Origin of stability of the high-temperature, low-pressure Rh2O3 III form of rhodium sesquioxide

We present a first principles study of the equilibrium structures and relative thermodynamic stability of the three observed polymorphs of rhodium(III) sesquioxide. The thermodynamic Gibbs free energies for each phase are calculated as a function of P and T based on the electronic total energy, as well as vibrational energy and vibrational entropy contributions in the local harmonic (LH) approximation. The results confirm that Rh₂O₃ I is a low-temperature, low-pressure form and Rh₂O₃ II is a high-pressure form. A breakdown in the LH approximation at high T is then discussed and to address this breakdown an empirically corrected local harmonic (ECLH) approximation is introduced. ECLH demonstrates that the high-temperature, low-pressure form Rh₂O₃ III is entropically stabilized and produces a partitioning of phase space that is consistent with published experimental investigations.     

Collisional excitation of rotation for a three-dimensional diatomic oscillator

S-matrix elements for rotational excitation have been calculated in a close coupling scheme which includes excited vibrational states. It is found that the rigid rotor approximation is not entirely justified and that only near rotational states need be included.     

The r-centroid approximation and generalized functions

The r-centroid approximation implies that molecular vibrational wavefunction products should behave similarly to relatively high sequence members of generalised functions.     

The linearly forced morse oscillator

An algebraic approach has been used to treat the linearly forced Morse-oscillator problem. It is shown that the dynamical algebra is equivalent to that for the M = 2 harmonic-oscillator case. Dissociation probabilities are calculated using a sudden approximation. They show a strong dependence on initial vibrational quantum number.     

The born approximation as a simple diagnostic method for direct molecular collisions with applications to Cl + HI and F + H2 reactions

Born approximation computations are presented and discussed for the Cl + HI → I + HCl and F + H₂ → H + HF reactions and their isotopic analogues. Most aspects of the role of reagent energy or the energy disposal in the products previously deduced from experiment or trajectory computations can be accounted for the Born approximation. The procedure used here neglects the interaction between non-bonded atoms. It does thereby provide a very simple computational scheme which requires as input only the spectroscopic constants of the reactants and products. In addition it offers simple qualitative interpretations of the trends in the results. The overall satisfactory agreement between the present results and past studies lends credibility to the basic propensity rule provided by the Born approximation: The most probable transitions are those that minimize the momentum transfer to the nuclei. The principle is discussed with special reference to exothermic (E′_T ? E_T) and endothermic transitions.The computations for Cl + HI indicate a decline of the reaction cross section with increasing kinetic energy and a strong enhancement by HI rotational energy. The surprisal analysis confirms the absence of vibrational population inversion for endothermic transitions. For the F + H₂ (and isotopic variants) reactions, the product-rotational state distribution extends nearly to the energy cut-off. The vibrational state distribution is somewhat different for para- and normal H₂ and, in general, the collision outcome is very sensitive to the initial rotational state of H₂ particularly at low translational energies. The HF/DF branching ratio is F + HD collisions is increasing with increase of the HD rotational state. The vibrational surprisal is essentially isotopically invariant.     

Simplified time-dependent self-consistent field approximation for intramolecular dynamics

The time-dependent Hartree approximation is applied to intramolecular dynamics of polyatomics with smooth, locally quadratic potential surfaces. It is shown that the full quantum solution is obtained from a certain single self-consistent trajectory. An extremely simple model results, pertinent to intramolecular energy transfer, vibrational lineshapes and unimolecular decay.     

Experimental and theoretical study of the rovibrational relaxation of CH4 and CD4 by Ar

Experimental results are reported for the vibrational relaxation of the lowest bending modes of CH₄ and CD₄ br Ar in the temperature range of 140–376 K. Theoretical calculations are carried out in the framework of the semiclassical coupled-states approximation using asymptotic expressions of (3j) symbols and a first-order perturbation treatment. The confrontation of experimental and theoretical rate constants confirms the crucial role of rotational energy transfer upon the vibrational relaxation transfer.     

Theoretical prediction of vibrational spectra. The a priori scaled quantum mechanical (SQM) force field and vibrational spectra of pyrimidine

The complete harmonic force field of pyrimidine has been computed at the ab initio Hartree—Fock level using a 4–21 Gaussian basis set. In order to compensate the systematic overestimations of the force constants at the aforementioned level of quantum mechanical approximation, the theoretical force constants were empirically scaled by using nine scale factors. (The values of all these scale factors were previously determined by fitting the theoretical force field of benzene to the observed vibrational spectra of benzene.) The resulting a priori scaled quantum mechanical (SQM) force field is regarded as the most accurate and physically the most correct harmonic force field for pyrimidine. This force field was then used to predict the vibrational spectra of pyrimidine-h₄ and pyrimidine-d₄. On the basis of these a priori vibrational spectra uncertain assignments have been confidently resolved. After a few reassignments, the mean deviations between the experimental and calculated frequencies are below 9 and 18 cm⁻¹ for the non-CH stretching in-plane and the out-of-plane vibrations, respectively. Computed IR intensities are generally in agreement with experiments at a qualitative level.     

A direct test of the vibrationally adiabatic theory of chemical reactions

The adiabaticity assumption of the vibrationally adiabatic theory of chemical reactions in the zero-curvature approximation is directly tested for the collinear H + H₂ reaction against calculations using exact wavefunctions. It is found that the symmetric stretch motion of the transition state is adiabatic to within 10% for total energies E ranging from 0.51 eV to 0.72 eV. For E below the zero-point energy of this symmetric stretch motion non-adiabaticity is substantial and is probably due to tunneling. For E above the first excited vibrational state energy of this symmetric stretch motion the adiabaticity assumption breaks down completely.     

The vibrational spectra of chloromethyl mercuric chloride,ClCH2HgCl

The Raman and i.r. spectra of ClCH₂HgCl are reported for the first time and a complete vibrational assignment is made on the basis of C_s symmetry. Force constant calculations based on an SVFF approximation indicate that the mercury—carbon stretching force constant is decreased by 30% on introduction of a chlorine atom into the methyl group of CH₃HgCl.     

Theoretical spectroscopic study of van der Waals systems

In this paper we discuss the application of three dimensional quantum models, in order to study the dynamics of vibrational predissociation of van der Waals molecules. In the first model the vibrations are described in the distorted-wave diabatic approximation while rotations are treated in the sudden approximation. The second model is related to the “Infinite order sudden approximation” and after a close coupling formalism for the vibrations, the bending motion is considered in an approximate way. We present the 3D quasibound levels and the rates for vibrational predissociation in a test case, the HeI₂.     

First-principles study of the phonon vibrational spectra and thermal properties of hexagonal MoS2

The phonon spectra and thermal properties of the hexagonal MoS₂ are investigated by using first-principles calculations within the density functional theory (DFT). Finite displacement method is used to calculate the phonon vibrational spectra and phonon density of states. The vibrational modes at the Gamma point are analyzed by using group theory. The temperature and pressure dependence of its thermal quantities such as the thermal expansion, the heat capacity at constant volume, the Gibbs energy and entropy are obtained based on the quasi-harmonic approximation (QHA). Our results show that both the thermal expansion coefficient α and the heat capacity C_V increase with T³ at low temperatures and gradually turn almost linear as the temperature increases. It is found that the entropy is sensitive to the temperature while the Gibbs free energy is more sensitive to the pressure change.     

Vibrational and electronic spectra of benzophenone in different phase states: Ab initio calculations and experiment

An ab initio method has been used to perform quantum mechanical calculations of the formation energy of different conformers of benzophenone: planar molecule, twisted molecule, planar molecule dimer, twisted molecule dimer; electronic and vibrational spectra of these conformers were also obtained. An assessment of the medium (solvent) influence on the optimal geometry, dipole moment and stability of different forms of benzophenone was performed in the self-consistent reaction field approximation. It is shown that the twisted conformer is more stable than the planar one (the difference of free energies is 32 kJ/mol for free molecules) and it becomes even more stable with the increase in solvent polarity. The calculated electronic and vibrational spectra agree well with the experimental data and properly reflect the complication of the vibrational spectrum when passing from the gaseous phase to the condensed state of benzophenone. The difference between spectral properties of the two dimer forms allows their identification from the spectra and qualitative explanation of the observed peculiarities of phosphorescence of the amorphous phase of benzophenone by the stabilization of different conformers.     

Distorted wave calculations of vibrational excitation in CO2+He and CO2+Ar collisions

Cross sections for the vibrational excitation and relaxation of CO₂ through collisions with He and Ar atoms have been computed using several approximate methods. They all employ the infinite-order sudden approximation for the rotational motion. The vibrational motion is treated using both exact close-coupling and distorted wave techniques. The latter approximate method permits the extension of the calculation to much higher collision energies. The validity of the distorted wave approximation is examined and is shown to be particularly good for the dominant inelastic processes in He+CO₂, leading to errors of the order of 7%. These become progressively greater for smaller cross sections. The excitation cross sections are reported for several vibrational transitions over an extended energy range up to 1.36 eV.     

Erratum: Thermodynamic perturbation theory of a dense fluid of polar and polarizable spheres

A method is described for determination of the dissociation energy D₀ for hydrogen bonded dimers B…H-A using only measurements of rotational transition intensities at a single temperature. Application in the particular case HCN…HF gives D₀ = 18.5 ± 1.1 kJ mol^?1. By taking account of the vibrational modes of HCN…HF in the harmonic oscillator approximation, D_e is estimated as 25.6 ± 1.6 kJ mol^?1.     

Structural relaxations and energy effects of intramolecular motions inN,N-dimethylnitramine: A theoretical study

The equilibrium geometry of theN,N-dimethylnitramine molecule and changes in the energy and structural parameters due to the internal rotation of the nitro group and the inversion of the N atom in the amino fragment were calculated by the restricted Hartree-Fock (RHF) method and at the second-order Møller-Plesset (MP2) level of perturbation theory with inclusion of electron correlation using the 6–31 G^* and 6–31 G^** basis sets. The one-dimensional potential functions of these motions calculated at the RHF/6–31 G^* level were approximated by a truncated Fourier and power series, respectively. The frequencies of torsional and inversion transitions were determined by solving direct vibrational problems for a non-rigid model,i.e., taking into account the molecular geometry relaxation. The equilibrium conformation of the molecular skeleton ofN,N-dimethylnitramine is nonplanar. Transition states of the internal rotation of the nitro group and inversion of the amine N atom are characterized by pronounced concerted changes in its bond angles and the length of the N?N bond. In the MP2/6–31 G^* approximation, the height of the barrier to internal rotation calculated taking into account the difference in the zero-point vibrational energies is equal to 9.7 kcal mol^?1. Inversion in the amino fragment is accompanied by a relatively small energy change at the barrier height of ?1.0 kcal mol^?1 calculated in the same approximation.     

Fermi-coupled spherically adapted effective states in the collisionless multiphoton excitation of SF6

A calculation method for the collisionless multiphoton excitation of SF₆ by intense CO₂ laser light up to a chain of parallel nv₃, (n - 1)v₃ + v₂ + v₆ … vibrational-rotational ladders linked by Fermi interaction is described. Spherically adapted effective states suitable to the purpose are defined, and matrix elements for multiphoton excitation in the rotatingwave approximation effective hamiltonian formalism are given in this basis. The method is aimed at the investigation of population transfer between the cited parallel vibrational ladders, and is suitable for computer-calculation programmation.     

Stability and vibrational spectra of toroidal isomers of C 240

To study the thermodynamic and mechanical stability of toroidal isomers of C ₂₄₀, we use a semi-empirical tight-binding theory and calculate their electronic structure, cohesive energy and vibrational spectra within the harmonic approximation. From these, we deduce their free energy at temperatures up to 1500K. The results are also compared to the isomer with icosahedral symmetry. Finally, we discuss within this approach, their stability and abundance.     

Fully converged sudden rotation total integral cross sections for 4He + H2 (ν = 0, j = 0) → 4He + H2 (ν′ = 1, j′)

Total integral cross sections for ⁴He + H₂ (ν = 0, j = 0) → ⁴He + H₂ (ν′ = 1, j′ = 0, 2) have been calculated in the total energy range 1.2 to 5.5 eV, according to a quantal sudden approximation for the H₂ rotational degrees of freedom and a close coupling expansion of the vibrational degree of freedom. Convergence of the above cross sections is investigated by employing four vibration basis sets in the close coupling calculations, i.e., ν = 0,1, ν = 0,1, 2, ν = 0, 1, 2, 3 and ν = 0, 1, 2, 3, 4. Between 4.2 and 5.5 eV calculations were done with three vibration basis sets; ν = 0.–4, ν = 0–5, and ν = 0–6. It is found that at least four vibrational basis functions are needed to converge (to within 5–10%) these cross sections in the above energy range. Comparison of breathing sphere calculations and summed sudden rotation results shows good agreement for the (weakly anisotropic) Mies-Krauss potential. However, as expected the former results underestimate the vibrational 0 → 1 total integral cross sections.