear displacement of the dimethylaminoethyl group. They correspond to two enantiomeric structures and a Cs structure, which have nearly equal energies. The energy barrier between the enantiomeric structures and the Cs structure is calculated to be about 1 kcal/mol. The small barrier readily causes an intramolecular interconversion of the two enantiomers through the Cs structure and thus results in the optical inactivity of taspine. CNDO/S calculations show that the electronic spectra of the enantiomer and the Cs structure are quite similar. These calculated spectra are in good agreement with the observed electronic spectra.     

Transient-state transport in some finite systems. Part II. Further time-lag theory for transport through a simple (two-stage) cascade

General expressions are derived for the time-lags in transport through a simple (two-stage) cascade, based only upon the conservation of mass condition and hence independent of any assumed equation of flow. By considering the expressions so obtained in relation to Fick's equation, particular results are deduced for two special cases: (a) when the diffusion coefficient, D, is a function only of the concentration of diffusant and (b) when D = constant.     

First-principles calculations of AlN nanowires and nanotubes: atomic structures, energetics, and surface states

We explore the atomic and electronic structures of single-crystalline aluminum nitride nanowires (AlNNWs) and thick-walled aluminum nitride nanotubes (AlNNTs) with the diameters ranging from 0.7 to 2.2 nm by using first-principles calculations and molecular dynamics simulations based on density functional theory (DFT). We find that the preferable lateral facets of AlNNWs and thick-walled AlNNTs are {1010} surfaces, giving rise to hexagonal cross sections. Quite different from the cylindrical network of hexagons revealed in single-walled AlNNTs, the wall of thick-walled AlNNTs displays a wurtzite structure. The strain energies per atom in AlNNWs are proportional to the inverse of the wire diameter, whereas those in thick-walled AlNNTs are independent of tube diameter but proportional to the inverse of the wall thickness. Thick-walled AlNNTs are energetically comparable to AlNNWs of similar diameter, and both of them are energetically more favorable than single-walled AlNNTs. Both AlNNWs and AlNNTs are wide band gap semiconductors accompanied with surface states located in the band gap of bulk wurtzite AlN.     

An adiabatic linearized path integral approach for quantum time correlation functions: electronic transport in metal-molten salt solutions

We generalize the linearized path integral approach to evaluate quantum time correlation functions for systems best described by a set of nuclear and electronic degrees of freedom, restricting ourselves to the adiabatic approximation. If the operators in the correlation function are nondiagonal in the electronic states, then this adiabatic linearized path integral approximation for the thermal averaged quantum dynamics presents interesting and distinctive features, which we derive and explore in this paper. The capability of these approximations to accurately reproduce the behavior of physical systems is demonstrated by calculating the diffusion constant for an excess electron in a metal-molten salt solution.     

Inelastic neutron scattering spectrum of cyclotrimethylenetrinitramine: a comparison with solid-state electronic structure calculations

Solid-state geometry optimizations and corresponding normal-mode analysis of the widely used energetic material cyclotrimethylenetrinitramine (RDX) were performed using density functional theory with both the generalized gradient approximation (BLYP and BP functionals) and the local density approximation (PWC and VWN functionals). The structural results were found to be in good agreement with experimental neutron diffraction data and previously reported calculations based on the isolated-molecule approximation. The vibrational inelastic neutron scattering (INS) spectrum of polycrystalline RDX was measured and compared with simulated INS constructed from the solid-state calculations. The vibrational frequencies calculated from the solid-state methods had average deviations of 10 cm(-1) or less, whereas previously published frequencies based on an isolated-molecule approximation had deviations of 65 cm(-1) or less, illustrating the importance of including crystalline forces. On the basis of the calculations and analysis, it was possible to assign the normal modes and symmetries, which agree well with previous assignments. Four possible "doorway modes" were found in the energy range defined by the lattice modes, which were all found to contain fundamental contributions from rotation of the nitro groups.