Volume 69, Issue 3, 01 August 1978
Index of content:

Kinetic instabilities in first order phase transitions
View Description Hide DescriptionLinear stabilityanalysis is used to show that an homogeneous system in the early ’’aging’’ stage of a first order phase transition is unstable to heterogeneous development. A detailed analysis appropriate to precipitation out of a solution is presented although only the most general features of a first order phase transition are actually necessary. A linear dispersion relation is constructed which can also be applied to an initially heterogeneous system and which predicts heterogeneous development in general agreement with observed Liesegang ring formation.

Application of molecular orbital method to crystalline solids: Calculation of the electronic energy bands of diamond‐type crystals
View Description Hide DescriptionThe electronic energy band structures of diamond‐type crystals (C, Si, Ge, and α‐Sn) are calculated by use of extended Hückel theory, taking into account all interactions between atoms up to the sixth neighbors. Reasonable overall agreement is obtained with experiments or other calculations when the four parameters included are adjusted to fit the experimental energies at two points in the Brillouin zone, zone center and conduction band minimum. This suggests the possibility of a reliable utility of this method for the systematic study of electronic structures of Si, Ge, and α‐Sn as well as diamond.

A b i n i t i o SCF calculations on molecular silicon dioxide
View Description Hide DescriptionA b i n i t i o SCF calculations are performed on molecular silicon monoxide and dioxide. These computations show that the electronic ground state for molecular SiO_{2} is ^{1}Σ^{+} _{ g } and has a D _{∞h } geometry, and that molecular SiO_{2} is bound with respect to SiO(^{1}Σ^{+}) and O(^{1} D). Vibrational frequencies are computed in order to aid in the identification of this enigmatic species.

A b i n i t i o SCF MO calculations of the potential surfaces of thiocarbonyls. I. ? ^{1} A _{1} and ? ^{3} A _{2} electronic and ? ^{3} A _{2}(b _{1}) vibrational states of F_{2}CS
View Description Hide DescriptionA b i n i t i o SCF MO calculations using an STO‐3G basis set have been carried out to obtain the potential energy surfaces of the ground ? ^{1} A _{1} and lowest triplet ? ^{3} A _{2} states of F_{2}CS. The calculated equilibrium geometry of the ground state is in good agreement with the experimental geometry. Using a suitable analytic approximation to the triplet state potential surface, energies of the stack of triplet state inversion vibrational levels associated with a double minimum potential curve along the out‐of‐plane bending coordinate have been calculated. Good agreement with experiment is obtained.

A b i n i t i o effective core potentials including relativistic effects. II. Potential energy curves for Xe_{2}, Xe^{+} _{2}, and Xe*_{2}
View Description Hide DescriptionPotential energy curves for the ground ^{1}Σ^{+} _{ g } state of Xe_{2}, the first four states of the Xe^{+} _{2} ions, and the eight Xe*_{2} excimer states corresponding to the addition of a 6sσ_{ g }Rydberg electron to these ion cores have been computed using averaged relativistic effective core potentials (AREP) and the self‐consistent field approximation for the valence electrons. The calculations were carried out using the LS‐coupling scheme with the effects of spin–orbit coupling included in the resulting potential energy curves using an empirical procedure. A comparison of nonrelativistic and averaged relativistic EP’s and subsequent molecular calculations indicates that relativistic effects arising from the mass–velocity and Darwin terms are not important for these properties of Xe_{2} molecules. Spectroscopic constants for Xe^{+} _{2} are in good agreement with all electron CI calculations suggesting that the computed values for Xe*_{2} excimers should be reliable. The lifetime for the O _{ u } ^{+} state of the Xe_{2}* is computed to be 5.6 nsec which is in the range of the experimentally determined values.

A b i n i t i o studies of AuH, AuCl, HgH and HgCl_{2} using relativistic effective core potentials
View Description Hide DescriptionRelativistic effective core potentials (ECP) are derived for Au and Hg atoms, where the ECP incorporates the Coulomb and exchange contributions of the core orbitals, the core‐orthogonality terms for the valence orthogonality terms for the valence orbitals, and the effect of the ’’mass–velocity’’ and ’’Darwin’’ relativistic effects on the valence orbitals. The results of atomic valence‐electron (VE) calculations with the ECP’s compare favorably with relativistic Hartree–Fock and Dirac–Hartree–Fock calculations and with experiment, when the effects of spin–orbit coupling are included in the VE calculations. Nonrelativistic calculations, by contrast, lead to erroneous predictions and to differences in excitation energies of 1.5–3.5 eV. The large relativistic effects in the atoms carry over into the AuH, AuCl, and HgCl_{2} molecules, as they are important in determining correct bond lengths and bond energies and in influencing the charge distributions. Similarly large relativistic effects are encountered in ionization potentials calculated for HgCl_{2} from orbital energies and from SCF calculations. Spin–orbit coupling is introduced to compare with the experimental photoelectron spectrum. An extensive study of the lowest electronic states of HgH is presented, where the effects of spin–orbit coupling are critical in describing the potential energy curves of the excited ^{2}Π_{1/2} and 2^{2}Σ^{+} _{1/2} states.

Dielectric friction and molecular reorientation
View Description Hide DescriptionWe present a theory of the effect of dielectricfriction on molecular reorientation. This theory is based on a rotational Smoluchowski equation with fluctuating torques due to polarization fluctuations. This theory predicts several interesting consequences of dielectricfriction which should be susceptible to experimental test: In contrast to previous theories, dielectricfriction is shown to have a decreased effect for higher l rotational correlation functions. The theory also leads to unusual results for molecular reorientation in polar mixtures.

Friction on a rotating dipole
View Description Hide DescriptionA formula is derived for the viscous and dielectricfriction on a steadily rotating spherical dipole for the case of an arbitrary ’’slipping coefficient’’. In the perfect slip limit, I recover the Nee–Zwanzig formula for dielectricfriction at zero frequency, given that a simple Debye dispersion describes the dielectric response of the medium.

Brownian dynamics study of transitions in a polymer chain of bistable oscillators
View Description Hide DescriptionThe potential of a bistable oscillator is taken as two quadratic wells separated by a quadratic barrier. The Brownian motion of a particle in such a field has been computer simulated for a variety of values of the barrier height and friction constant. The rate of passage over the barrier conforms well to Kramers’ theory. A chain in which each of the bonds is a bistable oscillator was then studied as a model of conformational transitions in a polymer. One question investigated was to what degree do the transitions occur cooperatively. The bond transition rates are found to compare fairly well with a Kramers‐like theory, with no cooperativity. However, a direct examination of the correlation between transitions shows some enhancement of the transition rate of near neighbors immediately following the transition of a bond.

Optical oscillator strengths for argon
View Description Hide DescriptionAn analytic atomic independent particle model is used to calculate optical oscillator strengths for 3p–n s and 3p–n d transitions in Ar. The results are compared to experiment and Hartree–Fock calculations.

Relaxation of the squeezing mode in free liquid films, measured by laser light scattering
View Description Hide DescriptionThe experimental setup to prepare free liquid films (from solutions of hexadecyltrimethylammoniumbromide) and to perform light scattering experiments on these films is described. Dynamic light scattering experiments concerning the relaxation of the squeezing mode (i.e., periodic thickness fluctuations) are reported for films of thickness between 35 and 100 nm and for mode wavelengths between 2.3 and 17.9 μm. In part of the wavelength regime good agreement is found between the experiments and existing hydrodynamic and classical colloidal interaction theories.

Electric and magnetic field spectra of the T _{1}←S _{0} transition in crystalline 1,4‐naphthoquinone
View Description Hide DescriptionThe pure electronic T _{1}←S _{0} transition of naphthoquinone single crystals has been investigated in electric and magnetic fields. The factor group states have been assigned ; their energies with respect to their mean value at 20 238 cm^{−1} are as follows: B _{ u }=−1.20 cm^{−1}; A _{ g }=−0.54 cm^{−1}; A _{ u }=+0.45 cm^{−1}; B _{ g }=+1.29 cm^{−1}. The molecular spin splitting parameters have been evaluated from the measured crystals spin splittings as follows: X=0 cm^{−1} Y=−0.16 cm^{−1} Z=+0.16 cm^{−1}. The molecular triplet state in the crystal is assigned as a superposition of the two n–π* states of the free molecule: ‖T _{1}≳ =‖n–π*^{3} B _{2}≳−0.08‖n–π*^{3} A _{2}≳. This assignment is in agreement with the observed polarization and intensity distribution among the spin sublevels; it also explains the direction of the change of dipole moment upon excitation which—in the crystal—does not coincide with the polar axis of the molecule and makes it possible to determine its sign along the polar axis of the free molecule.

Evolution of the spectrum of the solvated electron in BeF_{2} aqueous glasses at 76 K
View Description Hide DescriptionEvidence is presented for a spontaneous shift from infrared‐to‐ red‐to‐green in the overall spectrum of the electron trapped in an aqueous glass at 76 K following nanosecond pulse radiolysis. As with the alcohols, after the pulse the infrared absorption decays, there is a growth‐then‐decay of absorbance at intermediate wavelengths and net growth of absorption due to the equilibrated trapped electron state, e ^{−} _{vis}. This progressive transition was not characterised by a single‐step process and was discernible in aqueous glasses containing 7.5 or 10.7M BeF_{2} in D_{2}O. At higher BeF_{2} concentrations, or with LiBr as glass‐forming electrolyte, no growth of e ^{−} _{vis} was observed, probably because of concurrent loss of e ^{−} _{vis} in those glasses, as in LiCl and other glasses. BeF_{2} glasses of trapped electrons showed several other features of interest: (i) wavelength‐ selective bleaching of the e ^{−} _{vis} band indicates that it is composed of a broad ’’green’’ band (λ_{max}, 530–590 nm) which bleaches homogeneously, and a broad ’’red’’ region which bleaches inhomogeneously. (ii) λ_{max} for e ^{−} _{vis} changes with BeF_{2} concentration, being blue shifted with increasing concentration , with both green and red underlying structures shifting slightly. (iii) No absorption due to F^{−} _{2} was found following pulse radiolysis in these glasses at 76 K. (iv) Several recent findings with LiCl are mimicked by F^{−} _{2} glasses. For instance, G (e ^{−} _{vis}) increases and G (e ^{−} _{ir}) decreases as the electrolyte concentration is increased, while the combined yield remains constant at 1.8±0.1.

Rotational relaxation within the ^{1} B _{2u }(S _{1}) state of benzene
View Description Hide DescriptionRelaxation from nonequilibrium rotational distributions to a Boltzmann‐like distribution within the zero point level of S _{1} benzene vapor is studied using ground state benzene and argon as collision partners. The initial distributions are established by excitation with a narrow‐band (0.3 cm^{−1}) laser tuned to various positions within the rotational contour of the 6^{0} _{1} absorption band. The course of rotational relaxation is then followed by observations of the dependence of rotational contours in fluorescence bands upon gas pressure. Arguments are given to suggest that relaxation approximates a single‐step process, with collisions taking the initial nonequilibrium distribution directly to a broad distribution of J′K′ levels reminiscent of the Boltzmann distribution. The rate constant for this relaxation is about 9×10^{7} torr^{−1} sec^{−1} for benzene as a collision partner, which is about eight times the gas kinetic value. This constant is observed for each of two different initial distributions. It is likely that switching of electronic energy in collisions between S _{1} benzene and rotationally equilibrated S _{0} benzene makes a substantial contribution to this relaxation. The rate constant for relaxation in argon collisions is much smaller and depends on the initial distribution, being 1.5×10^{7} and 3.5×10^{7} torr^{−1} sec^{−1} for the two cases measured. Some applications of these data to rotational effects in radiationless transitions are discussed.

Excitation of the b ^{1}Σ^{+} _{ g } state of O_{2} by low energy electrons
View Description Hide DescriptionRate coefficients for excitation of the b ^{1}Σ^{+} _{ g } state of O_{2} by low energyelectrons have been measured using a drift tube technique. The time dependence of the absolute intensity of the 762 nm band emission was measured for O_{2} densities between 10^{16} and 2×10^{18} molecules/cm^{3}. When corrected for electron attachment, ionization, and metastable diffusion, the number of b ^{1}Σ^{+} _{ g } molecules produced per centimeter of electron drift and per O_{2} molecule calculated from the 762 nm emission varied from 1.3×10^{−18} cm^{2} at E/N=5×10^{−17}V cm^{2} to 2.1×10^{−16} cm^{2} at E/N=2×10^{−15}V cm^{2}. These values of electric field to oxygen density ratio E/N correspond to mean electronenergies of 0.75 and 6 eV, respectively. Measured decay constants for the 762 nm radiation yield a value for the product of the diffusion coefficient and the O_{2} density of (5.0±0.3) ×10^{8} cm^{−1} sec^{−1} and a quenching coefficient for the b ^{1}Σ^{+} _{ g } state of (3.9±0.2) ×10^{−17} cm^{3} sec^{−1}. Comparison of measured excitation coefficients with values calculated using a recommended set of electron collision cross sections for O_{2} show that the cross sections for direct excitation of the b ^{1}Σ^{+} _{ g } state are accurate near threshold and suggest that essentially all of the O_{2} molecules excited to levels at and above 1.63 eV result in the formation of molecules in the b ^{1}Σ^{+} _{ g } state.

The far infrared absorption spectrum of ethylene in the liquid phase
View Description Hide DescriptionThe far infrared absorption spectra of liquid ethylene have been measured at −145, −130, and −70°C. We attempt to account for the absorption on the basis of the quadrupole induced dipole interaction. We point out certain discrepancies and anomalies regarding the cancellation effect in the liquid phase.

Variational treatment of the proton–phonon system in KDP
View Description Hide DescriptionFerroelectric KDP is best described through an Ising Hamiltonian in a transverse field, coupled linearly to the phonon system. The soft optical mode is coupled to the order parameter, whereas the dependence of the transition temperature on deuteration follows from the coupling of the tunneling frequency to another optical branch. After unitary transformations of the Hamiltonian, in which parts of the phonon coupling are dealt with, an analytic upper bound for the free energy of the KDP system is found using Bogoliubov’s inequality. This allows a choice from the class of different canonical transformations of that one leading to the lowest free energy bound. Then, in a mean field approximation, the effective coupling constant is found to be a solution of an implicit analytic function, which is solved numerically for different coupling strengths. In the ferroelectric region a strong temperature dependence of the effective coupling is found; crossing into the paraelectric region, its value changes smoothly for weak and abruptly for medium coupling strengths. These results parallel the behavior found in phonon coupled exciton systems.

The photoelectron spectra of the chloramines NH_{2}Cl, NHCl_{2}, NCl_{3} and the methyl chloramines CH_{3}NHCl, CH_{3}NCl_{2}, and (CH_{3})_{2}NCl
View Description Hide DescriptionThe complete series of chlorinated and methylated derivatives of ammonia have been prepared in the pure state and studied by Hei ultraviolet photoelectron spectroscopy. The nonmethyl derivatives were also studied using NeI radiation. Assignments are made on the basis of observed substitution effects, and the spectra are compared with the analogous phosphorus compounds. The first band in all the spectra (arising from ionization of the nitrogen lone pair), shows interesting trends both in position and in bandwidth.

One‐phonon scattering of atoms in three dimensions by a simplified continuum model of a surface: Thermal desorption
View Description Hide DescriptionA model of thermal desorption of atoms from surfaces is presented. The treatment is quantum mechanical, and calculations are made using the first‐order distorted‐wave Born approximation, within the one‐phonon approximation. The atom–surface interaction potential is a Morse potential, and the modal properties of the surface are those of a bulk continuum, the work being a natural continuation of some earlier atom–surface scattering work of Goodman. Our conclusions are inconsistent with some of those of Bendow and Ying and Ying and Bendow, who reported pre‐exponential factors τ_{0} of order 10^{−5} s in the standard Frenkel formula for desorption; our values of τ_{0} are more in accord with the previously accepted values, of order 10^{−12} s. We apply the model to the astrophysical system H–C, and to interpretation of some experimental data on the systems He–Ar, He–Kr, and He–Xe; we find satisfactory agreement with experiment.

Energies and relative cross sections of singlet–triplet transitions in methyl‐substituted 1,3‐butadienes by ion‐impact spectroscopy
View Description Hide DescriptionThe energies of the 1 ^{3} B _{ u }←? ^{1} A _{ g } and 1 ^{3} A _{ g }←? ^{1} A _{ g } transitions of a number of methyl‐substituted 1,3‐butadienes have been determined by ion (He^{+} and H_{2} ^{+}) ‐impact energy‐loss spectroscopy. The observed values were relatively invariant at 3.2 and 4.9 eV, respectively, except in the case of 2,4‐dimethyl‐1,3‐pentadiene where triplet states at 3.5 and 4.4 eV indicate a nonplanar conformation or conformations. The relative cross section for the 1 ^{3} B _{ u }←? ^{1} A _{ g } transition in the He^{+}‐impact spectrum of t r a n s‐1,3‐pentadiene was observed to increase slightly relative to that for the 1 ^{3} A _{ g }←? ^{1} A _{ g } transition and substantially relative to that for the 1 ^{1} B _{ u }←? ^{1} A _{ g } transition on decreasing the ion energy from 3.5 to 1.5 keV. Cross sections for all three transitions decreased on changing the projectile from 3.0 keV H^{+} to 3.0 keV H_{2} ^{+} and from the latter to 3.0 keV He^{+}. Finally, the relative cross section for the 1 ^{1} B _{ u },2 ^{1} A _{ g }←? ^{1} A _{ g } transitions is decreased only slightly (by up to a factor of 2) on adding up to four methyl groups whereas the 1 ^{3} B _{ u }←? ^{1} A _{ g } and 1 ^{3} A _{ g }←? ^{1} A _{ g } relative cross sections suffer a decrease of about a factor of 10 for He^{+} impact and a bit less for H_{2} ^{+} impact.