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Volume 63, Issue 7, 01 October 1975

Time‐dependent wavefunctions for two independent perturbations
View Description Hide DescriptionA method of investigating the time development of two independent perturbations on a nuclear or electronic spin ensemble is presented. Without introducing unduly restrictive assumptions, a set of linear dependent differential equations is obtained, suitable for further numerical analysis. An explicit and general wavefunction Ψ^{(1)}(t) is derived for the presence of one time‐dependent perturbation. Explicit expressions for Ψ^{(2)}(t), the wavefunction of the spin ensemble under the influence of two time‐dependent perturbations, have been determined for various specific experimental conditions. The coefficients of expansion of Ψ^{(2)}(t) are presented in a form directly applicable for the determination of density matrices in an interaction representation. Qualitative conclusions based on these expressions are in agreement with reported experimental observations.

CS(A ^{1}Π→X ^{1}Σ^{+}) fluorescence from photodissociation of CS_{2} and OCS
View Description Hide DescriptionThe CS(A ^{1}Π→X ^{1}Σ^{+}) fluorescence resulting from photodissociation of CS_{2} and OCS by vacuum ultraviolet emission lines extending from λλ686–1239 Å has been investigated. With the assumption that the electronic transition moment is constant, the Franck–Condon factors for the emission system and the populations of the vibrational levels of the CS(A ^{1}Π) electronic state have been determined. The population data are approximately represented by a Poisson distribution, which is predicted from a theoretical model. A population inversion between the v=0 and 1 levels of the CS(A ^{1}Π) state is found. The cross sections for the production of fluorescence are also presented.

Vibrational energy transfer in polyatomic molecule collisions. I. High order corrections to the transition probabilities of vibrational energy transfer
View Description Hide DescriptionAn expansion technique of the evolution operator using the MAGNUS formalism enabled us to study the transition probability at one, two, three, and four quanta of vibration between the oscillators of two polyatomic molecules during a collision. In this paper the collisions are supposed to be not energetic enough to cause a series of multiple transitions, and the theory allowed us to study the validity of the first approximation of Born. At the same time the present work proposes a preliminary approach to the influence of the cubic and quartic potential constants and of the vibrational resonance on the vibrational transitions induced by collisions between polyatomic molecules. The theory is then applied to the collision CO_{2}–He.

Vibrational energy transfer in polyatomic molecule collisions. II. Role of multiquantum transitions during very energetic collisions
View Description Hide DescriptionIn a previous paper the processes of vibration energy transfer during a collision between two polyatomic molecules were studied using an operational calculation approach. This has enabled us to present analytical expressions for the probabilities of various events occuring during the collision of two diatomic molecules. A comparison with previous numerical calculations confirms the presence and the influence during these transfers of mechanisms which alter the characteristics of the nonperturbed oscillators and of multiquantum transitions.

Multiconfiguration studies of some low‐lying bound states of VH
View Description Hide DescriptionMulticonfiguration calculations using a hybrid of multiconfiguration self‐consistent field (MCSCF) and configuration interaction (CI) methods in a basis of Slater‐type atomic orbitals (STO’s) of nominal accuracy are carried out for some low‐lying bound states of VH. All the lowest states of the symmetries, ^{3}Σ^{−}, ^{5}Σ^{−}, ^{3}Π, ^{5}Π, ^{3}Δ, ^{5}Δ, ^{3}Φ, and ^{5}Φ, that dissociate to the ground states of the constituent atoms are bound and so are some of the excited states that have higher‐energy atomic dissociation products. The ground state is the lowest ^{5}Δ state for which the spectroscopic constants are computed to be R _{ e }=3.33 bohr, D _{ e }=1.87 eV, and ω_{ e }=1585 cm^{−1}. Potential curves and the computed spectroscopic constants are presented for the lowest states of all the above symmetries.

The a ^{3}Σ^{+} → X ^{1}Σ^{+} and b ^{3}Π → X ^{1}Σ^{+} band systems of SiO and the a ^{3}Σ^{+} → X ^{1}Σ^{+} band system of GeO observed in chemiluminescence
View Description Hide DescriptionChemiluminescence from SiO and GeO has been produced in a flowing gas system utilizing the reactions Si(^{3} P) + N_{2}O → SiO(b ^{3}Π,a ^{3}Σ^{+}) + N_{2} ΔH = −150 kcal/mole Ge(^{3} P) + N_{2}O → GeO(a ^{3}Σ^{+}) + N_{2} ΔH = −130 kcal/mole. An analysis of the chemiluminescencespectrum has shown that the emission originates in the b ^{3}Π and a ^{3}Σ^{+} states and terminates in the ground electronic state of SiO. The measured value of the spin–orbit coupling constant for the b ^{3}Π state was 75 cm^{−1}. No vibrational constants for either the a ^{3}Σ^{+} or b ^{3}Π states could be determined. T _{0} for the b ^{3}Π state was found to be 33 853 cm^{−1} while that for the a ^{3}Σ^{+} state was found to be 33 409 cm^{−1}. An analysis of the chemiluminescence of GeO was found to originate from the a ^{3}Σ^{+} state and terminate in the electronic ground state. T _{0} for the a ^{1}Σ^{+} state of GeO was found to be 27 552 cm^{−1}. Good agreement between the experimentally observed vibronic band intensities and those calculated using the Rydberg–Klein method has been obtained.

Low‐energy (≲3 eV) electron attachment to molecules in very‐high pressure gases: C_{2}H_{5}Br
View Description Hide DescriptionSignificant changes have been observed in both the magnitude and the energy dependence of the rate of attachment of slow (≲3 eV) electrons to bromoethane (C_{2}H_{5}Br) in either N_{2} or Ar gases with increasing density of these media from 500 to 25 000 Torr for N_{2} and from 500 to 42 000 Torr for Ar. The observed density and energy dependences of the attachment rates are discussed on the basis of two plausible reaction schemes involving either one or two states of C_{2}H_{5}Br^{−}. On the basis of the one‐state reaction scheme, determinations were made of the absolute rate of formation of C_{2}H_{5}Br^{−}* and of the relative magnitudes of the rates for dissociation and autoionization of the metastable C_{2}H_{5}Br^{−}* ion as a function of the mean electron energy 〈ε〉. On the basis of the same reaction scheme, the lifetime of C_{2}H_{5}Br^{−}* was estimated to be ?13 psec in the mean energy range 0.3–1 eV. Although the vertical attachment energy for the C_{2}H_{5}Br molecule is ∼0.75 eV, the present results imply that its adiabatic electron affinity is positive (≳0 eV).

Resolution corrections in total scattering cross section measurements
View Description Hide DescriptionAn expression is derived for the resolution correction based on the measured incident beam profile in the detector plane. The results are valid for any experimental configuration. Comparison is made with earlier treatments of this correction. The result given here will permit more accurate analysis of total scattering cross section measurements. Sample calculations are described and applied to recent determinations of the He–He potential. Finally, an expression is obtained for the small‐angle elastic differential cross section which can be used to deconvolute experimental measurements.

Gas phase ion chemistry of HNO_{3}
View Description Hide DescriptionThe ion chemistry of HNO_{3} is studied at 298 °K. The attachment of thermal electrons to HNO_{3} to produce NO^{−} _{2} is found to have a rate constant of (5±3) ×10^{−8} cm^{3}/sec. HNO_{3} reacts rapidly (k∼10^{−9} cm^{3}/sec) with a large variety of negative ions including Cl^{−}, NO_{2} ^{−}, O_{2} ^{−}, and CO^{−} _{3}. HNO_{3} is also found to bond strongly to NO_{3} ^{−}. The proton affinity of HNO_{3} is determined to be 176±7 kcal/mole. The present results indicate a strong similarity between protonated HNO_{3} and hydrated NO_{2} ^{+}, suggesting that these ion species are identical. The implication of the present results for atomospheric ion chemistry is discussed.

Vibrational relaxation of small molecules in the liquid phase: Liquid nitrogen doped with O_{2}, CO, and CH_{4}
View Description Hide DescriptionThe vibrational relaxation time of liquid nitrogen doped with CH_{4}, CO, and O_{2} at 77 °K has been measured by pulsed laser and spectroscopic techniques. Rate constants for V→Venergy transfer from N_{2} to the dopants and V→Trelaxation times have been obtained. These rates are consistent with a simple model which essentially treats the liquid as a high density gas where isolated binary collisions cause vibrational relaxation.

Three‐dimensional quantum mechanical studies of D+H_{2}→HD+H reactive scattering. II
View Description Hide DescriptionThree‐dimensional quantum mechanical calculations are carried out for the reactive scattering of D+H_{2}→DH+H on the Yates–Lester potential surface. The differential and total cross sections as well as the S‐matrix elements are obtained and are compared with the corresponding results obtained on the Porter–Karplus potential surface. The differential cross sections and the distributions over final angular momentum states are in much better agreement with the experimental measurements than the previous results obtained on the Porter–Karplus surface. However, the calculated threshold energy for the reaction seems too high whereas the threshold on the Porter–Karplus potential seems too low. These dynamic attributes are discussed in terms of the two‐body potentials between the atom and the molecule.

Hyperfine structure in the red emission system of NbN
View Description Hide DescriptionA detailed study of hyperfine structure observed in the 0,0 band of the ^{3}Φ (a _{β}) →^{3}Δ (a _{β}) system of NbN has shown that the secondary hyperfine effects observed in this structure are not due to a perturbation in the ^{3}Δ state but rather to the presence of a nonnegligible hyperfine effect in the ^{3}Φ excited state. Calculations of the intensity factors corresponding to the observed transitions confirm this hypothesis and give results in excellent agreement with experiment.

The dynamical structure factor S (Q,ω) of solid α‐N_{2}
View Description Hide DescriptionWe report the first results of a classical computer simulation(molecular dynamics) study of the dynamical structure factor S (Q,ω) for a simple model of a homonuclear diatomic solid in the α‐N_{2} structure. For a particular wave vector Q the peaks in S (Q,ω) can be identified with phonons and their associated widths as inverse lifetimes. The model consists of 250 molecules arranged with periodic boundary conditions in the cubic P a3 structure and interacting via a Mie–Lennard‐Jones (12–6) potential between their ends. Two runs were carried out with parameters such that for solid α‐N_{2} they corresponded to the conditions (T=17 K, a=5.65 Å) and (T=35 K, a=5.684 Å). In neither case do the phonon peaks agree well with the predictions of quasiharmonic lattice dynamics. Moreover, at the higher temperature many of the S (Q,ω) peaks show a large quasielastic peak which we interpret as being because of ’’rotational diffusion’’ of the molecules.

A b i n i t i o force constants for the HCN molecule: SCF and CI results
View Description Hide DescriptionForce constants for HCN have been determined from both the one‐electron model, SCF, and correlated, CI, wavefunctions. Using SCF wavefunctions, the stretching force constant for the CH bond, K _{11}, is 9% larger than experimentally determined values and the CN stretch, K _{22}, is 23% larger. When electron correlation is included through the use of configuration interactionwavefunctions the agreement of computed and experimental force constants is greatly improved; K _{11} is 5% larger than the experimental value and K _{22} is 9% larger. The force constants are determined by making least square polynomial fits to computed points on the potential surface. Force constants for both stretch and bending modes are reported through quartic terms.

Experimental observations of gas phase–adsorbed phase interactions during counterdiffusion in porous alumina
View Description Hide DescriptionThe binary gas systems helium–argon, helium–nitrogen, helium–1‐butene, and argon–1‐butene were counterdiffused through a plug of porous alumina at 135° and 150 °C and 1–3 atm pressure in a Wicke–Kallenbach experiment. The helium, nitrogen, and argon were essentially nonadsorbing; the butene was significantly adsorbed and diffused along the surface. Knudsen flow existed within the pores at most experimental conditions, i.e., the gas–gas molecular collisions were negligible in comparison with gas–surface collisions. The results showed that gas‐adsorbed phase collisions can have significant effects at conditions typical of laboratory and industrial practice. Strong evidence of interactions between all gas‐phase molecules and adsorbed butene molecules was observed whenever the butene was present. Both helium and argon fluxes were significantly less when counterdiffused with 1‐butene than when counterdiffused with nonadsorbing gases. The butene flux was markedly less when diffused against the argon than when diffused against the helium. The collisional effects were so strong in the argon–butene system that at low pressure the adsorbed 1‐butene was driven in a direction counter to the concentration‐gradient driving force. Apparently the efficiency of momentum transfer during the argon‐adsorbed butene collision was much greater than during the gaseous butene‐adsorbed butene collision.

Configuration and interstitial relaxation processes
View Description Hide DescriptionA theory of orientational and interstitial relaxation processes is presented in which the phenomena are characterized as transitions between nonstationary zeroth order configurations. A number of different mechanisms are separated according to the relative timescales of the libron (interstitial) motion and relaxation and the phonon motions. These mechanisms lead to differing temperature dependences that should be amenable to experimental verification. The full (many) phonon participation is included and gives a polaronlike character to the relaxing libron (interstitial). The present theory of activated rate processes departs from the conventional transition state theory. The concept of the activation energy barrier to relaxation is seen to originate from an ensemble average of nuclear tunneling rates from the individual librational levels.

^{87}Rb spin–lattice relaxation study of the ferroelectric phase transition in RbH_{2}PO_{4}
View Description Hide DescriptionThe temperature dependences of the ^{87}Rb laboratory (T _{1}) and rotating frame (T _{1ρ}) spin–lattice relaxation times were measured in RbH_{2}PO_{4}. The relaxation rates are determined by two competing effects: by a ’’fast’’ soft mode relaxation mechanism which dominates at lower temperatures near the ferroelectric transition, and by a ’’slow’’ high temperature motion mechanism which is rate determining above 220 °K. The soft mode spectrum was found to be flat between 18 and 320 kHz. The ’’uncorrelated’’ order parameter correlation time τ_{ a }=4×10^{−13} sec at 200 °K is of the same order as in other KH_{2}PO_{4} ferroelectrics.

Vibration–vibration energy transfer in HF dimers
View Description Hide DescriptionA theory of vibration–vibration energy transfer is developed for hydrogen fluoride molecules based on the model of energy transfer through the interaction of H of one HF molecule with F of the other in a nonrigid hydrogen‐bond dimer. The theory is applied to HF(n)+HF(0) →HF(n−1)+HF(1)+ΔE for values of the vibrational quantum number up to 5. Calculations at 300 °K show the rapid energy exchange for these processes. Particularly fast rates are found for the collisions involving high vibrational states with small values of the energy mismatch. Reasonable agreement between the present theory and experiment is found for the deactivation processes with n=2, 3, 4, and 5.

Kinetics of concentration fluctuations in a binary alkali–silicate system
View Description Hide DescriptionLaser light scattering was applied to a potassium–silicate system to observe the growth of supercritical concentration fluctuations. The Rayleigh and Brillouinspectra of our glass samples were measured as a function of heat treatment time duration and temperature. From the spectra we obtained the Landau–Placzek ratios and Brillouin shifts for each heat treatment interval and temperature. In glass forming melts, critical points may occur in regions of high shear viscosity; here because of the low mobility, relaxation times for concentration fluctuations are on the order of many hours. Thus, heat treatment followed by rapid quenching ’’freezes in’’ the fluctuations characteristic of the treatment temperature, and consequently the light scatteringmeasurements detect the high temperature structure. The measurements reported here provide the first direct evidence for a phase transition in a potassium–silicate system. From the equilibrium Landau–Placzek ratios, the spinodal temperatures were calculated. We also discuss the relaxation times for the system and the critical exponents.

On the relation between gaseous ion mobility and diffusion coefficients at arbitrary electric field strengths
View Description Hide DescriptionA generalized Einstein relation for gaseous ions is shown to be accurate even at high electric field strengths, provided care is taken in the evaluation of the ion temperature. Comparison with experiment is made for K^{+}ions in He, Ne, and Ar. The validity of this relation means that gaseous ion diffusion coefficients can be calculated from the more easily measured mobilities.