Bulletin of the American Physical Society
APS March Meeting 2014
Volume 59, Number 1
Monday–Friday, March 3–7, 2014; Denver, Colorado
Session W26: Focus Session: Explicitly Correlated Methods and Quantum Few-Body Systems |
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Sponsoring Units: DCOMP Chair: Sergiy Bubin, University of Rochester Room: 502 |
Thursday, March 6, 2014 2:30PM - 3:06PM |
W26.00001: Applications of the Stochastic Variational Method Invited Speaker: Kalman Varga The variational method complemented with the use of explicitly correlated Gaussian basis functions is one of the most powerful approaches currently used for calculating the properties of few-body systems. Despite its conceptual simplicity, the method offers great flexibility, high accuracy, and can be used to study diverse quantum systems, ranging from small atoms and molecules to light nuclei, hadrons, quantum dots, and Efimov systems. One of the biggest computational issue is the optimal choice of basis parameters. The stochastic variational method is a random trial and error approach which proved to be very efficient in minimizing the variational energy. The basic computational foundations are discussed, recent advances in the applications of the stochastic variational method in physics and chemistry are reviewed, and the strengths and weaknesses of the explicitly correlated Gaussians approach are compared with other few-body techniques. [Preview Abstract] |
Thursday, March 6, 2014 3:06PM - 3:18PM |
W26.00002: Perspectives and Current the Development of Non-Born-Oppenheimer Atomic and Molecular Quantum Mechanical Variational Calculations using Explicitly Correlated Gaussian Basis Functions Keeper L. Sharkey The development of highly accurate theoretical quantum mechanics models for atomic and molecular calculations is crucial for the verification of the results of high-resolution experimental spectroscopy. High accuracy in the calculations can be achieved by not assuming the Born-Oppenheimer approximation (non-BO) and by using the variational principle. The non-relativistic Hamiltonian describing the internal state of the considered system used in the approach is obtained by separating out the center-of-mass motion from the laboratory frame Hamiltonian. The wave functions used in the calculations are expanded in terms of explicitly correlated Gaussian (ECG) functions. The optimization of the Gaussian non-linear parameters is aided by the analytical energy gradient determined with respect to these parameters. Examples of some very accurate calculations of small atoms and diatomic molecules will be presented. The presentation will also include a discussion of the extension of the approach to perform non-BO calculations of bound states of small triatomic molecules (e.g. H$_3^+$). [Preview Abstract] |
Thursday, March 6, 2014 3:18PM - 3:30PM |
W26.00003: Low-energy D-wave positronium-hydrogen scattering Denton Woods, P. Van Reeth, S.J. Ward We are investigating the four-body Coulomb process of positronium-hydrogen (Ps-H) scattering below the Ps(n=2) excitation threshold using the Kohn variational method and variants. Our Ps-H $^1D$-wave phase shifts compare reasonably well with the close-coupling results [1,2], but our $^3D$-wave phase shifts are appreciably lower. In an attempt to improve the accuracy of these, we are employing a sectors-based approach [3] and the modification of the short-range Hylleraas terms with an exponential in the $r_{12}$ coordinate. We are investigating the use of the Born approximation for higher partial waves. We plan also to present our latest S-wave and P-wave results using the Kohn variational method [4]. \\[4pt] [1] H.R.J. Walters \emph{et al}, Nucl. Instrum. Methods B \textbf{221}, 149-159 (2004).\\[0pt] [2] J. Blackwood \emph{et al}, Phys. Rev. A \textbf{65}, 032517 (2002).\\[0pt] [3] Zong-Chao Yan and Y.K. Ho, Phys. Rev. A \textbf{59}, 2697 (1999).\\[0pt] [4] Denton Woods, S. J. Ward and P. Van Reeth, http://meetings.aps.org/link/BAPS.2013.DAMOP.Q1.122 (and references within). [Preview Abstract] |
Thursday, March 6, 2014 3:30PM - 4:06PM |
W26.00004: Asymptotic Expansions, 1/Z Expansions, and the Critical Nuclear Charge Invited Speaker: Gordon Drake The quantum mechanical three-body problem defies analytic solution, and so computationally intensive approximation methods involving, for example, variational calculations with large correlated basis sets must be used. This talk will review recent work to explore the outer fringes of the quantum mechanical three-body problem for heliumlike atoms. Asymptotic expansions provide a surprisingly simple and accurate account of highly excited Rydberg states with high angular momentum. $1/Z$ expansions, where $Z$ is the nuclear charge, provide results for an entire isoelectronic sequence within a single calculation. Its radius of convergence is thought to be related to the critical nuclear charge $Z_c$ for a state to be bound. For $Z < Z_c$, there may still be quasibound states (shape resonances) imbedded in the scattering continuum. Relationships amongst all three topics will be discussed, and new results presented for both asymptotic expansions and the critical nuclear charge. [Preview Abstract] |
Thursday, March 6, 2014 4:06PM - 4:18PM |
W26.00005: Stability of positron--atom complexes in ground and excited states Sergiy Bubin, Oleg Prezhdo Using a variational method with an explicitly correlated Gaussian basis set we have studied the stability of weakly bound positron--atom complexes in the ground and lowest excited states with higher spin multiplicity. Our calculations provide rigorous theoretical confirmation that a positron can be attached to the lowest quartet state of Li and triplet state of Be. The result is particularly notable for the positron--Be complex, as the excited triplet state lies below the autoionization threshold. The simultaneous existence of the ground and meta-stable excited states of positronic Li and Be opens up new possibilities for the experimental detection of positron--atom complexes. [Preview Abstract] |
Thursday, March 6, 2014 4:18PM - 4:30PM |
W26.00006: Challenges in calculating molecular systems with Coulomb interactions Nikita Kirnosov, Keeper Sharkey, Ludwik Adamowicz The highly accurate quantum mechanical calculations are not only crucial for high-resolution experimental data verification, but may also serve as a guide in the field of exotic systems exploration. Including all non-relativistic effects in a single-step variational approach and rigorously separating out the center of mass motion allows us to build a reliable model for calculating bound states of molecular systems with Coulomb interactions. In these calculations the wave function of the system is expanded in terms of explicitly correlated Gaussian (ECG) basis functions. Examples of calculations of energies and other properties of some molecular systems will be presented. [Preview Abstract] |
Thursday, March 6, 2014 4:30PM - 4:42PM |
W26.00007: Developments for a Relativistic Four-Component Many-1/2-Fermion Theory Benjamin Simmen, Edit M\'atyus, Markus Reiher Explicitly correlated configuration interaction methods have proven to be highly successful in the study of non-relativistic many-electron systems. They are also suited for pre-Born--Oppenheimer calculations where nuclei and electrons are treated on equal footing. Relativistic quantum chemistry is based on the no-pair approximation and provides a four-component Hamiltonian capturing the essential aspects of special relativity for molecular systems. Two fundamental issues arise when aiming at four-component pre-Born--Oppenheimer calculations. The concept of a center of mass cannot be exploited for the Dirac--Coulomb Hamiltonian: It is not possible to separate the overall motion of the system through a linear transformation of the one-particle Cartesian coordinates [1]. Second, a finite number of basis functions leads to an artificial decrease of the bound state energies since the Dirac--Coulomb Hamiltonian is not bounded from below [2]. Kinetic balance solves this for Slater determinants, but its explicitly correlated variant is considerably more involved.\\[4pt] [1] B. Simmen, E. M\'atyus, M. Reiher; Mol. Phys. 111; 2086 (2013)\\[0pt] [2] B. Simmen, M. Reiher; In: Many-Electron Approaches in Physics, Chemistry and Mathematics; Eds.: V. Blum, L. Delle Site; Springer (in press); (2014) [Preview Abstract] |
Thursday, March 6, 2014 4:42PM - 4:54PM |
W26.00008: Correlation-bound anion states Vamsee Voora, Kenneth Jordan In a correlation-bound anion, the excess electron is bound to the molecule in a diffuse non-valence orbital and electron correlation is crucial for the electron binding. Examples of such anions include Xe$_{\mathrm{n}}^{\mathrm{-}}$ clusters and certain (H$_{\mathrm{2}}$O)$_{\mathrm{n}}^{\mathrm{-}}$ clusters. Using many-body methods we have characterized correlation-bound anion states of C$_{\mathrm{60}}$, C$_{\mathrm{6}}$F$_{\mathrm{6}}$ and several large acenes. The correlation-bound anion states of these species are related to the image potential states of graphene. Modeling correlation-bound anion states presents challenges for \textit{ab initio }approaches. Hartree-Fock based approaches such as MP2 and CCSD fail to describe these states. The key to treating these species theoretically is to employ a method that allows the singly occupied orbital to relax in the presence of the long-range correlation effects. A model potential approach accounting for image effects for describing the binding of the excess electron will be presented for C$_{\mathrm{60}}$. [Preview Abstract] |
Thursday, March 6, 2014 4:54PM - 5:06PM |
W26.00009: Particle Number Conserving Approach to the Collective States in a Small Fermi-System Jennifer Glick, Vladimir Zelevinsky The standard Bardeen-Cooper-Schrieffer (BCS) description of pairing theory, random phase approximation (RPA) and Hartree-Fock-Bogoliubov (HFB) methods, routinely used in macroscopic many-body physics when the dimension of the Hamiltonian matrix is prohibitively large, include features which are not well suited to describe mesoscopic systems such as nuclei or cold atoms in traps. Two important disadvantages are the non-conservation of exact particle number through the introduction of quasiparticles, and the absence of a non-trivial paired solution in the discrete spectrum with weak pairing. We develop the pairing theory based on the exact particle number conservation, whose first applications to the ground state physics presented in [A. Volya and V. Zelevinsky, in {\sl 50 Years of Nuclear BCS}, World Scientific, 2012] demonstrated that such an approach avoids well known deficiencies of the standard treatment, especially in the region of weak pairing. Now, we use the method for low-lying collective excitations which in many cases are even more sensitive to conservation laws. We show that the RPA version based on solving the operator equations of motion is reduced to the set of recurrence relations for neighboring systems which precisely conserve the exact particle number. [Preview Abstract] |
Thursday, March 6, 2014 5:06PM - 5:18PM |
W26.00010: Nearly-exact calculation of chromium dimer binding with auxiliary-field quantum Monte Carlo Wirawan Purwanto, Shiwei Zhang, Henry Krakauer The binding of the strongly correlated Cr$_2$ molecule has long resisted accurate theoretical description, and Cr$_2$ has become a landmark test for many-body computational methods. We first performed exact auxiliary-field quantum Monte Carlo (AFQMC) calculations using a moderately-sized basis set. In parallel, phaseless AFQMC\footnote{% Zhang and Krakauer, \textit{Phys. Rev. Lett.} \textbf{90}, 136401 (2003)} calculations were carried out using the same and larger basis sets to remove the finite-basis errors from the exact AFQMC calculations. Results on Cr$_2$ ground-state properties, including binding energy, equilibrium distance, and vibrational frequency, are in excellent agreement with experiment. [Preview Abstract] |
Thursday, March 6, 2014 5:18PM - 5:30PM |
W26.00011: Imaginary-time nonuniform mesh method for solving the multidimensional Schr\"odinger equation Alberto Hernando de Castro, Jiri Vanicek An imaginary-time nonuniform mesh method for diagonalizing multidimensional quantum Hamiltonians is proposed and used to find the first 50 eigenstates and energies of up to $D=5$ strongly interacting spinless quantum Lennard-Jones particles trapped in a one-dimensional harmonic potential. We show that the use of tailored grids allows exploiting the symmetries of the system---in our case the $D!$ degeneracy derived from all possible permutations of distinguishable particles---reducing drastically the computational effort needed to diagonalize the Hamiltonian. This leads to a favorable scaling with dimensionality, requiring for the 5-dimensional system four orders of magnitude fewer grid points than the equivalent regular grid. Solutions to both bosonic and fermionic counterparts of this strongly interacting system are constructed, the bosonic case clustering as a Tonks-Girardeau crystal exhibiting the phenomenon of fermionization. The numerically exact excited states are used to describe the melting of this crystal at finite temperature. [Preview Abstract] |
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