Dipole moments and static dipole polarizabilities are calculated for neon and the molecules HF, H2O, NH3, CH4 and CO from SCF and correlated wavefunctions. The construction of appropriate gaussian-type basis sets is discussed and the convergence of the correlation contributions to the polarizability is analysed. The effect of vibrational averaging is also investigated. The polarizabilities as obtained from the coupled electron pair approximation (CEPA) with the most extended basis sets differ from experimental values by less than 1·5 per cent in all cases. The calculated polarizability anisotropies appear to be correct to about 5–15 per cent. The correlation contributions to the polarizabilities are found to vary from 3 to 12 per cent.

PNO-CI and PNO-CEPA studies of electron correlation effects

Publisher Summary The purpose of this chapter is to provide information on the recent developments in perturbation theory. In recent years, there is a great increase of interest in the application of perturbation theory to the fundamental problems of quantum chemistry. Perturbation theory is designed to deal systematically with the effects of small perturbations on physical systems when the effects of the perturbations are mathematically too difficult to calculate exactly, and the properties of the unperturbed system are known. The new applications have been mainly to atoms where the reciprocal of the atomic number, l/Z, provides a natural perturbation parameter. These may be divided into two groups. The first consists of calculations of energy levels, and is a natural outgrowth of Hylleraas's classic work on the 1/Z expansion for two-electron atoms. The applications in the second group are to the calculation of expectation values and other properties of atoms and molecules, and are of much more recent origin. There are two principal reasons for the success of these new applications: (1) sufficient accuracy is frequently obtained from knowledge of a first-order perturbed wave function, and (2) a great advantage of perturbation theory is that the functional form of the perturbed wave function is shaped by the perturbation itself.

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Recent Developments in Perturbation Theory

Accepting a commission to review progress in the subject embodied in our title is, perhaps, to take up something of a ‘poisoned chalice’. One of us, contributing on this same topic more than 20 years ago at the 1979 International Symposium on Aromaticity in Dubrovnik, wrote1 “A cynic would say that there are actually only two difficulties in discussing the subject of ‘aromaticity’ and ‘ring currents’sdeciding what is meant by ‘ring current’, and assigning a meaning to the term ‘aromaticity’!” That comment, though ostensibly facetious, had serious intent: it did encapsulate, with only a modicum of exaggeration, the problems that inherently beset any assessment such as the one attempted at Dubrovnik1 and in the present review. At the heart of the matter lies the undeniable fact that neither ring currents nor aromaticity are physical observables. Nevertheless, the intervening period has seen the ring-current idea, at least, become generally less controversial and more accepted than it once was. At the time of our opening quotation, one of us and Haigh had just published an exhaustive review2 of the ring-current concept covering the period up to about 1980sthe end of what might now be regarded as the era of semiempirical calculations in this field.2 This review2 (1979/1980) concluded that “the ‘ring current’ picture has proved itself ... to have great power in rationalising, at least qualitatively, the magnetic properties of π-electron systems. It is so pictorial that one can almost feel what is happening when a [conjugated] molecule is subjected to a magnetic field. Whatever advances the future may bring, it may be that the favourite habitat of the ‘ring current’ will be that in which it was born and brought up, namely, that of semi-empirical π-electron theory”. In other words, these authors were sanguine that, at the time (ca. 1980), the ring-current idea was gently coming to the end of its natural, useful life. However, as recently as 1997, when reviewing progress concerning the status of the ring-current model during the decade and a half or so after 1980s a period in this field that we have dubbed3 ‘the ab initio era’sthe present authors3 were initially somewhat surprised to find themselves concluding that “the ‘ring-current’ idea has well survived the first 15 years of the ab initio era.” Lazzeretti’s subsequent magnum opus4 on ring currents has more than confirmed this. By contrast, the sheer fact that in 2001sthe very first year of the 21st centurysthe American Chemical Society has seen fit to run this particular issue of Chemical Reviews shows that the concept of Aromaticity is as elusive as it ever was (see section II). There are three reasons for our not feeling obliged or inclined to present, in this review, an exhaustive, systematic, or historical critique of the ring-current concept itself. First, as we have just claimed, the idea of a ring current seems more secure now than it was 20 years ago, and it would appear that less apology or justification is needed for invoking it. Second, we ourselves have, in any case, only recently updated 1349 Chem. Rev. 2001, 101, 1349−1383

https://www.fc.up.pt/pessoas/jfgomes/documentos/ArtigosPDF/ChemRev,%20101,%201349-83(2001).pdf

Aromaticity and ring currents.

Homoatomic triple bonds between main-group elements have been restricted to alkynes, dinitrogen, and a handful of reactive compounds featuring trans-bent heavier elements of groups 13 and 14. Previous attempts to prepare a compound with a boron-boron triple bond that is stable at ambient temperature have been unsuccessful, despite numerous computational studies predicting their viability. We found that reduction of a bis(N-heterocyclic carbene)-stabilized tetrabromodiborane with either two or four equivalents of sodium naphthalenide, a one-electron reducing agent, yields isolable diborene and diboryne compounds. Crystallographic and spectroscopic characterization confirm that the latter is a halide-free linear system containing a boron-boron triple bond.

https://science.sciencemag.org/content/sci/336/6087/1420.full.pdf

Ambient-temperature isolation of a compound with a boron-boron triple bond.

The self‐consistent perturbation theory developed in earlier papers is extended to the open‐shell case. Density matrices for both shells are calculated iteratively until first‐order self‐consistency is achieved. A numerical application indicates the importance of considering both shells separately when discussing the effects of polarization on the charge density and the spin density.

Self‐Consistent Perturbation Theory. II. Extension to Open Shells

In Hartree-Fock theory and its various generalizations, it is customary to solve an eigenvalue problem involving an effective one-body Hamiltonian. The eigenvectors determine the Fock-Dirac density matrix, which also appears in the effective Hamiltonian, and solution proceeds iteratively until self-consistency is achieved.An alternative (necessary and sufficient) condition for a solution is that the density matrix ($\ensuremath{\rho}$) is idempotent and commutes with the Hamiltonian (h). The change in $\ensuremath{\rho}$, accompanying a change $\ensuremath{\Delta}$ in h, can then be expressed as a perturbation series. Formulas for the perturbation, to all orders, are obtained in terms of the unperturbed Hamiltonian and density matrix. It is also shown that the whole perturbation may be obtained directly, without separating the orders, and that the approach is related to earlier steepest-descent methods.

Roy Mcweeny

Papers

Perturbation Theory for the Fock-Dirac Density Matrix