The electrostatic calculation of molecurlar energies - III. The binding energies of saturated molecules

1954 ◽  
Vol 226 (1165) ◽  
pp. 193-205 ◽  
Keyword(s):  
Binding Energy ◽  
Valence Bond ◽  
Binding Energies ◽  
Wave Functions ◽  
Complex Molecules ◽  
Electron Orbital ◽  
Hydride Molecule ◽  
Paired Electron ◽  
Bond Functions ◽  
Good Agreement

A technique for calculating the binding energy of any saturated molecule is developed.The method is based on an application of the electrostatic theorem, discussed in earlier parts, to paired-electron orbital wave functions.These wave functions include both molecular-orbital and valence-bond functions as special cases.The resulting numerical computations are sufficiently simple to be carried through without approximation even for complex molecules. The method is applied to the lithium molecule and the lithium hydride molecule, and yields results in good agreement with experiment. The choice of wave functions for calculations on other molecules is discussed.

A DFT study of spherands containing five anisyl groups — Highly preorganized to bind the alkali metal

2006 ◽  
Vol 84 (8) ◽  
pp. 1045-1049 ◽  
Author(s):  
Shabaan AK Elroby ◽  
Kyu Hwan Lee ◽  
Seung Joo Cho ◽  
Alan Hinchliffe
Keyword(s):  
Density Functional Theory ◽  
Binding Energy ◽  
Density Functional ◽  
Ionic Radius ◽  
Binding Energies ◽  
Cavity Size ◽  
X Ray Diffraction ◽  
Functional Theory ◽  
X Ray ◽  
Good Agreement

Although anisyl units are basically poor ligands for metal ions, the rigid placements of their oxygens during synthesis rather than during complexation are undoubtedly responsible for the enhanced binding and selectivity of the spherand. We used standard B3LYP/6-31G** (5d) density functional theory (DFT) to investigate the complexation between spherands containing five anisyl groups, with CH2–O–CH2 (2) and CH2–S–CH2 (3) units in an 18-membered macrocyclic ring, and the cationic guests (Li+, Na+, and K+). Our geometric structure results for spherands 1, 2, and 3 are in good agreement with the previously reported X-ray diffraction data. The absolute values of the binding energy of all the spherands are inversely proportional to the ionic radius of the guests. The results, taken as a whole, show that replacement of one anisyl group by CH2–O–CH2 (2) and CH2–S–CH2 (3) makes the cavity bigger and less preorganized. In addition, both the binding and specificity decrease for small ions. The spherands 2 and 3 appear beautifully preorganized to bind all guests, so it is not surprising that their binding energies are close to the parent spherand 1. Interestingly, there is a clear linear relation between the radius of the cavity and the binding energy (R2 = 0.999).Key words: spherands, preorganization, density functional theory, binding energy, cavity size.

The electrostatic calculation of molecular energies - IV. Optimum paired-electron orbitals and the electrostatic method

1956 ◽  
Vol 235 (1201) ◽  
pp. 224-234 ◽  
Keyword(s):  
Simple Procedure ◽  
Wave Functions ◽  
Optimum Form ◽  
Method Of Calculation ◽  
Hartree Fock ◽  
Electron Orbital ◽  
Electrostatic Method ◽  
Valence States ◽  
Paired Electron ◽  
Electrostatic Interpretation

Equations which determine the optimum form of paired-electron orbitals are derived. It is shown that for large nuclear separations these equations become the Hartree-Fock equa­tions for appropriate valence states of the separated atoms. An electrostatic interpretation of chemical bonding is developed using optimum paired-electron orbital functions. For these wave functions this simple procedure yields results identical with those obtained by the conventional method of calculation based on the Hamiltonian integral. Numerical computations by the electrostatic method are also discussed.

The binding energies of atomic nuclei III. Nuclear forces and the ground state of oxygen 16

1959 ◽  
Vol 253 (1273) ◽  
pp. 186-198 ◽  
Keyword(s):  
Binding Energy ◽  
Electron Scattering ◽  
Ground State ◽  
Binding Energies ◽  
Wave Functions ◽  
Unperturbed System ◽  
Core Radius ◽  
Nuclear Forces ◽  
Potential Core ◽  
Atomic Nuclei

The r. m. s. radius and the binding energy of oxygen 16 are calculated for several different internueleon potentials. These potentials all fit the low-energy data for two nucleons, they have hard cores of differing radii, and they include the Gammel-Thaler potential (core radius 0·4 fermi). The calculated r. m. s. radii range from 1·5 f for a potential with core radius 0·2 f to 2·0 f for a core radius 0·6 f. The value obtained from electron scattering experiments is 2·65 f. The calculated binding energies range from 256 MeV for a core radius 0·2 f to 118 MeV for core 0·5 f. The experimental value of binding energy is 127·3 MeV. The 25% discrepancy in the calculated r. m. s. radius may be due to the limitations of harmonic oscillator wave functions used in the unperturbed system.

A variational method for calculating magnetic shielding constants in molecules

1957 ◽  
Vol 243 (1233) ◽  
pp. 264-273 ◽  
Keyword(s):  
Variational Method ◽  
Molecular Orbital ◽  
Diamagnetic Susceptibility ◽  
Valence Bond ◽  
Wave Functions ◽  
Magnetic Shielding ◽  
Magnetic Nucleus ◽  
Shielding Constants ◽  
Good Agreement

The general variational method is applied to the problem of calculating magnetic shielding constants in molecules. Using approximate variation functions together with simple molecular-orbital and valence-bond wave functions calculations have been made for the molecules hydrogen, methane, ethylene and acetylene. An approximation using the calculated diamagnetic susceptibility is used for electrons which are not localized near the magnetic nucleus considered. The results are in good agreement with experiment and in particular it is shown that the shielding constant for acetylene should lie between those for methane and ethylene.

The binding energies of s-shell nuclei

1969 ◽  
Vol 47 (24) ◽  
pp. 2825-2834 ◽  
Author(s):  
J. Law ◽  
R. K. Bhaduri
Keyword(s):  
Binding Energy ◽  
Long Range ◽  
Hard Core ◽  
Nucleon Nucleon ◽  
Interference Term ◽  
Binding Energies ◽  
Wave Functions ◽  
A Value ◽  
Range Part ◽  
Central Forces

We have calculated the binding energies of 4He and 3H with soft- and hard-core nucleon–nucleon potentials. With central forces, using harmonic-oscillator wave functions, we find that accurate results can be obtained by taking only the long-range part of the potential and its second-order perturbative term. When tensor forces are present, the long-range interference term is also included in the calculation. In this case, the method is not accurate and underbinds these nuclei by about 1 MeV per particle. Ignoring Coulomb forces, our method yields a value of 18.5 MeV for the binding energy of 4He with the Hamada–Johnston potential.

Binding energy of the triton

1951 ◽  
Vol 204 (1079) ◽  
pp. 476-488 ◽  
Keyword(s):  
Binding Energy ◽  
Magnetic Moments ◽  
Coulomb Repulsion ◽  
Coherent Scattering ◽  
High Energy ◽  
Binding Energies ◽  
Wave Functions ◽  
Variation Method ◽  
The Difference ◽  
High Energy Scattering

The variation method is employed to calculate the binding energy of the triton assuming charge-independent, two-body, Yukawa shape interactions between nucleons in which tensor forces are included. More complete trial wave functions are used than employed hitherto in such calculations, and it is found that an interaction of Yukawa shape with constants adjusted to fit the observed data on the binding energy, quadrupole moment and magnetic moment of the deuteron, the low-energy and high-energy scattering of neutrons by protons, the photodisintegration of the deuteron and the coherent scattering of slow neutrons gives an approximately correct binding energy for the triton. Calculations are also carried out with interactions of the same type but with different constants. The exchange character of the forces remains unimportant. It is confirmed that the difference in the binding energies of 3 H and 3 He can be ascribed to the effect of Coulomb repulsion between the protons in the latter nucleus. The wave functions found are used to compute the magnetic moments of the two nuclei but do not contain sufficient admixture of P component to explain the observed values.

PRESSURE EFFECT ON THE INTERFACE EXCITONS IN A TYPE-II ZnTe/CdSe HETEROJUNCTION

2003 ◽  
Vol 17 (27n28) ◽  
pp. 1425-1435 ◽  
Author(s):  
Z. Z. GUO ◽  
X. X. LIANG ◽  
S. L. BAN
Keyword(s):  
Binding Energy ◽  
Ground State ◽  
Pressure Effect ◽  
Light Hole ◽  
Binding Energies ◽  
Wave Functions ◽  
Type Ii ◽  
Band Bending ◽  
Effective Masses ◽  
Transfer Method

A variational method is used to study the ground-state binding energies of interface light-hole excitons in ZnTe/CdSe type-II heterojunctions under the influence of hydrostatic pressure. The finite triangle potential well approximation is introduced considering the band bending near the interface. The asymptotic transfer method is adopted to obtain the sub-band energies and wave functions of the electrons and light holes. The pressure influence on the band offsets, the effective masses and the dielectric constant are considered in the calculation. The obvious pressure-induced increase of the exciton binding energy is demonstrated and the influences of the pressure-depended parameters on the binding energy are compared.

scholarly journals Electrostatically assisted macroion association

2021 ◽  
Vol 24 (3) ◽  
pp. 33502
Author(s):  
J. Reščiš
Keyword(s):  
Monte Carlo ◽  
Molecular Docking ◽  
Binding Energy ◽  
Short Range ◽  
Dynamic Equilibrium ◽  
Model System ◽  
Binding Energies ◽  
Effective Attraction ◽  
Theoretical Results ◽  
Good Agreement

A model system of highly asymmetric polyelectrolyte with directional short-range attractive interactions was studied by canonical Monte Carlo computer simulations. Comparison of MC data with previously published theoretical results shows good agreement. For moderate values of binding energies, which matches those of molecular docking, a dynamic equilibrium between free and dimerized macroions is observed. Fraction of dimerized macroions depends on macroion concentration, binding energy magnitude, and on the valency of small counterions. Divalent counterions induce an effective attraction between macroions and enhance dimerization. This effect is most notable at low to moderate macroion concentrations.

A qualitative investigation of the wave functions of metallic uranium

1958 ◽  
Vol 247 (1249) ◽  
pp. 199-213 ◽  
Keyword(s):  
Wave Function ◽  
Binding Energy ◽  
Binding Energies ◽  
Wave Functions ◽  
Atomic Sphere ◽  
Maximum Charge ◽  
Self Consistent ◽  
Self Consistent Field ◽  
Negative Binding Energy ◽  
Metallic Uranium

The potential field and wave functions in metallic uranium have been calculated approximately by determining Hartree self-consistent fields for the four configurations (6 d ) 6 , (5 f ) 2 (6 d ) 2 (7 s ) 2 , (5 f ) 4 (6 d ) 2 , and (5 f ) 6 using the Wigner–Seitz boundary condition at the surface of the equivalent atomic sphere. In the self-consistent field obtained for each configuration, wave functions falling to zero at the surface of the sphere were evaluated for the outer electrons. The differences between the Hartree ∊-parameters for the two boundary conditions were used to give an indication of the relative band widths. The (5 f ) wave function has its principal maximum inside the (6 s ) (6 p ) shell, but is appreciable at the surface of the sphere and must participate in bonding. The binding energy of an electron in the (5 f ) wave function is 0.3934 rydbergs in the configuration (5 f ) 2 (6 d ) 2 (7 s ) 2 as given by the Hartree ∊-parameter. The (6 d ) function has its maximum charge density at the boundary and, with a binding energy of 0.1749 rydbergs in the same configuration, is likely to form a good metallic band. The (7 s ) function has a large negative binding energy and is not likely to occur. In the configuration (5 f ) 2 (6 d ) 2 (7 s ) 2 the band widths of the (5 f ), (6 d ) and (7 s ) functions are in the ratio 1:9∙8:22∙7. As the number of (5 f ) electrons is increased all the binding energies decrease and the band widths increase. At the same time the (6 s ) and (6 p ) functions are markedly perturbed, the functions (5 s ), (5 p ) and (5 d ) to a lesser extent.

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