Tight-binding Total Energy Calculations Research Articles

Atom Equivalent Energies for the Rapid Estimation of the Heat of Formation of Explosive Molecules from Density Functional Tight Binding Theory.

Atom equivalent energies have been derived from which the gas-phase heat of formation of explosive molecules can be estimated from fast, semiempirical density functional tight binding total energy calculations. The root-mean-square deviation and maximum deviation of the heats of formation from the experimental values for the set of 45 energetic molecules compiled by Byrd and Rice [ J. Phys. Chem. A, 2006, 110, 1005-1013] are 10.4 and 25.5 kcal/mol, respectively, using 4 atom equivalent energies and 7.4 and 15.0 kcal/mol, respectively, using 7 atom equivalent energies. These errors are around a factor of 2-3 larger than those obtained from density functional theory calculations but are smaller than those obtained from other semiempirical electronic structure methods. Heats of formation calculated with density functional tight binding theory using the 4 and 7 atom equivalent energies, the Byrd and Rice scheme, and the atom pair contribution method for a new set of 531 energetic molecules that contain only carbon, hydrogen, nitrogen, and oxygen are provided.

Snapshots of the Fragmentation for C70@Single-Walled Carbon Nanotube: Tight-Binding Molecular Dynamics Simulations.

In previously reported experimental studies, a yield of double-walled carbon nanotubes (DWCNTs) at C70@Single-walled carbon nanotubes (SWCNTs) is higher than C60@SWCNTs due to the higher sensitivity to photolysis of the former. From the perspective of pyrolysis dynamics, we would like to understand whether C70@SWCNT is more sensitive to thermal decomposition than C60@SWCNT, and the starting point of DWCNT formation, which can be obtained through the decomposition fragmentation of the nanopeapods, which appears in the early stages. We have studied the fragmentation of C70@SWCNT nanopeapods, using molecular dynamics simulations together with the empirical tight-binding total energy calculation method. We got the snapshots of the fragmentation structure of carbon nano-peapods (CNPs) composed of SWCNT and C70 fullerene molecules and the geometric spatial positioning structure of C70 within the SWCNT as a function of dynamics time (for 2 picoseconds) at the temperatures of 4000 K, 5000 K, and 6000 K. In conclusion, the scenario in which C70@SWCNT transforms to a DWCNT would be followed by the fragmentation of C70, after C70, and the SWCNT have been chemically bonding in the early stages. The relative stability of fullerenes in CNPs could be reversed, compared to the ranking of the relative stability of the encapsulated molecules themselves.

Atomic and electronic structures ofAg/Si(111)-c(12×2)surface: A first-principles study

Structural models for the $\text{Ag}/\text{Si}(111)\text{-c}(12\ifmmode\times\else\texttimes\fi{}2)$ phase were identified from a systematic search using tight-binding molecular dynamics and first-principles total-energy calculations. Our calculations showed that the low-energy $\text{c}(12\ifmmode\times\else\texttimes\fi{}2)$ and $6\ifmmode\times\else\texttimes\fi{}1$ structures can be derived from the well-known honeycomb chain-channel $3\ifmmode\times\else\texttimes\fi{}1$ model. Two $\text{c}(12\ifmmode\times\else\texttimes\fi{}2)$ models are found to have lower surface energies than both the $3\ifmmode\times\else\texttimes\fi{}1$ and $6\ifmmode\times\else\texttimes\fi{}1$ models, which is consistent with the experimental observation. A distinct feature of the $\text{c}(12\ifmmode\times\else\texttimes\fi{}2)$ structure is the dimer formation induced by lateral displacements of Ag atoms within the same row in the $6\ifmmode\times\else\texttimes\fi{}1$ phase. Different packing patterns of the Ag dimers with the same surface area can lead to either $6\ifmmode\times\else\texttimes\fi{}2$ or $\text{c}(12\ifmmode\times\else\texttimes\fi{}2)$ phase with very similar energies. Simulated scanning tunneling microscope images from our $\text{c}(12\ifmmode\times\else\texttimes\fi{}2)$ structure are in excellent agreement with the experimental measurement. Moreover, the lowest-energy $\text{c}(12\ifmmode\times\else\texttimes\fi{}2)$ structure identified from our calculations also reproduces the key features in the angle-resolved photoemission measurement.

SiH2 adsorption on the single dimer vacancy of the Si(100) surface

The energetic and structural properties ofSiH2 adsorbed on the single dimer vacancy (SDV) of theSi(100)-c(4 × 2) surface have been studied by using empirical tight-binding (ETB) total energy calculations. The adsorptionsof SiH2,SiH2 with a hydrogenadatom (SiH2+H)and SiH2 with twohydrogen adatoms (SiH2+2H) on the Si(100) surface with SDV structure have been studied. Threepossible sites (A, B and C) are found in each case. Adsorbing ofSiH2 or H on the SDV makes the structure of the SDV change. When a unit ofSiH2 is adsorbed on the SDV, the A site is more stable than the B site. IfSiH2+H orSiH2+2H is adsorbed on the SDV, the relative stability of the A site and B site reverses. The C siteis found to be the least stable site in all cases.

Diffusion of adatom in the selective epitaxial growth of Si(100): A molecular dynamics study

Tight-binding molecular dynamics simulation is performed for a Si adatom on the surface containing the {311} facet and the Si(100) surface to reproduce and explain the behavior of the {311} facet in the selective epitaxial growth of Si(100). In the simulation the adatom is observed to diffuse from the {311} facet to the Si(100) surface along the pathway of a trough between the dimer rows on Si(100) surface. By the tight-binding total energy calculation, it is also clarified that adatoms easily diffuse to the Si(100) surface because, after the adatom surmounts the first energy barrier to diffuse to the step edge near the {311} facet, there is no additional Schwoebel barrier and the other energy barriers gradually decrease to the top of the dimer row of Si(100). The pathway of the trough between dimer rows on the Si(100) surface is found to be energetically more favorable than the direct pathway to the dimer row from the tight-binding total energy calculation. Our tight-binding molecular dynamics simulation elucidates the mechanism responsible for the behavior of the {311} facet in the selective epitaxial growth of Si(100).

Resonance Raman spectroscopy(n,m)-dependent effects in small-diameter single-wall carbon nanotubes

This paper presents an accurate analysis of (i) the electronic transition energies ${E}_{22}^{S}$ and ${E}_{11}^{M}$, (ii) the radial breathing mode (RBM) frequencies ${\ensuremath{\omega}}_{\mathrm{RBM}}$, and (iii) the corresponding RBM intensities from 40 small-diameter single-wall carbon nanotubes (SWNTs) in the diameter range $0.7<{d}_{t}<1.3\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$. The electronic transition energies $({E}_{ii})$ are initially considered from nonorthogonal tight-binding total-energy calculations. To account for ${d}_{t}$-dependent many-body effects, a logarithmic correction, as proposed by Kane and Mele, is applied to both ${E}_{22}^{S}$ and ${E}_{11}^{M}$. The remaining discrepancies between the experimental and theoretical ${E}_{ii}$ values are shown to be proportional to the chirality-dependent effective masses of electrons and holes, as obtained from the electron energy dispersion relations. Chirality dependent screening effects are also identified in metallic SWNTs. For the RBM frequencies, a small deviation from the linear $1∕{d}_{t}$ behavior is observed, and this deviation is analyzed based on a chirality-dependent mode softening effect due to nanotube curvature. For those interested in sample characterization, the $(n,m)$ dependence of the resonance intensities is also addressed, the experimental results being compared with theoretical predictions based on matrix elements calculations. This analysis suggests that the (7,5), (7,6), and (6,5) SWNTs are more abundant in sodium dodecyl sulfate wrapped HiPco SWNTs in aqueous solution, in agreement with results previously reported for SWNTs grown by the CoMoCAT or alcohol methods.

Structure and growth of titanium buffer layers on Al2O3(0 0 0 1)

The structure of titanium films on α-Al2O3(0001) surfaces at room temperature was investigated through in situ reflection high energy electron diffraction (RHEED). The α-phase of titanium was observed to grow with the Ti(0001)∥Al2O3(0001), Ti[11̄00]∥Al2O3[21̄1̄0] and Ti[101̄0]∥Al2O3[11̄00] epitaxy. For up to 6 nm thick films, an other structure was found to co-exist with α-Ti. Its presence has dramatic consequences for the wetting of silver, which partly explains the non-trivial buffer effect of titanium at the silver/alumina interface. From the RHEED data, the extra structure is assigned to the high-pressure hexagonal ω-Ti phase. This is supported by tight-binding total energy calculations that demonstrate that the ω phase could actually be stabilized by the α-Al2O3(0001) substrate.

Structure and growth of titanium buffer layers on Al2O3(0001)

The structure of titanium films on α-Al2O3(0 0 0 1) surfaces at room temperature was investigated through in situ reflection high energy electron diffraction (RHEED). The α-phase of titanium was observed to grow with the Ti(0 0 0 1)∥Al2O3(0 0 0 1), Ti[1 1̄ 0 0]∥Al2O3[2 1̄ 1̄ 0] and Ti[1 0 1̄ 0]∥Al2O3[1 1̄ 0 0] epitaxy. For up to 6 nm thick films, an other structure was found to co-exist with α-Ti. Its presence has dramatic consequences for the wetting of silver, which partly explains the non-trivial buffer effect of titanium at the silver/alumina interface. From the RHEED data, the extra structure is assigned to the high-pressure hexagonal ω-Ti phase. This is supported by tight-binding total energy calculations that demonstrate that the ω phase could actually be stabilized by the α-Al2O3(0 0 0 1) substrate.

Structure and motion of basal dislocations in silicon carbide

$30\ifmmode^\circ\else\textdegree\fi{}$ and $90\ifmmode^\circ\else\textdegree\fi{}$ Shockley partial dislocations lying in ${111}$ and basal planes of cubic and hexagonal silicon carbide, respectively, are investigated theoretically. Density-functional-based tight-binding total-energy calculations are used to determine the core structure and energetics of the dislocations. In a second step their electronic structure is investigated using a pseudopotential method with a Gaussian basis set. Finally, the thermal activation barriers to glide motion of $30\ifmmode^\circ\else\textdegree\fi{}$ and $90\ifmmode^\circ\else\textdegree\fi{}$ Shockley partials are calculated in terms of a process involving the formation and migration of kinks along the dislocation line. The mechanism for enhanced dislocation movement observed under current injection conditions in bipolar silicon carbide devices is discussed.

A theoretical investigation of dislocations in cubic and hexagonal gallium nitride

In this article we review our theoretical work on dislocations in GaN. The methods applied are two distinct approximations to density functional theory: Density functional based tight-binding total energy calculations allow the prediction of low energy core structures and energies of extended defects embedded in larger regions of perfect material. However, whenever less approximate electronic structure calculations are required they are obtained in a localised basis pseudopotential approach. (© 2003 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Dislocations in diamond: Dissociation into partials and their glide motion

The dissociation of $60\ifmmode^\circ\else\textdegree\fi{}$ and screw dislocations in diamond is modeled in an approach combining isotropic elasticity theory with ab initio--based tight-binding total-energy calculations. Both dislocations are found to dissociate with a substantial lowering of their line energies. For the $60\ifmmode^\circ\else\textdegree\fi{}$ dislocation, however, an energy barrier to dissociation is found. We investigate the core structure of a screw dislocation distinguishing ``shuffle,'' ``mixed,'' and ``glide'' cores. The latter is found to be the most stable undissociated screw dislocation. Further, the glide motion of $90\ifmmode^\circ\else\textdegree\fi{}$ and $30\ifmmode^\circ\else\textdegree\fi{}$ partials is discussed in terms of a process involving the thermal formation and subsequent migration of kinks along the dislocation line. The calculated activation barriers to dislocation motion show that the $30\ifmmode^\circ\else\textdegree\fi{}$ partial is less mobile than the $90\ifmmode^\circ\else\textdegree\fi{}$ partial. Finally, high-resolution electron microscopy is performed on high-temperature, high-pressure annealed natural brown diamond, allowing the core regions of $60\ifmmode^\circ\else\textdegree\fi{}$ dislocations to be imaged. The majority of dislocations are found to be dissociated. However, in some cases, undissociated $60\ifmmode^\circ\else\textdegree\fi{}$ dislocations were also observed.

Calculation of thermodynamic quantities of metals and alloys by statistical moment method

The thermodynamic quantities of metals and alloys are studied using the moment method in the quantum statistical mechanics, going beyond the quasi-harmonic approximations. Including the power moments of the atomic displacements up to the fourth order, the free energy, specific heats Cv and Cp, mean square atomic displacements and thermal lattice expansion coefficients are derived explicitly in terms of the second and fourth order vibrational coupling constants. The thermodynamic quantities are calculated both for cubic (fcc and bcc) and closed packed hexagonal (hcp) metals. The Lennard–Jones type of potentials as well as the effective interatomic potentials derived from the tight-binding (TB) total energy calculation scheme are used. The calculated thermodynamic quantities are favorably compared with the experimental results. For the calculations of alloys, we investigate the effects of thermal lattice vibration on the long range order (LRO) parameter and order–disorder transitions of the ordered binary alloys.

Dislocations in diamond: Core structures and energies

The structures and core energies of dislocations in diamond are calculated using both isotropic and anisotropic elasticity theory combined with ab initio-based tight-binding total energy calculations. Perfect and dissociated 60° and screw dislocations are considered. Their possible dissociation reactions are investigated through a consideration of the calculated elastic energy factors and core energies. Dissociation into partials is energetically favored. We find that the double-period reconstruction of the 90° glide partial dislocation is more stable than the single-period reconstruction and that the glide set of 60° perfect dislocations is more stable than the shuffle set. Shuffle partials containing interstitials are less likely than those containing vacancies.

Stability of the period-doubled core of the 90 degrees partial in silicon

In a recent Letter [N. Lehto and S. Oberg, Phys. Rev. Lett. 80, 5568 (1998)], Lehto and Oberg investigated the effects of strain fields on the core structure of the 90-degree partial dislocation in silicon, especially the influence of the choice of supercell periodic boundary conditions in theoretical simulations. We show that their results for the relative stability between the two structures are in disagreement with cell-size converged tight-binding total energy (TBTE) calculations, which suggest the DP core to be more stable, regardless of the choice of boundary condition. Moreover, we argue that this disagreement is due to their use of a Keating potential.

Structures and Energetics of Regioisomers of C60 Dimer and Trimers

Ten different regioisomers of C60 trimers with intact cages were studied using the empirical tight-binding (TB) total energy calculation and the semiempirical PM3, AM1, and MNDO methods. We determined the stable atomic structure and energies of 10 (C60)3 regioisomers with ETBTEC, PM3, AM1, and MNDO calculations. The dimerization of C60 is exothermic according to the density-functional-based nonorthogonal tight-binding (DF-TB) method; the semiempirical PM3, AM1, and MNDO; and the ab initio 3-21G LDA and HF calculations, but it is endothermic in both the TB and the ab initio B3LYP6-31G*//4-21G B3LYP calculations. Therefore, according to the TB calculations, the most stable regioisomer of C60 trimers is equatorial. The energies of the trans-3(C2), trans-1(D2h), trans-2(C2), trans-4(Cs), cis-1 (C3ν), cis-2(Cs), cis-3(C2), cis-1(Cs), and cis-2(C3ν) regioisomers relative to the equatorial regioisomer are 13,19, 20, 30, 66, 99, 169, 215, and 673 meV, respectively.

Lowest-energy site for hydrogen in diamond

We investigate the locations, electronic energy levels and motion of hydrogen in diamond with tight-binding total energy calculations and Molecular Dynamics simulations. A lowest energy site for hydrogen in diamond is found. It is a sixfold degenerate site (with respect to the C-C bond), giving rise to a dangling bond and to a deep electronic level in the energy gap. The motion of the hydrogen atom in the diamond crystal is jumplike between these stable sites, starting at above $\ensuremath{\sim}400 \mathrm{K}.$ It is a coupled-barrier diffusion, with an activation energy of 0.9 eV.

Trimerization of C 60

Seven different regioisomers of C 60 trimers with intact cages have been calculated at the empirical tight-binding total energy calculation method. We analyze the atomic structure and energetics of seven different trimers except the sterically demanding cis-1. The trimers are formed by the linkage through a [2+2] cycloaddition. The energies of the trans-3, trans-1, trans-2, trans-4, cis-3 and cis- 2 regioisomers relative to the most stable equatorial regioisomer are 13, 19, 20, 30, 207 and 673 meV, respectively.

Stability and cap formation mechanism of single-walled carbon nanotubes

We use tight-binding total-energy calculations to investigate the energetics and the cap formation mechanism of single-walled carbon nanotubes. The present calculations of the edge energy and strain energy suggest the growth of armchair nanotubes to be energetically more favorable than the growth of zigzag nanotubes. The cap formation at the edge of both nanotubes is animated by the tight-binding molecular-dynamics simulations. The cap formation is immediately followed by the pentagon formation at the edge of both tubes. The role of transitions metals is further discussed.

Structural properties of cubic GaN epitaxial layers grown on β-SiC

Self-consistent tight-binding total energy calculations are performed to study the deposition of a few layers of cubic GaN on (100) β-SiC substrates. Cohesion energies, atomic displacements, dangling bond occupancies and surface reconstructions are calculated for a variety of epitaxial systems including monolayers of either Ga or N as well as single and double bilayers of GaN on either Si or C terminated substrates. The SiC substrates and Ga-N epitaxial layers are represented by 2×2 supercells of 9 Si and C monolayers plus the respective number of monolayers of Ga and N atoms. Depending on the system, surface atoms dimerize either symmetrically or asymmetrically resulting in either 2×1, c-2×2, or 2×2 surface reconstructions. At the substrate-epitaxial-layer interfaces, N binds stronger than Ga to either Si or C. Interface mixing is found to be energetically not advantageous for both C- and Si-terminated substrates, although for the latter the obtained small energy differences may suggest the possibility of mixing.

Determination of Vibrational Eigenfrequencies of Semiconductors Using Tight-Binding Total Energy Calculations

We calculate the eigenfrequencies of bulk semiconductors using tight-binding total energy calculations of an ideal and a distorted lattice. We correlate the obtained energy change with the harmonic force constants appearing as parameters in the expansion of the potential energy of the crys. tal lattice in terms of the displacement. A good agreement of the calculated q = 0 optical vibrational modes with the experimental values for Si, Ge, GaAs and GaP bulk crystals is obtained. The influence of a surface on the force constants and the vibrational frequencies is studied. PACS numbers: 63.20.—e