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Volume 72, Issue 3, 01 February 1980

The magnetic circular dichroism spectrum of carbon disulfide
View Description Hide DescriptionThe magnetic circular dichroism spectrum of carbon disulfide vapor in the 300–380 nm region is reported and analyzed. The signs of the A terms associated with the P and R rotational branches of the triplet bands are negative and positive, respectively. These data are used in an accompanying theoretical paper (following paper in this journal) to calculate the zero field splittings in the ^{3} A _{2} state of CS_{2}.

Theoretical analysis of the magnetic circular dichroism spectrum of carbon disulfide
View Description Hide DescriptionThe upper level of the near‐ultraviolet absorption system of carbon disulfide (the R system) is the B _{2} spin‐multiplet component of a ^{3} A _{2} state. A theoretical analysis of the magnetic circular dichroismspectrum of the R system shows that if, as has been assumed previously, the A _{1} and B _{1} spin‐multiplet components of the ^{3} A _{2} state are degenerate, they lie above the B _{2} component. This result is at variance with earlier conclusions. The only ordering of the spin‐multiplet components which is consistent with all available data is one in which the A _{1} and B _{1} components are nondegenerate, with both of these components lying below the B _{2} component. The available data are insufficient to assign the relative ordering of the A _{1} and B _{1} components.

Analytic solution of relaxation in a system with exponential transition probabilities. II. The initial transients
View Description Hide DescriptionUsing an exponential transition probability model normalized in the (0,∞) energy domain, we have obtained an analytical solution for the time‐dependent population density below threshold, c (x,t), in the form of the eigenfunction expansion where x is internal energy,t is time, A _{0} and A _{ j } are constants that depend on initial conditions, S and R _{ j } are solutions of a determinant of a matrix of coefficients and k _{0} ^{−1} and τ_{ j } are the relaxation times, the lowest of which (subscript 0) represents the reciprocal of the steady‐state rate constant. From c (x,t) we then obtain all other time‐dependent properties such as the non‐steady‐state rate constant and average energy, as well as incubation times and dead times for both number density and vibrational energy. Calculations relative to shock tube decomposition of N_{2}O, CO_{2}, and O_{2} in inert gas are compared with experiment, with generally good results. For the triatomics, average energy transferred per collision, as calculated from the experimental relaxation time, compares well with that calculated from the Schwartz–Slawsky–Herzfeld theory. The calculated diatomic rate constants (but not the relaxation and incubation times) are too low. Calculations relative to shock tube decomposition of cyclopropane are compared with numerical calculations of Malins and Tardy using a stepladder model. It is concluded that non‐steady‐state effects are unlikely in the cyclopropane shock tube work, and that diatomic rate constants are sensitive to rotational energy transfer.

Exponential transformation of molecular orbitals: A quadratically convergent SCF procedure. I. General formulation and application to closed‐shell ground states
View Description Hide DescriptionA new formulation is proposed for obtaining the SCF wave functions. It is based on an exponential transformation of spin–orbitals which obviates the use of Lagrangian multipliers. A general method is developed for determining explicit expressions for the successive derivatives of the energy with respect to the new variables. The total energy and the wave function are obtained by an iterative procedure, the convergence of which is shown to be quadratic. The method itself provides information as to the Hartree–Fock stability — or instability — of the SCF solution. The method of exponential transformation of molecular orbitals is applicable to closed‐shell systems, as well as to a large variety of open‐shell systems. As an illustration of the procedure the results of a b i n i t i o calculations for ammonia, methane, formaldehyde, and aziridine are given.

A single crystal EPR study of ground state triplet trimethylenemethane
View Description Hide DescriptionTrimethylenemethane, a ground state triplet, has been generated in a single crystal of methylenecyclopropane by γ irradiation at 77 K and studied by the electron paramagnetic resonance technique in the temperature range 4.2–106 K. From the observed anisotropy of the EPR spectra, the zero‐field splitting constants can be determined as D=0.0248 cm^{−1} and ‖E‖?0.0003 cm^{−1}, and the principal values of the protonhyperfine coupling tensor as −14, −38, and −26 MHz with an isotropic coupling of −26 MHz at 77 K. Computer simulations of some of the spectra were performed using a computer program developed for this investigation. Both the position and the intensity of the spectral lines were reproduced with a good result. The simulations gave a positive sign for the zero‐field splitting constant D. The zero‐field splitting is temperature dependent above c a. 20 K, probably due to an oscillating motion of the molecular plane. The hyperfine structure changes above c a. 80 K and becomes isotropic at 100 K. This change is attributed to an anisotropic rotation about the threefold symmetry axis of the molecule.

The photochemistry of nitrosyl halides: The X+NOX→X_{2}+NO(v) reaction (X=Cl, Br)
View Description Hide DescriptionThe primary and secondary photochemistry of NOBr and NOCl has been monitored by detecting infrared fluorescence from vibrationally excited NO following pulsed photolysis of the parent compound with a tunable laser. For wavelengths greater than 480 nm the primary photolysis of NOX to NO+X produces little if any vibrational excitation in the NO product. However, secondary photochemistry produces excited NO through the reaction X+NOX→X_{2}+NO(v). From the dependence of the rise time of NO fluorescence on the pressure of NOBr or NOCl at a constant pressure of added argon, it is found that the rate constants for the Br+NOBr and Cl+NOCl reactions are (5.16±0.28) ×10^{−12} and (5.40±0.47) ×10^{−12} cm^{3} molecule^{−1} sec^{−1}, respectively. The reaction of Br with NOBr produces more NO in v=3 and/or v=2 than in v=1. At 355 nm roughly half of the NO vibrational fluorescence is due to the primary dissociation NOX→X+NO(v).

Einstein A coefficients, oscillator strengths and lifetimes for some selected triplet–triplet transitions of N_{2}: A comparison between theory and experiment
View Description Hide DescriptionEinstein A coefficients, oscillator strengths and lifetimes have been calculated by an asymptotic expansion method, introduced by Chang and Karplus, for the N_{2}, B ^{3}Π_{ g }→A ^{3}Σ^{+} _{ u } (first positive), C ^{3}Π_{ u }→B ^{3}Π_{ g } (second positive), W ^{3}Δ_{ u }⇄B ^{3}Π_{ g } (Wu–Benesch) and B′ ^{3}Σ^{−} _{ u }→B ^{3}Π_{ g } (infrared afterglow) band systems, using theoretical electronic transition moments, R e (r), of Yeager and McKoy. Whenever possible, comparison has been made with those calculated from the electric dipole moment functions, R e (r̄), which are functions of r̄ centroids, obtained from band intensity or lifetime measurements. Excellent agreement has been obtained in the case of the second positive band system of molecular nitrogen. However, for all other cases, conventional R e (r̄) functions are found to be superior to the theoreticalR e (r) functions of Yeager and McKoy.

Surface tension of a simple fluid: Many body potential
View Description Hide DescriptionA general statistical mechanical expression is derived for the surface tension of a fluid with an arbitrary many body interaction potential, which reduces to the Kirkwood–Buff formula under the assumption of pairwise additivity. Sum rules for the inhomogeneous system with the many body potential are also presented. These are then used to show that the general expression for surface tension is formally equivalent to the fluctuation formula due to Yvon, and to a recent correlation function expression of Jhon, Desai, and Dahler.

Non‐Boltzmann, non‐Treanor vibrational level populations of electrical discharge excited nitrogen
View Description Hide DescriptionVibrational level population distributions of electrical discharge excited nitrogen were measured to v=5 using the electron beamfluorescence diagnostic technique. Measurements were made in the free jet expansion from an electrical discharge for both pure nitrogen and nitrogen–carbon monoxide mixtures. All measured distributions were highly non‐Boltzmann and also deviated from the Treanor quasisteady state distribution. A numerical matching technique was used to predict the shape of the vibrational population distribution for a given total vibrational population. The numerical results predict the shape of the distribution very well for all experimental conditions. The numerical modeling also showed that the deviation from Treanor conditions occurs because the V–V rates and electron excitation rates in the discharge are of the same order of magnitude for discharge pressures of a few Torr.

Riemann tensor theory of liquid state chain dynamics
View Description Hide DescriptionThe Riemann–Kirkwood–Fixman diffusion equation is applied to the analysis of rotational and torsional dynamics of alkane chains in liquids. It is found that the covariant metric can be calculated for chains of arbitrary length. For the three bond chain, butane, the covariant metric can be easily inverted and a diffusion equation for overall as well as internal rotation is derived. The internal torsional and overall rotational degrees of freedom are coupled by an internal angular momentum, originally proposed by Eckart. The time dependent torsion angle distribution function satisfies a diffusion equation with a nonlocal diffusion coefficient that is found to be in accord with our earlier work [J. Chem. Phys. 70, 2362 (1979)] and that of Pear and Weiner [J. Chem. Phys. 71, 212 (1979)].

Brownian dynamics simulation of alkane chain reorientation: A comparison of models
View Description Hide DescriptionOrientational time correlation functions and correlation times are determined using a Brownian dynamics and rigid body formalism and are compared with the results obtained from our previous Mori approach. It is found that the Mori method equipped with a minimum set of primary variables approximately represents the freely rotating chain. The correlation functions obtained from Brownian dynamics were found to display a rapid initial decrease, followed by a slow nearly exponential fall‐off. First and second rank correlation times for pentane, hexane, nonane, and undecane are reported.

Differential cross sections for the j=0→1 rotational excitation in HD–Ne collisions and their relevance to the anisotropic interaction
View Description Hide DescriptionIn a crossed molecular beam experiment, time‐of‐flight distributions of HD‐molecules scattered from Ne at an energy of 31.5 meV have been measured using the pseudorandom chopper method. Each time‐of‐flight spectrum shows a clearly resolved inelastic peak due to rotational excitation of HD from j=0 to j=1. With the aid of these spectra, together with additional measurements of the total differential cross section, the angular dependence of the differential cross section for the excitation j=0→1 is derived over a large angular range (20° to 120°). The sensitivity of the data to the interaction potential is carefully studied and the measured inelastic differential cross sections are compared with calculations based on interaction potentials recently proposed for this system.

The magnetic susceptibility of BH
View Description Hide DescriptionThe magnetic susceptibility of the BH molecule is calculated using large configuration interactionwave functions for the ^{1}Σ^{+}ground electronic state. The paramagnetic contribution to the susceptibility is determined in a sum over states where the set of Π configurations is restricted to ?400. BH is again found to be paramagnetic but with magnitude substantially reduced from coupled Hartree–Fock and multiconfiguration coupled Hartree–Fock perturbation results. The best configurational interaction calculations gave values of 5.984 and −3.279 (in parts per million cgs) for the susceptibility when the gauge origin was taken to be the B and the H nuclei, respectively.

Structural relaxation time of D_{2}O‐liquid water
View Description Hide DescriptionThe structural relaxation times (τ_{ T,P }) of D_{2}O‐liquid water were determined by employing the models of Nemethy and Scheraga (NS) and also Davis and Bradly (DB). We proposed a new model to obtaining τ_{ T,P } on the basis of the interstitial model proposed by Narten e t a l. from the study of x‐ray diffraction. The results for τ_{ T,P } obtained from the proposed models were compared with one another. The relaxation times for NS and DB are not in agreement with each other over the temperature range. The value of τ_{ T,P } for our model is close to that of DB at lower temperatures, but at higher temperatures the descrepancy between them increases. On the other hand, the quantity τ_{ T,P } of our model is very close to a rotational correlation time (τ_{ n d }) of a dipole in a D_{2}O molecule obtained by Hindman e t a l. over the temperature range. The value of τ_{ T,P } for the NS model is different from that of our model and also the correlation time τ_{ n d }. After the work for D_{2}O, we also applied our model to find the value of τ_{ T,P } for H_{2}O‐liquid water.

Molecular anions: The ground and excited states of LiF
View Description Hide DescriptionA b i n i t i o single configuration self‐consistent‐field calculations have been carried out for the electronic states of LiF^{−} arising from the Li(^{2} S)+F^{−}(^{1} S) and Li(^{2} P)+F^{−}(^{1} S) asymptotes. The ^{2}Σ^{+}ground state is found to be stable by 0.35 eV with respect to detachment to form LiF(^{1}Σ)+e ^{−}. The excited ^{2}Σ^{+} and ^{2}Π states are unstable and lie in the continuum of the ^{1}Σ^{+} neutral. However, stabilized SCF solutions for the excited states have been obtained in an energetic region in which electron scattering resonances have recently been predicted. The possible basis set dependence of this result is discussed. The LiF^{−} states are compared to a lithium atom polarized by a point negative charge.

A comparison between finite element methods and spectral methods as applied to bound state problems
View Description Hide DescriptionThe finite element and spectral methods are applied to two‐dimensional bound state problems. A comparison of the spectral method, which requires a global basis set expansion of the wave functions, and the finite element method, which requires no such such expansion, is presented. A procedure is given for formulating the finite element approach and for achieving fast and accurate results. The convergence of the finite element calculations is considered and shown to be well behaved. A discussion of the extension of the finite element method to higher dimensions is also included.

Sequential two‐photon absorption and singlet–singlet energy pooling in thiophosgene vapor
View Description Hide DescriptionEmission from the second excited singlet state of Cl_{2}CS vapor has been monitored following excitation with a tightly focused, pulsed dye laser in the region of the ground state to first excited singlet and triplet absorption systems. Excitation in the triplet bands produces prompt fluorescence from S_{2} as a result of sequential two‐photon absorption, S_{0}→^{ hν}T_{1}→^{ hν}S_{2}. Excitation in the bulk of the singlet bands produces no prompt fluorescence but does produce delayed fluorescence as a result of a bimolecular singlet–singlet energy pooling process, 2S_{1}→S_{2}+S_{0}.

Far infrared magnetic resonance of deoxyhemoglobin and deoxymyoglobin
View Description Hide DescriptionWe have used FIR magnetic resonance as a direct probe of the low lying electronic states of the high spin (S=2) ferrous ion in deoxyhemoglobin and deoxymyoglobin. In a variety of helium temperature experiments using different samples and different buffers, we have detected a broad absorption band at 3.5 cm^{−1} that is sensitive to the application of a magnetic field. This band is not observed in samples of oxy‐or carbonmonoxy‐hemoglobin. The integrated area of the absorption band agrees (via a Kramers–Kronig relation) with the measured values of the static susceptibility of deoxyhemoglobin at 1.2 °K. The large linewidth (3.5 cm^{−1}) of the observed band is thought to reflect the large number of conformational substates associated with slightly different structures of the protein.

Crossed beam study of the reaction H_{2} ^{+} (CO,H) HCO^{+} from 0.74 to 9.25 eV
View Description Hide DescriptionWe present a study of the reaction H^{+} _{2} (CO,H) HCO^{+} from 0.74 to 9.25 eV and the reaction H_{2} ^{+} (CO,H_{2}) CO^{+} at 1.9 eV. The proton transfer dynamics appear to follow the elastic spectator mechanism fairly well in the low energy regime. At higher energies, the cross section drops rapidly and the backward scattered intensity moves to barycentric speeds beyond the stripping limit. At low energies, the HCO^{+} products are highly excited, with 90% of the available energy in internal excitation. At higher energies beyond the spectator stripping limit, depletion of the most highly internally excited states occurs through dissociation and roughly 50% of the available energy appears in internal excitation. We present a correlation diagram analysis based upon the H_{2}CO^{+}surfaces of Vaz Pires e t a l. [J. Chem. Phys. 69, 3242 (1978)]. Low symmetry collisions lead to conical intersections of H_{2}CO^{+}surfaces in the entrance channel, providing a pathway for formation of ground state products through the ? ^{2} B _{2} state of H_{2}CO^{+}.

The concept of pressure in density functional theory
View Description Hide DescriptionUsing density functional theory, a prescription is given for determining the internal scalar pressure at a point within an atom or molecule. From this expression for the pressure, a thermodynamic expression for the energy is obtained in terms of the chemical potential of the reference system, forces acting on the system, the internal pressure and an additional component X[ρ]; namely, Here μ_{0} is the chemical potential in the absence of fields, v is the potential due to nuclei, φ is the potential due to electrons, P is the scalar pressure, and X[ρ] is defined by the formula where T[ρ] and K[ρ] are the exact kinetic energy and exchange–correlation functionals. The functional X[ρ] vanishes as N approaches infinity, or in Thomas–Fermi or Thomas–Fermi–Dirac approximation, yet it is necessary to account for chemical binding.