Equivalence of the deformed Rosen–Morse potential energy model and Tietz potential energy model

By applying the dissociation energy and the equilibrium bond length for a diatomic molecule as explicit parameters, we generate an improved expression for the deformed Rosen–Morse potential energy model. It is found that the deformed Rosen–Morse potential model and the well-known Tietz potential model are the same empirical potential function for diatomic molecules. With the help of the energy spectrum expression of the deformed Rosen–Morse potential model, we obtain exact closed-form expressions of diatomic anharmonicity constants $\omega _e x_e $ ω e x e and $\omega _e y_e $ ω e y e .     

The construction of the Gilmore–Perelomov coherent states for the Kratzer–Fues anharmonic oscillator with the use of the algebraic approach

By applying the algebraic approach and the displacement operator to the ground state, the unknown Gilmore–Perelomov coherent states for the rotating anharmonic Kratzer–Fues oscillator are constructed. In order to obtain the displacement operator the ladder operators have been applied. The deduced SU(1, 1) dynamical symmetry group associated with these operators enables us to construct this important class of the coherent states. Several important properties of these states are discussed. It is shown that the coherent states introduced are not orthogonal and form complete basis set in the Hilbert space. We have found that any vector of Hilbert space of the oscillator studied can be expressed in the coherent states basis set. It has been established that the coherent states satisfy the completeness relation. Also, we have proved that these coherent states do not possess temporal stability. The approach presented can be used to construct the coherent states for other anharmonic oscillators. The coherent states proposed can find applications in laser-matter interactions, in particular with regards to laser chemical processing, laser techniques, in micro-machinning and the patterning, coating and modification of chemical material surfaces.     

Viscosity and thermal conductivity of some refrigerants at moderate and high densities on the basis of Rainwater–Friend theory and the corresponding states principle

The initial density dependence of viscosity and thermal conductivity was formulated on the basis of Rainwater–Friend (RF) theory. In this work, we have first focused on the calculation of viscosity and thermal conductivity of moderately dense argon by using RF theory and an accurate ab initio potential function. This theory which was originally presented for spherical potentials have been adapted for calculation of viscosity and translational contribution of thermal conductivity of some refrigerants by introducing the corresponding states correlations for the second transport virial coefficients. Then the internal states contribution for the thermal conductivity has been determined based on the Mason–Monchick and modified Enskog theories. So, we have calculated the viscosity and thermal conductivity of some refrigerants, R32, R14, R12, R13, R22, R134a, R143a, R125, R123, R142b, at moderate densities up to about 2 mol dm⁻³. At high densities, beyond the validity range of RF theory, we have applied correlation expressions for the viscosity and thermal conductivity residual functions to calculate the viscosity and thermal conductivity of supercritical refrigerants and then compared with the available experimental data. In conclusion, we have shown that the RF theory in conjunction with the corresponding states residual functions present the reliable model for calculation of viscosity and thermal conductivity of refrigerants over a comparatively wide temperature and pressure range up to 65 MPa within the experimental errors.     

Thermal diffusion in Lennard–Jones fluids in the frame of the law of the corresponding states

This work is related to the definition of a reduced thermal diffusion coefficient thanks to numerical microscale molecular dynamics simulations. This cross transport process, also called Soret effect, couples mass flux and thermal gradient and is still largely misunderstood. For this study, we have applied a boundary driven non-equilibrium molecular dynamics algorithm on Lennard–Jones spheres mixtures. Simulations have been performed at a constant reduced supercritical state, using a van der Waals’ one fluid approximation in order to fulfil the law of the corresponding states. In binary mixtures, we have studied the molecular parameters and the molar fraction influences on thermal diffusion separately and then combined. It is shown that, on pressure and on thermal conductivity, the corresponding states law is fulfilled for a wide range of molecular parameters ratios. In this frame, we have then constructed simple correlations which relate thermal diffusion factor to the mixture parameters. Combining the relations obtained, a reduced thermal diffusion factor taking into account all the various contributions has been defined. Finally, it is shown that this relation enables us to estimate thermal diffusion in various binary and ternary mixtures of Lennard–Jones spheres representing alkanes with a maximum deviation of 15%.     

A corresponding states treatment of the liquid–vapor saturation line

In this work we analyze correlations for the maxima of products of some liquid–vapor saturation properties. These points define new characteristic properties of each fluid that are shown to exhibit linear correlations with the critical properties. We also demonstrate that some of these properties are well correlated with the acentric factor. An application is made to predict the properties of two new low global warming potential (GWP) refrigerants.     

Use of the Gerchberg–Saxton algorithm in optimal coherent anti-Stokes Raman spectroscopy

We are utilizing recent advances in ultrafast laser technology and recent discoveries in optimal shaping of laser pulses to significantly enhance the stand-off detection of explosives via control of molecular processes at the quantum level. Optimal dynamic detection of explosives is a method whereby the selectivity and sensitivity of any of a number of nonlinear spectroscopic methods are enhanced using optimal shaping of ultrafast laser pulses. We have recently investigated the Gerchberg–Saxton algorithm as a method to very quickly estimate the optimal spectral phase for a given analyte from its spontaneous Raman spectrum and the ultrafast laser pulse spectrum. Results for obtaining selective coherent anti-Stokes Raman spectra (CARS) for an analyte in a mixture, while suppressing the CARS signals from the other mixture components, are compared for the Gerchberg–Saxton method versus previously obtained results from closed-loop machine-learning optimization using evolutionary strategies.     

Theoretical study of the excited states and the redox potentials of unusually distorted ��-trifluoromethylporphycene

Quantum chemical calculations were performed to analyze the excited states and the redox potentials of a recently synthesised fluorine-containing porphycene, 2,7,12,17-tetraethyl-3,6,13,16-tetrakis(trifluoromethyl) porphycene. The reduction and oxidation potentials of the porphycenes measured by cyclic voltammetry were semiquantitatively reproduced using density-functional theory (DFT) and polarizable continuum model calculations, in which solvent effect and basis-sets extension effect were indispensable. Symmetry-adapted cluster configuration interaction and time-dependent (TD) DFT calculations were performed to analyze the visible region of the absorption spectra, and the results were in good agreement with the experimental data. The results of the calculations showed that both structural distortion and electronic effects cause specifically large stabilization of the LUMO level and become the origin of the particularly large positive-side shift of the reduction potential and the red-shift in the Q band absorption.     

Atoms-in-molecules calculation of dipole moments of the lowest Σ and Π states of LiH

AIM calculations of dipole and transition moment functions are reported for the lowest Σ and Π states of LiH using a relatively small basis. The functions obtained agree quite satisfactorily with the best ab initio calculations. The results seem to indicate that the AIM approach might become useful in producing missing input data to the DIM calculations of dipole and transition moment surfaces for molecular collision systems interacting with a laser field.     

A CAS SCF CI study of the 1Σ+g and 3IIu states of the C2 molecule and the 4Σ−g and 2IIu states of the C+2 ion

Ab initio calculations of the X ¹Σ⁺_g and a ³II_u states of C₂ and the X⁴Σ⁻_g and a²II_u states of the C⁻₂ molecular ion are performed to determine the corresponding potential curves around the potential minima and at the dissociation limits. A large Gaussian basis set augmented by three d-type polarization functions on each carbon center is used to approximate the molecular orbits. The calculations are done at the complete-active-space SCF and multi-reference configuration interactions level. Spectroscopic constants and rotation—vibration energies are derived from the ab initio calculated potentials. Good agreement between theory and experiment is obtained for the X¹Σ⁺_g and a ³II_u states of C₂. In the earlier tentative assignment of the observed electronic transition around 2490 Å to the ²Σ⁻_g ← ²II_u system in C⁺₂, the lower state is confirmed by the present calculations to be C⁺ ₂ (²II_u).     

X-ray photoelectron spectroscopy for detection of the different Si–O bonding states of silicon

X-ray photoelectron spectroscopy (XPS) was used to detect the bonding between a silica particle surface and attached silanes. In addition to the commonly recorded Si 2p spectrum, the Si 1 s level is also accessible when monochromatic Ag Lalpha X-rays are applied. Furthermore, the spectrum of the Si 1 s level shows a fine structure. After spectrum deconvolution, we assigned the fitted spectral peaks to Si-C bonds of the silanes and to the Si-O bonds of the silica network. The recorded Si 1 s spectra were deconvoluted into peaks originating from Si-C bonds and the Si-O-Si silica network. To check the results of spectrum deconvolution, several differently functionalized silanes containing stoichiometric amounts of heteroatoms were applied for silica surface modification. We conclude that spectra deconvolution of the Si 1 s signal is an appropriate means for quantification of surface attached silane molecules.     

Hamiltonian for the problem on the ground and excited electron–nuclear states of nano-objects of finite size with periodic structure: Oligomers

A Hamiltonian has been proposed to study ground and excited states of nano-objects with a periodic structure, which makes it possible to find a general solution as a linear combination of basis functions in the form of normal waves. Terms that allow obtaining easily the solution with varying degrees of accuracy are explicitly defined. The method is suitable for the analysis of both finite and infinitely extended objects, including segments with a periodic structure.     

Submillimeter-wave and far-infrared spectroscopy of high-J transitions of the ground and ν2 = 1 states of ammonia

Complete and reliable knowledge of the ammonia spectrum is needed to enable the analysis and interpretation of astrophysical and planetary observations. Ammonia has been observed in the interstellar medium up to J=18 and more highly excited transitions are expected to appear in hot exoplanets and brown dwarfs. As a result, there is considerable interest in observing and assigning the high J (rovibrational) spectrum. In this work, numerous spectroscopic techniques were employed to study its high J transitions in the ground and ν(2)=1 states. Measurements were carried out using a frequency multiplied submillimeter spectrometer at Jet Propulsion Laboratory (JPL), a tunable far-infrared spectrometer at University of Toyama, and a high-resolution Bruker IFS 125 Fourier transform spectrometer (FTS) at Synchrotron SOLEIL. Highly excited ammonia was created with a radiofrequency discharge and a dc discharge, which allowed assignments of transitions with J up to 35. One hundred and seventy seven ground state and ν(2)=1 inversion transitions were observed with microwave accuracy in the 0.3-4.7 THz region. Of these, 125 were observed for the first time, including 26 ΔK=3 transitions. Over 2000 far-infrared transitions were assigned to the ground state and ν(2)=1 inversion bands as well as the ν(2) fundamental band. Of these, 1912 were assigned using the FTS data for the first time, including 222 ΔK=3 transitions. The accuracy of these measurements has been estimated to be 0.0003-0.0006?cm(-1). A reduced root mean square error of 0.9 was obtained for a global fit of the ground and ν(2)=1 states, which includes the lines assigned in this work and all previously available microwave, terahertz, far-infrared, and mid-infrared data. The new measurements and predictions reported here will support the analyses of astronomical observations by high-resolution spectroscopy telescopes such as Herschel, SOFIA, and ALMA. The comprehensive experimental rovibrational energy levels reported here will permit further refinement of the potential energy surface to improve ammonia ab initio calculations and facilitate assignment of new high-resolution spectra of hot ammonia.     

DFT calculations with the symmetrized kohn–sham formalism for the electronic structure of the high-energy states of nitrogen dioxide

Quantum-chemical calculations of the electronic structure of the high-energy states of NO₂ were performed by the density functional method with symmetrized Kohn–Sham formalism. The results from the DFT calculation of the NO₂^* NO_2^* excited states agree well with experimental data and ab initio calculations. The reactivity of the long-lived excited state NO₂^*( [(C)\tilde]²A" ) NO_2^*\left( {{{\tilde{C}}^2}A'} \right) during photochemical conversion to NO₃ was investigated.     

A theoretical study of the lowest electronic states of azobenzene: the role of torsion coordinate in the cis–trans photoisomerization

In the present paper we report the results of a multiconfigurational computational study on potential-energy curves of azobenzene along the NN twisting to clarify the role of this coordinate in the decay of the S₂(*) and S₁(n*) states. We have found that there is a singlet state, S₃ at the trans geometry, on the basis of the doubly excited configuration n²*², that has a deep minimum at about 90° of twisting, where it is the lowest excited singlet state. The existence of this state provides an explanation for the short lifetime of S₂(*) and for the wavelength-dependence of azobenzene photochemistry. We have characterized the S₁(n*) state by calculating its vibrational frequencies, which are found to correspond to the recently observed transient Raman spectrum. We have also computed the potential-energy curve for the triplet T₁(n*) at the density functional theory B3LYP level, which indicates that in this state the isomerization occurs along the twisting coordinate.Acknowledgement The financial support from MIUR (project Modellistica delle proprietà spettroscopiche di sistemi molecolari complessi funds ex 60% and project Dinamiche molecolari in sistemi di interesse chimico funds ex 40%), from the University of Bologna (Funds for Selected Research Topics) is gratefully acknowledged.Contribution to the Jacopo Tomasi Honorary Issue     

Rényi entropy of the infinite well potential in momentum space and Dirichlet-like trigonometric functionals

The momentum entropic moments and Rényi entropies of a one-dimensional particle in an infinite well potential are found by means of explicit calculations of some Dirichlet-like trigonometric integrals. The associated spreading lengths and quantum uncertainty-like sums are also provided.     

The structure of the SF6 molecule and the SF 6 − anion excited states

The electronic and geometric structures of the ground state and a number of excited states of the SF₆ molecule and the SF ₆ ^– anion have been calculated by the discrete-variation method of the local density-functionals. The anion was found to possess a number of states stable toward the outer electron detachment, and at least one excited state stable toward dissociation. The adiabatic electron affinity (EA) was determined as 3.46 eV at the highest level of theory. This result is correlated to the high EAs of the isovalent compound SeF₆ and TeF₆; however, it does not agree with the presently accepted experimental estimate of 1.0 ± 0.2 eV for the SF₆EA value. The basic anion configuration is octahedral with a S-F bond length of 1.717 Å. The calculated limit for the highest dissociation channel of the ground state SF ₆ ^– SF ₅ ^– + F is 1.5 eV lower than the minimum of the total energy of the neutral molecule; this is in good agreement with experimental estimates.Institute for Chemical Physics, Russian Academy of Sciences, 142432 Chernogolovka. Translated from Izvestiya Akademii Nauk, Seriya Khimicheskaya, No. 3, pp. 641–649, March, 1992.