Bulletin of the American Physical Society
APS March Meeting 2016
Volume 61, Number 2
Monday–Friday, March 14–18, 2016; Baltimore, Maryland
Session V20: Explicitly Correlated Methods and Quantum FewBody SystemsFocus

Hide Abstracts 
Sponsoring Units: DMP DCOMP Chair: Sergiy Bubin, Nazarbayev University Room: 319 
Thursday, March 17, 2016 2:30PM  3:06PM 
V20.00001: Possibilities of the freecomplement methodology for solving the Schrödinger equation of atoms and molecules Invited Speaker: Hiroshi Nakatsuji Chemistry is a science of complex subjects that occupy this universe and biological world and that are composed of atoms and molecules. Its essence is diversity. However, surprisingly, whole of this science is governed by simple quantum principles like the Schrödinger and the Dirac equations. Therefore, if we can find a useful general method of solving these quantum principles under the fermionic and/or bosonic constraints accurately in a reasonable speed, we can replace somewhat empirical methodologies of this science with purely quantum theoretical and computational logics. This is the purpose of our series of studies  called “exact theory” in our laboratory. Some of our documents are cited below [18]. The key idea was expressed as the free complement (FC) theory (originally called ICI theory [3]) that was introduced to solve the Schrödinger and Dirac equations analytically. For extending this methodology to larger systems, order N methodologies are essential, but actually the antisymmetry constraints for electronic wave functions become big constraints. Recently [8], we have shown that the antisymmetry rule or `dogma' can be very much relaxed when our subjects are large molecular systems. In this talk, I want to present our recent progress in our FC methodology. The purpose is to construct “predictive quantum chemistry” that is useful in chemical and physical researches and developments in institutes and industries. [1] H. Nakatsuji, Acc. Chem. Res. 45, 1480 (2012). [2] H. Nakatsuji and H. Nakashima, TSUBAME eScience J. 11, 8, 24 (2014). [3] H. Nakatsuji, Phys. Rev. Lett. 93, 030403 (2004). [4] H. Nakatsuji and H. Nakashima, Phys. Rev. Lett. 95, 050407 (2005). [5] H. Nakatsuji, et al, Phys. Rev. Lett. 99, 240402 (2007). [6] H. Nakatsuji and H. Nakashima, J. Chem. Phys.142, 084117 (2015). [7] H. Nakashima and H. Nakatsuji, J. Chem. Phys. 139, 044112 (2013). [8] H. Nakatsuji and H. Nakashima, J. Chem. Phys. 142, 194101 (2015). [Preview Abstract] 
Thursday, March 17, 2016 3:06PM  3:18PM 
V20.00002: Natural generalization of Slater determinants to more than one dimension Denis Sunko The calculation of realistic $N$body wave functions for identical fermions is still an open problem in physics, chemistry, and materials science, even for $N$ as small as two. Here a fundamental algebraic structure of manybody Hilbert space is described, enabling theoretically wellfounded systematic investigation of wavefunction space. The structure allows an arbitrary manyfermion wave function to be written in terms of a finite number of antisymmetric functions called shapes, which cannot be constructed by combining onedimensional wave functions. Shapes naturally generalize the singleSlaterdeterminant form for the ground state to more than one dimension. Their number is exactly $N!^{d1}$ in $d$ dimensions. A general algorithm is given to list them all in terms of standard Slater determinants. Conversely, excitations which can be induced from the onedimensional case are bosonised into a system of distinguishable bosons, called Euler bosons, much like the electromagnetic field is quantized in terms of photons distinguishable by their wave numbers. Their wave functions are given explicitly in terms of elementary symmetric functions, reflecting the fact that the fermion sign problem is trivial in one dimension. The shapes are all possible vacua for the Euler bosons. [Preview Abstract] 
Thursday, March 17, 2016 3:18PM  3:30PM 
V20.00003: Configuration space method for calculating binding energies of exciton complexes in quasi1D/2D semiconductors. Igor Bondarev A configuration space method, pioneered by Landau and Herring in studies of molecular binding and magnetism[1], is developed to obtain universal asymptotic relations for lowest energy exciton complexes (trion, biexciton) in confined semiconductor nanostructures such as nanowires and nanotubes[2], as well as coupled quantum wells. Trions are shown to be more stable (have greater binding energy) than biexcitons in strongly confined quasi1D structures with small reduced electronhole masses. Biexcitons are more stable in less confined quasi1D structures with large reduced electronhole masses. The theory predicts a crossover behavior, whereby trions become less stable than biexcitons as the transverse size of the quasi1D nanostructure increases, which might be observed on semiconducting carbon nanotubes of increasing diameters. This method is also efficient in calculating binding energies for triontype electronhole complexes formed by indirect excitons in double coupled quantum wells, quasi2D nanostructures that show new interesting electroabsorption/refraction phenomena.  [1]Landau {\&} Lifshitz, Quantum Mechanics; C.Herring, RMP 34, 631 (1962). [2]I.V.Bondarev, PRB 90, 245430 (2014); PRB 83, 153409 (2011). [Preview Abstract] 
Thursday, March 17, 2016 3:30PM  3:42PM 
V20.00004: Tests for Wavelets as a Basis Set Thomas Baker, Glen Evenbly, Steven White A wavelet transformation is a special type of filter usually reserved for image processing and other applications. We develop metrics to evaluate wavelets for general problems on test onedimensional systems. The goal is to eventually use a wavelet basis in electronic structure calculations. We compare a variety of orthogonal wavelets such as coiflets, symlets, and daubechies wavelets. We also evaluate a new type of orthogonal wavelet with dilation factor three which is both symmetric and compact in real space. [Preview Abstract] 
Thursday, March 17, 2016 3:42PM  4:18PM 
V20.00005: How competitive are expansions in orbital products with explicitly correlated expansions Invited Speaker: Krzysztof Szalewicz Helium dimer potential is of great importance for metrology since several future measurement standards will be based on helium gas. Such potential can be used to predict all thermodynamic properties of diffuse helium gas (nonadditive threebody potential is needed for higher densities). The accuracy required by these standards is so high, that in the past work of our group we had to include nonadiabatic, relativistic, and quantum electrodynamics effects. The current state is that the largest contribution to the uncertainty of the helium dimer potential is due to the BornOppenheimer (BO) part of this potential. This uncertainty was reduced and became comparable to other uncertainties in the new calculations that will be presented. These calculations used explicitly correlated Gaussian (ECG) basis sets and represent nearly exact solutions of the Schr\"odinger equation in the BO approximation. Similar calculations were also performed in orbital basis sets using a multilevel approach up to the full configuration interactions level. Largest existing basis sets were used at each level so that our calculations represent the best results that can currently be obtained using orbitals. These results will be critically compared with those obtained using ECG bases. [Preview Abstract] 
Thursday, March 17, 2016 4:18PM  4:30PM 
V20.00006: New Types of Explicitly Correlated Gaussian Functions for NonBornOppenheimer Molecular? Calculations. Martin Formanek, Keith Jones, Sergiy Bubin, Ludwik Adamowicz In this work we explore the possibility of using a new functional form of Explicitly Correlated Gaussiantype functions (ECGs) for performing nonBornOppenheimer calculations of diatomic molecular systems. Namely we focus our attention on ECGs with preexponential factors in the form of sin/cos functions of the square of the internuclear distance (sin/cosECGs). These ECGs can be generated as linear combinations of ECGs with complex exponential parameters (complexECGs) The complexECGs were previously used to calculate energy levels of He atom [1] and with the sin/cosECGs the vibrational energy levels for the H$_2$ molecule described by an effective Morse potential were calculated [2]. The focus of this study is abinitio description of a real diatomic molecule, namely HD$^+$, within the framework where the BO approximation is not assumed using these basis sets. The aim is to compare their accuracy and efficiency with ECGs with preexponential factors in the form of even powers of the internuclear distance and to assess their potential usefulness in nonBO calculations of molecules with more than two nuclei. [1] S. Bubin and L. Adamowicz, J. Chem. Phys. 124, 224317 (2006) [2] M. Formanek, K.L. Sharkey, N. Kirnosov and L. Adamowicz, J. Chem. Phys. 141, 154103 (2014) [Preview Abstract] 
Thursday, March 17, 2016 4:30PM  4:42PM 
V20.00007: Complex explicitly correlated Gaussians for nonBornOppenheimer calculations of small molecules Sergiy Bubin, Ludwik Adamowicz NonBornOppenheimer calculations of molecular systems, where all particles are properly treated on an equal footing, represents a big challenge for the theory. Due to the huge difference in the masses of the electrons and nuclei the latter move more slowly and their correlation functions have distinct localization around the equilibrium internuclear separations. This feature is hard to implement in explicitly correlated variational approaches with Gaussian type basis functions while maintaining an analytic integrability of all necessary matrix elements. In this work we demonstrate that the difficulties can be overcome by using complex Gaussians. In our benchmark calculations on HD$^+$ molecular ion we have achieved excellent performance of this simple complex basis set that is on par or better than what was seen in previous NonBO calculations of small diatomic molecules. [Preview Abstract] 
Thursday, March 17, 2016 4:42PM  4:54PM 
V20.00008: How Large are Nonadiabatic Effects in Atomic and Diatomic Systems? Yubo Yang, Ilkka Kylanpaa, Norm Tubman, Jaron Krogel, Sharon HammesSchiffer, David Ceperley We have developed a fixednode quantum Monte Carlo method to simulate atoms and molecules without the BornOppenheimer approximation with sub milliHartree accuracy [1]. For this purpose, we construct trial wave functions with nodes that depend on both the electronic and ionic positions. We report groundstate energies and the ionization energies for the firstrow atoms and atomization energies for the firstrow hydrides. The latter show effects of the nonadiabatic coupling between electrons and nuclei. We discuss how the method scales to larger systems. [1] Y. Yang, I. Kyl\"{a}np\"{a}\"{a}, N. M. Tubman, J. T. Krogel, S. HammesSchiffer, D. M. Ceperley, J. Chem. Phys. \textbf{143}(12), 2015. [Preview Abstract] 
Thursday, March 17, 2016 4:54PM  5:06PM 
V20.00009: The structure of the secondorder nonBornOppenheimer density matriz D2: Eduardo Ludena, Peter Iza, Yosslen Aray, Mauricio Cornejo, Dik Zambrano Properties of the nonBornOppenheimer 2matrix are examined. Using a coordinate system formed by internal translationally invariant plus the total centerofmass coordinates it is shown that regardless of the point of reference selected, the operator for the reduced second order density matrix, 2RDM, solely depends upon the translationally invariant internal coordinates. We apply this result to examine the nature of the 2RDM extracted from the exact analytical solutions for model nonBornOppenheimer fourparticle systems of the CoulombHooke and Moshinsky types. We obtain for both these models explicit closedform analytic expressions for the electron and nuclear 2RDM. An explicit expression is also obtained for the electronnuclear 2RDM in the Moshinsky case, which shows coupling between the electron and nuclear coordinates. [Preview Abstract] 
Thursday, March 17, 2016 5:06PM  5:18PM 
V20.00010: Extracting g tensor values from experimental data with Markov Chain Monte Carlo methods Anagha Kulkarni, Weiwen Liu, Ryan Zurakowski, Matthew Doty Quantum Dot Molecules(QDMs) have emerged as a new platform for optoelectronic and spintronic devices.QDMs consist of multiple Quantum Dots (QDs) arranged in close proximity such that interactions between them can tailor their optical and spin properties.These properties can be tuned during growth and insitu by applying electric fields that vary the coupling between QDs,which controls the formation of delocalized molecularlike states.Engineering the formation of molecular states in QDMS can be used to achieve new functionalities unavailable with individual QDs. Using molecular engineering approaches to tailor QDMs require precise knowledge of parameters such as binding energies of charge complexes,magnitude of many body interactions or components of the g tensor.Precise values of these parameters are difficult to extract from either experimental measurements or theoretical calculations.We develop and demonstrate a Markov Chain Monte Carlo method for extracting elements of the g tensor for a single hole confined in a QDM from photoluminescence data obtained as a function of electric and magnetic fields.This method can be applied to extract precise quantitative values of other physical parameters from sparse experimental data on a variety of systems. [Preview Abstract] 
Thursday, March 17, 2016 5:18PM  5:30PM 
V20.00011: QUANTUM MONTE CARLO METHOD FOR HEAVY ATOMIC AND MOLECULAR SYSTEMS WITH SPINORBIT INTERACTIONS Cody Melton, Lubos Mitas We present a new quantum Monte Carlo (QMC) method that can treat spinorbit and other types of spindepentent interactions explicitly. It is based on generalization of the fixedphase and projection of the nonlocal operators with spinor trial wave functions. For testing the method we calculate several atomic and molecular systems such as Bi, W, Pb, PbH and PbO, some of them with both large and smallcore pseudopotentials. We validate the quality of the results against other correlated methods such as configuration interaction in twocomponent formalism. We find excellent agreement with extrapolated values for the total energies and we are able to reliably reproduce experimental values of excitation energies, electron affinity and molecular binding. We show that in order to obtain the agreement with experimental values the explicit inclusion of the spinorbit interactions is crucial. [Preview Abstract] 
Follow Us 
Engage
Become an APS Member 
My APS
Renew Membership 
Information for 
About APSThe American Physical Society (APS) is a nonprofit membership organization working to advance the knowledge of physics. 
© 2024 American Physical Society
 All rights reserved  Terms of Use
 Contact Us
Headquarters
1 Physics Ellipse, College Park, MD 207403844
(301) 2093200
Editorial Office
100 Motor Pkwy, Suite 110, Hauppauge, NY 11788
(631) 5914000
Office of Public Affairs
529 14th St NW, Suite 1050, Washington, D.C. 200452001
(202) 6628700