Bulletin of the American Physical Society
APS March Meeting 2011
Volume 56, Number 1
Monday–Friday, March 21–25, 2011; Dallas, Texas
Session Q40: Theoretical Methods and Algorithms for Chemical Physics |
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Sponsoring Units: DCP Chair: Donald Truhlar, University of Minnesota Room: A122/123 |
Wednesday, March 23, 2011 11:15AM - 11:27AM |
Q40.00001: Primordial Particles; Collisions of Inelastic Particles George Sagi Three-dimensional matter is not defined by Euclidian or Cartesian geometries. Newton's and Einstein's laws are related to the motions of elastic masses. The study of collisions of inelastic particles opens up new vistas in physics. The present article reveals how such particles create clusters composed of various numbers of particles. The Probability of each formation, duplets, triplets, etc. can be calculated. The particles are held together by a binding force, and depending upon the angles of collisions they may also rotate around their center of geometry. Because of these unique properties such inelastic particles are referred to as primordial particles, Pp. When a given density of Pp per cubic space is given, then random collisions create a field. The calculation of the properties of such primordial field is very complex and beyond the present study. However, the angles of collisions are infinite in principle, but the probabilities of various cluster sizes are quantum dependent. Consequently, field calculations will require new complex mathematical methods to be discovered yet. [Preview Abstract] |
Wednesday, March 23, 2011 11:27AM - 11:39AM |
Q40.00002: Aggregation of Thermal Particles in Simulation Iat Neng Chan Based on the Schrodinger Equation, energy levels are evaluated for charged particle or atom surrounded by few atoms imitated to atomic cavity situations under multipole or Lennard-Jones interactions. To examine the states of corresponding eigenvalues, the associated wave functions from simulation are plotted in three-dimension to elucidate the space distribution of particles. In cases for testing on effect of different adjacent atomic structures, concentration region of distribution is revealed from a series of results. The range of localization shown also is affected by the type and strength of interactions between particles and atoms, besides the number and position of surrounding atoms. The thermal effect considered in the computation is modeled by average over results from random fluctuation of atom positions for a given heating grade. Moreover, analysis with fuzzy conditions is applied to reduce the complicated and time-consumption approach, also for the training in science education. Even the investigation is limited and tentative, qualitative studies on different parameters and structures can provide the influence of factors and approximate information to compare with the experience evidences. [Preview Abstract] |
Wednesday, March 23, 2011 11:39AM - 11:51AM |
Q40.00003: Many Body Density Matrix Theory C.J. Tymczak One fundamental limitation of quantum chemical methods is the accuracy of the approximate many-body theoretical framework. Accurate many-body formalisms for quantum chemical methods do exist, but these methods are computationally very expensive. Methods also exist that are much less computationally expensive such as Hatree-Fock, Density Functional and the Hybrid Functional theories, but at a reduced representation of the exact many-body ground state. This severely limits either the system size that can be addressed accurately, or the accuracy of the representation. What is needed is a method that represents the many-body ground states accurately, but with a low computational cost. Recently, a method for determining the response, to any order of the perturbation, within the density matrix formalism has been discovered. This method opens up the possibility of computing the variational many-body ground states to unprecedented accuracy within a simplified computational approach. We report on the theoretical development of this methodology, which we refer to as Many Body Density Matrix Theory. This theory has many significant advantages over existing methods. One, its computational cost is equivalent to Hartree-Fock or Density Functional theory. Two it is a variational upper bound to the exact many-body ground state energy. Three, like Hartree-Fock, it has no self-interaction. And four, it is size extensive. [Preview Abstract] |
Wednesday, March 23, 2011 11:51AM - 12:03PM |
Q40.00004: Probing the Surface-to-Bulk Transition: A Closed-Form, Constant-Scaling Algorithm for Computing Subsurface Green Functions Matthew Reuter, Tamar Seideman, Mark Ratner A closed-form algorithm for computing subsurface Green functions---the blocks of a material's Green function between the surface and the bulk---is presented, where we assume the system satisfies a common principal layer approximation. By exploiting the block tridiagonal and nearly block Toeplitz structure of the Hamiltonian and overlap matrices, this method scales independently of the system size (constant scaling), allowing studies of large systems. As a proof-of-concept example, we investigate the decay of surface effects in an armchair graphene nanoribbon, demonstrating the persistence of surface effects hundreds of atomic layers ($\sim$0.5 $\mu$m) away from a surface. We finally compare the surface-to-bulk transitions of finite and semi-infinite systems, finding that finite systems exhibit amplified surface effects. [Preview Abstract] |
Wednesday, March 23, 2011 12:03PM - 12:15PM |
Q40.00005: Projecting the phase-space trajectory of multidimensional non-equilibrium systems onto a discrete set of states: a Projective Dynamics approach Katja Schaefer, M.A. Novotny Phase-space trajectories, which are either continuous or possess small discontinuities, can be projected onto a discrete set of states with nearest neighbor coupling. The pointwise projection leads for non- equilibrium system to a non-Markovian process, even if the dynamics of the original system is Markovian. However, using time-averaged transition-rates a Markov process can be obtained, which has the same overall properties as the original dynamics of the system. The projected process defines a new dynamics, which only in the limit $t\rightarrow \infty$ obtains the property on the time-scale of the averaging procedure. We demonstrate the Projective Dynamics method in theory and applications to absorption processes, which in general are not describable through equilibrium or steady-state models. We show the discrete set of states $\{\zeta_k\}$ can be chosen arbitrarily (with slight restrictions) for all systems. [Preview Abstract] |
Wednesday, March 23, 2011 12:15PM - 12:27PM |
Q40.00006: Finding lowest saddle point Qing Lu, Minghai Li, Akihiro Kushima, Xi Lin A history-penalized basin filling algorithm is presented in this work which identifies the lowest saddle point starting from any given initial state on any given potential energy hypersurface. The natural analogy of this algorithm is filling a barrel with water; by monitoring the location where leakage occurs one identifies the lowest opening on the wall of the barrel. The successful implementation of this algorithm relies on insightful choices of the penalty function, penalty function combination, and peak refinement. Several types of penalty functions are implemented to study two classical systems, the ad-cluster surface diffusion and supercooled binary Lennard-Jones liquid, and one quantum system of the topological soliton migration. The most efficient penalty function is found to be a triangle penalty function with uniform forces and large 3N+1-dimensional volume. The combination of penalty functions dramatically improves the computational efficiency. The lowest saddle point can be precisely located by the basin filling algorithm coupled with a few standard peak-refinement methods. [Preview Abstract] |
Wednesday, March 23, 2011 12:27PM - 12:39PM |
Q40.00007: The Reaction of Carbon Dioxide with Water Clusters: an Ab Initio Metadynamics Study Gregoire Gallet, Fabio Pietrucci, Wanda Andreoni Simulations are often invoked as aid to understand and optimize carbon capture and sequestration processes. The hydration of carbon dioxide (CO$_{2})$ offers an excellent test case for assessing the reliability of computational schemes. We present a density-functional-theory study of the reaction of CO$_{2}$ with water clusters. The first step was to validate DFT results in different approximations of the exchange and correlation functional with respect to quantum chemical methods for the structure, binding energies and vibrational frequencies of several isomers. Next, simulations of the reactions leading to the formation of carbonic acid were performed using metadynamics as accelerating procedure. This method allows us both to identify the reaction mechanisms and to obtain an estimate of the free energy barriers via the reconstruction of the free energy profiles. Comparisons were drawn with previous static calculations of the barriers. As reference, a similar calculation in liquid water will be presented. [Preview Abstract] |
Wednesday, March 23, 2011 12:39PM - 12:51PM |
Q40.00008: Triplet Pairing and Odd-Electron Densities in Constrained-Pairing Mean-Field Theory Jason K. Ellis, Carlos A. Jimenez-Hoyos, Gustavo E. Scuseria Describing strong (also known as static or non-dynamical) correlation caused by degenerate or nearly degenerate orbitals near the Fermi level remains a theoretical challenge, particularly in molecular systems. Constrained-pairing mean-field theory (CPMFT) has been quite successful capturing the effects of static correlation in bond formation and breaking in closed- shell molecular systems. This method uses singlet electron entanglement to model static correlation at \textit{mean field} cost. The present work extends the previous formalism to include triplet pairing, allowing a description of same-spin correlation and open-shell species. Additionally, a spin-orbital extension of the ``odd-electron'' formalism of Yamaguchi and co-workers is presented as a method for understanding triplet radical character in molecules. Results from representative systems are presented. [Preview Abstract] |
Wednesday, March 23, 2011 12:51PM - 1:03PM |
Q40.00009: Dynamical Mean-Field Theory for Quantum Chemistry Nan Lin, Chris Marianetti, Andrew Millis, David Reichman The dynamical mean-field concept of approximating an unsolvable many-body problem in terms of the solution of an auxiliary quantum impurity problem, introduced to study bulk materials with a continuous energy spectrum, is here extended to molecules, i.e. finite systems with a discrete energy spectrum. Application to chains and small clusters of hydrogen atoms yields ground state energies which are competitive with leading quantum chemical approaches at intermediate and large interatomic distances, and provides good approximations to the excitation spectrum. The method is a promising approach to the strong correlation problems of quantum chemistry. [Preview Abstract] |
Wednesday, March 23, 2011 1:03PM - 1:15PM |
Q40.00010: Constrained Active Space Unrestricted Mean-Field Approaches for Controlling Spin-Contamination Takashi Tsuchimochi, Gustavo E. Scuseria We have recently shown that unrestricted Hartree-Fock (UHF) variationally reduces to high-spin restricted open-shell Hartree-Fock when constraints are imposed on the eigenvalues of the spin density matrix [T. Tsuchimochi and G. E. Scuseria, J. Chem. Phys. {\bf 133}, 141102 (2010)]. We here generalize these ideas and propose to control spin-contamination in UHF by releasing the constraints in an active space while imposing them elsewhere. If the active space is properly chosen, our constrained UHF (CUHF) method greatly benefits from a controlled broken-symmetry effect while avoiding the massive spin contamination arising in the traditional UHF. We apply L$\rm{\ddot{o}}$wdin's projection operator to CUHF and obtain multireference wave functions with moderate computational cost. We report results on singlet-triplet energy gaps to show that our constrained scheme outperforms fully unrestricted methods. This constrained approach can be readily used in Kohn-Sham (KS) density functional theory with similar favorable effects, provided that spin-contamination is given by the KS orbitals as in UHF. [Preview Abstract] |
Wednesday, March 23, 2011 1:15PM - 1:27PM |
Q40.00011: Nuclear quantum effects using selective mode excitation in water Sriram Ganeshan, Marivi Fernandez-Serra Recently, Ceriotti et. al. [1] introduced a comprehensive framework to use a custom-tailored Langevin equation with correlated-noise in the context of MD simulations. One of the interesting applications of these thermostats is that, such a framework can be used to selectively excite normal modes whose frequency falls within a prescribed, narrow range [2]. The general idea of this work is to understand whether, the selective excitation of modes in some systems like water is enough to reproduce the necessary nuclear quantum effects at a given temperature. Ceriotti et. al has also implemented their colored noise thermostat (Langevin) to the PIMD of TIP4P/F model [3]. In this work we study how the TIP4P/f responds to the selective mode excitation using the delta-thermostats. We apply this delta thermostat to the molecular dynamics of TIP4P/F [4] water force field, a model explicitly fitted with the lack of zero point ionic vibrations. TIP4P/F provides us an ideal platform to study the effect of selective mode excitation on water. We address the question of whether selective mode excitations are enough to generate the nuclear quantum effects in water. This work will also provide a way to identify the dominant modes for which the quantum effects are important. [1] Chem. Theory Comput.6, 1170 (2010) [2] Proc. Comp. Sci. 1, 1601 (2010), [3] J. Chem. Phys. 131, 024501 (2009), [4] J. Chem. Phys 133, 124104 (2010). [Preview Abstract] |
Wednesday, March 23, 2011 1:27PM - 1:39PM |
Q40.00012: \textit{Ab Initio} Composite Methods Angela Wilson, Wanyi Jiang, Gbenga Oyedepo, Marie Laury In this brief presentation, we highlight recent developments of the \textit{ab initio} composite method, the correlation consistent Composite Approach (ccCA). Recent work has enabled ccCA to be utilized for 3d transition metals, as well as for species for which a multireference wavefunction is required. We overview the development, as well as applications of the method to the prediction of spectroscopic and thermodynamic properties of molecules. [Preview Abstract] |
Wednesday, March 23, 2011 1:39PM - 1:51PM |
Q40.00013: Distortion of scanning-tunnelling-spectroscopy images of isolated molecules induced by electron correlation Massimo Rontani, Dimitrios Toroz, Stefano Corni Scanning tunnelling spectroscopy (STS) visualizes electron states in both extended systems and nano-objects, as quantum dots and molecules. Whereas bulk quantum states are insensitive to electron number fluctuations, an energy gap opens each time a new electron is injected by the STS tip into a sufficiently small system. This gap originates from the interaction of the next incoming electron with the others already present in the system. In this Coulomb blockade regime a fundamental question is whether the wave function of the ``quasi-particle'' added to the system -imaged by the STS tip- is sensitive to electron-electron interaction. Here we show that the STS images of single planar molecules with metal centres predicted by ab initio many-body calculations differ qualitatively from their uncorrelated counterparts. We find in the maps resolved at the Fermi energy that correlation significantly removes spectral weight from the metal atom, as well as the overall weight is remarkably reduced. This change may be measured and compared with STS images of molecules without the metal center, whose many-body and uncorrelated versions are alike. [Preview Abstract] |
Wednesday, March 23, 2011 1:51PM - 2:03PM |
Q40.00014: Maximizing the hyperpolarizability poorly determines the potential Rolfe Petschek, Timothy Atherton, Joseph Lesnefsky, Greg Wiggers Increasing the non-linear response of materials to an electric field, characterized by quantities such as the first hyperpolarizibility $\beta$, is a mattter of importance for applications. We optimized the zero frequency $\beta$ of a one-dimensional potential well containing a single electron by freely adjusting the shape of that potential. It is shown that with careful optimization the maximum hyperpolarizability converges quickly with increasing numbers of parameters in the potential to approximately 0.708951 of the proven upper bound. The Hessian of $\beta$ at the maximum makes it clear that there is a very wide range of nearby, nearly optimal potentials: with several measures of differences between potentials, this Hessian has only two large eigenvalues with the others diminishing quickly. The optimum potentials are substantially different and more affected by small eigenvectors than the wavefunctions. Thus, wavefunctions are superior for describing the conditions that optimize the hyperpolarizability. Prospects for a concise description of the two important constraints on near-optimum potentials and wavefunctions are discussed. [Preview Abstract] |
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