Tables for Determining Atomic Wave Functions and Energies
TL;DR: In this paper, a table has been constructed so that wave functions and energies, for any atomic state having $1s, $2s$ and $2p$ electrons, can be computed by variational means.
Abstract: Tables have been constructed so that wave functions and energies, for any atomic state having $1s$, $2s$ and $2p$ electrons, can be computed by variational means Exchange terms are included, so that singlet and triplet states can be minimized separately By using the tables a state can be calculated in a few hours A few of the possible states have been worked out The best parameters, the total energies and the term values are given for the states $(1{s}^{2})^{1}S,(1s,2s)^{1}S,^{3}S;(1,2p)^{1}P,^{3}P; (1{s}^{2},2s)^{2}S; (1{s}^{2},2p)^{2}P; (1{s}^{2},2{s}^{2})^{1}S; (1{s}^{2},2s,2p)^{1}P,^{3}P; (1{s}^{2},2{p}^{2})^{1}S,^{1}D,^{3}P; (1{s}^{2},2{s}^{2},2p)^{2}P; (1{s}^{2},2{s}^{2},2{p}^{6})^{1}S$; of the atoms He, Li, Be, B, C, N, O, F, Ne, Na and Mg The intramultiplet separations have been computed, including the spin-spin interaction when necessary: the check with experiment being fairly satisfactory By the use of an empirical correction rule, term values can be predicted to within a few hundred wave numbers
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TL;DR: In this paper, it was shown that the only obstacle to the evaluation of wave functions of any required degree of accuracy is the labour of computation, and that all necessary integrals can be explicitly evaluated.
Abstract: This communication deals with the general theory of obtaining numerical electronic wave functions for the stationary states of atoms and molecules. It is shown that by taking Gaussian functions, and functions derived from these by differentiation with respect to the parameters, complete systems of functions can be constructed appropriate to any molecular problem, and that all the necessary integrals can be explicitly evaluated. These can be used in connexion with the molecular orbital method, or localized bond method, or the general method of treating linear combinations of many Slater determinants by the variational procedure. This general method of obtaining a sequence of solutions converging to the accurate solution is examined. It is shown that the only obstacle to the evaluation of wave functions of any required degree of accuracy is the labour of computation. A modification of the general method applicable to atoms is discussed and considered to be extremely practicable.
1,036 citations
Abstract: Explicit formulas and numerical tables for the overlap integral S between AO's (atomic orbitals) of two overlapping atoms a and b are given. These cover all the most important combinations of AO pairs involving ns, npσ, and npπ AO's. They are based on approximate AO's of the Slater type, each containing two parameters μ [equal to Z/(n—δ)], and n—δ, where n—δ is an effective principal quantum number. The S formulas are given as functions of two parameters p and t, where p=½(μa+μb)R/aH , R being the interatomic distance, and t=(μa—μb)/(μa+μb). Master tables of computed values of S are given over wide ranges of p and t values corresponding to actual molecules, and also including the case p=0 (intra‐atomic overlap integrals). In addition, tables of computed S values are given for several cases involving 2‐quantum s, p hybrid AO's.Hybrid S values for any desired type of hybrid can be obtained very easily from the tables as simple linear combinations of non‐hybrid S values. It is shown how S values correspondin...
868 citations
TL;DR: The electronic correlation energy in 3-and 4-electron atomic systems is compared to previously well-established correlation energies in 2-and 3-electrons atoms as discussed by the authors, and it is shown that the distribution of correlation energy between radial and angular correlation parallels that of the 2-Electron system very closely.
195 citations
01 Nov 1959
TL;DR: The electronic correlation energy in 3-and 4-electron atomic systems is compared to previously well established correlation energies in 2-and 3-electrons atoms as discussed by the authors, which suggests a convenient scheme for constructing a semi-empirical method for estimating atomic energies rather accurately, however, a similar analysis for molecules in terms of the internuclear parameters suggests there may be inherent difficulties in constructing such a scheme for the molecular case.
Abstract: The electronic correlation energy in 3- and 4-electron atomic systems is compared to previously well established correlation energies in 2-electron atoms. It is shown that the distribution of correlation energy in the K shell of these atoms between radial and angular correlation parallels that of the 2-electron system very closely. It is found, however, that the correlation in the L shell of the Be ground state is almost purely angular correlation energy. There is negligible correlation energy associated with K-L interaction. Analysis of the Z dependence of the correlation energy of 4 electron atoms shows a term linear in Z. It is suggested that this term arises from degeneracies existing in the limit of infinite Z, and a tabulation of states expected to have this property is given. The analysis suggests a convenient scheme for constructing a semiempirical method for estimating atomic energies rather accurately. It is pointed out that a similar analysis for molecules in terms of the internuclear parameters suggests there may be inherent difficulties in constructing such a scheme for the molecular case. (auth)
185 citations
TL;DR: In this paper, the theory of the transformation from molecular orbitals to sets of equivalent orbitals is discussed for the general case when there is more than one occupied molecular orbital of given symmetry and more than 1 equivalent set.
Abstract: The theory of the transformation from molecular orbitals to sets of equivalent orbitals is discussed for the general case when there is more than one occupied molecular orbital of given symmetry and more than one equivalent set. The general transformation is worked out for molecules whose component atoms possess inner shells and lone pairs of electrons. The theory is illustrated by reference to some simple molecules such as water and ammonia. Finally, it is shown how the expression for the total energy of a molecule can be divided up in such a way that the interactions between its localized parts are dealt with separately. The significance of lone pairs of electrons in determining the shape of molecules is pointed out.
153 citations