Directed Valence as a Property of Determinant Wave Functions

Zimmerman, Howard K.; Rysselberghe, Pierre Van

doi:10.1063/1.1747344

Cited by 30 publications

(13 citation statements)

References 4 publications

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“…In this work, we implement this approach and demonstrate its viability even for moderately large molecules. The discussion of the most probable electron arrangement has a long history in chemistry . Recently, Scemama et al investigated the maxima of

| Ψ |^{2}

for the water molecule similarly to the current work, and the current author developed single electron densities based on the maxima of

| Ψ |^{2}

…”

Section: Introductionmentioning

confidence: 77%

Maxima of : A connection between quantum mechanics and Lewis structures

Lüchow

2014

J Comput Chem

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The maxima of squared electronic wave functions |Ψ|2 are analyzed for a number of small molecules. They are in principle observables and show considerable chemical insight from first principles. The maxima contain substantial information about the relative electron positions in a molecule, such as the pairing of opposite spin electrons and the Pauli repulsion which are lost in the electron density. Single bond and double bond as well as polar bond pairs and lone pairs are obtained from the maximum analysis. In many cases, we find a correspondence to the electron arrangements in molecules as assumed by Lewis in 1916.

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| Ψ |^{2}

for the water molecule similarly to the current work, and the current author developed single electron densities based on the maxima of

| Ψ |^{2}

…”

Section: Introductionmentioning

confidence: 77%

Maxima of : A connection between quantum mechanics and Lewis structures

Lüchow

2014

J Comput Chem

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“…This may be particularly serious in the discussion of shapes, for these are, to a large extent, decided by the mutual effects of electrons on one another. For example, inethane is tetrahedral because the Pauli principle requires that four electrons with parallel spins in the 2s and three 2 p orbitals of carboil will be, with greatest probability, a t the corners of a regular tetrahedron (11). Moreover charge effects favor this shape also.…”

Section: Introductionmentioning

confidence: 99%

Equivalent Orbitals and the Shapes of Excited Species

Linnett¹

1958

Can. J. Chem.

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The electron distributions in the ground states of C?H?, HCO, and NH?, and in one excited state of each species, have been considered by transforming the sinlple molecular orbitals into equivalent ones. I n the light of these considerations, the shapes and dimensions of the above species in these states have been discussed. I t is found that a considerable degree of understanding can be achieved though there is uncertainty in the interpretation in some cases. INTRODUCTIONThe object of this paper is to discuss some ways in which the shapes of n~olecules and radicals in their ground and excited states are decided by their electronic structures. The molecule C2Hp and the radicals HCO and N H 2 will be co~lsidered as examples. An extensive treatment of this type of problem has been given by Walsh (lo), his approach being that of simple molecular orbital (M.O.) theory. This method, in its simple form, implies that the total energy can be represented to a satisfactory approximation by the sum ol a number of one-electron energies of values corresponding to the orbitals that are occupied. Clearly this is an overapproximation, for interelectronic effects arising both from their charge and from the consequences of the Pauli principle (i.e. effects of multiplicity) are ignored. T o some extent, of course, in drawing diagrams in his papers, Walsh has taken account of these effects, for the graphs of energy against angle are not computed from a number of one-electron calculations but are derived on a more enlpirical basis.Simple A11.O. theory, because interelectronic effects are ignored, is clearly an oversii~lplification. This may be particularly serious in the discussion of shapes, for these are, to a large extent, decided by the mutual effects of electrons on one another. For example, inethane is tetrahedral because the Pauli principle requires that four electrons with parallel spins in the 2s and three 2 p orbitals of carboil will be, with greatest probability, a t the corners of a regular tetrahedron (11). Moreover charge effects favor this shape also. Also NH3 is pyramidal because of the presence of the lone pair and of the interaction of this with the bonding pairs (7). Consideration of shapes should therefore include interelectron effects as well as one-electron effects, and consequently the simple M.O. procedure is not wholly satisfactory.The approach used in this paper will be that based on the representation of the molecular wave function in terms of equivalent orbitals which are linear combinations of the basic one-electron molecular orbitals, for these allow an easier appreciation of the electron distribution, and a more reasonable assessment of the effects of electron interactions. This procedure has been used previously by the author to discuss the bonding in the ground and some excited states of the diatomic molecules and ions formed by carbon, nitrogen, and oxygen (5). Equivalent orbitals of this type are to be preferred when electron distributioils are being considered (4). I t was found that the fo...

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“…The interaction arising fro111 the Pauli exclusion principle is in general more important than that arising fro111 electrostatic repulsions and the arrangeinents of electron pairs given in Table I can be deduced from a consideration of this interaction alone ignoring electrostatic repulsions. I t has been shoarn by several authors (2)(3)(4)(5)(6)(7)(8)(9)(10) that, by assigning the electrons to appropriate s, @, and d atomic orbitals, writing the coinplete antisym-metric wave function for these electrons, thereby taking account of the I'auli exclusion principle, and then calculatiilg the most probable distribution of the electrons, the arrangements of electron pairs that are obtained are identical with those given in Table I. The same results call be obtained in a si~nple qualitative manner as follows.…”

mentioning

confidence: 99%

“…For four electrons of the same spill 01-four pairs of opposite spin the most probable arrangement, i.e. that which inaxiillizes their distance apart or gives thein equivalent seg~nents of the available spherical space, is the tetrahedral arrangement (8). Four electrons of the same spin or lour pairs of opposite spill may be regarded as occup)ring four equivalent tetrahedrally directed seginents of the available spherical volumc, i.e.…”

mentioning

confidence: 99%

Electron Correlation and Molecular Shape

Gillespie¹

1960

Can. J. Chem.

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I t is proposed that the arrangements of the electron pairs in the valency shell of a central atom of a polyatomic molecule can be predicted by considering the equilibrium arrangements of similar particles on the surface of a sphere with a n appropriate law of force between the particles. The arrangements resulting from an inverse square law of force, corresponding to electrostatic repulsions, and a force which is proportional to l / r n where n is large, corresponding to Pauli forces, are considered specifically. It is shown that the arrangements predicted agree with those found experimentally for ~nolecules containing only non-transitional elements. The possible arrangements for seven, eight, and nine pairs of electrons in a valency shell are discussed in detail. A method is suggested for predicting the arrangements of electron pairs in valency shells containing lone pairs which can OCCLIPY alternative non-equivalent positions. The effect of the interactions of electron pairs on bond lengths in certain molec~~les is discussed. The extension of the same principles t o molecules containing transitional elements is briefly outlined.I t was shown recently by Gillespie and Nyholnl (1) that the shapes of a wide range of molecules can be correctly predicted by ineans of the sinlple rule that the electron pairs, including both shared (i.e. bonding) pairs and unshared (i.e. lone) pairs, of the valency shell of a central atom of a polyatoinic nlolecule adopt certain definite arrangements which depend only on their total number as shown in Table I. These arrangements are a consequence of the mutual interactions of the valency shell electrons due to (i) electrostatic repulsions, and to (ii) the operation of the Pauli exclusion principle, as a consequence of which electrons of the same spin tend to lieep as far apart as possible while electrons of opposite spin tend to be drawn together (2). The interaction arising fro111 the Pauli exclusion principle is in general more important than that arising fro111 electrostatic repulsions and the arrangeinents of electron pairs given in Table I can be deduced from a consideration of this interaction alone ignoring electrostatic repulsions. I t has been shoarn by several authors (2-10) that, by assigning the electrons to appropriate s, @, and d atomic orbitals, writing the coinplete antisymlManz4scri@t received Janz~ary 22, 1960. Coztribz4tion front the Departnte,zt of Clretnistry, 11.lcil.laster University, Ilantilton, Ontario. Can.

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Directed Valence as a Property of Determinant Wave Functions

Cited by 30 publications

References 4 publications

Maxima of : A connection between quantum mechanics and Lewis structures

Maxima of : A connection between quantum mechanics and Lewis structures

Equivalent Orbitals and the Shapes of Excited Species

Electron Correlation and Molecular Shape

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