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.

Topologically partitioned dynamic polarizabilities using the theory of atoms in molecules

1996 ◽  
Vol 74 (6) ◽  
pp. 976-987 ◽  
Author(s):  
Christof Hättig ◽  
Bernd A. Hebβ ◽  
Georg Jansen ◽  
János G. Ángyán
Keyword(s):  
Atomic Charge ◽  
Atoms In Molecules ◽  
Basis Set ◽  
Dynamic Polarizability ◽  
Hartree Fock ◽  
Molecular Charge ◽  
Dynamic Charge ◽  
Atomic Polarizability ◽  
Dynamic Polarizabilities ◽  
Dipole Polarizabilities

Frequency-dependent distributed polarizabilities have been determined from time-dependent Hartree–Fock calculations, using the partitioning of the molecular space suggested by Bader's topological theory of atoms in molecules. The basis set dependence of the distributed dynamic polarizabilities is analyzed in terms of the first few Cauchy moments, for the carbon monoxide, water, cyanogen, urea and benzene molecules. Two alternative relocalization schemes have been considered in order to reduce the number of distributed dynamic polarizability parameters. The first one, closely related to the atomic polarizability model of Bader, leads to atomic charge–dipole and dipole–dipole polarizabilities, describing the response of the molecular charge distribution to a uniform external field, in terms of atomic charges and dipoles. The second scheme, similar to that suggested by Stone, retains the fully distributed description of the dynamic charge-flow polarizabilities, while all two-center dipole–dipole and charge–dipole contributions are condensed in one-center dynamic dipole–dipole polarizabilities. Key words: Bader-partitioning, distributed dynamic polarizabilities, Cauchy-moments, benzene, polarizability of; urea, polarizability of.

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.

Polarizations of atomic and molecular charge distributions

1969 ◽  
Vol 47 (12) ◽  
pp. 2308-2311 ◽  
Author(s):  
R. F. W. Bader ◽  
I. Keaveny ◽  
G. Runtz
Keyword(s):  
Electric Field ◽  
Charge Distribution ◽  
Primary Response ◽  
Fundamental Nature ◽  
Charge Distributions ◽  
Molecular Charge ◽  
A Charge

It is shown that the dominant polarization of a molecular charge distribution in the region of a nucleus of an atom which employs p orbitals in its bonding (Be → F, Mg → Cl) is quadrupolar in nature, and dipolar for an atom which employs s orbitals (H, He, Li, Na). That these polarizations are of a fundamental nature is demonstrated by showing that they represent the primary response of a charge distribution to an electric field, whether it be internal or external, static or dynamic.

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.

Polaronic and Bipolaronic Enhancement of Second Hyperpolarizabilities in Dithienyl Polyenes from Ab Initio Quantum Methods

1999 ◽  
Vol 597 ◽  
Author(s):  
Steven Trohalaki ◽  
Robert J. Zellmer ◽  
Ruth Pachter
Keyword(s):  
Ab Initio ◽  
Density Functional ◽  
Valence Bond ◽  
Closed Shell ◽  
Functional Theory ◽  
Molecular Conformations ◽  
Hartree Fock ◽  
Molecular Charge ◽  
Field Methodology ◽  
Moller Plesset

AbstractSpangler and He [1,2] have shown that dithienyl polyenes form extremely stable bipolaronic dications when oxidatively doped in solution. Previous theoretical studies applied empirical methods to predict bipolaronic enhancement of hyperpolarizabilities for simple polyenes [3,4]. Here, we employ density functional theory to optimize the gas-phase molecular conformations of neutral, cationic, and dicationic forms of a series of dithienyl polyenes, where the number of ethene units, N, is varied from 1–5. Ab initio Hartree-Fock, generalized valence bond, configuration interaction, and Møller-Plesset calculations demonstrate that the dications are farily well described with a closed shell and therefore have little biradicaloid character. Second hyperpolarizabilities, γ, are subsequently calculated using ab initio Hartree-Fock theory and a finite field methodology. As expected, γ increases with the number of ethene units for a given molecular charge. The cations also show the largest increase in γ with N. For a given value of N, the cations display the largest γ values. However, if we treat the dication as a triplet, which might be present in solution, then it displays the largest γ.

scholarly journals Hartree-Fock Charge Distributions for 1p-Shell Nuclei

1976 ◽  
Vol 56 (5) ◽  
pp. 1497-1502 ◽  
Author(s):  
R. S. Bhalerao ◽  
A. T. Dhavale
Keyword(s):  
Hartree Fock ◽  
Charge Distributions
Sign in / Sign up

Export Citation Format

Share Document