Spin Symmetry States Research Articles

Bootstrap embedding with an unrestricted mean-field bath.

A suite of quantum embedding methods have recently been developed where the Schmidt decomposition is applied to the full system wavefunction to derive basis states that preserve the entanglement between the fragment and the bath. The quality of these methods can depend heavily on the quality of the initial full system wavefunction. Most of these methods, including bootstrap embedding (BE) [M. Welborn et al; J. Chem. Phys. 145, 074102 (2016)], start from a spin-restricted mean-field wavefunction [call this restricted BE (RBE)]. Given that spin-unrestricted wavefunctions can capture a significant amount of strong correlation at the mean-field level, we suspect that starting from a spin-unrestricted mean-field wavefunction will improve these embedding methods for strongly correlated systems. In this work, BE is generalized to an unrestricted Hartree-Fock bath [call this unrestricted BE (UBE)], and UBE is applied to model hydrogen ring systems. UBE's improved versatility over RBE is utilized to calculate high spin symmetry states that were previously unattainable with RBE. Ionization potentials, electron affinities, and spin-splittings are computed using UBE with accuracy on par with spin-unrestricted coupled cluster singles and doubles. Even for cases where RBE is viable, UBE converges more reliably. We discuss the limitations or weaknesses of each calculation and how improvements to RBE and density matrix embedding theory these past few years can also improve UBE.

Deuterated forms of H3+ and their importance inastrochemistry.

At the low temperatures (approx. 10 K) and high densities (approx. 100 000 H2 molecules per cm-3) of molecular cloud cores and protostellar envelopes, a large amount of molecular species (in particular those containing C and O) freeze-out onto dust grain surfaces. It is in these regions that the deuteration of H3+ becomes very efficient, with a sharp abundance increase of H2D+ and D2H+. The multi-deuterated forms of H3+ participate in an active chemistry: (i) their collision with neutral species produces deuterated molecules such as the commonly observed N2D+, DCO+ and multi-deuterated NH3; (ii) their dissociative electronic recombination increases the D/H atomic ratio by several orders of magnitude above the D cosmic abundance, thus allowing deuteration of molecules (e.g. CH3OH and H2O) on the surface of dust grains. Deuterated molecules are the main diagnostic tools of dense and cold interstellar clouds, where the first steps toward star and protoplanetary disc formation take place. Recent observations of deuterated molecules are reviewed and discussed in view of astrochemical models inclusive of spin-state chemistry. We present a new comparison between models based on complete scrambling (to calculate branching ratio tables for reactions between chemical species that include protons and/or deuterons) and models based on non-scrambling (proton hop) methods, showing that the latter best agree with observations of NH3 deuterated isotopologues and their different nuclear spin symmetry states. This article is part of a discussion meeting issue 'Advances in hydrogen molecular ions: H3+, H5+ and beyond'.

Hartree-Fock Ground State of the Three-Dimensional Electron Gas

In 1962, Overhauser showed that within Hartree-Fock (HF) the electron gas is unstable to a spin-density wave state. Determining the true HF ground state has remained a challenge. Using numerical calculations for finite systems and analytic techniques, we study the unrestricted HF ground state of the three-dimensional electron gas. At high density, we find broken spin symmetry states with a nearly constant charge density. Unlike previously discussed spin wave states, the observed wave vector of the spin-density wave is smaller than 2k(F). The broken-symmetry state originates from pairing instabilities at the Fermi surface, a model for which is proposed.

Spin symmetry breaking in bilayer quantum Hall systems

Based on the construction of generalized Halperin wave functions, we predict the possible existence of a large class of broken spin symmetry states in bilayer quantum Hall structures, generalizing the recently suggested canted antiferromgnetic phase to many fractional fillings. We develop the appropriate Chern-Simons theory, and establish explicitly that the low-lying neutral excitation is a Goldstone mode and that the charged excitations are bimerons with continuously tunable (through the canted antiferromagnetic order parameter) electric charge on the individual merons.

Molecular-beam infrared–infrared double-resonance spectroscopy study of the vibrational dynamics of the acetylenic C–H stretch of propargyl amine

The acetylenic C–H stretch spectrum of propargyl amine near 3330 cm−1 has been measured at 0.0002 cm−1 (6 MHz) resolution with a tunable color-center laser in an electric-resonance optothermal spectrometer. The spectrum has been fully assigned through IR–IR double resonance measurements employing a tunable, microwave sideband-CO2 laser. The 10 μm spectrum of propargyl amine displays splittings in the two nuclear spin symmetry states arising from amino-proton interchange, allowing double-resonance assignment of the –NH2 group resultant proton nuclear spin quantum number in the highly fragmented 3 μm spectrum. The experimental state density is consistent with a (2J+1) increase that is expected if all near-resonant states are coupled. From this J-dependent growth in the state density we determine the density of states at J=0 to be 22 states/cm−1. This value is in reasonable agreement with the direct state count result of 16 states/cm−1. The unperturbed transition frequencies for the two different nuclear spin species at a given rotational level do not coincide, differing on average by about 50 MHz. The nonresonant coupling effects which produce effective splittings in the 10 μm spectrum appear to survive into the high state density regime. The measured IVR lifetimes are on the order of 500 ps for the low Ka values studied here (Ka<4) and show a Ka-dependence with the IVR rate increasing as Ka increases. The statistical properties of the spectrum have been compared to predictions from random matrix theory. The level spacings are not well represented by Wigner statistics as would be expected for underlying chaotic classical dynamics. However, the intensity fluctuations are consistent with a χ2-distribution, expected for classically chaotic systems, as measured by Heller’s F-statistic.

Rotational states of the NH+4 ion in (NH4)2SnCl6 by inelastic neutron scattering

The tunnel splitting of the librational ground state of a NH+4 ion in (NH4)2 SnCl6 has been analyzed by ’’incoherent’’ inelastic neutron scattering. Ground state splittings of 2.96±0.04 and 1.51±0.03 μeV have been observed at T=6 K and are interpreted as transitions between A?T and T?E spin symmetry states, respectively. With increasing temperature the observed tunnel splitting shifts towards smaller energies but fails to show significant lifetime broadening. The first excited librational state is observed at 13.4±0.5 meV. An excitation with E?30 meV probably corresponds to the second excited librational state. Above 70 K classical reorientational motion gives rise to quasielastic scattering. From the temperature dependence of the quasielastic linewidth an activation energy EA=590±30 K is obtained. A three dimensional rotational potential is discussed in view of the above data. The temperature dependence of the tunneling states is compared with current theories.

Proton N.M.R. study of the dynamics of the ammonium ion in ferroelectric langbeinite, (NH4)2Cd2(SO4)3

The proton N.M.R. lineshape of polycrystalline Langbeinite, (NH4)2Cd2(SO4)3, has been studied in the temperature range 300 K to 1·8 K. The resonance line is motionally narrowed over the entire temperature range, and the low temperature proton line shows clear evidence for tunnelling motion of the ammonium ion between spin-symmetry states. From a computer simulation of the lineshape, we obtain an estimate for the tunnelling splitting parameter, J, of the torsional ground state of the ammonium ion, as 375 ± 125 gauss. For an undistorted tetrahedral crystal field this corresponds to a tunnelling splitting Δ = 4J = 6·3 ± 2·1 MHz. Pulsed proton N.M.R. studies have also been carried out on the above compound at 30·8 MHz and 48·2 MHz and the spin-lattice relaxation time (T 1) has been measured by the π - t - π/2 pulse sequence as a function of temperature down to 77 K. At 30·8 MHz, a T 1 minimum of 13 ms occurs at 105·8 K, and is ascribed to random reorientations of the NH4 + ion. An activational energy barrier of 0·74 ± 0·1 kcal/mole and an associated pre-exponential factor of 8·0 × 10-13 s are calculated for the above motional process, and the value of the activation energy is correlated with the tunnelling splitting of the torsional ground state. An anomaly in T 1 has been observed at the ferroelectric Curie point (95 K), indicating the order-disorder nature of the transition. This is the first experimental evidence relating to the nature of the transition in Langbeinite.

Evidence for nuclear spin symmetry states in solid silane

The existence of nuclear spin symmetry states associated with the protons and deuterons in solid silane is inferred from minima in a plot of nuclear spin-lattice relaxation times versus temperature.