Relaxations of molecular charge distributions and the vibrational force constants in diatomic hydrides

1969 ◽  
Vol 47 (16) ◽  
pp. 3061-3074 ◽  
Author(s):  
R. F. W. Bader ◽  
J. L. Ginsburg
Keyword(s):  
Charge Distribution ◽  
Force Constant ◽  
Covalent Binding ◽  
Force Constants ◽  
Static Charge ◽  
Hartree Fock ◽  
Polynomial Fit ◽  
Molecular Charge ◽  
Static Charge Distribution ◽  
Ionic Binding

The force constants for LiH, HF, NaH, and HCl are calculated from Hartree–Fock wavefunctions by a polynomial fit of the forces exerted on the nuclei as a function of the internuclear separation. The magnitude of the force constant is interpreted in terms of the relaxation of the molecular charge distribution induced by the nuclear displacement. In LiH or NaH, for which the molecular charge distribution exhibits the characteristics of ionic binding, two distinct relaxations are evident: a relaxation in the region of the cationic core and a relaxation of the density localized on the proton. The relaxation of the charge density in the vicinity of the Li+ or Na+ core opposes the motion of either nucleus while the relaxation of the density localized on the proton facilitates the displacement of the nuclei. In HF or HCl the relaxation of the molecular charge distribution is dominated by one continuous region of charge increase (for bond contraction) or decrease (for bond extension) over the whole of the binding region, a relaxation which facilitates the motion of the nuclei. Thus the relaxation of a molecular charge distribution and its effect in determining the magnitude of the force constant is dominated by the same features of the static charge distribution which serve to distinguish ionic from covalent binding.

A view of bond formation in terms of molecular charge distributions

1968 ◽  
Vol 46 (6) ◽  
pp. 953-966 ◽  
Author(s):  
R. F. W. Bader ◽  
A. K. Chandra
Keyword(s):  
Charge Distribution ◽  
Bond Formation ◽  
Atomic Charge ◽  
Maximum Error ◽  
Calculated Density ◽  
Hartree Fock ◽  
Charge Distributions ◽  
Molecular Charge ◽  
Nuclear Separation ◽  
Order Of Magnitude

The process of bond formation as a function of internuclear separation for H2 and Li2 is interpreted in terms of the changes in the charge distributions and the forces which they exert on the nuclei. The charge distributions are calculated from extended Hartree–Fock wave functions which reduce to the Hartree–Fock atomic functions for infinite nuclear separation. The results for H2 indicate that at separations greater than 5 a.u. the net attractive force exerted on the approaching nuclei arises from a simultaneous inwards polarization of the atomic charge distributions. For separations less than 5 a.u. the nuclei are bound by the force exerted by the delocalized component of the charge distribution. The density distributions and forces for He2 over a range of internuclear separations are compared with those for H2 to contrast the formation of stable and unstable molecular species in terms of their respective charge distributions.The final section of the paper examines in detail the changes in the Hartree–Fock molecular charge distribution which arise from the inclusion of electron correlation in the wave function. The maximum error in the Hartree–Fock charge distribution for H2 is found to be in the region between the nuclei, where it overestimates the charge density by approximately 1%. The errors in the Hartree–Fock charge distribution for Li2 are found to be of the same order of magnitude as the uncertainty in the calculated density distribution itself.

Study of charge transfer in FeTi

1983 ◽  
Vol 41 ◽  
pp. 296-297
Author(s):  
J. Taft∅
Keyword(s):  
Charge Transfer ◽  
Charge Distribution ◽  
Electron Scattering ◽  
Periodic System ◽  
Electron Distribution ◽  
Scattering Amplitude ◽  
Transition Elements ◽  
Hartree Fock ◽  
Cscl Structure ◽  
The Right

It is well known that for reflections corresponding to large interplanar spacings (i.e., sin θ/λ small), the electron scattering amplitude, f, is sensitive to the ionicity and to the charge distribution around the atoms. We have used this in order to obtain information about the charge distribution in FeTi, which is a candidate for storage of hydrogen. Our goal is to study the changes in electron distribution in the presence of hydrogen, and also the ionicity of hydrogen in metals, but so far our study has been limited to pure FeTi. FeTi has the CsCl structure and thus Fe and Ti scatter with a phase difference of π into the 100-ref lections. Because Fe (Z = 26) is higher in the periodic system than Ti (Z = 22), an immediate “guess” would be that Fe has a larger scattering amplitude than Ti. However, relativistic Hartree-Fock calculations show that the opposite is the case for the 100-reflection. An explanation for this may be sought in the stronger localization of the d-electrons of the first row transition elements when moving to the right in the periodic table. The tabulated difference between fTi (100) and ffe (100) is small, however, and based on the values of the scattering amplitude for isolated atoms, the kinematical intensity of the 100-reflection is only 5.10-4 of the intensity of the 200-reflection.

Bonded Force Constant Derivation of Lysine-Arginine Cross-linked Advanced Glycation End-Products

2018 ◽  
Author(s):  
Anthony Nash ◽  
Nora H de Leeuw ◽  
Helen L Birch
Keyword(s):  
Molecular Dynamics ◽  
Force Constant ◽  
Computational Study ◽  
Force Constants ◽  
Quantum Mechanical ◽  
Advanced Glycation ◽  
Partial Charges ◽  
Cross Links ◽  
Complete Set ◽  
Dynamics Simulations

<div> <div> <div> <p>The computational study of advanced glycation end-product cross- links remains largely unexplored given the limited availability of bonded force constants and equilibrium values for molecular dynamics force fields. In this article, we present the bonded force constants, atomic partial charges and equilibrium values of the arginine-lysine cross-links DOGDIC, GODIC and MODIC. The Hessian was derived from a series of <i>ab initio</i> quantum mechanical electronic structure calculations and from which a complete set of force constant and equilibrium values were generated using our publicly available software, ForceGen. Short <i>in vacuo</i> molecular dynamics simulations were performed to validate their implementation against quantum mechanical frequency calculations. </p> </div> </div> </div>

RAMAN SPECTRA OF TITANIUM DI-, TRI-, AND TETRA-CHLORIDES

2001 ◽  
Vol 15 (28n30) ◽  
pp. 3865-3868 ◽  
Author(s):  
H. MIYAOKA ◽  
T. KUZE ◽  
H. SANO ◽  
H. MORI ◽  
G. MIZUTANI ◽  
...  
Keyword(s):  
Force Constant ◽  
Raman Spectra ◽  
Normal Mode ◽  
Raman Band ◽  
Normal Mode Analysis ◽  
Force Constants ◽  
Mode Analysis ◽  
Oxidation Number

We have obtained the Raman spectra of TiCl n (n= 2, 3, and 4). Assignments of the observed Raman bands were made by a normal mode analysis. The force constants were determined from the observed Raman band frequencies. We have found that the Ti-Cl stretching force constant increases as the oxidation number of the Ti species increases.

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