Diatomic Molecules H2 Research Articles

Orbital contraction and covalent bonding.

According to Ruedenberg's classic treatise on the theory of chemical bonding [K. Ruedenberg, Rev. Mod. Phys. 34, 326-376 (1962)], orbital contraction is an integral consequence of covalent bonding. While the concept is clear, its quantification by quantum chemical calculations is not straightforward, except for the simplest of molecules, such as H2 + and H2. This paper proposes a new, yet simple, approach to the problem, utilizing the modified atomic orbital (MAO) method of Ehrhardt and Ahlrichs [Theor. Chim. Acta 68, 231 (1985)]. Through the use of MAOs, which are an atom-centered minimal basis formed from the molecular and atomic density operators, the wave functions of the species of interest are re-expanded, allowing the computation of the kinetic energy (and any other expectation value) of free and bonded fragments. Thus, it is possible to quantify the intra- and interfragment changes in kinetic energy, i.e., the effects of contraction. Computations are reported for a number of diatomic molecules H2, Li2, B2, C2, N2, O2, F2, CO, P2, and Cl2 and the polyatomics CH3-CH3, CH3-SiH3, CH3-OH, and C2H5-C2H5 (where the single bonds between the heavy atoms are studied) as well as dimers of He, Ne, Ar, and the archetypal ionic molecule NaCl. In all cases, it is found that the formation of a covalent bond is accompanied by an increase in the intra-fragment kinetic energy, an indication of orbital contraction and/or deformation.

Empirical quality criteria for the approximation of the electronic term of a diatomic molecule by the Morse formula

A brief review of the latest results of the application of the approximation of the potential of a diatomic molecule by the Morse model function in applied spectroscopy is presented. The functions of the electronic terms of the diatomic molecules BeH, F2, H2, HCl, and Be2 are compared with their two alternative approximations by the Morse function. As a criterion, we used the differences between the original (approximated) term and its Morse models, which, combined with the dependence of the anharmonicity of the original terms on the vibrational quantum number ωexe(v), allowed to formulate some generalizations about the deformation of the form the original term in the approximations. Simulation always leads to an increase in the bond energy in the range of 7-50% and to an increase in the number of vibrational levels. In favorable cases, the contour shape is reproduced with a deviation of no more than 100-200 cm-1 in the lower part of the potential well. Key words: Morse formula, diatomic molecule, anharmonicity, electronic terms, vibrational structure.

Accurate Prediction of Thermodynamic Functions of H2 and LiH Using Theoretical Calculations

Thermodynamic functions of two diatomic molecules gas, H2 and LiH, from theoretical point of view were predicted. The Schrodinger equation was analytically solved with the generalized Morse potential using Nikiforov–Uvarov method. The energy eigenvalues were obtained for the two cases (i) constant effective mass and (ii) position-dependent effective mass. The partition function of two diatomic molecules gases H2 and LiH was analytically obtained. Thermodynamic functions of the gases such as specific heat in constant pressure and volume, entropy, and enthalpy were determined and compared with experimental data. We could find an interesting point from our theoretical calculations. The results indicated that the calculated thermodynamic functions are in agreement with experimental data when the generalized Morse potential with variable mass was considered. This means that one can obtain best theoretical results by setting variable mass parameters.

Quantum dissipative systems beyond the standard harmonic model: Features of linear absorption and dynamics.

Current simulations of ultraviolet-visible absorption lineshapes and dynamics of condensed phase systems largely adopt a harmonic description to model vibrations. Often, this involves a model of displaced harmonic oscillators that have the same curvature. Although convenient, for many realistic molecular systems, this approximation no longer suffices. We elucidate nonstandard harmonic and anharmonic effects on linear absorption and dynamics using a stochastic Schrödinger equation approach to account for the environment. First, a harmonic oscillator model with ground and excited potentials that differ in curvature is utilized. Using this model, it is shown that curvature difference gives rise to an additional substructure in the vibronic progression of absorption spectra. This effect is explained and subsequently quantified via a derived expression for the Franck-Condon coefficients. Subsequently, anharmonic features in dissipative systems are studied, using a Morse potential and parameters that correspond to the diatomic molecule H2 for differing displacements and environment interaction. Finally, using a model potential, the population dynamics and absorption spectra for the stiff-stilbene photoswitch are presented and features are explained by a combination of curvature difference and anharmonicity in the form of potential energy barriers on the excited potential.

Nuclear spin-independent effects of parity nonconservation in molecule of hydrogen

Theoretical concepts and calculation results of the spatial parity nonconserving (PNC) effects of electron-electron and electron-nucleus nuclear spin-independent interactions in diatomic homonuclear molecule H2 of parahydrogen are presented. The magnetic dipole transition between the states with the same rotational number of the vibrational band in the H2 ground electronic state is considered. It is shown that in this situation these effects are of the same order of magnitude. The H2 molecule is therefore the first example of molecular system where the electron-electron PNC interaction can be directly observed. Since the constants of the electron-nucleus PNC interaction have been already accurately measured in atomic experiments, the electron-electron PNC interaction constant also can be extracted from the future experiments. In other atoms and molecules the electron-electron PNC interaction is usually deeply screened by the electron-nucleus one. Since the nuclei of H2 contain no neutrons, in such future experiments on the PNC effect observation one can, in principle, measure the Weinberg angle (free parameter of the standard model) with unprecedented accuracy.

Analytical Insight into the Effect of Electric Field on Molecular Properties of Homonuclear Diatomic Molecules

Background: The diatomic molecules represent one of the most active classes of materials, and they have been widely used as active materials for important applications. Objective: In this study, the effect of external electric field on molecular properties of four homonuclear diatomic molecules H2, C2, Cl2, and Br2 has been analyzed. Methods: All the calculations are based on the density functional theory (DFT) at the B3LYP/6- 311++G(3df,3pd) level through the Gaussian 09W program package. Results: The studied molecular properties include total energy, density of state (DOS) analysis, frontier molecular orbital energies HOMO and LUMO, energy gap, absorption threshold, internuclear separation, harmonic vibrational frequency, bond force constant, molecular dipole moment, polarizability, chemical potential, chemical hardness and electrophilicity. Conclusion: It has been observed that the interaction of molecules with external electric fields can be used to control and improve the basic properties of homonuclear diatomic molecules for their exploitation in some significant applications in spintronics. Keywords: B3LYP, DFT, diatomic molecules, energy gap, external field.

Observing electron localization in a dissociating H2+ molecule in real time

Dissociation of diatomic molecules with odd number of electrons always causes the unpaired electron to localize on one of the two resulting atomic fragments. In the simplest diatomic molecule H2+ dissociation yields a hydrogen atom and a proton with the sole electron ending up on one of the two nuclei. That is equivalent to breaking of a chemical bond—the most fundamental chemical process. Here we observe such electron localization in real time by performing a pump–probe experiment. We demonstrate that in H2+ electron localization is complete in just 15 fs when the molecule’s internuclear distance reaches 8 atomic units. The measurement is supported by a theoretical simulation based on numerical solution of the time-dependent Schrödinger equation. This observation advances our understanding of detailed dynamics of molecular dissociation.

Information entropies for the Morse potential using the J-matrix method

Information entropies, such as Shannon, Fisher and Rényi entropies, with their associated quantities, are calculated and discussed for the Morse potential in the position (r) and momentum (p) spaces using the J-matrix method. The entropies, for the s-wave, are numerically obtained for the diatomic molecules H2 and LiH. It is the first information entropy calculation for real diatomic molecules using the Morse potential. Interesting characteristic features of the entropy densities are shown, where the position and momentum space information entropies satisfy the uncertainty relations.

Study of the 2-channel systems using the J-matrix method

ABSTRACTThe partial widths and the branching ratios have been calculated for 2-channel systems, using the diagonalisation of a 2-channel full Hamiltonian and the J-matrix quantities related to the free Hamiltonian, for resonance states with different orbital angular momentum ℓ(ℓ = 0, 1, 2, 3) and different charge z (z = +1, 0, − 1) for Noro and Taylor potential. Moreover, the 1- and 2-channel Morse potential have been investigated for the two diatomic molecules H2 and LiH. The basis used is the Laguerre basis. Two approximate methods have been used to calculate the widths and the ratios associated with a spinless projectile‒target system. Many results are reported here for the first time, including the results of ℓ ≠ 0 and z ≠ 0 in 2-channel Noro and Taylor potential, and the results for the two diatomic molecules. The comparison of our outcome with earlier studies, wherever possible, on energies, branching ratios and partial widths, is discussed.

A general transformation to canonical form for potentials in pairwise interatomic interactions.

A generalized formulation of explicit force-based transformations is introduced to investigate the concept of a canonical potential in both fundamental chemical and intermolecular bonding. Different classes of representative ground electronic state pairwise interatomic interactions are referenced to a chosen canonical potential illustrating application of such transformations. Specifically, accurately determined potentials of the diatomic molecules H2, H2(+), HF, LiH, argon dimer, and one-dimensional dissociative coordinates in Ar-HBr, OC-HF, and OC-Cl2 are investigated throughout their bound potentials. Advantages of the current formulation for accurately evaluating equilibrium dissociation energies and a fundamentally different unified perspective on nature of intermolecular interactions will be emphasized. In particular, this canonical approach has significance to previous assertions that there is no very fundamental distinction between van der Waals bonding and covalent bonding or for that matter hydrogen and halogen bonds.

Encapsulation of diatomic molecules in fullerene C60: implications for their main properties.

The endohedral complexes of diatomic guest molecules H2, N2, O2, F2, HF, CO, LiH, LiF, BN, and BeO with C60 have been characterized computationally by employing second-order Møller-Plesset (MP2) theory and its density-fitting local (DF-LMP2) variant. The interaction energies, equilibrium geometries, dipole moments and harmonic vibrational frequencies of these complexes have been systematically calculated. It was found that all guest molecules are stabilized inside the C60 cage, with the most pronounced stabilization effect (of about 50 kcal mol(-1)) observed for the polar covalent BeO and BN molecules. It is noteworthy that the normally short-lived BN molecule is the only guest molecule that was found to chemisorb on the inner surface of C60. When encapsulated, all guest molecules (except for BN) exhibit bond elongation (up to 0.07 Å) and, consequently, a red shift in vibrational stretching frequencies. In fact, the calculated vibrational properties of the H2@C60 complex agree well with those derived from experiment. The C60 geometry is not perturbed significantly upon encapsulation, but a subtle tendency to decrease the carbon-carbon bond alternation is observed. Polar guest molecules inside C60 are located at an off-center position and a significant decrease in their dipole moments upon encapsulation is observed. The importance of explicitly taking into account electron correlation effects, as well as full geometry relaxation, to yield a correct description of the complexes investigated is clearly demonstrated. The present results may serve as a guide for future attempts to synthesize such complexes employing the "molecular surgery" approach.

Application of the Coulomb spheroidal basis for diatomic molecular calculations

Characteristics of Rydberg states for diatomic molecules H2, HeH+, C2+,N2+ are calculated in the basis of Coulomb spheroidal wave functions. The results are compared to the more sophisticated calculations and efficiency of the Coulomb spheroidal basis for molecular calculations is examined

Autoionization rate constants of zero electron kinetic energy Rydberg states

We have calculated the vibrational and rotational autoionization rate constants for diatomic molecules H2, N2, and HCl in high Rydberg states by employing the density matrix formulation with the inverse Born–Oppenheimer approximation basis set. The purpose is to simulate the main radiationless processes occurring in zero electron kinetic energy (ZEKE) spectroscopy. The quantum numbers and the energy dependences of the calculated autoionization rate constants are represented as the scaling laws via nonlinear regression. These data provide a suitable starting point for quantitative study of the intricate dynamics involved in ZEKE Rydberg states.

An analytic algebraic approach to study the influence of molecular alignment and orientation on multiphoton excitation in intense laser fields

The influence of molecular alignment and orientation on multiphoton vibrational excitation of diatomic molecules H2, HD, and D2 is studied by an analytical algebraic approach. The explicit expressions of the time-evolution operator and the excitation probability are given. The long-time average absorbed energy spectra and the time-dependent absorbed energy are obtained. Results show that the impact of molecular orientation on the multiphoton resonant excitation is decided by the molecular type and molecular anharmonicity. This is valuable for controlling the vibrational excitation of molecules, which is relevant to the whole field of molecular physics and physical chemistry. Furthermore, good agreement with numerical simulation is achieved.

A QUASICLASSICAL TRAJECTORY STUDY OF REACTIVE SCATTERING ON AN ANALYTICAL POTENTIAL ENERGY SURFACE FOR GeH2 SYSTEM

A quasiclassical trajectory method was employed to study reaction Ge+H 2 (v=0, j=0) and reverse reaction H+GeH (v=0, j=0) on an analytical potential energy surface obtained from simplified many-body expansion method with fitting to B3P86/CC-pVTZ calculations around a global minimum and a long-range van de Waals well plus spectroscopy data for diatomic molecules GeH and H2 . Reaction probabilities from both reaction and reverse reaction were calculated. Dominant reaction is complex-forming reaction Ge+H2 (v=0, j=0) → GeH2 , and its cross section is 10 times bigger than that of complex-forming reaction from the reverse reaction. There is no threshold effect for complex-forming reaction and the cross sections for both complex-forming reactions decrease with the increase of collision energy. Life time of complex is shown to be decreasing with increase of collision energy. Dominant reverse reaction is reaction H + GeH (v=0,j=0) → Ge+H2 ; the reaction probability decreases with the increase of collision energy and differential cross section shows that this reverse reaction has almost equal angular distribution at low collision energy and mostly forward scattering at high collision energy.

Effects of the internuclear vector on the photoelectron angular distributions of H2 +

We study the photoelectron angular distributions (PADs) of diatomic molecule H2 + irradiated by intense laser fields using a nonperturbative scattering theory. We find that the internuclear vector may change the PADs. The PADs have qualitative changes with the increasing of the internuclear distance. The molecular orientation affect the symmetry of the PADs. When the internuclear vector is vertical or parallel to the laser polarization vector, the PADs are four-fold symmetric; for other case the PADs are two-fold symmetric. Due to the modulation effect resulting from the molecular multi-core nature, the size of the jet and the main lobe can be enlarged or reduced. The molecular modulation effect become obvious for large internuclear distance.

Anatomy of bond formation: Insights from the analysis of domain‐averaged Fermi holes in momentum space

AbstractAlongside conventional domain‐averaged Fermi hole (DAFH) analysis in position space, we examine an alternative representation in momentum space. As examples, we consider the processes of splitting the chemical bonds in the simple diatomic molecules H2, N2, and LiH, as representatives of nonpolar single, nonpolar multiple, and polar bonding. We believe that the additional information provided by the complementary description in momentum space contributes to a better understanding of the phenomenon of chemical bonding. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009

Influence of Young-type interference on the forward-backward asymmetry in electron emission fromH2in collisions with80−MeVbare C ions

We use the forward-backward angular asymmetry in the electron emission cross sections in fast ion impact ionization of H2 as a probe of the inversion symmetric coherence in homonuclear diatomic molecules. The electron energy dependence of the asymmetry parameter for H2 exhibits oscillatory structure due to Young-type interference in contrast to atomic targets such as He. The asymmetry parameter technique provides a selfnormalized method to reveal the interference oscillation independent of theoretical models and complementary measurements on atomic H target. DOI: 10.1103/PhysRevA.74.060701 PACS numbers: 34.50.Fa, 34.50.Gb Angular distribution of various types of radiations particles and photons is known to be quite sensitive to various effects associated with different physical processes in atomic, nuclear, plasma physics and other branches of physics. In fast ion-atom ionization, the long range Coulomb interaction of the final state electrons with the target and the projectile ions influences the evolution of the electron wave function and thereby the angular distribution of electron emission. Such two-center effect is known to cause a large forward-backward asymmetry 1‐4 in the electron emission spectrum. The electron emission spectrum from the simplest diatomic molecule H2 manifests yet another important aspect of interference 5 in ion-atom ionization besides the wellknown mechanisms such as soft collision, two-center effect and binary encounter 1‐4,6‐8. Since the two indistinguishable H atoms in the H2 molecule may be considered as the coherent emission sources of phase coupled electrons in a large impact parameter collision, their contributions add coherently and an interference effect should be observed. Therefore, the electron emission from H2 may be viewed as a natural coherent system which is similar to Young’s double slit interference phenomenon 5. We demonstrate here that the additional mechanism of Young-type interference plays a major role in the angular asymmetry of electron double differential cross section DDCS and asymmetry parameter itself would be a sensitive test to study the interference for a diatomic molecular target. Following the initial theoretical studies on the interference effect in electron scattering 9 and photoionization 5, very recently the evidence of Young-type interference was found in the fast-ion collisions with H2 10‐12. Ideally one would have expected an oscillation in the DDCS spectrum due to interference. But a steep fall of the DDCS by about four or five orders of magnitude see below does not allow one to observe the oscillation directly. The oscillations, thereby, were observed in the DDCS ratios H2-to-2H which was explained due to the interference. However, the experiments using H are rare due to the experimental constraint and oscillations in the DDCS ratios were observed 4,12 in such experiment with H. Theoretical DDCS for atomic, or effective atomic H have also been employed 10,11 in the absence of an atomic H target. In such cases, the shapes of the oscillations are sensitive to the atomic parameters such as the effective atomic number Zeff which is model dependent. So far oscillations have not been observed based on the H2 DDCS data only. In this work we present a method based on the analysis of the asymmetry parameter which is independent of normalization procedures and permits therefore to observe the interference effect directly in the H2 data only. By eliminating the need for the data on atomic H is an important step forward in the study of this

The absorption line profiles of H2O near 1.39 μm in binary mixtures with N2, O2, and H2 at low pressures

The absorption line profiles of water vapor in binary mixtures with diatomic molecules H2, N2, and O2 have been recorded on a diode laser spectrometer. The profiles of several lines of the 101 band have been studied near 1.39 μm with a spectral resolution of 3 × 10−4 cm−1. The pressure of the binary mixtures was varied from 0 to 200 Torr. The experimental data obtained have been used to test the Voigt, Rautian-Sobel’man, and Galatry theoretical models of a spectral line profile. The coefficients of collisional narrowing have been determined from the results of the fitting.

The role of the electrodes in a molecular conductor: an eigenchannel analysis

In order to investigate the role of the electrodes in a molecular conductor, we have studied the effects of diatomic molecules H2 and O2 on the eigenchannels of a nanocontact formed by two Au(100) electrodes with finite cross sections by first principles calculations combined with non-equilibrium Green's function technique. Two cases where the axes of the molecules are placed along the electrode axis and vertically to the electrode axis are studied. We find that the maximum number of the eigenchannels and their energy ranges are always determined by the band structure of the electrodes. The molecules only modify the electron transmission probability of each channel.