Upper and lower bounds for the second-order energy in the SchrÖdinger perturbation theory are studied by means of operator inequalities and inner projections. It is shown that the variation problems associated with Hylleraas's upper bound and Hirschfelder-Prager's lower bound over a linear manifold have simple explicit solutions. The approach is tested numerically on some selected examples with good results.

A simple, ‘free electron’ like model for the saline hydrides is discussed. To zeroth order the valence electrons are assumed to form a free gas. Effects of band structure are included in the perturbation theory. Straightforward calculations on crystalline MgH2, using pseudopotential parameters determined from metal data, yield good values for the lattice parameters and the equilibrium density.

The electron momentum distribution in NaHC2O4 · H2O has been studied using the gamma-ray Compton scattering technique and quantum-mechanical ab initio MO-LCAO-SCF calculations. An ionic model for the crystal gives Compton profiles in good agreement with the experimental observations. The effect of the crystal field on the energies of the molecular orbitals and on the Compton profiles is discussed.

This review is primarily concerned with theoretical calculations of momentum densities and Compton cross sections for molecular systems. Qualitative properties of a momentum space representation are given. A comparison between experimental and theoretical cross sections within the impulse approximation is made. Ab initio calculations for small molecules, like the nitrogen and water molecules, are studied. Various approaches to treat large molecules are studied and compared for the formamide and p-benzoquinone molecules. Some comments on calculations for solid state systems are given.

The correlation between electrons with parallel spins is studied in the momentum-space representation by means of so-called correlation quotients. Plots of these functions for the beryllium, neon, argon and zinc atoms are given and analysed in a simple model.

Compton profiles and expectation values for pn are computer for the water, ammonia and methane molecules using large scale configuration interaction wavefunctions.

The momentum densities for the diatomic molecules N2, CO and NF have been evaluated by means of Fourier transforms of natural spin orbitals obtained from valence configuration interaction calculations. The densities are analysed in terms of their u and T symmetries for various states of the neutral and the singly-ionized molecules. Some general properties of distributions in momentum space are discussed. Numerical data are given for Compton profiles for the molecules considered.

Compton profiles of formamide and p-benzoquinone have been measured with 60 keV gamma-rays. The experimental results are compared with profiles derived from localised molecular orbital and iterative extended Hückel methods and, in the case of formamide, also an ab initio self-consistent field calculation. All theories predict profiles which are in fairly good agreement with experiment, with exception of the localised molecular orbital model which underestimates the profile at low momenta.

Valence Compton profiles and momentum expectation values for some small and medium-sized molecules are calculated and analysed using Fourier transformed wavefunctions obtained by means of the semi-empirical (iterative) extended Huckel, CNDO/2 and INDO methods. Particular attention is paid to the alleged insensitivity of the molecular profile, and the question of bond profile transferability is briefly discussed in an INDO localized picture.

The electronic structure of the esters of the isothiocyanic acid is calculated in an iterative extended Hückel method. Contour diagrams of the valence electron density are given. The odour character of these molecules is discussed in terms of the electronic structure obtained and the theories of smell put forward by Amoore and Wright respectively.

The use of Mulliken's "ionic Hamiltonian" to obtain excited state orbitals is investigated. When compared with the ordinary virtual orbital method it is found to give improved charge distributions for the excited orbitals, but seems to be of less value for improving excitation energies in a minimal-basis calculation. As examples, INDO calculations have been carried out on the ethylene, formaldehyde, and pyridine molecules.

International Journal of Quantum ChemistryVolume 7, Issue 5 p. 1037-1037 Book Review The quantum theory of atoms, molecules and photons. Author: John Avery. Published by: McGraw-Hill, London, 1972. Price £5·50. No. of pages: 378 Peter Lindner, Peter Lindner Quantum Chemistry Group, Uppsala University, Uppsala, SwedenSearch for more papers by this author Peter Lindner, Peter Lindner Quantum Chemistry Group, Uppsala University, Uppsala, SwedenSearch for more papers by this author First published: September 1973 https://doi.org/10.1002/qua.560070519AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat No abstract is available for this article. Volume7, Issue5September 1973Pages 1037-1037 RelatedInformation

AbstractA simple, “nearly free electron” model for the dihydrides of Be, Mg, Ca, Sr and Ba is investigated. To zeroth order the valence electrons are assumed to form a free gas. Effects of band structure are included in second‐order pseudopotential perturbation theory. The stability of three probable crystal structures is investigated, and lattice parameters are calculated for two different choices of the pseudopotential.

International Journal of Quantum ChemistryVolume 4, Issue 2 p. 217-218 Letter to the Editor Lower bounds for ε2 in the 1/z-expansion for heliumlike ions† Peter Lindner, Peter Lindner Quantum Chemistry Group, Uppsala University, Uppsala, SwedenSearch for more papers by this author Peter Lindner, Peter Lindner Quantum Chemistry Group, Uppsala University, Uppsala, SwedenSearch for more papers by this author First published: March 1970 https://doi.org/10.1002/qua.560040208Citations: 5 † Sponsored in part by the Air Force Office of Scientific Research (OSR) through the European Office of Aerospace Research (OAR) United States Air Force under Grant EOOAR-69-0043. AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat No abstract is available for this article.Citing Literature Volume4, Issue2March 1970Pages 217-218 RelatedInformation

By use of the cusp condition for electronic wavefunctions the exact asymptotic behavior of the atomic form factor is determined. The relation between the pair distribution function and the incoherent scattering function for large wave vector is pointed out.

The stability of a Hartree–Fock determinant under a splitting of the doubly occupied orbitals with simultaneous symmetry projection is studied. As a consequence of the spin degeneracy, the energy is given by the lowest root to a secular equation. It is found that even for an infinitesimal splitting of the orbitals there will be a discontinuous, finite lowering of the energy for both closed-shell and open-shell states. Numerical illustrations are given by the Li and Be atoms, the H4 molecule, and the benzene molecule.

The spin-degeneracy problem in the alternant molecular-orbital (AMO) method, as applied to excited states of the benzene molecule, is investigated. The results obtained using the full nine-dimensional triplet spin space and the five-dimensional quintet space show in the one-parameter method an energy improvement over the ones obtained by a conventional AMO treatment of 0.659 eV for the B31u state and 0.975 eV for the A31g state. When two mixing parameters are used the corresponding improvements are much smaller, 0.029 eV and 0.032 eV, respectively. Results are also presented for some additional states, not occurring in the ordinary AMO method.

The alternant‐molecular‐orbital (AMO) method as applied to the benzene molecule is reconsidered. A variational treatment was performed to determine the singlet spin function which gives the best total energy in the five‐dimensional spin space available. It is found that an AMO function containing two mixing parameters and an optimized spin function gives an energy improvement over the ordinary one‐parameter AMO method, utilizing a single spin function, by 0.452 eV. Optimization of the spin function alone gives an energy lowering which is 57% of this value, while a two‐parameter function with the usual spin function gives 86%. On a reconsidéré l'application de la méthode des orbitales moléculaires alternantes (AMO) à la molécule de benzène. Par un calcul variationnel on a déterminé celle des fonctions singulettes de l'espace de spin à cinq dimensions, qui donne la meilleure énergie totale. On trouve qu'une fonction AMO à deux paramètres combinée à une fonction de spin optimisée donne une amélioration de l'énergie de 0.452 eV, sur la méthode AMO ordinaire à un seul paramètre et une seule fonction de spin. Une optimisation de la fonction de spin seulement donne 57% de cette valeur‐ci, tandis qu'une fonction à deux paramètres avec la fonction de spin ordinaire donne 86%. Die alternierende Molekülorbitalmethode (AMO) wurde noch einmal auf das Benzolmolekül angewendet. Mit einer Variationsberechnung wird die Singulett‐Spinfunktion des fünfdimensionalen Spinraum bestimmt, die die beste Gesamtenergie liefert. Man findet das eine AMO‐funktion mit zwei Parametern und einer optimisierten Spinfunktion eine Energieverbesserung über die gewöhnliche AMO‐Methode mit einem Parameter und einer einzigen Spinfunktion, von 0.452 eV gibt. Optimisierung der Spinfunktion allein gibt 57% dieses Wert, während eine Zweiparameterfunktion mit der gewöhnlichen Spinfunktion 86% gibt.

π-electron energies ofcis- andtrans-stilbene and the benzyl radical have been calculated by use of the semiempirical method proposed byPariser, Parr andPople. Special attention is devoted to differences in total energies between the two isomers and to the steric hindrance in thecis-form.