Adiabatic Curves Research Articles

Charge transfer of doubly charged and trebly charged ions with atomic hydrogen at thermal energies

The charge transfer of doubly charged and trebly charged ions of C, N, O, and Ne with atomic hydrogen at thermal energies is studied. Adiabatic potential-energy curves and radial coupling matrix elements are presented. The collision cross sections are calculated after transforming to a diabatic basis. For the trebly charged ions, there exists at least one exit channel into which charge transfer is highly probable. Cross sections for doubly charged ions are sensitive to the energy-level structure of the ionic species.

The quenching of Na(3 2P) by H2: Interactions and dynamics

An eight-configuration diatomics-in-molecules formalism with symmetrically orthogonalized diabatic input is used to calculate the three lowest potential energy surfaces and nonadiabatic couplings for Na+H2 collisions. The singlet diatomic input for NaH and the singlet and triplet diatomic input for H−2 are chosen to reproduce the accurate adiabatic curves for those cases, and the diatomic input for H2 is based on theoretical interpretations of the resonance states. Trajectory calculations are carried out using the calculated 2 2A′ potential surface and nonadiabatic couplings, and the choice of H−2 input is found to sensitively affect the H2 vibrational excitation in the resonance-line quenching process. One H−2 curve, based on the work of Wadehra and Bardsley, yields an amount of vibrational excitation similar to that observed experimentally. The resulting set of potential energy surfaces provides a reasonable microscopic interpretation of the chemical dynamics of the quenching process Na(3p2P)+H2(v = 0, low j) →Na(3s2S)+H2(v′,j′).

Theoretical analysis of the reaction atomic fluorine + molecular hydrogen (v = 0) .fwdarw. hydrogen fluoride (v = 0, 1, 2, 3) + atomic hydrogen

A simple model is presented for the low-energy resonance in the P/sub 02/ reactive transmission probability for collinear dynamics. Detailed quantum-dynamical calculations on the Muckerman-5 surface are reported. These dynamical results suggest that the model adequately captures the physics underlying the low-energy resonance. In addition, an analysis of the vibrationally adiabatic potential-energy curves for the exit channel provides an explanation for the decay of the HF(v = 3) threshold obtained by using both quantum and quasi-classical reverse dynamical calculations on this potential-energy surface. The resonance model and the analysis of the vibrationally adiabatic potential-energy curves provide some insight into features of the potential-energy surface that need to be determined accurately before full a priori theoretical predictions can be expected to provide quantitatively meaningful results.

Rapid ways of predicting static-bed and cross-flow drier performance

A rapid method is described for analysing and predicting the performance of static-bed and cross-flow driers. The first step of the procedure uses a graphical construction to establish the effective adiabatic equilibrium curves. These can be used to carry out a broad qualitative analysis of moisture transfer operations in the absence of kinetic data. In a subsequent step, known solutions for isothermal non-equilibrium sorption are applied to these curves to derive moisture and temperature profiles and histories, air flow requirements and other design parameters of interest. No numerical solutions of the relevant model equations are required and the method is quite generally valid for any arbitrary form of moisture isotherms. Sample illustrations are given for deep-bed and cross-flow drying operations.

Shock adiabatic curves of metals

Shock adiabatic curves of metals

A Model for Drying on Adiabatic Saturation Lines

A model is developed to simulate continuous steady state evaporation. The process is one that proceeds along adiabatic saturation curves. Aerodynamic effects of dryer air and circulation flow flux are combined with dryer temperature and humidity to compute evaporation rates. The calculation method requires several iteration loops and a computer program to do the work is described. Curves are presented of evaporation rates as affected by temperature, humidity, nozzle heat transfer efficiency and circulation flow quantity. Optimization of process cost and energy are discussed.

The theoretical study of predissociation in diatomics. the case of the O 2 B' 3Σ −u state

The predissociation of excited O 2 has been studied theoretically with the aid of a simple model describing the Rydberg-valence crossing which occurs in the B and B' 3Σ − u states. Calculations of the decay rates have been performed by means of a method described previously. The energy shifts caused by the interaction of a discrete state with the dissociative continuum have been computed by the Fano method. Isotopic effects and the dependence of decay rates and energy shifts on the minimum energy gap between the adiabatic curves have been emphasized.

Evaluation of the temperature responses in colorimetric measurements of chemisorption enthalpies on metal films

An analysis was performed of various estimates of the adiabatic temperature Ttot that corresponds to the total heat liberated by a gas dose adsorbed on a metal film in the calorimeter for measurement of chemisorption enthalpies. Besides the two common procedures consisting either in the construction of the adiabatic temperature-time curve or in the extrapolation of the single-exponential cooling part of the actual temperature-time curve to zero time, we have examined estimates of Ttot by extrapolating the cooling exponential to the mid-point between zero time and the temperature maximum (t = tmax/2). Model calculations have shown the merit of the latter extrapolation, particularly in the cases of slow heat evolution. This has been verified on the data measured in the chemisorption of methane and ethane on molybdenum films. Extrapolation to tmax/2 has turned out to be a simple and reasonably reliable procedure for handling the data obtained in film calorimeters.

Transfer of oscillator strength in regions of avoided crossings. Atomic spectra for non-integer values of Z. application to the NI 4S o- 4P sequences

We report FOTOS calculations for the oscillator strengths of the N 1s 22s 22p 3 4S 0 → (1s 22s2p 4, 1s 22s 22p 23s) 4P iso-electronic sequences. Except for NeIV, excellent agreement with recent experimental values is found. Since this system exhibits a considerably localized valence-Rydberg (v-R) mixing, we have used it as a model for a study of the behavior of oscillator strengths in situations analogous to avoided crossings of molecular adiabatic curves. The two-state approximation (TSA) explains the observed spectroscopic data reasonably well. Our calculations extend to non-integer values of the nuclear charge for which we obtain Hartree-Fock as well as correlated wavefunctions. The notion introduced here, i.e. the use of non-integer Z to study the behavior of energy levels and oscillator strengths in atomic systems, is theoretically equivalent to the study of Born-Oppenheimer curves in diatomic molecules and constitutes a useful alternative for the rigorous study of avoided crossings.

ChemInform Abstract: CALORIMETRIC STUDY OF THE GLASSY STATE. XIII. THERMODYNAMIC PROPERTIES OF NORMAL AND DEUTERATED ORTHOBORIC ACID CRYSTALS

Thermal properties of normal and deuterated orthoboric acids were studied through the measurements of heat capacity in the temperature range from 13 to 370 K by using an adiabatic calorimeter and differential thermal analysis curves above room temperature. For both crystals, the heat capacity anomaly was found around 290 K in the heat capacity values dependent upon the thermal history of the specimen; i.e., the endothermic or exothermic enthalpy relaxation was observed in this temperature range. This behavior is of characteristic to the glass transition and is considered to be ascribed to the freezing-in phenomenon of the motion of rearrangement of the protons in hydrogen bondings. The enthalpy relaxation curves were analyzed with the exponential law and the characteristic time constant toward the equilibrium state was longer for enthalpy-excessive side than for enthalpy-deficient side. The glass transition temperature at which the endothermic relaxation time becomes 1 ks is 296.6 K for normal orthoboric ...

Diabatic states of the H+-Xe collisional system

Diabatic states of the H+-Xe collisional system have been calculated using the projected-valence-bond (PVB) method. The two lowest diabatic 1 Sigma + PVB states are found to cross at an internuclear distance R=4.7a0. For collision energies E<or approximately=1 keV no transition takes place at this crossing since it is strongly avoided in the corresponding adiabatic energy curves. On the other hand it is shown that Demkov-type transitions occurring at larger distances (R approximately=6.7a0) are responsible for the near-resonant charge-exchange processes in H++Xe collisions. The PVB results, in conjunction with diabatic states for spin-orbit coupling, are used in quantum calculations of differential cross sections. The results are compared with previous theoretical and experimental data.

Determination of the adiabatic curve indices for mixtures of real gases

Determination of the adiabatic curve indices for mixtures of real gases

Molecular study of theH+-Kr collisional system

Ab initio calculations have been performed to provide the basis for a molecular study of the elastic and the lowest charge-transfer channels in ${\mathrm{H}}^{+}$ + Kr collisions. The adiabatic ground-state potential-energy curve agrees satisfactorily with that predicted from elastic scattering experiments. In the Hartree-Fock treatment, the charge transfer into $\mathrm{H}(1s)+{\mathrm{Kr}}^{+}(4{p}^{5})$ appears to be mainly caused by a double virtual electronic transition via a doubly excited state. A "projected valence bond" (PVB) treatment involving single-configuration diabatic states built from projected H and Kr atomic orbitals is also presented. With such diabatic states the charge-exchange process is suitably described as occurring directly under the effect of an exponentially decreasing coupling between closely lying and almost parallel energy curves. The defects of the PVB approximation arising at small internuclear distances ($R$) are discussed. Diabatic states for the spin-orbit coupling are suggested for studying the population sharing between the $\ensuremath{\Omega}={0}^{+}$ states dissociating into $\mathrm{H}+{\mathrm{Kr}}^{+}(4{p}^{5}:^{2}P_{\frac{3}{2}},^{2}P_{\frac{1}{2}})$. A procedure involving a basis change from the adiabatic states at small $R$ to the PVB states at large $R$, together with the diabatic states for spin-orbit coupling is proposed to solve effectively the relevant scattering close-coupling equations.

Calculation of adiabatic radial and angular-momentum matrix elements using variational wavefunctions for H2+

Several adiabatic energy curves and wavefunctions for H2+ are calculated using a variational treatment. The agreement with exact adiabatic energies is excellent. Further, these variational wavefunctions are used to evaluate the radial matrix elements 〈α‖d/dR‖β〉 and the angular-momentum matrix elements 〈α‖iLy‖β〉 which are needed for treating atom–atom collisions by use of expansions in molecular states.

Approximate equation of state of condensed substances

The functions entering into the equation of state of Mie-Gruneisen solids are constructed approximately. In [1] an approximate equation of state was proposed for solids whose adiabatic curves obey a linear relationship between the velocity of the shock wave D and the mass velocity U; the slope of the shock adiabatic curve was equal to 1.5. In the present work, the dimensionless variables proposed in [2] are used to construct an equation of state which is free from the above-mentioned limitation. The equation of state found is used to make calculations of the shock compression of porous metals, in particular, of copper, with values of the porosity not differing significantly from unity.

Interactions of excited (n=3) and ground-state helium atoms: Potential curves and inelastic processes

Adiabatic potential-energy curves have been calculated for the interaction of several $n=3$ triplet states of helium with ground-state helium. Mechanisms for excitation-transfer in collisions of $3^{3}S$ and $3^{3}P$ with ground-state atoms are suggested by the results of these calculations. A deexcitation cross section corresponding to $3^{3}S\ensuremath{\rightarrow}2^{3}P$ excitation-transfer has been calculated using the Stueckelberg-Landau-Zener approximation and is consistent with existing measurements. The existence of a small hump in the potential curve causes the cross section to decrease rapidly at low energies. Thus, a strong temperature dependence of effective cross sections is expected. A possible mechanism for associative ionization is also discussed.

Theoretical study of curve crossing: ab initio calculations on the four lowest 1Σ+ states of LiF

The potential curves of the four lowest 1Σ+ states of LiF have been studied by ab initio configuration interaction methods, using a contracted Gaussian basis set of better than double-ζ quality, augmented with diffuse basis functions on the fluorine atom. The choice of orbitals and selection of configurations were carried out with the objective of obtaining a balanced treatment of the four states and of the different regions of the potential curves. ``Generalized valence-bond'' orbitals, obtained from ground-state MCSCF calculations, together with ``improved virtual orbitals,'' were found suitable for the construction of the configuration functions. The latter were energy selected from all single and double excitations relative to a set of 12 ``reference configurations,'' chosen to include all contributions found important for any of the four states at any internuclear distance. The expected avoided crossing between the lowest covalent and ionic structures is found at an internuclear distance of about 11 bohr, compared to the experimentally deduced value of 14 bohr, due to the considerable difficulty in obtaining a balanced description of the electron correlation of the separated species, particularly the F− ion. A set of diabatic potential curves was generated from the two lowest adiabatic curves by a novel procedure based on the Rittner model of the ionic state. A set of adjusted adiabatic potentials was obtained from the diabatic curves after shifting the ionic diabatic curve downward by 0.42 eV to correct for the error in the computed electron affinity of the fluorine atom, resulting in a shift of the avoided crossing to the correct internuclear distance of 14 bohr. The dipole moments of the four states were computed as a function of internuclear distance and were interpreted in terms of the electronic structure.

Properties of the adiabatic energy curves for the ground states of H 2+, HD +, and D 2+

Equilibrium internuclear distances, energies, and force constants are reported for the diatomic molecules H 2 +, HD +, and D 2 + at the adiabatic level of approximation. The differences between these values and those calculated previously at the Born-Oppenheimer level of approximation are analyzed.

Shock compression of two-component paraffin-tungsten mixtures

Up to pressures of 2 mbar, curves have been recorded experimentally for the shock compression of paraffin and for two paraffin-tungsten mixtures, containing 66.2 and 84.0 wt.% tungsten. It is shown that over the whole range of pressures investigated experimentally, the mixture shock adiabatic curves satisfy the principle of additivity. Attention is called to the great potential of the method of weighting additives for the investigation of light media at high shock pressures. The criteria for the applicability of the principle of additivity have been analyzed.

Diatomic interhalogens: Systematics and implications of spectroscopic interatomic potentials and curve crossings

Spectroscopically derived potential curves for the low-lying excited states of the homonuclear and heteronuclear diatomic interhalogens are systematized by taking cognizance of the spin-orbit state of the dissociation products. Observed regularities lead to the prediction of a bound B (3Π0+) state of F2 with r′e ≃ 1.9 Å, D′e ≃ 3300 cm−1. Several of the heteronuclear interhalogens show evidence of a strong interaction between the B (3Π0+) state and a repulsive Y (O+) state, leading to the formation of a new B′(O+) state. An analysis of these interactions has led to the construction of sets of diabatic potentials consistent with the best estimated adiabatic curves and thus to the determination of the crossing points rx and interaction strengths V12(rx). The patterns of V12(rx) values suggest that they depend mainly upon the spin-orbit coupling constant of the excited atomic dissociation product. Reported also are repulsive segments of potential curves deduced for the Y (O+) states for a series of 1Π states and a few higher-lying (Z) states, the latter two series from analysis of existing continuum absorption data. Repulsive interactions in all four families of states studied [3Π0+, 1Π1, Y(O+), and Z] show clear regularities governed by steric effects. Implications of the present results with respect to the theory of interatomic forces, predissociation phenomena, and the scattering of ground state halogen atoms are discussed.