Large Zero-point Energy Research Articles

Ground-State Properties of Two-Dimensional 3He-4He Mixtures: Energetics and Structures

Using a variational Jastrow wavefunction extended to include a three-body correlation function and a hypernetted chain (HNC) and Fermi hypernetted chain (FHNC) scheme with contribution from elementary diagrams, we analyze ground-state energies and structural properties of two-dimensional3He-4He mixtures. The mixtures are in equilibrium at lower density compared to a pure4He system because of the large zero-point energy and statistical correlations due to the fermionic nature of3He. We evaluate the lowering of ground-state energies as a function of the impurity concentration and total density of mixtures. Comparing the results with boson3He-4He mixtures, we evaluate the energy shifts coming from the statistics and analyze the enthalpy to study the miscibility and mobility of each component of the mixture.

Configuration interaction calculations of the structure and energetics of the high symmetry isomers of the O +4 cation

The identification of the oxygen dimer cation, O + 4, by cryogenic matrix-isolation IR and ESR spectroscopies, and as the important core-cation in the ionization of gas-phase O 2 clusters, has led to theoretical investigations of the stable isomeric structures available to this species. The open-shell quartet spin state favoured by O + 4 together with its highly symmetric structures means that ab initio all-electron calculations are bedevilled by difficulties including spin contamination, symmetry breaking and con- figurational convergence. The QCISD(T) approximation used in the calculations reported here seems to account for these computational problems. The 4B u state of the trans-planar (C 2h) isomers is found to be the most stable structure, though the 4B 3g state of the rectangular (D 2h) isomer, calculated as of 4 kcal mol −1 higher energy, is so because of the influence of a large zero-point vibration energy.

The quantum dynamics of hydrogen and deuterium on the Pd(111) surface: A path integral transition state theory study

The surface diffusion constant for hydrogen and deuterium on the palladium(111) surface is calculated using quantum mechanical transition state theory. The rate constants for diffusion into the subsurface layer are also calculated. Quantum effects are seen to be most important for the surface/subsurface transition and cause an inverse isotope effect in which the rate for deuterium is greater than the rate for hydrogen. The results of ground and excited state wave function calculations show localized hydrogenic states, despite large zero point energies, and that the preferred binding site can vary with isotope between surface and subsurface sites. In addition, estimates of the tunneling rate between the surface and subsurface are in qualitative agreement with the low temperature transition state results.

低温でのクラスター形成による同位体分離

The isotope enrichment by the formation of neutral and ionic clusters is discussed. In the free jet expansion, the heavier isotopes are enriched in the neutral clusters and the lighter isotopes are preferentially eliminated from the neutral clusters. In the free jet seeded with ions, the enrichment of heavier isotopes in the ionic clusters is greatly enhanced compared to that in the neutral clusters. This is mainly due to the large zero-point energy difference in the bond energies between the neutral and ionic clusters. The enrichment factor for ionic clusters decreases with the growth of cluster size and converges to that for the neutral ones. The deuteron-held heavy hydrogen clusters D3+(D2)n are found to be thermochemically more stable than the proton-held hydrogen clusters H3+(H2)n with n=2~9. This is due to the tighter bond formation with n≤6 and to the more favorable entropy effect with n=7~9 for the clusters D3+(D2)n.

Detection of Quadrupole Interactions by Muon Level Crossing Resonance

Abstract The positive muon proves to be a very versatile and sensitive magnetic resonance probe: implanted in virtually any material its polarisation may be monitored via the asymmetry in its radioactive decay, giving information on the sites occupied by the muon in lattices or molecules, and the local fields experienced at these sites. The scope of these experiments has been greatly extended by the development of a technique of cross relaxation or level crossing resonance which allows quadrupole splittings on nuclei adjacent to the muon to be measured. The principles of the technique and the conditions necessary for detection of the spectra are described, together with a number of applications. Of especial interest is the manner in which muons mimic the behaviour of protons in matter. In metal lattices, for instance, muons invariably adopt the same interstitial sites as do protons in the dilute hydride phases, so that they can be used to study problems of localisation and diffusion common to those of hydrogen in metals. Studies of the muon level crossing resonance in copper have given valuable information on the crystallographic site, electronic structure and low temperature mobility of the interstitial defect. In semiconductors, muons are expected to trap at other impurities - notably acceptors - in processes analogous to the passivation of dopants by hydrogen. Muon resonance offers the exciting prospect of spectroscopic study of these passivation complexes. In molecular materials, substitution of protons by muons can be thought of rather like deuteration. Muons implanted in ice produce a significant change in the quadrupole coupling constant of adjacent 17O nuclei which may be traced to the effects of the large muon zero point energy; the resonance spectrum also exhibits temperature dependent features which may be informative on the nature and lifetime of defects in the ice structure. Muon level crossing resonance has already been studied in an oxide superconductor and this relatively young field is now wide open for quadrupole interaction studies in other materials, using a variety of nuclei.

Calculation of van der Waals spectra for H2HF, D2HF, and H2DF

Calculations of spectra for the excitation of the van der Waals modes in the weakly bound complexes H2HF, D2HF, and H2DF are reported. An ab initio potential energy surface has been computed using the coupled electron pair approximation with a large basis set. The rovibrational bound states for the complexes are calculated using a variational method. A self-consistent field approach is used to optimize the basis sets for bending and stretching motion in the van der Waals complex. The calculated spectra compare very well with those measured in near-infrared experiments. The computations provide a systematic analysis of the relative stability and rigidity of the different complexes, the very large zero-point energy effects, and the unusual nature of the rovibrational wave functions in these van der Waals molecules. The predicted spectra contain some new bands with surprisingly large intensities that might be detectable in experiments.

Optical properties of III–V semiconductor quantum wires and dots

I review here the brief history and present status of research on the optical properties of III–V semiconductor quantum wires and dots. These efforts are driven in part by predictions of interesting linear and nonlinear optical properties for these structures. Experimental work has focused on various schemes to make uniform arrays of structures. New techniques developed for making these arrays have been followed by the observation of large zero-point energies and subband splittings for electrons, and modified exciton binding energies and selection rules for optical transitions in quantum wires.

Temperature dependence of electron scavenging in ethanol and ethanol-O-d

Inefficient scavenging of solvated electrons (e/sup -//sub s/) may provide understanding of details which are difficult to explore for nearly diffusion-controlled processes. Alcohols as solvents permit use of organic reagents, exhibit interesting dynamic solvation effects, and are particularly appropriate for dry-electron scavenging. Sixteen scavengers, with k/sub e/sub aq/sup -/// in the range 10/sup 7/ to 10/sup 9/ M/sup -1/ s/sup -1/, have been investigated in ethanol from 150 to 298 K. Values of the activation energy were higher for two efficient scavengers, approximately 4.5 kcal/mol for CCl/sub 4/ and HClO/sub 4/, than approximately 3.8 kcal/mol for inefficient scavengers such as toluene, with no evident pattern. Activation contributes little to differences in k/sub e/sup -//sub s//. Many of the inefficient scavengers were moderately efficient as dry-electron (e/sup -/) scavengers at 298 K. For toluene 63% of dry electrons were scavenged at 298 K by C/sub 37/ = 1.8 M, but at 123 K by only C/sub 37/ = 0.43 M. Temperature-dependent ionization C/sub 6/H/sub 5/CH/sub 3//sup -/ ..-->.. C/sub 6/H/sub 5/CH/sub 3/ + e/sup -//sub s/ is indicated. At 298 K and large combined concentrations of toluene (k/sub e/sup -//sub s// approximately equal to 10/sup 7/ M/sup -1/ s/sup -1/) andmore » biphenyl (k/sub e/sup -//sub s// approximately equal to 10/sup 9/ M/sup -1/ s/sup -1/), toluene converts e/sup -/ to e/sup -//sub s/, measured as biphenylide ion. Localization of e/sup -/ by solvent, which is less efficient in C/sub 2/H/sub 5/OD, competes with scavenging and C/sub 37/ decreases with decreasing temperature to a constant limiting value at approximately 150 or approximately 125 K which is approximately 25 to 50% of the value at 298 K. Localization and scavenging are activationless at low temperature and the isotope effect disappears. It is proposed that e/sup -/ scattering in the liquid maintains a large zero-point kinetic energy which is available for resonances, e.g., benzene, to account for activationless scavenging. Analogously, localization is attributed to C/sub 2/H/sub 5/OH/sup -/. 1 table; 9 figures.« less

EPR of methylene. Temperature dependence in a xenon matrix

The EPR spectra of CH2 and CD2 were examined between 2.18 and 9.2 °K in a xenon matrix. The zero-field splitting and linewidths of the randomly oriented triplet CD2 were temperature independent below 4.2 °K which is consistent with the currently accepted model in which the trapped methylene occupies its lowest discrete tortional level in the matrix. Increasing the temperature above 4.2 °K produces a decrease in the zero-field splitting of CD2 and an increase in linewidth. The zero-field splitting for CH2 exhibited a temperature dependence between 4.2 and 2.18 °K. The variation of the zero-field splitting parameters could be described by a thermal activation energy of about 30 cm−1 for CD2 and approximately 14 cm−1 for CH2. These relative magnitudes are likely a consequence of the fact that CH2 has a larger zero-point energy than CD2 and therefore requires a smaller energy of activation to jump or tunnel to a random orientation. The temperature dependence of the homogeneous broadening of the z1 and z2 EPR spectral lines of CD2 could be described by a thermal activation energy between 36 and 42 cm−1. The mechanism for the line broadening is probably the same for the decrease in D, and the difference in experimental activation energies probably arises from uncertainties in the deconvolution of the spectral linewidth into a homogeneous and an inhomogeneous part. It was also found that methylene in a xenon matrix could be warmed to 50 °K before significant diffusion with subsequent reactive recombination takes place.

Compression of SolidHe3andHe4to 20 000 Bars

For purposes of comparison, we have measured the compression of both solid ${\mathrm{He}}^{3}$ and ${\mathrm{He}}^{4}$ at 4.2 \ifmmode^\circ\else\textdegree\fi{}K up to 20 000 bars pressure. The relative volume changes of the solid samples were measured in a direct piston displacement apparatus. It was found that both isotopes fit a Murnaghan finite strain relation. From this compressibilities were computed. Within experimental error, the two isotopes have the same compressibility throughout the range. As might be expected from its larger zero-point energy, ${\mathrm{He}}^{3}$ has the slightly greater molar volume at all pressures.

Transmission of Slow Neutrons by LiquidHe4. II

The Los Alamos slow-neutron total scattering cross sections in liquid ${\mathrm{He}}^{4}$ are analyzed using the general scattering theory expected to be valid at short and medium neutron wavelenths. With the approximate mean kinetic energies and partial mean square forces per liquid atom derived previously, the theory is in fair agreement with the data below about 8 A; it breaks down at longer wavelengths. The analysis of the data is then inverted by attempting to solve the following problem: is it possible to find with the cross-section data a set of liquid parameters, at a given liquid temperature, such that the cross sections computed with them would represent the data at wavelengths larger than 8-9 A. This problem receives an affirmative solution inasmuch as the neutron data liquid parameters turn out to be in fair agreement with the approximate liquid parameters obtained by an entirely different method. The scattering cross sections recalculated with the new parameters represent the data fairly well out to 12-13 A. A direct, practically experimental, proof has been obtained for the existence of a very large zero-point kinetic energy in liquid ${\mathrm{He}}^{4}$ over a wide temperature interval. The significance of these results for the derivation, with neutron and x-ray data, of mean kinetic and potential energies, and mean square forces, per atom, in liquids is discussed.

Interatomic Correlations in LiquidHe4

The direct correlation functions, of generally short-range character over most of the liquid temperature interval, have been obtained with the liquid ${\mathrm{He}}^{4}$ x-ray scattering data of Reekie, using the 701 IBM Electronic Calculator. The geometrical simplicity of these functions when compared with the indirect correlation functions, of more intuitive physical significance, is automatically demonstrated. They closely satisfy two types of integral test relations, and this fact proves their over-all correct character and the internal consistency of the numerical analysis.The previously obtained indirect correlation functions will be used here in studying the interference properties of the liquid in slow-neutron scattering processes, in the limiting static approximation. At temperatures not too close to the critical region, the static interference integrals are always negative as a result of the preponderant destructive interference effects arising from the local density defects from the mean density, outweighing the local density excesses. At short and moderate neutron wavelengths, where the use of the static interference integrals is better justified, the total slow-neutron scattering cross sections in liquid ${\mathrm{He}}^{4}$, and in liquids in general, always increase with increasing temperature. The static interference integrals will be shown to provide an additional integral test on the indirect correlation functions. The latter were found to satisfy this test relation with good accuracy.Part of this paper is devoted to a numerical evaluation of mean kinetic energies per liquid ${\mathrm{He}}^{4}$ atom as a function of the temperature. The existence of a large zero-point kinetic energy of the liquid as compared with the kinetic energy of thermal origin is demonstrated. Furthermore, the previously given qualitative proof of the kinetic energy origin of the lambda transition could be made semiquantitative. Finally, root-mean-square forces acting on a liquid atom are evaluated, this physical quantity of elementary character having become, in principle at least, accessible through the experimental investigation of slow-neutron scattering properties of liquids.