The Interpretation of molecular wave functions: the development and application of Roby's method for electron population analysis

1982 ◽  
Vol 304 (1488) ◽  
pp. 533-565 ◽  
Keyword(s):  
Population Analysis ◽  
Chem Phys ◽  
Wave Functions ◽  
Multiple Bonds ◽  
Electron Population ◽  
Polarization Functions ◽  
Bond Strengths ◽  
Extended Basis ◽  
Two Hybrid ◽  
Single Bonds

An extensive investigation has been made of Roby’s (Molec. Phys. 27, 81 (1974)) projection-density method for electron population analysis, particularly as applied to extended basis molecular wave functions. In the developed method maximum possible populations are ascribed to atomic s.c.f. orbitals and minimum possible populations to polarization functions. Roby populations are reported for a range of diatomic and simple polyatomic molecules. For a given coordination number, the Roby atomic population n A reflects the electronegativities of an atom and its ligands. By equipartition of shared populations, atomic charges may also be defined. The two-centre shared populations s AB = n A + n B — are found to be coherent indicators of bond strengths. For conventional single bonds, s AB can often be roughly interpreted as S AB » 2 S ab ,where S ab is the overlap integral between the two hybrid atomic orbitals defined by a localized molecular orbital representing the A -B bond. Multiple bonds can be interpreted similarly. Multi-centre shared populations s ABC , s ABCD are helpful in descriptions o f the bonding in B 2 H 6 and P 4 . The Roby projector technique is particularly useful in determining the unique effects of polarization functions. Several wave functions for NF 3 and SO 3 are examined in detail, and the sulphur d functions are confirmed as the most important polarization functions. Various technical aspects of the Roby method are also explored, and the method is shown to have some significant advantages over the widely used Mulliken ( J. chem. Phys. 23, 1833 (1955)) method of population analysis.

Population Analysis with Hydrogen 2 p Polarization Functions Included in the INDO Basis Set

1980 ◽  
Vol 35 (12) ◽  
pp. 1350-1353
Author(s):  
J. C. Facelli ◽  
R. H. Contreras
Keyword(s):  
Ab Initio ◽  
Population Analysis ◽  
Basis Set ◽  
Ab Initio Methods ◽  
Mulliken Population Analysis ◽  
Indo Method ◽  
Hydrogen Atoms ◽  
Mulliken Population ◽  
Electron Population ◽  
Polarization Functions

Abstract Mulliken population analysis with 2p polarization functions included in the AO basis set of the INDO method has been performed for a set of molecules containing hydrogen as well as first row atoms. It is found that this enlargement of the basis set yields an increasing electron population in hydrogen atoms, in agreement with trends found in “ab initio” methods.

scholarly journals From “inverted” to “superdirect“ bonds: a general concept connecting substituent angles with sigma bond strengths. The case of the CC bonds in hydrocarbons.

2021 ◽  
Author(s):  
Rubén Laplaza ◽  
Julia Contreras-García ◽  
Franck Fuster ◽  
François Volatron ◽  
Patrick Chaquin
Keyword(s):  
Dissociation Energy ◽  
General Concept ◽  
Bond Energies ◽  
Multiple Bonds ◽  
Cyclic Molecules ◽  
Central Bond ◽  
Bond Strengths ◽  
The Mean ◽  
Single Bonds ◽  
Sigma Bond

<div>The C-C dissociation energy with respect to geometry frozen fragments (BE) has been calculated for C2H6 as a function of  = H-C-C angles. BE decreases rapidly when  decreases from its equilibrium value to yield the so-called “inverted bonds” for  < 90°; on the contrary BE increases</div><div>when  increases to yield somehow “superdirect” bonds, following a sigmoidal variation. The central bond in Si2H6, Ge2H6 and N 2H4 as well as the C-H bond in CH3-H behaves similarly. The concept of “invertedness”/”directedness” is generalized to any CC sigma bond in hydrocarbons and characterized by the mean angle value <> of substituents. Using dynamic orbital forces (DOF) as indices, the intrinsic  bond energies are studied as a function of <> for formally single bonds in a</div><div>panel of 22 molecules. This energy decreases from the strongest “superdirect” bonds in butadiyne, (<> = 180°) or tetrahedrylacetylene to the weakest “inverted bond” in cyclobutene, tetrahedrane, bicyclobutane and [1.1.1]propellane (<> = 60°), according to a sigmoidal variation. The <> parameter appears as a crude, but straightforward and robust, index of strain in cyclic molecules. Sigma bonds in multiple bonds of a panel of 11 molecules have most of time <> values less than 90°</div><div>and are significantly weaker than standard single bonds. Thus they can be considered as formally inverted or near inverted.</div><div><br></div>

Electron Population Analysis by Full-Potential X-Ray Absorption Simulations

1999 ◽  
Vol 82 (11) ◽  
pp. 2398-2401 ◽  
Author(s):  
Yves Joly ◽  
Delphine Cabaret ◽  
Hubert Renevier ◽  
Calogero R. Natoli
Keyword(s):  
Population Analysis ◽  
Full Potential ◽  
Electron Population ◽  
X Ray ◽  
X Ray Absorption

AIM study on the transferability of the oxygen atom in linear ethers

2000 ◽  
Vol 78 (12) ◽  
pp. 1535-1543 ◽  
Author(s):  
Antonio Vila ◽  
Enrique Carballo ◽  
Ricardo A Mosquera
Keyword(s):  
Dipole Moment ◽  
Oxygen Atom ◽  
Potential Energy ◽  
Critical Points ◽  
Wave Functions ◽  
Electron Population ◽  
Alkyl Radicals ◽  
Energy Interaction ◽  
Interaction Dipole Moment ◽  
Oxygen Atoms

The integrated values of the electron population, electron energy, nucleus–electron potential energy interaction, dipole moment and volume of the oxygen atoms, and the main properties of the O—C bond critical points, were determined by employing the theory of atoms in molecules and 6-31++G**//6-31G* wave functions for a series of 25 unbranched alkyl monoethers. These results were used to assess the degree of approximate transferability of the oxygen atom along this series in terms of the particular alkyl radicals bonded to it. It has been found that a set of six different oxygen atoms is necessary to classify all the computed values. It can be established that the oxygen atoms bonded to propyl and larger radicals can be treated, in practice, as a transferable fragment, while those bonded to at least one smaller radical are specific. Though the total HF energy and the available experimental heats of formation are well fitted by a traditional additivity scheme that distinguishes only among O, CH2, and CH3 units, it has been found that the energy properties are influenced by the size of the molecule.Key words: transferability, AIM theory, ethers.

Beschreibung der Richtung des elektrischen Dipolmomentvektors 14 durch Slater-Orbitalexponenten, / The Direction of the Electric Dipole Moment Vector μ⃗ as Inferred from Slater Orbital Exponents

1975 ◽  
Vol 30 (7-8) ◽  
pp. 550-553
Author(s):  
Paul Machmer
Keyword(s):  
Dipole Moment ◽  
Electric Dipole Moment ◽  
Electric Dipole ◽  
Population Analysis ◽  
Electron Population ◽  
Slater Orbital ◽  
Moment Vector ◽  
Molecular Ground State ◽  
Heteronuclear Molecules ◽  
Orbital Exponents

By means of Slater orbital exponents it is possible to differentiate between the positive and the negative end of the permanent electric dipole of diatomic heteronuclear molecules. Thus Slater orbital exponents hold a clue to the direction of the electric dipole moment vector μ⃗ of the molecular ground state. A comparison with electron population analysis is made.

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