Showing papers on "Ground state published in 1969"

On Next‐Nearest‐Neighbor Interaction in Linear Chain. II

Abstract: Ground‐state properties of the Hamiltonian H=12J ∑ i=1N σi·σi+1 + 12Jα ∑ i=1N σi·σi+2 (σN+1 ≡ σ1, σN+2 ≡ σ2) are studied for both signs of J and −1 ≤ α ≤ 1 to gain insight into the stability of the ground state with nearest‐neighbor interactions only (α = 0) in the presence of the next‐nearest‐neighbor interaction. Short chains of up to 8 particles have been exactly studied. For J > 0, the ground state for even N belongs always to spin zero, but its symmetry changes for certain values of α. For J < 0, the ground state belongs either to the highest spin (ferromagnetic state) or to the lowest spin and so to zero for even N. The trend of the results suggests that these facts are true for arbitrary N and that the critical value of α is probably zero. Upper and lower bounds to the ground‐state energy per spin of the above Hamiltonian are obtained. Such bounds can also be obtained for the square lattice with the nearest‐ as well as the next‐nearest‐neighbor interaction.

Ground State of a One‐Dimensional N‐Body System

Abstract: The problem of N quantum‐mechanical equal particles interacting pairwise by inverse‐cube forces (``centrifugal potential'') in addition to linear forces (``harmonical potential'') is considered in a onedimensional space. An explicit expression for the ground‐state energy and for the corresponding wavefunction is exhibited. A class of excited states is similarly displayed.

Gibbs states of a one dimensional quantum lattice

Abstract: A one dimensional infinite quantum spin lattice with a finite range interaction is studied. The Gibbs state in the infinite volume limit is shown to exist as a primary state of a UHF algebra. The expectation value of any local observables in the state as well as the mean free energy depend analytically on the potential, showing no phase transition. The Gibbs state is an extremal KMS state.

Improved Quantum Theory of Many‐Electron Systems. V. The Spin‐Coupling Optimized GI Method

Abstract: The previously developed GI methods have an arbitrary aspect since they are based on a particular representation of the symmetric group. Here we remove this arbitrariness by optimizing the representation, that is, optimizing the spin‐coupling scheme simultaneously with the optimization of the orbitals. The resulting wavefunctions, called the spin‐coupling optimized GI or SOGI wavefunctions, have all of the general properties of GI wavefunctions including the independent particle interpretation and are found as the solutions to a set of coupled differential equations which differ from the GI equations only in that the equations are constructed from a different representation of the symmetric group. We have applied this method to the ground state and some excited states of Li, to the ground states of Be^+ and B^(++) and to the ground state of LiH. In each of these cases, we found that the SOGI wavefunction was only slightly different from the G1 wavefunction and led to very similar energies and other spatial properties. For the spin density at the nucleus, however, SOGI led to much better results. In order to illustrate the effects of spatial symmetry on the SOGI orbitals, we examined the lowest ^1B_(1g), ^3A_(2g), and ^3E_u states of square H_4 and the ^2Σ_u^+ state of linear symmetrical H_3. We find that in three of these cases optimization of the spin representation is crucial to providing an adequate description of the state. To investigate how the SOGI method would describe chemical reactions, the SOGI wavefunctions were computed for several other nuclear configurations of the H_3 system along the reaction path. These calculations showed that the spin coupling changed significantly during the reaction H_2 + H⇆H + H_2 and that the variation of the SOGI orbitals provides a clear description of the changes in bonding which occur during this reaction.

Temperature Dependence of Dissociative Attachment in N2O

Abstract: The attachment of low‐energy electrons (<4 eV) by the reaction e+N2O → O−+N2 has been studied as a function of gas temperature from approximately 160 to 1040°K. The ions produced by a monoenergetic electron beam are detected by total ion collection or by mass analysis. The kinetic energy distributions of the O− ions have also been measured and found to be relatively insensitive to the electron energy when the latter exceeds 1.5 eV, in which case the most probable ion energy is 0.38 eV. The shape and magnitude of the cross section below 2 eV is found to be sensitive to gas temperature throughout the range studied. The differences in shape and threshold observed by previous workers occur below 2 eV and to a large extent may be reconciled in terms of the differing gas temperatures employed. The temperature insensitive portion of the cross section is ascribed to electron capture into the highest‐energy N2O− state connected to electronic ground state N2 + O−. The O− kinetic energy distributions arising therefr...

Use of the CNDO Method in Spectroscopy. IV. Small Molecules: Spectra and Ground‐State Properties

Abstract: The modified CNDO method has been applied to the study of the electronic‐absroption spectra of several small molecules; namely, formaldehyde, formic acid, formamide, allene, ketene, and diazomethane, with quite satisfactory results. The lowest energy excited state of the last three compounds has been assigned as the state which arises from a π → π′* transition. A study has also been made of the calculation of ground‐state properties from the spectroscopic parameterization. It has been concluded that although this method can give reasonable estimates of these properties, it is most reliable when used to evaluate ground‐state properties which depend upon calculated eigenvalues.

Ring Puckering in Five‐Membered Rings. II. The Microwave Spectrum, Dipole Moment, and Barrier to Pseudorotation in Tetrahydrofuran

Abstract: The microwave spectrum of tetrahydrofuran has been studied. Nine complete rotational spectra have been observed. These arise from the ground and eight excited states. All of these states are less than 200 cm−1 from the ground state. The rotational constants and dipole moments exhibit a strong nonlinear dependence on the quantum number of the excited state. Vibration–rotation interaction is strong and the spectra of the first four states deviate from that of rigid rotor spectra. These deviations permit the determination of two energy separations: Δ01 = 0.67 cm−1 and Δ23 = 1.5 cm−1. All of the results are interpreted in terms of a model of restricted pseudorotation with a potential function of [30(1‐cos2φ) / 2] + [40(1‐cos4φ) / 2] cm−1, where φ is the angle of pseudorotation. The dipole moment varies from 1.52 to 1.76 D depending upon the pseudorotation state. The details of this variation indicate that the twisted configuration is at lower energy than the bent configuration.

Infinite Square-Well Potential with a Moving Wall

Abstract: The problem of a particle in a one-dimensional infinite square-well potential with one wall moving at constant velocity is treated by means of a complete set of functions which are exact solutions of the time-dependent Schrodinger equation. Comparison is made with a first-order perturbation treatment, and numerical results are presented for a particle initially in the ground state.

Some remarks on the ground state of infinite systems in statistical mechanics

Abstract: We investigate the ground states of infinite quantum lattice systems. It is shown in particular that a positive energy operator is associated with these states.

Low-Energy Scattering of Electrons by Helium

Abstract: The close-coupling equations for electron-helium scattering have been solved in the energy range near the $n=2$ thresholds. Cross sections for elastic scattering from both ground and excited states, for excitation of the ground state to the $n=2$ states ($2^{3}S$, $2^{1}S$, $2^{3}P$, and $2^{1}P$), and for excitation and de-excitation processes involving only the $n=2$ levels are presented and compared with experimental evidence on total metastable production, on angular distributions of excitation cross sections to the $n=2$ levels, and on processes involving only the $n=2$ states. The percentage polarization of light emitted by electron-impact excitation to the $2^{3}P$ and $2^{1}P$ states is computed and compared with experiment. The calculations indicate the importance of resonances in near threshold excitation and de-excitation processes in He. An attempt has been made to understand the resonant structure by considering both the energy dependence of the eigenphases of the many-channel $S$ matrix produced by solving the close-coupling equations and the energy dependence of eigenvalues of the related time-delay matrix.

Atom–Molecule Kinetics Using ESR Detection. V. Results for O+OCS, O+CS2, O+NO2, and H+C2H4

Abstract: The wide‐temperature‐range, fast‐flow reactor with ESR detection used in previous papers of this series has been further improved so that rate coefficients of nearly 1013 cm3 mole−1·sec−1 can now be measured by the pseudo‐first‐order method. Results have been obtained over the temperature range 273°–808°K for the reaction O+OCS→CO+SO, over 227°–538°K for O+CS2→CS+SO, and over 297°–543°K for O+NO2→NO+O2 In Arrhenius form the rate coefficients are (cm3 mole−1·sec−1) k1 = 1.9 × 1013exp(− 4530 / RT); k2 = 1.2 × 1013exp(− 1050 / RT); k3 = 1.0 × 1013exp(− 580 / RT). The product SO in [1] and [2] was measured in its 3Σ ground state, and excited vibrational states could not be detected by ESR under our experimental conditions, although the SO must have been so excited initially. Stoichiometry and mechanisms are discussed. The H + C2H4 reaction was also measured in room‐temperature helium and argon, and in helium at 525°K. The data were obtained over a pressure range of about 0.5–2.5 mm, and the pressure dependenc...

Evidence for Luminescence Involving Arsenic Vacancy-Acceptor Centers in p -Type GaAs

Abstract: The observed similarity in the temperature behavior of peak shift, half-width, and intensity of the 1.37-eV band in $p$-type GaAs and the self-coactivated luminescence in ZnS substantiate a previously proposed model of recombination at an arsenic vacancy bound to an acceptor (Zn or Cd). The excitation spectra obtained through the use of GaAs laser diodes show a shoulder at 1.46 eV, just on the lower-energy side of the absorption edge. The shoulder is ascribable to absorption at the luminescence center responsible for the 1.37-eV band. Approximate configuration-coordinate curves are constructed for the centers in both Zn- and Cd-doped GaAs crystals from the experimental values of the low-temperature emission and excitation peak energies, the vibration frequency of the center in its excited state, and the activation energy for the temperature dependence of intensity. The non-Gaussian shape of the emission band is explained in terms of a small displacement between the minima of the configuration-coordinate curves. A vibration energy of 0.011 eV is determined for the excited state of the center, and a value between 0.011 and 0.0344 eV for the ground state of the center.

Band Structure and Impurity States

Abstract: A general formulation of the theory of electron impurity states in a lattice in the extended zone scheme is presented. The dependence of the impurity states on the band structure is discussed, and it is shown that the existence of secondary extrema in the band structure may produce additional bound and resonant states. A prescription is given for computing such states and for estimating the probabilities of transitions to them from the ground state; some properties of these transition probabilities are discussed. Solutions of onedimensional models are presented explicitly.

Dissociation energy of Li2 from laser-excited fluorescence

Abstract: The fluorescence spectra B 1Πu − X 1Σg+ of the molecular species 6Li2, 6Li7Li, and 7Li2, excited by the cw lines of the argon ion laser, have been observed and analyzed. Based on a short Birge–Sponer extrapolation of the vibrational levels of the ground state, the dissociation energy for the Li2 molecule has been determined to be D00 = 1.026 ± 0.006 eV. This value, combined with the dissociation limit of the upper state determined by Loomis and Nusbaum, proves that there is a hump of about 0.12 ± 0.04 eV above the asymptote of the potential curve of the Li2 B 1Πu state. Improved rotational and vibrational constants of the ground state of Li2 have also been obtained. A new technique is described which utilizes collision‐induced rotational transfer to facilitate the υ′, J′ assignment of the excited levels.

Fluorescence spectra of some retinyl polyenes.

Abstract: The fluorescence and absorption spectra of two series of retinyl1 polyenes have been measured. One series consists of the retinyl–carbon moiety with different end groups, these being the alcohol, acetate, acid, oxime, and methyl‐amine. The second group comprises the trans, 11‐cis, 13‐cis, and 9‐cis stereoisomers of retinol (vitamin A). The spectra of the first series have been measured at room temperature and 77°K in both hydrocarbon and methanol solvents. The acetate and acid have also been studied as crystals. The relative shapes and the degree of overlap of the absorption and fluorescence spectra are discussed in terms of simple potential‐energy diagrams. It is shown that the bands are severely Franck–Condon forbidden on two counts; first, by virtue of the bond alternation in the ground state that leads to a gross change in geometry of the nuclear framework on excitation, and second, from steric hindrance that occurs at various points in the retinyl–carbon framework. The spectra reported here show how an end group or a bend in the chain can affect the nature of the vibrational envelope. The effect of an environment is shown to be particularly pronounced upon Franck–Condon forbidden bands. The quantum yields of fluorescence at room temperature have been determined for the trans, 11‐cis, 13‐cis, and 9‐cis retinols, and trans‐retinyl acetate. The yields at room temperature are given in both hydrocarbon and polar solvents. The intensity of the fluorescence as a function of temperature has been estimated in some cases. Fluorescence could not be detected from retinyl acid and retinylidene methylamine at room temperature. The emission yield is shown to be correlated with the relative shapes of the ground‐ and excited‐state potential‐energy surfaces. It is suggested that vibrational relaxation in the excited state is the major process deactivating excited polyenes in fluid solution. The efficiency of this deactivating process is much reduced by increasing the viscosity of the environment. This process may be of great significance when polyenes are employed in photobiology. The radiative lifetime of trans‐retinol in methanol calculated from the data is 2.35 nsec.

Self‐Consistent Theory of Bond Alternation in Polyenes: Normal State, Charge‐Density Waves, and Spin‐Density Waves

Abstract: The unrestricted Hartree–Fock theory is used to investigate bond alternation in C4N+2H4N+2 cyclic polyenes. The possible ground states are examined as functions of the parameters in the Pariser–Parr–Pople model Hamiltonian. We show that charge‐density‐wave ground states do not exist for physical values of the input parameters. The normal, or molecular‐orbital, ground state does give rise to a negligible bond alternation at large N, in agreement with previous workers. Spin‐density‐wave ground states exist for most values of the parameters and have lower energy than the normal ground states. These states do not exhibit bond alternation when the sigma‐bond compression is the same as that used to obtain the normal energy.

High energy limit in rearrangement collisions

Abstract: The cross section for particle exchange from ground state to ground state in a three-particle collision is investigated. An asymptotic expansion for high incident energies can be given if the Fourier transforms of the interaction potentials allow an expansion in powers of 1/k for largek, which includes Coulomb interaction. It is shown that in general the first and second Born approximations provide the asymptotically leading terms. For special mass ratios, scattering into special (critical) angles becomes predominant. These angles, which are independent of energy, can also be determined employing classical arguments. Near the critical angles single terms of either the first or second Born approximation become dominant. If the exchanged mass is small, the interaction between the two heavy masses cancels near forward direction, implying the validity of the impact parameter theory. The results are discussed for Coulomb interaction as the simplest example (electron exchange). Here, the contributions by critical scattering are small unless the energies become exceedingly large.

Electron Nuclear Double Resonance in an Organic Molecule in a Triplet Ground State. Spin Densities and Shape of Diphenylmethylene Molecules in Diphenylethylene Single Crystals

Abstract: The electron nuclear double resonance spectra of the protons in diphenylmethylene molecules in the ground triplet state in a single crystal of 1,1′‐diphenylethylene have been studied. The values, in the fine structure principal axis system, of the components of the proton–electron hyperfine interaction tensor have been determined and tabulated. Both the values of the 7 distinguishable spin densities and the molecule geometry, which give best fit to the measurements, have been given. Calculations made by the method of intermediate neglect of differential overlap have been compared with the experimental results.

Far‐Infrared Spectrum and the Barrier to Pseudorotation of Silacyclopentane

Abstract: The far‐infrared spectrum arising from the transitions between the pseudorotational levels in silacyclopentane has been observed. Thirteen absorption maxima were found for the υ = 0 (radial ground) state and eight for the υ = 1 state. For each series a potential of the form V = (V2 / 2) (1 + cos2φ) predicts frequencies which agree very closely with the observed values. The values of V2, which represent the barriers to pseudorotation, were found to be 1362 ± 25 cm−1 for the radial ground state and 1301 ± 50 cm−1 for the first excited state. The pseudorotation constants for the two radial states were found to be B0 = 1.966 and B1 = 2.033 cm−1. The observed pseudorotation barrier of 3.89 kcal/mole represents the energy required to go from the more stable C2 half‐chair conformation to the Cs envelope form and is higher than expected from previously derived formulas.