arXiv subjects
Publications and source records attributed to C. J. Tymczak.
Using first principles calculations, we show the high hydrogen storage capacity of a new class of compounds, metalloboranes. Metalloboranes are transition metal (TM) and borane compounds that obey a novel-bonding scheme. We have found that the transition metal atoms can bind up to 10 H2 molecules.
A novel Gaussian-Sinc mixed basis set for the calculation of the one-electron electronic structure within a uniform magnetic field in three dimensions is presented. The one-electron system is used to demonstrate the utility of this new methodology and is a first step in laying the foundation for further development of many-electron atomic and molecular methodology. It is shown in this manuscript how to effectively calculate all basis set integrals, which includes the mixed Gaussian-Sinc integrals, with a fast and accurate method. The Sinc basis is invariant to the choice of the position of the Coulomb potential, as opposed to traditional grid based methods. This invariance guarantees that the choice of the grids origin has no effect on the electronic structure calculation. This is because the Coulomb potential is treated properly in this methodology, as opposed to DVR methodologies. The off-diagonal terms are sparse but very important around the Coulomb singularity. In general, five to six significant digits of accuracy on all converged results without the linear dependency problems of the Gaussian methodologies are achievable. This methodology is applied to calculate the ground state energy of H atom, $H_2^{+}$ ion and $H_3^{2+}$ ion in magnetic fields up to a magnetic field strength of 2.35x$10^13$ G (10,000 au). From these calculations it is shown that $H_3^{2+}$ ion is unstable without relativistic considerations.
For any graph $G$ on $n$ vertices and for any {\em symmetric} subgraph $J$ of $K_{n,n}$, we construct an infinite sequence of graphs based on the pair $(G,J)$. The First graph in the sequence is $G$, then at each stage replacing every vertex of the previous graph by a copy of $G$ and every edge of the previous graph by a copy of $J$ the new graph is constructed. We call these graphs {\em self-similar} graphs. We are interested in delineating those pairs $(G,J)$ for which the chromatic numbers of the graphs in the sequence are bounded. Here we have some partial results. When $G$ is a complete graph and $J$ is a special matching we show that every graph in the resulting sequence is an {\em expander} graph.
We report on the utility of using Shannons Sampling theorem to solve Quantum Mechanical systems. We show that by extending the logic of Shannons interpolation theorem we can define a Universal Lattice Basis, which has superior interpolating properties compared to traditional methods. This basis is orthonormal, semi-local, has a Euclidean norm, and a simple analytic expression for the derivatives. Additionally, we can define a bounded domain for which band-limited functions, such as Gaussians, show quadratic convergence in the representation error in respect to the sampling frequency. This theory also extends to the periodic domain and we illustrate the simple analytic forms of the periodic semi-local basis and derivatives. Additionally, we show that this periodic basis is equivalent to the space defined by the Fast Fourier Transform. This novel basis has great utility in solving quantum mechanical problems for which the wave functions are known to be naturally band-limited. Several numerical examples in single and multi-dimensions are given to show the convergence and equivalence of the periodic and bounded domains for compact states.
Using density functional theory (DFT) and quantum Monte Carlo (QMC) calculations we show that the B12Hn and B12Fn (n = 0-4) quasi-planar structures are energetically more favorable than the corresponding icosahedral clusters. Moreover, we show that the fully planar B12F6 cluster is more stable than the 3D counterpart. These results open up the possibility of designing larger boron based nanostructures starting from quasi-planar or fully planar building blocks.
We investigate the symmetry of the boron buckyball and a related boron nanotube. Using large-scale ab-initio calculations up to second-order Møller Plesset perturbation theory, we have determined unambiguously the equilibrium geometry/symmetry of two structurally related boron clusters: the B80 fullerene and the finite-length (5,0) boron nanotube. The B80 cluster was found to have the same symmetry, Ih, as the C60 molecule since its 20 additional boron atoms are located exactly at the centers of the 20 hexagons. Additionally, we also show that the (5,0) boron nanotube does not suffer from atomic buckling and its symmetry is D5d instead of C5v as has been described by previous calculations. Therefore, we predict that all the boron nanotubes rolled from the α-sheet will be free from structural distortions, which has a significant impact on their electronic properties.
Based on our comprehensive theoretical investigation and known experimental results for small boron clusters, we predict the existence of a novel aromatic inorganic molecule, B12H6. This molecule, which we refer to as borozene, has remarkably similar properties to the well-known benzene. Borozene is planar, possesses a large first excitation energy, D3h symmetry, and more importantly is aromatic. Furthermore, the calculated anisotropy of the magnetic susceptibility of borozene is three times larger in absolute value than for benzene. Finally, we can show that borozene molecules may be fused together to give larger aromatic compounds with even larger anisotropic susceptibilities.
We present a time-reversible Born-Oppenheimer molecular dynamics scheme, based on self-consistent Hartree-Fock or density functional theory, where both the nuclear and the electronic degrees of freedom are propagated in time. We show how a time-reversible adiabatic propagation of the electronic degrees of freedom is possible despite the non-linearity and incompleteness of the self-consistent field procedure. Time-reversal symmetry excludes a systematic long-term energy drift for a microcanonical ensemble and the number of self-consistency cycles can be kept low (often only 2-4 cycles per nuclear time step) thanks to a good initial guess given by the adiabatic propagation of the electronic degrees of freedom. The time-reversible Born-Oppenheimer molecular dynamics scheme therefore combines a low computational cost with a physically correct time-reversible representation of the dynamics, which preserves a detailed balance between propagation forwards and backwards in time.
We present parallelization of a quantum-chemical tree-code [J. Chem. Phys. {\bf 106}, 5526 (1997)] for linear scaling computation of the Coulomb matrix. Equal time partition [J. Chem. Phys. {\bf 118}, 9128 (2003)] is used to load balance computation of the Coulomb matrix. Equal time partition is a measurement based algorithm for domain decomposition that exploits small variation of the density between self-consistent-field cycles to achieve load balance. Efficiency of the equal time partition is illustrated by several tests involving both finite and periodic systems. It is found that equal time partition is able to deliver 91 -- 98 % efficiency with 128 processors in the most time consuming part of the Coulomb matrix calculation. The current parallel quantum chemical tree code is able to deliver 63 -- 81% overall efficiency on 128 processors with fine grained parallelism (less than two heavy atoms per processor).
Linear scaling quantum chemical methods for Density Functional Theory are extended to the condensed phase at the $Γ$-point. For the two-electron Coulomb matrix, this is achieved with a tree-code algorithm for fast Coulomb summation [J. Chem. Phys. {\bf 106}, 5526 (1997)], together with multipole representation of the crystal field [J. Chem. Phys. {\bf 107}, 10131 (1997)]. A periodic version of the hierarchical cubature algorithm [J. Chem. Phys. {\bf 113}, 10037 (2000)], which builds a telescoping adaptive grid for numerical integration of the exchange-correlation matrix, is shown to be efficient when the problem is posed as integration over the unit cell. Commonalities between the Coulomb and exchange-correlation algorithms are discussed, with an emphasis on achieving linear scaling through the use of modern data structures. With these developments, convergence of the $Γ$-point supercell approximation to the ${\bf k}$-space integration limit is demonstrated for MgO and NaCl. Linear scaling construction of the Fockian and control of error is demonstrated for RBLYP/6-21G* diamond up to 512 atoms.
A translationally invariant formulation of the Hartree-Fock (HF) $Γ$-point approximation is presented. This formulation is achieved through introduction of the Minimum Image Convention (MIC) at the level of primitive two-electron integrals, and implemented in a periodic version of the ONX algorithm [J. Chem. Phys, {\bf 106} 9708 (1997)] for linear scaling computation of the exchange matrix. Convergence of the HF-MIC $Γ$-point model to the HF ${\bf k}$-space limit is demonstrated for fully periodic magnesium oxide, ice and diamond. Computation of the diamond lattice constant using the HF-MIC model together with the hybrid PBE0 density functional [Theochem, {\bf 493} 145 (1999)] yields $a_0=3.569$Åwith the 6-21G* basis set and a $3\times3\times3$ supercell. Linear scaling computation of the HF-MIC exchange matrix is demonstrated for diamond and ice in the condensed phase
The recent work of Delabaere and Trinh (2000 J. Phys. A 33 8771) discovered the existence of ${\cal P}{\cal T}$-symmetry breaking, complex energy, $L^2$ solutions for the one dimensional Hamiltonian, $P^2+iX^3+iαX$, in the asymptotic limit, $α\to -\infty$. Their asymptotic analysis produced questionable results for moderate values of $α$. We can easily confirm the existence of ${\cal P}{\cal T}$-symmetry breaking solutions, by explicitly computing the low lying states, for $|α| < O (10)$. Our analysis makes use of the Multiscale Reference Function (MRF) approach, developed by Tymczak et al (1998 Phys. Rev. Lett. 80 3678; 1998 Phys. Rev. A 58, 2708). The MRF results can be validated by comparing them with the converging eigenenergy bounds generated through the Eigenvalue Moment Method, as recently argued by Handy (2001a,b). Given the reliability of the MRF analysis, its fast numerical implementation, high accuracy, and theoretical simplicity, the present formalism defines an effective and efficient procedure for analyzing many related problems that have appeared in the recent literature.
We devise a new and highly accurate quantization procedure for the inner product representation, both in configuration and momentum space. Utilizing the representation $Ψ(ξ) = \sum_{i}a_i[E]ξ^i R_β(ξ)$, for an appropriate reference function, $R_β(ξ)$, we demonstrate that the (convergent) zeroes of the coefficient functions, $a_i[E] = 0$, approximate the exact bound/resonance state energies with increasing accuracy as $i \to \infty$. The validity of the approach is shown to be based on an extension of the Hill determinant quantization procedure. Our method has been applied, with remarkable success, to various quantum mechanical problems.