Imaging the Structure of the Trimer Systems 4He3 and 3He4he2
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What Is the Shape of the Helium Trimer? a Comparison with the Neon and Argon Trimers Dario Bressanini* and Gabriele Morosi
ARTICLE pubs.acs.org/JPCA What Is the Shape of the Helium Trimer? A Comparison with the Neon and Argon Trimers Dario Bressanini* and Gabriele Morosi Dipartimento di Scienze Chimiche e Ambientali, Universita' dell'Insubria, Via Lucini 3, 22100 Como, Italy ABSTRACT: Despite its apparent simplicity and extensive theoretical investiga- tions, the issue of what is the shape of the helium trimer is still debated in the literature. After reviewing previous conflicting interpretations of computational studies, we introduce the angleÀangle distribution function as a tool to discuss in a simple way the shape of any trimer. We compute this function along with many different geometrical distributions using variational and diffusion Monte Carlo methods. We compare them with the corresponding ones for the neon and argon fl trimers. Our analysis shows that while Ne3 and Ar3 uctuate around an 4 equilibrium structure that is an equilateral triangle, He3 shows an extremely broad angleÀangle distribution function, and all kinds of three-atom configura- 4 tions must be taken into account in its description. Classifying He3 as either equilateral or linear or any other particular shape, as was done in the past, is not sensible, because in this case the intuitive notion of equilibrium structure is ill defined. Our results could help the interpretation of future experiments aimed at measuring the geometrical properties of the helium trimer. ’ INTRODUCTION candidate for the Efimov effect, first discussed in nuclear physics. 1 Weakly bound van der Waals noble gases clusters in the last The recent paper of Kolganova et al. provides a nice review of the literature of this field of research. -
First-Principles Calculations of Helium Cluster Formation in Palladium Tritides
FIRST-PRINCIPLES CALCULATIONS OF HELIUM CLUSTER FORMATION IN PALLADIUM TRITIDES A Thesis Presented to The Academic Faculty by Pei Lin In Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the School of Physics Georgia Institute of Technology August 2010 FIRST-PRINCIPLES CALCULATIONS OF HELIUM CLUSTER FORMATION IN PALLADIUM TRITIDES Approved by: Professor Mei-Yin Chou, Advisor Professor Andrew Zangwill School of Physics School of Physics Georgia Institute of Technology Georgia Institute of Technology Professor James Gole Professor David Sholl School of Physics School of Chemical and Biomolecular Georgia Institute of Technology Engineering Georgia Institute of Technology Professor Phillip N. First Date Approved: May 10, 2010 School of Physics Georgia Institute of Technology To my beloved family iii ACKNOWLEDGEMENTS I owe my sincere gratitude to all who have helped me, encouraged me, and believed in me through this challenging journey. Foremost, I am deeply indebted to my thesis advisor, Professor Mei-Yin Chou, for every advice and opportunity she provided me through the years of my education. Her exceptional insight and broad-minded guidance led me the way to be a critical-thinking and self-stimulating physicist, which would be my greatest asset in the future. I owe my sincere thanks to Professor Andrew Zangwill, Professor James Gole, Professor Phillip First, and Professor David Sholl for their precious time being in my thesis defense committee. I am thankful to our previous and current group members Dr. Amra Peles, Dr. Li Yang, Dr. Zhu Ma, Dr. Wolfgang Geist, Dr. Alexis Nduwinmana, Dr. Jia-An Yan, Dr. Wen-Ying Ruan, Dr. -
Ionization Dynamics of Helium Dimers in Fast Collisions with Heþþ
week ending PRL 106, 033201 (2011) PHYSICAL REVIEW LETTERS 21 JANUARY 2011 Ionization Dynamics of Helium Dimers in Fast Collisions with Heþþ J. Titze,1 M. S. Scho¨ffler,2 H.-K. Kim,1 F. Trinter,1 M. Waitz,1 J. Voigtsberger,1 N. Neumann,1 B. Ulrich,1 K. Kreidi,3 R. Wallauer,1 M. Odenweller,1 T. Havermeier,1 S. Scho¨ssler,1 M. Meckel,1 L. Foucar,4 T. Jahnke,1 A. Czasch,1 L. Ph. H. Schmidt,1 O. Jagutzki,1 R. E. Grisenti,1 H. Schmidt-Bo¨cking,1 H. J. Lu¨dde,5 and R. Do¨rner1,* 1Institut fu¨r Kernphysik, Goethe-Universita¨t Frankfurt am Main, Max-von-Laue-Str.1, 60438 Frankfurt, Germany 2Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, California, 94720, USA 3GSI Helmholtzzentrum fu¨r Schwerionenforschung GmbH, Planckstr. 1, 64291 Darmstadt, Germany 4Max-Planck-Institut fu¨r Kernphysik, Saupfercheckweg 1, 69117 Heidelberg, Germany 5Institut fu¨r Theoretische Physik, Goethe-Universita¨t Frankfurt am Main, Max-von-Laue-Str. 1, 60438 Frankfurt, Germany (Received 23 September 2010; published 20 January 2011) By employing the cold target recoil ion momentum spectroscopy technique, we have investigated the þ þ (He , He ) breakup of a helium dimer (He2) caused by transfer ionization and double capture in collisions with alpha particles (E ¼ 150 keV=u). Surprisingly, the results show a two-step process as well as a one-step process followed by electron exchange. In addition, interatomic Coulombic decay [L. S. Cederbaum, J. Zobeley, and F. Tarantelli, Phys. Rev. Lett. 79, 4778 (1997).] is observed in an ion collision for the first time. -
Chem 1A, Fall 2015, Final Exam December 14, 2015 (Prof
Chem 1A, Fall 2015, Final Exam December 14, 2015 (Prof. Head-Gordon)2 Name: ________________________________________ Student ID:_____________________________________ TA: _______________________________ Contents: 14 pages 1. Multiple choice (15 points) 2. Molecular orbitals and quantum mechanics (12 points) 3. Acid-Base Equilibria (13 points) 4. Electrochemistry (12 points) 5. Thermochemistry (12 points) 6. Chemical Kinetics (8 points) Total Points: 72 points (+ 2 bonus points) Instructions: Closed book exam. Basic scientific calculators are OK. Set brains in high gear and go! Thanks for taking our class, and best wishes for success today, and beyond. Some possibly useful facts. Molar volume at STP = 22.4 L 23 -1 N0 = 6.02214 × 10 mol 1 V = 1 J / C -18 -1 -9 Ry = 2.179874 × 10 J = 1312 kJ mol 1 nm = 10 m 15 Ry = 3.28984 × 10 Hz 1 kJ = 1000 J -23 -1 k = 1.38066 × 10 J K 1 atm = 760 mm Hg = 760 torr ≈ 1 bar -34 h = 6.62608 × 10 J s 1 L atm ≈ 100 J T (K) = T (C) + 273.15 -31 me = 9.101939 × 10 kg F = 96,485 C / mol 8 -1 c = 2.99792 × 10 m s -14 Kw = 1.0 × 10 (at 25C) Gas Constant: R = 8.31451 J K-1 mol-1 or -19 1eV = 1.602×10 J R = 8.20578 × 10-2 L atm K-1 mol-1 1 J = 1 kg m2 s-2 1 Some possibly relevant equations: Quantum: Thermodynamics: E = hν λν = c λ deBroglie = h/p = h/mv Ekin (e-) = hν - Φ = hν - hν0 p = mv Particle in a box (1-D Quantum): ΔG° = ΔH° - TΔS° 2 2 2 En = h n /8mL ; n = 1, 2, 3.. -
Experimental Observation of Helium Dimer
Grand Valley State University ScholarWorks@GVSU Peer Reviewed Articles Chemistry Department 12-11-1992 The Weakest Bond: Experimental Observation of Helium Dimer Fei Luo George C. McBane Grand Valley State University, [email protected] Geunsik Kim Clayton F. Giese W. Ronald Gentry Follow this and additional works at: https://scholarworks.gvsu.edu/chm_articles Part of the Biological and Chemical Physics Commons ScholarWorks Citation Luo, Fei; McBane, George C.; Kim, Geunsik; Giese, Clayton F.; and Gentry, W. Ronald, "The Weakest Bond: Experimental Observation of Helium Dimer" (1992). Peer Reviewed Articles. 6. https://scholarworks.gvsu.edu/chm_articles/6 This Article is brought to you for free and open access by the Chemistry Department at ScholarWorks@GVSU. It has been accepted for inclusion in Peer Reviewed Articles by an authorized administrator of ScholarWorks@GVSU. For more information, please contact [email protected]. The weakest bond: Experimental observation of helium dimer Fei Luo, George C. McBane, Geunsik Kim, Clayton F. Giese, and W. Ronald Gentry Chemical Dynamics Laboratory, University of Minnesota, 207 Pleasant Street SE, Minneapolis, Minnesota 55455 (Received 9 November 1992; accepted 11 December 1992) Helium dimer ion was observed after electron impact ionization of a supersonic expansion of helium with translational temperature near 1 mK. The dependence of the ion signal on source pressure, distance from the source, and electron kinetic energy was measured. The signal was determined to arise from ionization of neutral helium dimer. INTRODUCTION servation2 several years ago that it is possible to attain temperatures as low as 0.3 mK in extreme pulsed expan He2 has been the only rare gas dimer not experimen sions of pure helium from room temperature sources. -
Cold Few-Atom Systems with Large S-Wave Scattering Length
Cold Few-Atom Systems With Large s-Wave Scattering Length Doerte Blume, Qingze Guan Experiment: The University of Oklahoma Maksim Kunitski, Reinhard Doerner,… Supported by the NSF. Frankfurt University Cold Few-Atom Systems With Large s-Wave Scattering Length Or Possibly Better: Low-Energy Few-Body Physics Doerte Blume, Qingze Guan Experiment: The University of Oklahoma Maksim Kunitski, Reinhard Doerner,… Supported by the NSF. Frankfurt University Three Few-Body Systems Cold molecular system: Helium dimer, trimer, tetramer,… Nuclear systems: Deuteron, triton, Alpha particle,… Small ultracold alkalis: For fermions, in presence of trap. For bosons, in free space. Pushing toward: Beyond energetics… Beyond statics… Common Characteristic? Large s-Wave Scattering Length 1) Helium-helium (van der Waals length !"#$ ≈ &. ()*): 3 4 1) He- He: )+ = −./. (&)* 4 4 2) He- He: )+ = (0*. 12)* “Naturally” large scattering length. No deep-lying bound states. Tunability? 2) Deuteron (nuclear force around 1 Fermi = (*3(&m): 47* 1) Singlet (4 = *, 6 = (): )+ = −8.. 0Fermi 47( 2) Triplet (4 = (, 6 = *): )+ = &. .1Fermi 3) Ultracold atoms: Feshbach resonances provide enormous tunability. 4Helium-4Helium Example: One Vibrational Bound State Radial wave true He-He potential (calculations to be function: presented use the full potential) F(/% ZR model: (%D->) ;HI(−?/->) 4 4 • He- He bound state energy 89:7;5 = −1.3mK. • No < > * bound states. • Two-body s-wave scattering length -> = 171-*. • Two-body effective range ?;@@ = 15.2-* (alternatively, two- body van der Waals length ?A9B = 5.1-*). 1K = 8.6 × 10−5 eV 1eV= $ × %. '() × (*('+, 1-* = *. .%/01234567 Braaten, Hammer, Physics Reports Three Bosons with 428, 259 (2006). Large |"#|: Efimov Effect ( ( &'( &'(,, $ = + + ∑./0 1(2 3.0 + 1,2 3' − 3( 2 3( − 3, . -
Spectroscopy and Quantum Mechanics of the Helium Dimer
ienc Sc es al J c o i u m r e n a h l C Heidari A, Chem Sci J 2016, 7:2 Chemical Sciences Journal DOI: 10.4172/2150-3494.1000e112 ISSN: 2150-3494 EditorialResearch Article OpenOpen Access Access + Spectroscopy and Quantum Mechanics of the Helium Dimer (He2 ), Neon + + + Dimer (Ne2 ), Argon Dimer (Ar2 ), Krypton Dimer (Kr2 ), Xenon Dimer + + + (Xe2 ), Radon Dimer (Rn2 ) and Ununoctium Dimer (Uuo2 ) Molecular Cations A Heidari* Faculty of Chemistry, California South University, 14731 Comet St. Irvine, CA 92604, USA Some of the simplest of all molecules are the Helium dimer, Neon decades. In addition, these cations for the sake of their small atoms and dimer, Argon dimer, Krypton dimer, Xenon dimer, Radon dimer and need to identify and separations gains increasing importance. In this + + + + + + Ununoctium dimer molecular cations, He2 , Ne2 , Ar2 , Kr2 , Xe2 , Rn2 editorial, the molecular structure and thermodynamic parameters and + and Uuo2 . Because of their simplicity and importance, these molecular properties of these cations have also been investigated and calculated cations have received considerable attention from experimentalists (Figures 2 and 3). as well as theoreticians [1-11]. The exact solution of the electronic Schrödinger equation for these cations plays an important role in investigating the molecular structure of more complex systems. In this editorial, some of approximation as well as exact solutions of the Schrödinger equation for these cations have been studied and one the exact solutions have been considered in details. By making use of the perturbation theory, cosmological perturbation theory and also homotopy perturbation method with the help of the linear extrapolation techniques, we have presented a simpler novel method to obtain the numerical exact solution. -
Fantasy Versus Reality in Fragment-Based Quantum Chemistry
The Journal PERSPECTIVE of Chemical Physics scitation.org/journal/jcp Fantasy versus reality in fragment-based quantum chemistry Cite as: J. Chem. Phys. 151, 170901 (2019); doi: 10.1063/1.5126216 Submitted: 31 August 2019 • Accepted: 6 October 2019 • Published Online: 4 November 2019 John M. Herberta) AFFILIATIONS Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, USA a)[email protected] ABSTRACT Since the introduction of the fragment molecular orbital method 20 years ago, fragment-based approaches have occupied a small but growing niche in quantum chemistry. These methods decompose a large molecular system into subsystems small enough to be amenable to electronic structure calculations, following which the subsystem information is reassembled in order to approximate an otherwise intractable supersys- tem calculation. Fragmentation sidesteps the steep rise (with respect to system size) in the cost of ab initio calculations, replacing it with a distributed cost across numerous computer processors. Such methods are attractive, in part, because they are easily parallelizable and there- fore readily amenable to exascale computing. As such, there has been hope that distributed computing might offer the proverbial “free lunch” in quantum chemistry, with the entrée being high-level calculations on very large systems. While fragment-based quantum chemistry can count many success stories, there also exists a seedy underbelly of rarely acknowledged problems. As these methods begin to mature, it is time to have a serious conversation about what they can and cannot be expected to accomplish in the near future. Both successes and challenges are highlighted in this Perspective. -
Imaging the He2 Quantum Halo State Using a Free Electron Laser
Imaging the He2 quantum halo state using a free electron laser Stefan Zellera,1, Maksim Kunitskia,Jorg¨ Voigtsbergera, Anton Kalinina, Alexander Schotteliusa, Carl Schobera, Markus Waitza, Hendrik Sanna, Alexander Hartunga, Tobias Bauera, Martin Pitzera, Florian Trintera, Christoph Goihla, Christian Jankea, Martin Richtera, Gregor Kastirkea, Miriam Wellera, Achim Czascha, Markus Kitzlerb, Markus Braunec, Robert E. Grisentia,d, Wieland Schollkopf¨ e, Lothar Ph. H. Schmidta, Markus S. Schoffler¨ a, Joshua B. Williamsf, Till Jahnkea, and Reinhard Dorner¨ a,1 aInstitut fur¨ Kernphysik, Goethe-Universitat¨ Frankfurt, 60438 Frankfurt, Germany; bPhotonics Institute, Vienna University of Technology, 1040 Vienna, Austria; cDeutsches Elektronen-Synchrotron, 22607 Hamburg, Germany; dGSI Helmholtz Centre for Heavy Ion Research, 64291 Darmstadt, Germany; eDepartment of Molecular Physics, Fritz-Haber-Institut, 14195 Berlin, Germany; and fDepartment of Physics, University of Nevada, Reno, NV 89557 Edited by Marlan O. Scully, Texas A&M University, College Station, TX, and approved November 3, 2016 (received for review June 30, 2016) Quantum tunneling is a ubiquitous phenomenon in nature and One of the most extreme examples of such a quantum halo crucial for many technological applications. It allows quantum par- state can be found in the realm of atomic physics: the helium ticles to reach regions in space which are energetically not accessi- dimer (He2). The dimer is bound by only the van der Waals ble according to classical mechanics. In this “tunneling region,” the force, and the He–He interaction potential (Fig. 1D) has a mini- particle density is known to decay exponentially. This behavior is mum of about 1 meV at an internuclear distance of about 3 A˚ universal across all energy scales from nuclear physics to chem- [0.947 meV/2.96 A˚ (5)]. -
Page 1 of 16 Fall 2011: 5.112 PRINCIPLES of CHEMICAL SCIENCE Problem Set #4 Solutions This Problem Set Was Graded out of 99 Points
Page 1 of 16 Fall 2011: 5.112 PRINCIPLES OF CHEMICAL SCIENCE Problem Set #4 solutions This problem set was graded out of 99 points Question 1 (out of 7 points) (i) For each pair, determine which compound has bonds with greater ionic character. (3 points) (a) NH3 or AsH3: The N-H bond is more ionic than the As-H bond since the difference in electronegativity of N and H (3.0 vs. 2.2) is greater than the difference between As and H (2.2 vs. 2.2). (b) SiO2 or SO2: S and O have similar electronegativities (3.0 and 3.4) whereas for Si and O the difference is greater (1.9 vs. 3.4) so the Si-O bonds have greater ionic character. (c) SF6 or IF5: S and I have very similar electronegativities (2.6 and 2.7), thus the bonds are very similar. S-F bonds may have a slightly higher ionic character, but it would be difficult to determine experimentally. (ii) In which molecule, O=C=O or O=C=CH2, do you expect the C–O bond to be more ionic? (2 points) The C–O bond in O=C=O will have greater ionic character because O is more electronegative than the carbon in the CH2 fragment, so in absolute values, the C in CO2 has twice as much charge removed as the C attached to one O and the CH2 fragment. (iii) In which molecule do you expect the bonds to be more ionic, CCl4 or SiCl4? (2 points) The difference in electronegativity between C and Cl is less than the difference between Si and Cl, so the bonds in SiCl4 will be have greater ionic character. -
Few-Body Approach to Diffraction of Small Helium Clusters by Nanostructures
Few-body approach to diffraction of small helium clusters by nanostructures1 Gerhard C. Hegerfeldt2 Institut f¨ur Theoretische Physik, Universit¨at G¨ottingen Bunsenstr. 9, 37073 G¨ottingen, Germany and Thorsten K¨ohler3 Max-Planck-Institut f¨ur Str¨omungsforschung Bunsenstr. 10, D-37073 G¨ottingen, Germany Abstract We use few-body methods to investigate the diffraction of weakly bound systems by a transmission grating. For helium dimers, He2, we obtain explicit expressions for the transition amplitude in the elastic channel. 1 1. Introduction In recent years typical optics experiments have been carried over to atoms, among them diffraction by double slits [1] and by transmission gratings which were produced by nanostructure techniques [2, 3]. The usual wave-theoretical methods of classical optics (Huygens, Kirchhoff) seem to give excellent descriptions of these experiments [4] so that apparently not much more than a good textbook on classical optics seems to be needed. This simple picture, however, has changed. Recently Sch¨ollkopf and Toennies [2, 5, 6] have performed impressive diffraction experiments with helium dimers and helium clusters consisting of up to 26 atoms. A typical diffraction pattern arXiv:quant-ph/9809031v1 11 Sep 1998 is shown in Fig. 1. The helium dimer He2, discovered a few years ago [8, 2], has an extremely low binding energy of −0.11 µeV [7], with no excited states. The binding energy is much smaller than the incident kinetic energy of typical experiments. Its diameter is estimated to be about 6 nm [9]. Present day slit widths are as low as 50 nm and a further reduction is expected. -
Arxiv:1006.2667V1 [Physics.Atm-Clus] 14 Jun 2010 Ulse N Hs E.Lt.14 541(2010) 153401 104, Lett
published in: Phys. Rev. Lett. 104, 153401 (2010) Single photon double ionization of the helium dimer T. Havermeier1, T. Jahnke1, K. Kreidi1, R. Wallauer1, S. Voss1, M. Sch¨offler1, S. Sch¨ossler1, L. Foucar1, N. Neumann1, J. Titze1, H. Sann1, M. K¨uhnel1, J. Voigtsberger1, A. Malakzadeh1, N. Sisourat2, W. Sch¨ollkopf3, H. Schmidt-B¨ocking1, R. E. Grisenti1,4 and R. D¨orner1 1Institut f¨ur Kernphysik, J. W. Goethe Universit¨at, Max-von-Laue-Str.1, 60438 Frankfurt, Germany 2 Institut f¨ur physikalische Chemie, Universit¨at Heidelberg, Im Neuenheimer Feld 229, 69120 Heidelberg, Germany 3 Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, 14195 Berlin, Germany 4 GSI Helmholtzzentrum f¨ur Schwerionenforschung GmbH Planckstr. 1, 64291 Darmstadt, Germany Abstract We show that a single photon can ionize the two helium atoms of the helium dimer in a distance up to 10 A.˚ The energy sharing among the electrons, the angular distributions of the ions and electrons as well as comparison with electron impact data for helium atoms suggest a knock-off type double ionization process. The Coulomb explosion imaging of He2 provides a direct view of the nuclear wave function of this by far most extended and most diffuse of all naturally existing arXiv:1006.2667v1 [physics.atm-clus] 14 Jun 2010 molecules. 1 2 4 The helium dimer ( He2) is an outstanding example of a fragile molecule whose existence was disputed for a long time because of the very weak interaction potential[1] (see black 4 curve in Fig. 1). Unequivocal experimental evidence for He2 was first provided in 1994 in diffraction experiments[2] by a nano-structured transmission grating.