Morse Potential Energy Research Articles

The electron affinities of NO and O2

In the 1970s, experimental values of the EA of O2 and NO clustered around two values, 0.43 and 0.9eV for O2 and 0.025 and 0.8eV for NO. We report new ground state adiabatic electron affinities (AEA), AEA-X: NO; 0.84±0.05 and O2; 0.9±0.05eV. Excited state EA, AEA∗ for spin orbital coupling states of NO are 0.27 and 0.25±0.02eV. The activation energies for thermal electron attachment to the X state are both 0.8±0.05eV. These were obtained by a least squares analysis of electron capture detector data using a two state model incorporating other literature data and their random uncertainties, including AEA, NO, 0.85±0.08eV and AEA∗ O2; 0.45 and 0.43±0.01eV. Morse Potential energy curves illustrate the assignments.

Negative Ion Mass Spectra, Electron Affinities, Gas Phase Acidities, Bond Dissociation Energies, and Negative Ion States of Cytosine and Thymine

Negative ion Morse potential energy curves for cytosine (C) and thymine (T) consolidate electron affinity, gas-phase acidity, bond dissociation energy, photoelectron spectrum, electron impact, transmission, and transfer data. We have previously published experimental adiabatic electron affinities for guanine, 1.51 ± 0.05; adenine, 0.95 ± 0.05; C, 0.56 ± 0.05; uracil, 0.80 ± 0.05; and T, 0.79 ± 0.05 (all in eV). These values were obtained from half-wave reduction potentials in aprotic solvents and verified by AM1 semiempirical multiconfiguration configuration interaction (AM1-MCCI) calculations. We present a computer simulation of thermal charge-transfer experiments to support these values. Unpublished negative chemical ionization mass spectrometry data support our gas-phase acidities: for A, G, and T, 14.1; for U, 14.2; and for C, 14.3 (all in eV). We use dipole-bound and valence-state electron affinities previously obtained from photoelectron spectra (Schiedt, J.; Weinkauf, R.; Neumark, D. M.; Schlag, E. W. Chem. Phys. 1998, 239, 511). We interpret monoenergetic electron beam spectra reported in the literature to obtain vertical electron affinities, negative ion distributions, and limits to bond dissociation energies for C and T (Huels, M. A.; Hahndorf, I.; Illenberger, E.; Sanche, L. J. Chem. Phys. 1998, 108, 1309).

EPR investigations of bonding and activation of nitrogen oxides by surface complexes of transition metal ions

EPR spectroscopy has been used to investigate changes occurring at the molecular level during coordination and activation of NO and N2O small pollutant molecules on Cu/ZSM-5 and Mo/SiO2 catalysts, respectively. It is shown that the activation of nitric oxide occurs by formation of a bent η1{CuNO}11 surface adduct with rehybridization of the NO Orbitals. The spin Hamiltonian parameters of this species have been analyzed in detail, leading to a molecular and electronic picture of the complex. The mechanism along which N2O is decomposed upon interaction with surface Mo5+ species involves dissociative metal-to-ligand electron transfer. The reaction was monitored by EPR using naturally abundant and95Mo-enriched molybdenum. The dynamics of the N-O bond cleavage is discussed in terms of two-dimensional Morse potential energy surfaces. From the EPR parameters of the resultant O− radical, the spin density distribution and the stabilization energy were calculated.

Vibrationally resolved oxygen K→Π ∗ spectra of O 2 and CO

A near-edge X-ray absorption fine-structure (NEXAFS) study of the O K→Π ∗ excitation in CO (534 eV) and O 2 (531 eV) molecules has been carried out. A Franck–Condon analysis of the transitions has been accomplished assuming a Morse potential energy curve for the core hole states. The vibrational constants of O 2 are in agreement with values expected from the equivalent core molecule OF. The values of the lifetime widths of the Π ∗ excited states are Γ O 2 =149±10 meV and Γ CO=158±8 meV. The measured lifetime width of O 2 is an upper limit to the true value as unresolved spin–orbit structure is believed to be present, which may cause an additional broadening of ∼5 meV. In spite of this, it is substantially smaller than the hitherto accepted value of 180 meV, necessitating a re-evaluation of most previously published data.

Exploring the Morse Potential: MorsePotential.mcd

The goal of the 'Exploring the Morse Potential' document is to provide hands on practice with the Morse potential energy function and the units used for calculating this potential. In the document is a step-by-step description of how to create the Morse potential function for HCl.

Characterization of homonuclear diatomic ions by semi-empirical Morse potential energy curves.: 3. Rare-gas positive ions revisited

The Morse parameters for all the Rg 2 + and ground- and D-state curves for the X 2 − are reported. Based on the isoelectronic equivalence and new literature data for the ground states of I 2 −, Ne 2 + and Ar 2 + [Ramos et al., Phys. Rev. A 56 (1997) 1913; Signorell et al., J. Chem. Phys. 107 (1997) 10819; Zanni et al., J. Chem. Phys. 107 (1997) 7613] the literature high-resolution photoelectron spectra [Hall et al., J. Phys. B 28 (1995) 2435] can be analyzed to give accurate D 0, υ e and some r e for all the states. For some curves, the absorption spectra must be used. To do this the selected values of ground-state Rg 2 + parameters are: Ne 2 + (1.28±0.01 eV, 175±2 pm, 569±4 cm −1); Ar 2 + (1.314±0.001 eV, 256±2 pm, 307±1 cm −1); Kr 2 + (1.18±0.01 eV, 272±2 pm, 162±2 cm −1); Xe 2 + (1.007±0.005 eV, 308.5±2 pm, 128±5 cm −1).

Characterization of Homonuclear Diatomic Ions by Semiempirical Morse Potential Energy Curves. 2. The Rare Gas Positive Ions

Morse potential energy curves for the lowest six states of the rare gas positive ion dimers have been calculated on the basis of experimental data. For the ground states, there are sufficient measured data to define the curves completely. For the excited states of all the positive ion dimers except neon, there are sufficient measured data to define the curves. To obtain these curves, new assignments of vibrational progressions in high-resolution photoelectron spectra previously published are made and the vertical ionization potentials obtained. The vertical ionization potentials are used to determine the internuclear distances. The ground state ionic and neutral radii for Ne to Xe are 63, 93, 105, and 123 pm and 112, 152, 168, and 194 pm, respectively. “Virtual” covalent radii for Ne to Xe are 69, 98, 111, and 126 pm. The curves are consistent with the van der Waals radii of Ne to Xe, which are 154, 188, 200, and 218 pm. From the correlation between the Morse parameters of the isoelectronic ions and the n...

Characterization of Homonuclear Diatomic Ions by Semiempirical Morse Potential Energy Curves. 1. The Halogen Anions

Morse potential energy curves for the homonuclear diatomic halogen anions and their excited states were constructed using experimental data available from the literature. All of the curves are uniquely or overdetermined. The properties of the negative ions have been related to those of the neutral by using three dimensionless parameters, kA, kB, and kR, to modify the Morse curves of the neutral. The magnitudes of the parameters are reasonably consistent and suggest ranges for other homonuclear diatomic ions. A set of Morse potential energy curves is predicted for astatine anions on the basis of the consistency of these parameters. These curves are a significant improvement over those presented 10 years ago because of the existence of additional experimental data. In cases where the curves are overdetermined, these data agree very well with the calculated Morse potentials. Estimates for internuclear distances were made on the basis of the assumption of the additivity of radii. Agreement with available expe...

Avoided resonance overlapping beyond the energy independent formalism. II. Electronic predissociation

The transition between the diabatic and the adiabatic zero order representation when the electronic potential coupling increases, is studied in the partitioning method (PM) and in the complex coordinate method (CCM) implemented in a discrete variable representation (DVR). The model is a C+ type predissociation in a diatomic system with a crossing between a Morse potential energy curve and an exponentially repulsive curve. In the weak coupling regime (isolated diabatic metastable states), both methods confirm the linear variation of the resonance widths with the strength of the electronic interaction, as expected in a perturbative treatment. When the coupling is large in the diabatic representation (strong overlap regime), the formation of narrow resonances supported by the upper adiabatic potential can be related, in PM, to the process of avoided resonance overlapping among interfering states. The complete change of representation can be described in the initial diabatic basis set in PM. However, the full energy dependence of the discrete-continuous matrix elements must then be taken into account. The deformation and the final splitting of a diffuse spectral line with increasing coupling is re-examined in terms of these energy dependent eigenvalues of the effective Hamiltonian. The use of the appropriate representation, either diabatic or adiabatic, according to the strength of the electronic coupling, has been found decisive in CCM so as to observe the correct migration of the resonance positions towards the zero order adiabatic states, and the decrease of their widths. No relevant results have been obtained for the intermediate strength of the coupling in CCM. Analytical expressions for the derivative coupling matrix elements (∂/∂R) in the fixed node DVR (corresponding to the particle-in-a-box wave functions) have been established.

A non-unique relationship between potential energy surface barrier and dynamical diffusion barrier: fcc (111) metal surface

We present results from molecular dynamics simulations of the diffusion of a single metal atom on the surface of a fcc (111) metal. The central point that is addressed is the relationship between features of the potential energy surface and the diffusion rate when the surface (energy) corrugation is small. The systems considered here are Ag and Ag(111) and Rh on Rh(111). The interatomic forces were predicted using an approximation to the many-body non-self-consistent density functional based corrected effective medium theory (with acronym MD/MC-CEM), and an empirical Morse potential energy surface. Both potential energy forms are completely specified by the properties of the bulk systems, with the former also predicting very good values of surface energies on low Miller index surfaces and diffusion barriers on fcc (001) surfaces. Diffusion rates were extracted from the long time behavior of the adatom's mean square displacement and were found to obey an Arrhenius-type dependence on temperature. Good agreement with experimental diffusion rates was found with both potential energy surfaces. A different potential energy surface with much larger energy corrugation also yields agreement with experiment. We conclude that diffusion on these atomically smooth surfaces is governed by correlated dynamical behavior which eliminates the possibility of a unique extraction of the corrugation profile from experimental data.

Continuum approximation of the morse potential lattice sums in cubic crystals

Using the continuum approximation of Born and his coworkers, several lattice sums of the Morse potential energy function are calculated for cubic lattices. The results are found to be in good to excellent agreement with the actual values.

Morse pe-curves of AlH

Morse potential energy curves forC1∑+ andC1∑+ of AlH have been constructed. The energy values have been found to increase from vibrational levels 0 to 6 and decrease from vibrational levels 7 to 50 with the corresponding centre and half-width in the stateC1∑+. InC1∑+ state the energy values have been found to increase from vibrational levels 0 to 28 and decrease from vibrational levels 29 to 50 with the corresponding centre and half-width.

A COMPUTER SIMULATION OF THE STRUCTURE OF AMORPHOUS ALLOY Fe-P(II)——THE DEPENDENT RELATION OF THE STRUCTURE OF Fe100-xPx ON THE CONCENTRATION

In this paper, the model that we constructed to simulate the DPRHS of Fe100-xPx(x= 25, 20, 15) is taken as the primary configuration. This configuration is then subjected to relaxation under the quasi-dynamical equilibrim boundary through the tail truncated Morse potential (energy minimization). The total energy, reduced distribution function, coordination number distribution, angular distribution and homogeneity are obtained from the calculated data. The dependent relation of the structure of Fe100-x Px on the composition are discussed.

A COMPUTER SIMULATION OF THE STRUCTURE OF AMORPHOUS ALLOY Fe-P(I)——THE SHORT RANGE ORDER OF THE STRUCTURE OF Fe75P25 ALLOY

In this paper, the model that we constructed to simulate the structure of Fe75P25 is taken as the primary configuration. Then this configuration is subjected to relaxation under the quasi-dynamic equilibium boundary through th tail-truncated Morse potential (energy minimization). The total energy, reduced distribution function coordination number, angular distribution function and homogeneity are obtained from the calculated data. The short lange order in amorphous alloy Fe75P25 is disclssed.

Influence of heme-surrounding amino acid residues on the manganese (V)-nitrido bond in manganese-substituted hemoproteins: resonance Raman evidence for porphyrin core expansion and reduction of the manganese(V)-nitrido stretching force constant.

Nitridomanganese(V) protoporphyrin IX was prepared by hypochlorite oxidation of the corresponding manganese(III) protoporphyrin IX derivative in the presence of ammonium ion and by photolysis of the corresponding azidomanganese(III) complex. Myoglobin and horseradish peroxidase containing this novel protoporphyrin derivative were prepared for the first time. These remarkably stable species were examined by electronic absorption, electron paramagnetic resonance, and resonance Raman spectroscopies. The MnV-N stretching modes of the nitridomanganese(V)-substituted myoglobin and horseradish peroxidase were observed at 1010 and 1003 cm-1, respectively, by resonance Raman spectroscopy, while the MnV-N stretching frequency for nitridomanganese(V) protoporphyrin IX in 0.1 N aqueous NaOH was found at 1046 cm-1. The equilibrium dissociation energies of MnV-N bonds in these complexes were estimated from vibrational overtone spacings by introducing the Morse potential energy function, were found to be around 4.5 eV, and seemed independent of the surroundings of the manganese porphyrin, although its force constant decreased from 7.3 to 6.7 mdyn/A upon incorporation into apoprotein. The porphyrin ring modes of these nitridomanganese(V) derivatives were influenced greatly upon incorporation into apoproteins, suggestive of the occurrence of porphyrin core expansion. Upon this core expansion the MnV center moves into the mean plane of porphyrin plane, but the access of nitrido (N) toward MnV is restricted due to a steric hindrance from porphyrin pyrrole nitrogens. The resulting stretched MnV-N bond might cause lowering of the MnV-N stretching frequency upon incorporation into apoprotein.

Importance of kinetics and thermodynamics to the electron-capture detector

The kinetic model for the electron-capture detector (ECD) has been reviewed. Emphasis was placed on the agreement between thermodynamic and kinetic data obtained from the ECD and independent data obtained by other techniques. During the past five years, sufficient kinetic and thermodynamic data have been obtained to establish clearly the validity of the ECD model for non-dissociative electron capture and for exothermic dissociative electron attachment. In addition, new ECD data have been obtained for a kinetic mechanism of dissociative electron capture, which had been postulated but had not been demonstrated. This mechanism provides values for rate constants which have heretofore never been measured. All of the mechanisms have been illustrated by the use of Morse potential energy curves. A direct correspondence was shown to exist between the gas-phase mechanisms and mechanisms in solution observed with electrochemical techniques. As a result, fundamental kinetic and thermodynamic data can be obtained from the solution data. Correlations have been given which permit the calculation of electron affinities from half-wave reduction potentials.

The Analysis of Vibrational Spectra of Species Adsorbed at the electrode-solution interface: A theoretical model for the effects of potential on the observed spectra

Abstract : Interactions of electroactive species and adsorbates with the solvent, electrolyte and electrode are observed in the situ infrared spectrum of the interface. The analysis of these spectra is usually difficult, and conventional normal coordinate analysis, while useful for simple molecular systems which are undisturbed by the environment, is not well suited for systems whose vibrational structure is perturbed by external forces. We have recently formulated a Taylor series in symmetry-adaptable spherical harmonic functions which has been applied successfully to account for spectral perturbations observed in an electromechanical system. In the method, an adsorbed molecule is described as the sum of pair-wise potential energy functions which operate between the bonded and non-bonded atoms. Perturbations are introduced by additional pair-wise terms operating between the perturbing force center and the specific atoms in the molecule. In many systems, Morse or Lennard-Jones potential energy functions may be used. Cartesian force constants, from which the vibrations of the system are determined, are calculated from expansion of the pair-wise potential functions to second order using the symmetry-adapted from the Taylor series. The elements of the cartesian force constant matrix have been derived for the general case. Keywords: Infrared spectroelectrochemistry.

Importance of kinetics and thermodynamics to the electron-capture detector

The kinetic model for the electron-capture detector (ECD) has been reviewed. Emphasis was placed on the agreement between thermodynamic and kinetic data obtained from the ECD and independent data obtained by other techniques. During the past five years, sufficient kinetic and thermodynamic data have been obtained to establish clearly the validity of the ECD model for non-dissociative electron capture and for exothermic dissociative electron attachment. In addition, new ECD data have been obtained for a kinetic mechanism of dissociative electron capture, which had been postulated but had not been demonstrated. This mechanism provides values for rate constants which have heretofore never been measured. All of the mechanisms have been illustrated by the use of Morse potential energy curves. A direct correspondence was shown to exist between the gas-phase mechanisms and mechanisms in solution observed with electrochemical techniques. As a result, fundamental kinetic and thermodynamic data can be obtained from the solution data. Correlations have been given which permit the calculation of electron affinities from half-wave reduction potentials.

Infrared and raman spectroscopy of stressed polyethylene

AbstractPolyethylene films were stressed in uniaxial tension at room temperature while the infrared (FTIR) or Raman spectra were simultaneously measured. The purpose of these experiments was to gain an understanding of the molecular origins of the stress‐induced vibrational frequency shifts Δν and determine the mechanisms of molecular deformation and fracture of PE molecules with stress σ. The PE samples consisted of ultradrawn, high‐density, ultrahigh‐molecular‐weight, solid‐state‐extruded films and the stress was applied parallel to the nearly perfectly oriented orthorhombic crystal c‐axis direction. The experimental frequency shifting coefficients α = (∂ν/∂σ)σ→0 were compared with calculated α values determined from a vibrational analysis of an isolated PE chain using conformational energy minimization methods in which both harmonic and anharmonic (Morse) potential energy functions were used for the CC stretching modes in the valence force field. The following α values were obtained and are compared with theory (anharmonic case in parentheses, in cm−1/GPa): CC symmetric stretch, α(1127) = −5.9 (−5.3); CC asymmetric stretch, α(1059) = −11.2 to −5.7 (−5.8); CH2 rock, α(730/720) = −2.0 to −3.0 (−2.2); CH2 scissors, α(1472/1462) = −1.0 to −1.2 (−1.1); CH2 twist, α(1295) ≃ 0(0.8); CH2 wag, α(1370) undetermined owing to weak bands (−4.6); CH2 stretch α(3000) ≈ 0. The largest negative frequency shifts were observed for the CC stretching modes, in agreement with the calculations using the Morse potential. The harmonic potential for CC stretching resulted in small positive α values for both the CC stretching and CH2 wagging modes, while the other modes were unaffected by this choice of potential. The relative contribution of CC bond stretching and CĈC valence angle bending to the c‐axis strain was about 1:1, in agreement with experiment. The Young's tensile modulus of a PE chain was calculated as Ec = 267 GPa.

A computerised approach to some aspects of spectroscopy

Spectroscopy is an extremely diversified and wide-ranging subject and is perhaps best approached through a study of atoms and diatomic molecules, subsequently extended to include polyatomic molecules. Since the field is large an arbitrary selection of topics has had to be made to illustrate some of the applications of interactive computing. The Beer-Lambert law is widely encountered by students at an early stage and forms the basis of the program PHOTOMETER. This can be used not only for evaluating data from teaching experiments but also for real analyses of a routine or research nature. The concept of the quantisation of electronic energy is usually introduced via the Bohr treatment of the hydrogen atom and in HYDROGEN this treatment is extended to include one-electron ions up to and including 16O 7+. Even though it has now been superseded by wave mechanics, the Bohr theory is useful in that it permits the student to make quantitative calculations at an early stage, and to compare the results with experimental values to be found in the literature. In diatomic molecules, the presence of the second atom naturally introduces the idea of vibrational energy, and MORSECURVE produces detailed data which enable the complete Morse potential energy curve to be plotted. However, molecular vibrational energy is quantised and transitions between the energy levels in the ground electronic state form the basis of vibrational spectroscopy. The program VIBRATIONS calculates the vibrational energy levels of a diatomic molecule when the values of the fundamental frequency and anharmonicity constants are entered. If data for both the ground and an excited electronic state of a molecule are used, then MORSECURVE and VIBRATIONS, in conjunction, produce results which enable the drawing of transitions which give rise to vibrational fine structure in the electronic spectrum.