Bulletin of the American Physical Society
2005 APS March Meeting
Monday–Friday, March 21–25, 2005; Los Angeles, CA
Session W34: Theory and Modeling |
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Sponsoring Units: DCP Chair: Mark Ratner, Northwestern University Room: LACC 511A |
Thursday, March 24, 2005 2:30PM - 2:42PM |
W34.00001: Density of States of Weakly Disordered Two-Dimensional Frenkel Excitons Nouredine Zettili, A. Boukahil The Coherent Potential Approximation (CPA) is used to study the optical properties of weakly disordered two-dimensional Frenkel exciton systems with nearest neighbor interactions. The transition frequencies are assumed to have Gaussian distribution. An approximate complex logarithmic Green's function for a square lattice with nearest neighbor interactions is used in the CPA self-consistent equation to determine the coherent potential. We show that the CPA results are in excellent agreement with previous numerical investigations. [Preview Abstract] |
Thursday, March 24, 2005 2:42PM - 2:54PM |
W34.00002: TDDFT approach with Gaussian Augmented Plane Waves Thomas Chassai, Marcella Iannuzzi, Juerg Hutter The calculation of the electronic structure of large systems ($100\div 1000$ atoms) by methods based on Density Functional Theory has recently gained a more central role. However, the extensive study of quantities like the excited states and related properties, are still out of reach, due to the high computational costs. We present the new implementation of a hybrid method, the Gaussian Augmented Plane Waves (GAPW) method, where the electronic density is partitioned in its hard and soft contributions. The former are local terms naturally expanded in a Gaussian basis, whereas the soft contributions are expanded in Plane Waves by using a low energy cutoff, without loss in accuracy, even for all electron calculations. For the calculation of the excitation energies a recently developed, time-dependent density functional response theory (TD-DFRT) technique is joined with the GAPW procedure. Given a system that is initially in the ground state, TD-DFRT derives the excitation energies from the linear response of the density to the perturbation produced by an external electrical field. We demonstrate the accuracy of the TD-DFRT-GAPW method by the comparison with other TDDFT approaches, for a set of small molecules. Our results converge very fast with the PW cutoff, which means that at the same level of accuracy we can afford much larger systems at feasible computational costs. All the implementations have been done in the framework of the CP2K program package (http://cp2k.berlios.de). [Preview Abstract] |
Thursday, March 24, 2005 2:54PM - 3:06PM |
W34.00003: Parametrization and performance appraisal of the analytic and variational X$\alpha$ method Rajendra Zope, Brett Dunlap The linear combination of atomic orbitals, analytic and variational implementation of Slater's X$\alpha $ method that allows arbitrary scaling of the exchange-correlation potential around each atom has been formulated. The method is numerical integration free, and thus delivers machine-precision energies that are stationary in all respects. One choice of scaling uses the $\alpha $s that give exact atomic energies. We present the results of a performance assessment of this method by calculating the atomization energies and total energies of the G2 and extended G2 sets of molecules. Similar calculations for uniform $\alpha $ are also appraised. Minimizing the mean absolute error in both the X$\alpha $ energies and the Hartree-Fock energies shows that Slater's exchange functional with $\alpha $ = 0.7091 performs significantly better than the G\'{a}sp\'{a}r-Kohn-Sham exchange functional for these molecules and for equally weighted atoms H-Kr. The Office of Naval Research, directly and through the Naval Research Laboratory, and the DoD's High Performance Computing Modernization Program, through the Common High Performance Computing Software Support Initiative, Project MBD-5, supported this work. The calculations were performed at the Army Research Laboratory Major Shared Resource Center (ARL MSRC). [Preview Abstract] |
Thursday, March 24, 2005 3:06PM - 3:18PM |
W34.00004: Density fluctuations in the geometric cluster algorithm Jiwen Liu, Nigel B. Wilding, Erik Luijten We have extended the recently-developed geometric cluster Monte Carlo algorithm\footnote{J. Liu and E. Luijten, Phys.\ Rev.Lett.\ \textbf{92}, 035504 (2004).} to study the critical properties of fluid systems. Density fluctuations are introduced by exchanging clusters of particles between two identical cells. This allows the system to decompose into two coexisting phases of different densities. We exploit a mapping on the grand-canonical order-parameter distribution function to systematically locate the critical point. The method is illustrated for the standard Lennard-Jones fluid. Remarkably, even away from the percolation threshold, our cluster algorithm is able to suppress critical slowing-down, leading to a considerable efficiency improvement compared to grand-canonical Monte Carlo simulations already at moderate system sizes. Owing to the non-local nature of the geometric cluster moves, we anticipate that our method becomes particularly advantageous in the study of critical properties of fluids containing components of widely different sizes. [Preview Abstract] |
Thursday, March 24, 2005 3:18PM - 3:30PM |
W34.00005: Density Functional Perturbation Theory on a real space grid Eugene Kadantsev, M. J. Stott The real space implementation of the density functional perturbation theory is reported in which the quantities of interest are defined on a uniform grid, the kinetic energy operator is computed using a high-order finite-difference formula and first principles pseudopotentials are used for the ion-electron interaction. The linear response is obtained on the real space grid. It is applied to calculation of vibrational frequencies and polarizabilities of localized molecular systems, and it is straightforward to use the response in other physical quantities. [Preview Abstract] |
Thursday, March 24, 2005 3:30PM - 3:42PM |
W34.00006: Long Range Charge-Transfer Excitations in Time-Dependent Density Functional Theory Neepa Maitra Long-range charge-transfer excited states are notoriously badly underestimated in time-dependent density-functional theory (TDDFT). Yet charge-transfer is an important and ubiquitous phenomena in, for example, biological molecules, which are large enough that TDDFT appears the only practical approach. In this talk, I discuss how charge-transfer excitations between open-shell species is accurately recovered in {\it exact} TDDFT: in particular, the role of the step in the ground-state potential, and the severe frequency-dependence of the exchange-correlation kernel. [Preview Abstract] |
Thursday, March 24, 2005 3:42PM - 3:54PM |
W34.00007: 3d R-matrix calculations of electron scattering from extended molecular systems Stefano Tonzani, Chris H. Greene We have implemented a three-dimensional finite element approach [S. Tonzani and C.H. Greene, { J. Chem. Phys. 014111} {\bf 122}, (2005)], to solve the Schr\"{o}dinger equation for scattering of a low energy electron from a molecule. 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 as a local density functional. A local polarization potential based on density functional theory [F. A. Gianturco and A. Rodriguez-Ruiz , { Phys. Rev. A} {\bf 47}, 1075 (1993)] approximately describes the long range attraction to the molecular target induced by the scattering electron without adjustable parameters. We have used this approach successfully in calculations of cross sections for small and medium sized molecules (like SF6, XeF6, C60 and Uracil). This method will be very useful to treat the electron-induced dynamics of larger molecular systems, possibly of biological interest, difficult to tackle with more complex ab initio methods. This work has been supported by DOE-Office of Science and NERSC. [Preview Abstract] |
Thursday, March 24, 2005 3:54PM - 4:06PM |
W34.00008: The Transcorrelated Method Combined with the Variational Monte Carlo Calculation: Application to Atoms Naoto Umezawa, Shinji Tsuneyuki, Takahisa Ohno, Kenji Shiraishi, Toyohiro Chikyow The transcorrelated (TC) method is a useful approach to optimize the Jastrow-Slater-type many-body wave function $FD$. The basic idea of the TC method [1] is based on the similarity transformation of a many-body Hamiltonian ${\cal H}$ with respect to the Jastrow factor $F$: ${\cal H}_{\rm TC}=frac{1}{F} {\cal H} F$ in order to incorporate the correlation effect into ${\cal H}_{\rm TC}$. Both the $F$ and $D$ are optimized by minimizing the variance $\sigma^2=\int |{\cal H}_{rm TC}D - E D |^2 d^{3N} x$. The optimization for $F$ is implemented by the variational Monte Carlo calculation, and $D$ is determined by the TC self-consistent-field equation for the one-body wave functions $\phi_{\mu}(x)$, which is derived from the functional derivative of $\sigma^2$ with respect to $\phi_{mu}(x)$. In this talk, we will present the results given by the transcorrelated variational Monte Carlo (TC-VMC) method for the ground state [2] and the excited states of atoms [3]. [1]S. F. Boys and N. C. Handy, Proc. Roy. Soc. A, {\bf 309}, 209; {\bf 310}, 43; {\bf 310}, 63; {\bf 311}, 309 (1969). [2]N. Umezawa and S. Tsuneyuki, J. Chem. Phys. {\bf 119}, 10015 (2003). [3]N. Umezawa and S. Tsuneyuki, J. Chem. Phys. {\bf 121}, 7070 (2004). [Preview Abstract] |
Thursday, March 24, 2005 4:06PM - 4:18PM |
W34.00009: Dynamics of the photoisomerization process of {\it trans} - azobenzene: a time-dependent density functional study Norihisa Oyama, Yoshitaka Tateyama, Yoshiyuki Miyamoto, Takahisa Ohno Azobenzene is a typical molecule which shows a reversible photoisomerization, and has attractive considerable attention for molecular devices. The photoisomerization mechanism of {\it trans} - azobenzene, however, has been controversial for over a half century because of its ultra-fast reaction. In this work, we investigated the dynamics of the photoisomerization process of {\it trans}- azobenzene based on time-dependent density functional theory. Our calculations clearly indi-cate that the photoisomerization process for S$_1$ excitation occurs through a rotation channel against the widely-accepted inversion mechanism. In contrast, it was found that a direct isomeriza- tion does not occur for S$_2$ excitation, and a transition to S$_1$ occurs at about 100fs. This study was supported by ACT- JST, and FSIS and Special Coordination Funds of MEXT of the Japanese government. The calculations in this work were carried out partly using the Numerical Materials Simulator in National Institute for Materials Science, and partly using the NEC-SX5 at Cybermedia Center, Osaka University. [Preview Abstract] |
Thursday, March 24, 2005 4:18PM - 4:30PM |
W34.00010: Calculation of the dynamics of nonadiabatic transitions with multiple vibrational modes Kunio Ishida, Keiichiro Nasu We propose a new calculation method of the dynamics of nonadiabatic transition which is applicable to study coherent control of photoisomerizations. We show that we can obtain a good approximation of the real dynamics of the system with less computational cost by switching fully quantum mechanical (QM) calculation and classical (CM) calculation at every time step by evaluating a ``switching factor'' defined by \begin{equation} \eta = \max_{\phi_i,z_i} |\langle z_1 e^{i\phi_1},z_2 e^{i\phi_2},...,z_N e^{i\phi_N}|U|\Phi \rangle|^2, \end{equation} where $N$ is the number of the vibrational modes relevant to the photoisomerization, and $|\Phi \rangle$ shows the quantum mechanical state each wavepacket in the system. $|z_1e^{i\phi_1},z_2 e^{i\phi_2},...,z_N e^{i\phi_N} \rangle$ and $U$ denote the coherent state in $N$-dimensional space and a translation operator, respectively. The switching rule is:\\ ``When $\eta$ exceeds a threshold value $\eta_c$, we perform a QM calculation, and {\it vice versa}.''\\ By choosing an appropriate value of $\eta_c$ we obtain a approximated wavefunction at each time step which well-reproduces that derived by QM calculation. [Preview Abstract] |
Thursday, March 24, 2005 4:30PM - 4:42PM |
W34.00011: Fast sampling in the slow manifold: The momentum-enhanced hybrid Monte Carlo method Ioan Andricioaei We will present a novel dynamic algorithm, the MEHMC method, which enhances sampling and at the same time yielding correct Boltzmann weighted statistical distributions. The gist of the MEHMC method is to use momentum averaging to identify the slow manifold and bias along this manifold the Maxwell distribution of momenta usually employed in Hybrid Monte Carlo. Several tests and applications are to exemplify the method. [Preview Abstract] |
Thursday, March 24, 2005 4:42PM - 4:54PM |
W34.00012: Correlated geminal wave function: a resonating valence bond approach for quantum chemistry Michele Casula, Claudio Attaccalite, Sandro Sorella We introduce a simple correlated wave function, obtained by applying a Jastrow term to an antisymmetrized geminal power (AGP). Both the geminal and the Jastrow play a crucial role in determining its accuracy: the former permits the correct treatment of the nondynamic correlation effects, the latter allows a very rapid convergence of the geminal expansion by fulfilling the cusp conditions. The remarkable feature of this approach is that many resonating valence bonds (RVB) can be dealt simultaneously with a single determinant, at a computational cost growing with the number of electrons similarly to more conventional methods, such as Hartree-Fock or Density Functional Theory. Recently several atoms$[1]$ and molecules$[2]$ have been studied by using the RVB wave function; we have always obtained total energies, bonding lengths and binding energies comparable with more demanding multi configurational schemes. This ansatz opens the possibility to perform fully ab initio calculations of complex correlated molecular systems. We present preliminary results on benzene dimer and active site analogues of sulfur-iron proteins, which are still challenging compounds for quantum chemistry methods. \begin{description} \item{[1]} M. Casula, S. Sorella, JCP 119, 6500 (2003) \item{[2]} M. Casula, C. Attaccalite, S. Sorella, JCP 121, 7110 (2004) \end{description} [Preview Abstract] |
Thursday, March 24, 2005 4:54PM - 5:06PM |
W34.00013: Molecular vibrations and the rotating Eckart frame of the ArHCl van der Waals complex Florence J. Lin By changing its shape while conserving angular momentum, a polyatomic molecule can return to its initial shape with a different orientation (as a ``falling cat'' or a diver can do). Floppy atom-diatomic molecule van der Waals complexes are excellent candidates in which to observe this. It is shown that large-amplitude ``internal'' motions of an atom-diatomic molecule van der Waals complex with zero total angular momentum can lead to overall rotation of the complex in the center-of- mass frame, i.e., the internal motion and overall rotation are coupled. Using geometric mechanics, the net angle of overall rotation is explicitly described in terms of Jacobi coordinates. The net angle of overall rotation is the sum of a dynamic phase plus a geometric phase; the latter is also described in terms of a gauge potential and, alternatively, molecular rotational constants. This is demonstrated by numerically integrating Hamilton's equations using a potential energy surface determined by fitting to experimental data for the ArHCl van der Waals complex. [Preview Abstract] |
Thursday, March 24, 2005 5:06PM - 5:18PM |
W34.00014: Collective diffusion in an ordered adsorbate: kinetic lattice gas model approach Zbigniew W. Gortel, Magdalena A. Za{\l}uska--Kotur An approach to microscopic kinetics of an interacting lattice gas is proposed to derive an algebraic expression for the coverage dependence of the collective diffusion coefficient in an adsorbate, ordered by strong adatom--adatom repulsive intractions, populating a square lattice of adsorption sites. The starting point are Markovian Master equations for the time dependent probabilities of all accessible microstates of the gas in which jumps of adatoms from occupied to empty adsorption sites are accounted for. The transition rates between the microstates depend on the occupancy state of the adsorption sites around the jumping adatom. The diffusion coefficient is extracted from the lowest eigenvalue of a non--hermitian rate matrix in the long wavelength limit. The eigenvalue is evaluated using an anzatz for the left and the right eigenvectors of the rate matrix with the adsorbate ordering inscribed into the structure of the eigenvectors. Analytic results which have not been obtained yet by any other method are validated by Monte Carlo simulations of the diffusion process. [Preview Abstract] |
Thursday, March 24, 2005 5:18PM - 5:30PM |
W34.00015: First-Principles Hartree-Fock-Roothaan Study of Ground State of Ozone including Many-Body Effects Shekhar Gurung, M.M. Aryal, D.D. Paudyal, D.R. Mishra, N.B. Maharjan, B. Dhakal, R.H. Scheicher, Junho Jeong, T.P. Das Earlier investigations\footnote{www.aps.org/meet/march03/H12.009} by our group on the ground state of Ozone molecule have shown a sensitive dependence of the binding energy on the size of the variational basis set used and the treatment of many-body effects. We have recently carried out new investigations using some of the most extensive basis sets available for Oxygen atom including many-body effects through both perturbation procedure upto fourth order and configuration interaction. Results will be discussed for the total energy, binding energy and geometry of the ground state and excitation energy for the singlet isomeric state with equilateral triangle structure. [Preview Abstract] |
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W34.00016: Spontaneous Quantum Electrical Dipole Predicted in Triangular Molecules Ryan Requist, Philip B. Allen, Alexander G. Abanov, Tunna Baruah Triangular symmetric molecules are forbidden by symmetry to have a fixed electrical dipole moment. However, with orbital degeneracy and an odd electron count yielding an electronically degenerate ground state (as in Na$_3$), a quantum dipole moment is shown to exist. Unlike the fixed dipole of a water molecule, the moment does not point in a fixed direction, but lies in the plane of the molecule and takes quantized values $\mu_0$ along any direction of measurement in the plane. An electric field $\vec{F}$ in the plane leads to a linear Stark splitting $\pm \mu_0 |\vec{F}|$. Linear Stark splittings are suppressed in low fields by molecular rotation, just as the linear Stark shift of water is suppressed, but will be revealed in moderately large applied fields and low temperatures. With an increasing barrier to the free periodic Jahn-Teller motion of the nuclei, there is a crossover from the quantum dipole to the classical dipole of a rigidly distorted triangular molecule. Density functional theory calculations for Na$_3$, a simple model system, suggest that its dipole is classical, because there is a large barrier that obstructs free Jahn-Teller motion. [Preview Abstract] |
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