Electronic effect on the rotational energy of a diatomic molecule

The rotational hamiltonian for a diatomic molecule has been rederived from the total classical hamiltonian. This procedure directly introduces the effect of electronic motion which is ordinarily neglected in zero-order approximation. Kronig's rotational hamiltonian is discussed and shown to be an approximation of our findings. Our general result is then specialized to ¹Σ states, and the theory tested by calculating the observed fractional discrepancy between the experimentally determined H³⁵Cl energy level constant Y₀₂ and its predicted value from Dunham's theory. When all corrections are summed, the results are in good agreement with experiment.     

Selective guest encapsulation by a cobalt-assembled cage molecule

Metal-assembled resorcinarene-based cages enclose space and entrap organic molecules from water. Addition of cobalt(II) ions to a neutral, aqueous solution of a resorcinarene that has iminodiacetic acids attached to its upper rim results in the formation of cages. These cages not only entrap organic molecules, but they do so in a selective manner. Guests with optimum size, shape, and polarity are preferentially entrapped. For example, selection of p-xylene is twenty thousand times more favorable than that of m-xylene. The enthalpy of resorcinarene deprotonation and cage formation was calculated by performing calorimetry studies and ranged from -305 to -348 kJ mol(-1). The change in enthalpy of guest encapsulation varied by as much as 43 kJ mol(-1). The differences in change in free energy of guest encapsulation varied by -16 kJ mol(-1). The changes in enthalpy and free energy of guest encapsulation were used to calculate the changes in entropy, which ranged from -97 to +37 J mol(-1) K(-1). An enthalpy-entropy compensation of guest encapsulation was observed.     

Phenol as a guest molecule in clathrate compounds

Phenol, having favourable physical and chemical properties, can be enclosed as the guest component in the clathrates of tetracyano complexes. Six compounds of Hofmann and similar type clathrates M(NH₃)₂M' (CN)₄.nG and M(en)_m M'(CN)₄.nG were prepared and identified: Ni(NH₃)₂Pt.2C₆H₅OH; Ni(en)₂Pt(CN)₄.O.14C₆H₅OH; Ni(NH₃)₂Pt(CN)₄.C₆H₅OH.H₂O; Zn(NH₃)₂Ni(CN)₄.O.1C₆H₅OH.H₂O; Cu(NH₃)₂Ni(CN)₄. 2C₆H₅OH and Fe(NH₃)₂Ni(CN)₄.2C₆H₅OH. The phenol containing clathrates are more stable than clathrates containing other guest molecules. In the case of Ni(en)₂ Pt(CN)₄.O.14C₆H₅OH thermal loss of the guest molecule leaves the host lattice intact, but further heating results in the rupture of the host lattice. The compounds were capable in the solid state of sorbing other organic molecules once they had been heated to the temperature required for almost complete loss of guest molecule i.e. n→o.     

The influence of ultrashort excitations on the vibrational dynamics in a diatomic molecule

The problem of vibrational wave packet dynamics in the system of two electronic states of a diatomic molecule, where the states are coupled by infinitely short light pulses, is solved. The electronic states were modeled by shifted harmonic oscillators with different frequencies. Exact expressions for the probability densities of the wave packets in the ground and excited states were derived. The spatial, spectral, and temporal characteristics of the wave packets, namely, the range of motion, spatial width, mean energy, spectral width (the mean number of vibrational states in a wave packet), and the autocorrelation function, were calculated as functions of the molecular parameters (the frequency ratio and the distance between the potential minima) and of the delay time between the light pulses. The possibility of controlling the mean energy and spectral width of the wave packets in the ground electronic state by varying the delay time is considered. It was shown that "squeezed" wave packets can be prepared in the ground electronic state if the upper electronic state is shallow.     

Electric dipole moment of the diatomic AgBr molecule

Stark effect measurements on hyperfine components of the J = 3 – 2 rotational transition of ¹⁰⁷ Ag ⁷⁹ Br and ¹⁰⁹ Ag⁷⁹ Br at 11.5 GHz were carried out. The electric dipole moment derived for AgBr in its ground electronic and vibrational state is |μ_o| = 5.620 ± 0.030 D.     

Theory of swelling of a crosslinked substance in equilibrium with a solvent in various phases

In this paper the thermodynamic theory of a body in a liquid, crystalline or vaporized solvent is treated. The equilibrium swelling curves are discussed for the different states of the solvent. The slopes of the swelling curves are dependent on the differential enthalpy of dilution of the solvent and, additionally, on the enthalpies of vaporization, crystallization and sublimation of the solvent related to the state of the swelling agent. The slopes of the swelling curves are determined by the differential heat of vaporization, the differential heat of solution of the solvent or the differential heat of fusion according to the state of the swelling agent. Directly below the melting pointT _m,1, or directly above the boiling pointT _b,1 of the solvent the swelling curves change their slopes with a sharp bend. This phenomenon can be used to determine (₁/w ₁) at constant temperature and pressure, which means the change of the chemical potential ₁, with the change of the weight fractionw ₁ of the solvent. Using a simplified statistical thermodynamic relation it is possible to describe the principal courses of the swelling curves in all states of the solvent.     

Electric dipole moment of the diatomic if molecule

The electric dipole moment of the IF molecule has been determined by a study of the Stark effect on the hyperfine components of the J = 1 ← 0 rotational transition lying in the 17 GHz region. The production of molecules was by microwave discharge of I₂ and C₆F₁₀(CF₃)₂. A direct diagonalisation of the energy matrix of the total hamiltonian has been used and the electric dipole moment derived for the ground vibrational state of IF is |μ₀ |= 1.948(20)D.     

Thermal expansivity of tetrahydrofuran clathrate hydrate with diatomic guest molecules

The guest dynamics and thermal behavior occurring in the cages of clathrate hydrates appear to be too complex to be clearly understood through various structural and spectroscopic approaches, even for the well-known structures of sI, sII, and sH. Neutron diffraction studies have recently been carried out to clarify the special role of guests in expanding the host water lattices and have contributed to revealing the influence factors on thermal expansivity. Through this letter we attempt to address three noteworthy features occurring in guest inclusion: (1) the effect of guest dimension on host water lattice expansion; (2) the effect of thermal history on host water lattice expansion; and (3) the effect of coherent/incoherent scattering cross sections on guest thermal patterns. The diatomic guests of H 2, D 2, N 2, and O 2 have been selected for study, and their size and mass dependence on the degree of lattice expansion have been examined, and four sII clathrate hydrates with tetrahydrofuran (THF) have been synthesized in order to determine their neutron powder diffraction patterns. After thermal cycling, the THF + H 2 clathrate hydrate is observed to exhibit an irreversible plastic deformation-like pattern, implying that the expanded lattices fail to recover the original state by contraction. The host-water cage dimension after degassing the guest molecules remains as it was expanded, and thus host-guest as well as guest-guest interactions will be altered if guest uptake reoccurs.     

Collinear collision of an atom with a homonuclear diatomic molecule

The problem of collinear scattering of an atom from a homonuclear diatomic molecule is formulated in terms of a first-order nonlinear matrix differential equation for the variable coefficient of reflection. For a homonuclear molecule when the target Hamiltonian is invariant under the parity transformation, only transitions between even states or odd states are possible. This selection rule reduces the number of open or closed channels that contribute to the reflection and transmission coefficients. But for numerical calculation, under the conditions of the problem, one can approximate the target Hamiltonian by the Hamiltonian of a displaced harmonic oscillator. In this approximation, the reflectional symmetry of the Hamiltonian is not preserved and transitions between any two levels of the target are possible. To simplify the problem further, the interaction between the projectile and the target is assumed to be a sum of two Gaussian terms. For this combination of the potentials the many-channel interaction can be expressed analytically. By fitting the Lennard–Jones potential with a sum of two Gaussian potentials and solving the matrix differential equation, transition probabilities are obtained for the He? H₂ collision. The numerical results are compared with the results found by Secrest and Johnson, and by Clark and Dickinson.     

Quantum control of vibrational excitations in a heteronuclear diatomic molecule

Optimal control theory is applied to obtain infrared laser pulses for selective vibrational excitation in a heteronuclear diatomic molecule. The problem of finding the optimized field is phrased as a maximization of a cost functional which depends on the laser field. A time dependent Gaussian factor is introduced in the field prior to evaluation of the cost functional for better field shape. Conjugate gradient method^21,24 is used for optimization of constructed cost functional. At each instant of time, the optimal electric field is calculated and used for the subsequent quantum dynamics, within the dipole approximation. The results are obtained using both Morse potential as well as potential energy obtained using ab initio calculations.     

Vibrational excitation and dissociation of a diatomic molecule in the diffusion approximation

A numeric solution is given for the excitation of vibration and dissociation in the diffusion approximation for an O₂-Ar (oxygen-argon) mixture. The time of vibrational relaxation is calculated, and also the rate constant for dissociation. The diffusion approximation describes the processes satisfactorily for a gas whose particles differ little in mass.I am indebted to B. V. Kuksenko, A. I. Osipov, and M. N. Safaryan for discussions and valuable advice.     

On the variational solution of morphed molecular potential in a diatomic molecule

The general one-dimensional potential energy function, including centrifugal distortion, for a diatomic molecule is morphed with a series of Morse-like functions for each of the rotational quantum numbers $J$ . For each of the morphed potential, explicit formulae for the matrix elements of the complete energy matrix, on the basis of the solutions of the one-dimensional harmonic oscillator, are given and these may be used in connection with the variational procedure to solve the corresponding vibrational Schrödinger equation. From the set of vibrational levels $\{\text{ E}_\mathrm{vJ}\}, J = 0, 1, 2,{\ldots }$ the ro-vibrational transitions can be deduced.     

Classical study of the influence of induced rotation and anisotropy effects on energy transfer between an atom and a diatomic molecule

The lagrangian equations of motion for a mass 4 atom colliding with a mass 2 diatomic molecule are solved numerically in order to investigate the validity of some approximations often used in energy transfer theory. The results are shown to be very sensitive to the details of the intermolecular potential; the effect of induced rotation can change the vibrational energy transfer by an order of magnitude.     

Vibrational energy relaxation of a diatomic molecule in a room-temperature ionic liquid

Vibrational energy relaxation (VER) dynamics of a diatomic solute in ionic liquid 1-ethyl-3-methylimidazolium hexafluorophosphate (EMI(+)PF(6) (-)) are studied via equilibrium and nonequilibrium molecular dynamics simulations. The time scale for VER is found to decrease markedly with the increasing solute dipole moment, consonant with many previous studies in polar solvents. A detailed analysis of nonequilibrium results shows that for a dipolar solute, dissipation of an excess solute vibrational energy occurs almost exclusively via the Lennard-Jones interactions between the solute and solvent, while an oscillatory energy exchange between the two is mainly controlled by their electrostatic interactions. Regardless of the anharmonicity of the solute vibrational potential, VER becomes accelerated as the initial vibrational energy increases. This is attributed primarily to the enhancement in variations of the solvent force on the solute bond, induced by large-amplitude solute vibrations. One interesting finding is that if a time variable scaled with the initial excitation energy is employed, dissipation dynamics of the excess vibrational energy of the dipolar solute tend to show a universal behavior irrespective of its initial vibrational state. Comparison with water and acetonitrile shows that overall characteristics of VER in EMI(+)PF(6) (-) are similar to those in acetonitrile, while relaxation in water is much faster than the two. It is also found that the Landau-Teller theory predictions for VER time scale obtained via equilibrium simulations of the solvent force autocorrelation function are in reasonable agreement with the nonequilibrium results.     

Trajectory calculation results on the orientation of a diatomic molecule in collision with an atom

Orientational effects in collisions between a diatomic molecule and a noble gas atom are studied by classical trajectory calculations. A preferable ”perpendicular orientation“ of the molecule is found at the moment of closest approach of the atom. This orientational effect is more pronounced in collisions with heavy atoms.