Comparison of the Morse and Deng-Fan potentials for X-H bonds in small molecules

Parabolic-Gaussian Double Quantum Wells under a Nonresonant Intense Laser Field

In this paper, we investigate the electronic and optical properties of an electron in both symmetric and asymmetric double quantum wells that consist of a harmonic potential with an internal Gaussian barrier under a nonresonant intense laser field. The electronic structure was obtained by using the two-dimensional diagonalization method. To calculate the linear and nonlinear absorption, and refractive index coefficients, a combination of the standard density matrix formalism and the perturbation expansion method was used. The obtained results show that the electronic and thereby optical properties of the considered parabolic-Gaussian double quantum wells could be adjusted to obtain a suitable response to specific aims with parameter alterations such as well and barrier width, well depth, barrier height, and interwell coupling, in addition to the applied nonresonant intense laser field.

Harmonic-Gaussian Symmetric and Asymmetric Double Quantum Wells: Magnetic Field Effects

In this study, we considered the linear and non-linear optical properties of an electron in both symmetrical and asymmetrical double quantum wells, which consist of the sum of an internal Gaussian barrier and a harmonic potential under an applied magnetic field. Calculations are in the effective mass and parabolic band approximations. We have used the diagonalization method to find eigenvalues and eigenfunctions of the electron confined within the symmetric and asymmetric double well formed by the sum of a parabolic and Gaussian potential. A two-level approach is used in the density matrix expansion to calculate the linear and third-order non-linear optical absorption and refractive index coefficients. The potential model proposed in this study is useful for simulating and manipulating the optical and electronic properties of symmetric and asymmetric double quantum heterostructures, such as double quantum wells and double quantum dots, with controllable coupling and subjected to externally applied magnetic fields.

Magneto-transport and Thermal properties of TiH diatomic molecule under the influence of magnetic and Aharonov-Bohm (AB) fields

In this study, the effects of Aharonov-Bohm (AB) and magnetic fields on the thermodynamic and magneto-transport properties of TiH diatomic molecule using the Deng-Fan potential as a model are investigated. The functional analysis approach (FAA) is used to solve the Schrodinger equation in the presence of magnetic and AB fields with Deng-Fan potential. The energy equation, as well as the wave function, have been derived. The analytic expressions for the thermo-magnetic and transport properties of the Deng-Fan potential are derived using the energy equation and the partition function. These properties obtained are thoroughly analysed utilising graphical representations. Our analysis shows that the magnetic susceptibility of the TiH exhibits a diamagnetic behaviour, and the specific heat capacity behaviour agrees with the famous Dulong-Petit law when the system is subjected to AB field variations and a fixed magnetic field. Albeit, a slight anomaly is observed in the behaviour of the specific heat capacity. Our findings will be valuable in various fields of physics, including chemical and molecular physics and condensed matter physics, where the derived models could be applied to study other diatomic molecules and quantum dots, respectively.

Morse oscillator equation of state: An integral equation theory based with virial expansion and compressibility terms

A number of interaction energy types are employed in the vibrations studies, especially in the spectroscopic analysis, such as the harmonic oscillator and Morse oscillator. In this research, a derivation of an analytical formula of equation of state of Morse oscillator is considered by employing the approximations used in the simple fluids theory. The compressibility formula of the pressure and the virial expansion formula of the pressure using the solutions of the main equation of the simple fluids theory with one of the approximations of the theory are employed for the purpose of the derivation. The virial coefficients of the total Morse oscillator pressure (the first order one, and the second order one) are found for Morse oscillator with respect to the fractional volume of the components, where we conclude that the first order term is proportional to the absolute temperature directly and depends on the diameter of the particles, while we concluded that the second order coefficient term is more complicated than the first order one with temperature, and also, depends on the three Morse oscillator parameters and the diameter of the particles. Besides, we conclude that the total pressure of Morse oscillator, generally, depends on the minimum energy of the well of Morse oscillator, the width parameter of Morse oscillator, and the equilibrium bond distance of the oscillator, in addition to their dependence on the absolute temperature of the components, and the diameter of the particles. The formula of the Morse oscillator equation of state which is found in this research can be applied to multiple materials described using Morse oscillator such as lots of dimers in the vibrations spectroscopy.

From vibrational spectroscopy and quantum tunnelling to periodic band structures – a self-supervised, all-purpose neural network approach to general quantum problems

A general, feedforward neural network strategy for the treatment of a broad range of quantum problems including rotational and vibrational spectroscopy, tunnelling and band structure calculations is presented in this study.

Vibrational energies of some diatomic molecules for a modified and deformed potential

A molecular potential model is proposed and the solutions of the radial Schrӧdinger equation in the presence of the proposed potential is obtained. The energy equation and its corresponding radial wave function are calculated using the powerful parametric Nikiforov–Uvarov method. The energies of cesium dimer for different quantum states were numerically obtained for both negative and positive values of the deformed and adjustable parameters. The results for sodium dimer and lithium dimer were calculated numerically using their respective spectroscopic parameters. The calculated values for the three molecules are in excellent agreement with the observed values. Finally, we calculated different expectation values and examined the effects of the deformed and adjustable parameters on the expectation values.

Bound-state solutions and thermal properties of the modified Tietz-Hua potential

An approximate solutions of the radial Schrödinger equation was obtained under a modified Tietz–Hua potential via supersymmetric approach. The effect of the modified parameter and optimization parameter respectively on energy eigenvalues were graphically and numerically examined. The comparison of the energy eigenvalues of modified Tietz–Hua potential and the actual Tietz–Hua potential were examined. The ro-vibrational energy of four molecules were also presented numerically. The thermal properties of the modified Tietz–Hua potential were calculated and the effect of temperature on each of the thermal property were examined under hydrogen fluoride, hydrogen molecule and carbon (ii) oxide. The study reveals that for a very small value of the modified parameter, the energy eigenvalues of the modified Tietz–Hua potential and that of the actual Tietz–Hua potential are equivalent. Finally, the vibrational energies for Cesium molecule was calculated and compared with the observed value. The calculated results were found to be in good agreement with the observed value.

Diatomic molecule energies of the modified Rosen−Morse potential energy model

We solve the Schrödinger equation with the modified Rosen−Morse empirical potential model to obtain rotation-vibrational energy spectra and unnormalized radial wave functions. The vibrational energy levels calculated with the modified Rosen−Morse potential model for the 61Πu state of the 7Li2 molecule and the X3Π state of the SiC radical are in better agreement with the Rydberg−Klein−Rees data than the predictions of the Morse potential model.

Molecular energies of the improved Tietz potential energy model

We solve the Schrödinger equation with the improved Tietz empirical potential energy model. The rotation-vibrational energy spectra and the unnormalized radial wave functions have been obtained. The vibrational energy levels predicted by using the improved Tietz potential model for the 51Δg state and C1Πu state of the Na2 molecule are in good agreement with the experimental Rydberg−Klein−Rees data.

Molecular energies of the improved Rosen−Morse potential energy model

We solve the Schrödinger equation with the improved Rosen−Morse empirical potential energy model. The rotation-vibrational energy spectra and the unnormalized radial wave functions have been obtained. The interaction potential energy curves for the 33Σg+ state of the Cs2 molecule and the 51Δg state of the Na2 molecule are modeled by employing the improved Rosen−Morse potential and the Morse potential. Favourable agreement for the improved Rosen−Morse potential is found in comparing with the Rydberg−Klein−Rees potential. The vibrational energy levels predicted by using the improved Rosen−Morse potential for the 33Σg+ state of Cs2 and the 51Δg state of Na2 are in better agreement with the Rydberg−Klein−Rees data than the predictions of the Morse potential.

Displacement matrix elements of Deng-Fan oscillators

Analytic expressions for matrix elements of integral powers of the displacement of the coordinate from equilibrium for the Deng-Fan oscillator have been derived. A comparison is made with the corresponding matrix elements for the Morse oscillator. These matrix elements are useful in high overtone spectroscopy and in models for DNA melting.

Modeling temperature dependent kinetic isotope effects for hydrogen transfer in a series of soybean lipoxygenase mutants: The effect of anharmonicity upon transfer distance

Soybean lipoxygenase-1 (SLO) catalyzes the oxidation of linoleic acid. The rate-limiting step in this transformation is the net abstraction of the pro-S hydrogen atom from the center of the 1,5-pentadienyl moiety in linoleic acid. The large deuterium kinetic isotope effect (KIE) for this step appears in the first order rate constant ((D)k(cat) = 81 ± 5 at T = 25 °C). Furthermore, the KIE and the rate for protium abstraction are weakly temperature dependent (E(A,D) - E(A,H) = 0.9 ± 0.2 kcal/mol and E(A,H) = 2.1 ± 0.2 kcal/mol, respectively). Mutations at a hydrophobic site about 13 Å from the active site Fe(III), Ile(553), induce a marked temperature dependence that varies roughly in accordance with the degree to which the residue is changed in bulk from the wild type Ile. While the temperature dependence for these mutants varies from the wild type enzyme, the magnitude of the KIE at 25 °C is on the same order of magnitude. A hydrogen tunneling model [Kuznetsov, A.M., Ulstrup, J. Can. J. Chem. 77 (1999) 1085-1096] is utilized to model the KIE temperature profiles for the wild type SLO and each Ile(553) mutant. Hydrogenic wavefunctions are modeled using harmonic oscillators and Morse oscillators in order to explore the effects of anharmonicity upon computed kinetic observables used to characterize this hydrogen transfer.

Absolute Intensities of CH Stretching Overtones in Alkenes

We have measured the CH stretching vibrational spectrum of ethene gas in the regions corresponding to 1-5 quanta in the CH stretching vibration with Fourier transform infrared and conventional absorption spectroscopy and have determined the corresponding oscillator strengths. We have calculated the CH stretching vibrational oscillator strengths for a series of alkenes: ethene, propene, 1,3-butadiene, cis-2-butene, and trans-2-butene. The CH stretching intensities are calculated with a simple Morse oscillator local mode model for CH groups and with the harmonically coupled anharmonic oscillator local mode model for CH2 and CH3 groups. The local mode parameters, frequencies, and anharmonicities are obtained from experiments. The harmonic coupling coefficients and the dipole moment functions are calculated with a range of ab initio methods. These include self-consistent-field Hartree-Fock, density functional, correlated, and multireference theories, combined with basis sets ranging from double- to quadruple-zeta quality augmented with polarization and diffuse functions. Variation in calculated oscillator strengths with the choice of ab initio method is systematically studied and compared with observed intensities. From this comparison between the calculated and observed values, we can quantitatively understand the relative usefulness of various ab initio dipole moment functions in calculations of vibrational oscillator strength for alkenes.

Cis-cis and trans-perp HOONO: Action spectroscopy and isomerization kinetics

The weakly bound HOONO product of the OH+NO2+M reaction is studied using the vibrational predissociation that follows excitation of the first OH overtone (2nu1). We observe formation of both cis-cis and trans-perp conformers of HOONO. The trans-perp HOONO 2nu1 band is observed under thermal (223-238 K) conditions at 6971 cm(-1). We assign the previously published (warmer temperature) HOONO spectrum to the 2nu1 band at 6365 cm(-1) and 2nu1-containing combination bands of the cis-cis conformer of HOONO. The band shape of the trans-perp HOONO spectrum is in excellent agreement with the predicted rotational contour based on previous experimental and theoretical results, but the apparent origin of the cis-cis HOONO spectrum at 6365 cm(-1) is featureless and significantly broader, suggesting more rapid intramolecular vibrational redistribution or predissociation in the latter isomer. The thermally less stable trans-perp HOONO isomerizes rapidly to cis-cis HOONO with an experimentally determined lifetime of 39 ms at 233 K at 13 hPa (in a buffer gas of predominantly Ar). The temperature dependence of the trans-perp HOONO lifetime in the range 223-238 K yields an isomerization barrier of 33+/-12 kJ/mol. New ab initio calculations of the structure and vibrational mode frequencies of the transition state perp-perp HOONO are performed using the coupled cluster singles and doubles with perturbative triples [CCSD(T)] model, using a correlation consistent polarized triple zeta basis set (cc-pVTZ). The energetics of cis-cis, trans-perp, and perp-perp HOONO are also calculated at this level [CCSD(T)/cc-pVTZ] and with a quadruple zeta basis set using the structure determined at the triple zeta basis set [CCSD(T)/cc-pVQZ//CCSD(T)/cc-pVTZ]. These calculations predict that the anti form of perp-perp HOONO has an energy of DeltaE0=42.4 kJ/mol above trans-perp HOONO, corresponding to an activation enthalpy of DeltaH298 (double dagger 0)=41.1 kJ/mol. These results are in good agreement with statistical simulations based on a model developed by Golden, Barker, and Lohr. The simulated isomerization rates match the observed decay rates when modeled with a trans-perp to cis-cis HOONO isomerization barrier of 40.8 kJ/mol and a strong collision model. The quantum yield of cis-cis HOONO dissociation to OH and NO2 is also calculated as a function of photon excitation energy in the range 3500-7500 cm(-1), assuming D0=83 kJ/mol. The quantum yield is predicted to vary from 0.15 to 1 over the observed spectrum at 298 K, leading to band intensities in the action spectrum that are highly temperature dependent; however, the observed relative band strengths in the cis-cis HOONO spectrum do not change substantially with temperature over the range 193-273 K. Semiempirical calculations of the oscillator strengths for 2nu1(cis-cis HOONO) and 2nu1(trans-perp HOONO) are performed using (1) a one-dimensional anharmonic model and (2) a Morse oscillator model for the OH stretch, and ab initio dipole moment functions calculated using Becke, Lee, Yang, and Parr density functional theory (B3LYP), Møller-Plesset pertubation theory truncated at the second and third order (MP2 and MP3), and quadratic configuration interaction theory using single and double excitations (QCISD). The QCISD level calculated ratio of 2nu1 oscillator strengths of trans-perp to cis-cis HOONO is 3.7:1. The observed intensities indicate that the concentration of trans-perp HOONO early in the OH+NO2 reaction is significantly greater than predicted by a Boltzmann distribution, consistent with statistical predictions of high initial yields of trans-perp HOONO from the OH+NO2+M reaction. In the atmosphere, trans-perp HOONO will isomerize nearly instantaneously to cis-cis HOONO. Loss of HOONO via photodissociation in the near-IR limits the lifetime of cis-cis HOONO during daylight to less than 45 h, other loss mechanisms will reduce the lifetime further.