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Notes: Summary A comparative study was undertaken on the innervation of mucous and granular glands in frog skin. Results obtained by the Falck-Hillarp fluorescence technique and cholinesterase staining indicated that both types of glands receive exclusively adrenergic innervation. Electron microscopy was used to investigate the innervation pattern at the ultrastructural level. The distribution of nerve terminals was found to differ in the two types of glands. In the mucous gland, terminals were found at a distance of about 0.5 μm from the basement membrane but never within the gland parenchyma. In the granular gland, the terminals were located between smooth muscle cells and also in direct contact with the secretory epithelium but never outside the basement membrane.

Notes: Summary Preliminary ultrastructural studies on the effects of 5,6-Dihydroxytryptamine (5,6-DHT) on the anterior byssus retractor muscle (ABRM) of Mytilus show degeneration of 2 types of monoaminergic nerves after 10 days of drug treatment. One type contained large granular vesicles (560–1,680 Å) while the other had small granular vesicles (200–640 Å). These axons may possibly represent serotonergic and dopaminergic nerves, thought to innervate this muscle. Two other types of profiles seemed to be unaffected by the drug. One conforms to cholinergic nerves while the other has a predominance of large opaque vesicles (1,200–2,500 Å). The significance of these findings is discussed in the light of recent observations on the neurotoxic effects of 5,6-DHT on vertebrate and molluscan nerves.

Notes: Summary The unicellular hatching glands (UHGs) of four species of salmonid fish, Salmo gairdneri, Salmo trutta, Salvelinus fontinalis and Salvelinus pluvius were studied by light and electron microscopy. The UHGs are distributed on the epidermis of head and yolk sac, and on the epithelium of the mouth and gills. Since these cells are large and include dilated cisternae of the endoplasmic reticulum from the primitive to the mature stages they are conspicuous. Around the Golgi complexes, there are consecutive figures showing synthesis of secretory granules with close relationships to the Golgi vesicles. The secretory granules grow in size and vary in density during maturation; some have enclosed cytoplasmic structures. At the hatching stage, they are discharged with some cytoplasmic structures from the UHG which is located in the superficial layer of epithelium. After exhaustion of the secretory granules, the remainder of the contents of UHGs is liberated.

Notes: Summary A multilamellate body (MLB), bearing close resemblance to an array of annulate lamellae, has been observed in several adenohypophysial cell types of the teleost, Hemihaplochromis philander. In longitudinal section, each MLB comprises a ladder-like row of 12–50 sausage-shaped profiles, termed lamellae. A few lamellae in each section show connections with the endoplasmic reticulum. Apposition of paired lamellar membranes at regularly spaced intervals results in a beaded appearance, whereby sites of membrane apposition are probable pore sites. The MLB differs from annulate lamellae in having poorly developed pores and closer packing of lamellae. It is suggested that the MLBs described here, may represent annulate lamellae at a stage of development or break-down when pores are incomplete.

Notes: Summary Images have been obtained from freeze-etch replicas of neurohypophyses which are consistent with the view that orderly arranged aggregates of membrane particles occur in regions where fragments of membrane are being added to and taken away from the plasma membrane during secretion. Aggregates of particles included rosette-like and necklace-like patterns similar to those described by other authors at sites of exocytosis and endocytosis.

Notes: Summary The fibers of drum and trunk muscles of the Tigerfish, Therapon jarbua, differ greatly in diameter. The myofibrils of the trunk muscles are irregularly oriented, while those of the drum muscles are rolled into spiral or concentric bands. Both muscle types possess the sarcomere structure typical of cross-striated musculature. However, the myofibrils of the drum muscles differ greatly in sarcomere length and width from those in the trunk musculature. The trunk muscles contain few mitochondria, whereas in the drum muscles mitochondria are abundant. The sarcoplasmic reticulum (SR) of the drum muscles takes the form of elongated tubes in both the A and the I region; that of the trunk musculature consists of small vesicles. Of the two muscle types, the drum muscle contains more SR. With respect to the form of the T system, the trunk musculature is of the Z type and the drum muscles of the A-I type. The drum muscle displays a considerably greater number of motor endplates; these lack typical junctional folds and have mitochondria with very few cristae. No fat could be demonstrated in either the drum or the trunk muscles. However, the concentration of glycogen is higher in the drum muscle than in the musculature of the trunk.

Notes: Summary In ciliated cells of thymic cysts in Nude mice, ciliary rootlets are constantly and closely related to smooth endoplasmic reticulum and clear vesicles. This special association suggests that this structure does not play only an anchoring role but must be involved in the general metabolism of the cilium.

Notes: Summary In Nassarius reticulatus the nuclei and nucleoli undergo important morphological changes from the zygote to the 16-cell stage. In the zygote and in the trefoil (2-cell) and 4-cell stage, several agranular, fibrillar nucleolus-like bodies 1 μm diameter are present in the interphase nucleus. Granular nucleoli first appear at the 8-cell stage. These nucleoli have fibrillar and granular regions. The granular regions are made up predominantly of ribosome-like osmiophilic granules. From the 16 and 32-cell stage onwards, the one or two spherical nucleoli of each nucleus measure 2.5 μm in diameter and show a concentric organization with a very dense central region surrounded by a broad peripheral zone containing numerous granules, possibly of ribonucleoprotein. At the same time the number of ribosome-like particles increase in the karyoplasm and that of ribosomes in the cytoplasm. These findings are surprising because in eggs with radial cleavage, which have been subjected to more detailed analysis, the first granular nucleoli appear after the end of the cleavage, at the blastula or gastrula stage. The early appearance of granular nucleoli which seem to be characteristic of several eggs with spiral cleavage is discussed in connection with biochemical data on RNA-synthesis.

Notes: Summary The fine structure of the endothelium lining the femoral and mesenteric veins in the rabbit was examined following the infusion of concentrations of adrenaline varying from 0.5 to 5.0 μg/kg. Control animals were infused with saline. Vesiculation of the endothelial cells was observed following each infusion of adrenaline, the effect being most marked with the highest dose used. It is suggested that this vesiculation may be associated with the release of antihaemophilic globulin and/or plasminogen activator from the endothelial cells.

Notes: Summary The ultrastructure of coronet cells of the saccus vasculosus has been studied in specimens of Anguilla anguilla (L.) at different stages of its life cycle. At all the stages observed coronet cells are composed of a basal and an apical part, the latter bearing globules with primary vesicles. In the larva (a marine form) and in the fully metamorphosed small eel at the time of entry into freshwater the narrow lumen and the vesicles within the apical globules are filled with electron-dense material. In forms in which adaptation to freshwater has occurred, the saccus lumen appears expanded, the apical globules are better developed, and the electron-dense material has disappeared. It is suggested that the two situations observed represent different functional states of the organ, in relation to different conditions of environmental salinity.

Notes: Summary 6-hydroxydopamine (6-OHDA) was shown to cause ultrastructural changes in adrenocortical cells of lizards and rats. These changes comprised the formation of dense bodies with lamellar and crystalloid patterns, a decrease in the number of mitochondria and structural alterations of mitochondria. Alterations in adrenocortical cells of lizards and rats differed in both qualitative and quantitative aspects. Adrenomedullary cells were not affected as a rule. Only in young animals did 6-OHDA cause deposits of an electrondense material in medullary cells. An attempt was made to obtain information on amine uptake into cortical cells using the Falck-Hillarp technique to analyse the in-vivo and in-vitro uptake of noradrenaline (NA) into the adrenal cortex in adult rats. Extraneuronal uptake into heart and spleen was studied as well. Our results suggest that NA is taken up into cortical cells, particularly into nuclei, after exposure to 10-4 gm/ml in-vitro indicating that uptake of 6-OHDA is also likely. Investigations using labelled 6-OHDA are required for further elucidating its extraneuronal uptake.

Notes: Summary The ciliary body of the cat was investigated by fluorescence histochemistry and electron microscopy in an attempt to clarify its sympathetic innervation. Subconjunctival doses of 5-hydroxydopamine (5-OHDA) or 6-hydroxydopamine (6-OHDA) were given to establish the precise location of the sympathetic nerve terminals. The distribution of noradrenergic fibers and terminals was shown by fluorescence histochemistry to be sparse in the trabecular meshwork and the anterior portion of the ciliary muscle, but dense in the subepithelial tissue. The small and large dense core vesicles which occur in many nerve endings of the subepithelial tissue adjacent to the pigmented epithelial layer increased in electron density following the administration of 5-OHDA. Many degenerating nerve endings were found in the same region of animals treated with 6-OHDA. In contrast, there were few noradrenergic terminals in the ciliary muscle except for a portion of the smooth muscle which was shown to be dually innervated. The noradrenergic fibers in the subepithelial region and the trabecular meshwork may play an important role in aqueous secretion and outflow.

Notes: Summary In the lamina ganglionaris, the first optic ganglion of the fly, the inventory of cell types as well as the patterns of their connections are well known from light microscopic investigations. Even the synaptic contacts are known with relative completeness. However, the structural details visible on electron micrographs are very difficult to interpret in functional terms. This paper concentrates on two aspects: 1) the synaptic complex between a retinula cell axon and four postsynaptic elements, arranged in a constant elongated array (it is suggested that all synapses in which the retinula cell is presynaptic are of this kind), and 2) the “gnarl” complex in which a presynaptic specialization in one neuron is separated from another neuron by a complicated glial invagination. The participation of glia at postsynaptic sites seems to be quite common in this ganglion. Occasionally it seems that a glia cell is the only postsynaptic partner facing a presynaptic specialization within a neuron.

Notes: Summary Rabbit ovarian preovulatory follicles and in particular the overlying surface epithelium were studied by morphological and ultrahistochemical means at different times after mating. By light microscopy an increase of cytoplasmic granules was found in the surface epithelium at the follicle apex 4 h after mating. The granules increased in amount and showed maximal accumulation 8–9 h after mating. They then disappeared at the same time as the connective tissue elements in the underlying tunica albuginea and theca externa disintegrated. Transmission electron microscopy showed that the membrane-bounded granules or dense bodies fused with one another and by 8 h after mating they often changed character and appeared more electron lucent. Furthermore, open communications were found between altered granules and vacuoles and between vacuoles and the extracellular space below the epithelium. Acid phosphatase reaction product was localized to the granules and Golgi cisternae. Not all the dense bodies were enzyme positive. At later stages, close to the time of follicle rupture, the epithelial cells were attenuated and thin, with only a few granules. By scanning electron microscopy it was found that the epithelial cells at the follicle apex increased in size approaching the time of follicle rupture and that their microvilli decreased in number and in size. At 8 h and later, the contours of intracellular granules could be visualized. The results of this study were similar to those found when rabbits were induced to ovulate by HCG-stimulation. This further strengthens the hypothesis that the surface epithelium contributes proteolytic enzymes which help to disintegrate the follicle apex prior to rupture.

Notes: Summary Using the unlabeled antibody peroxidase-antiperoxidase (PAP) technique at the electron microscopic level, it was demonstrated that the hormones of the posterior pituitary of Rana temporaria are located in separate vasotocinergic and mesotocinergic nerve fibres. This observation confirms the results of our previous immunocytochemical studies at the light microscopic level.

Notes: Summary Epidermal septate junctions of Nereis sp. and Cirriformia sp. fixed with OsO4 or glutaraldehyde/OsO4 display variable structure in electron micrographs. In transverse section the septa are often indistinct and obscured by opaque material that fills the junctional cleft. Septa (spaced at 180–280 Å) are more clearly defined in slightly oblique transverse section; they exhibit an electron lucent center and appear to be linked by arms. En face views of the junction show a honeycomb pattern. Cytoplasmic faces of junctional membranes are backed with plaques opposite the septa. Lanthanum used as a tracer delineates junctional structure in negative contrast. In transverse section a chain-like lattice is present in the junctional cleft. En face views show parallel rows of pleated elements often linked by arms into honeycomb arrays. Oblique sections demonstrate that these pleated elements are continuous with the chain-like lattice seen in transverse sections. Lanthanum does not pass entirely through the junction. Lanthanum reveals that the septa have a very intricate substructure, but it is difficult to visualize the architecture that could generate the various images presented by these junctions when seen in different orientations. However, it is clear that these junctions possess some features that are diagnostic of several supposedly different types of septate junctions in invertebrates.

Notes: Summary The effects of various concentrations of 6-hydroxydopamine (6OHDA) on rat adrenocortical cells in tissue culture were studied with phase contrast and electron microscopy. With 40 mg/l of 6-OHDA the first signs of alteration as revealed by microcinematography appeared in isolated cortical cells as early as 15 min after addition of the drug. There was a cessation of movement of cell organelles and an immobilisation of membrane undulations followed by the development of dark inclusion bodies. The cells underwent increasing shrinkage and collapsed by 11/2 h. Chromaffin cells were not affected until 45 min after exposure to the drug and neurons were the most resistant population. However 61/2 h after application of the drug most cells in the culture were dead. 6-OHDA applied in different doses and to adrenal expiants did not alter the sequence of events. Ultrastructurally cortex cells underwent damage along two lines: they either showed lytic changes or developed various types of dense bodies before reaching the lytic stage. Treatment of cortical cells with 40 mg/l 5-or 6-OHDA followed by exposure to buffered 2% glyoxylic acid and heat did not produce a fluorescence within the cells. Microspectrofluorimetry on amine models with noradrenaline, 5- and 6-OHDA revealed that neither 5-nor 6-OHDA are capable to form a fluorophore with glyoxylic acid.

Notes: Summary Electron microscopy of testicular biopsies obtained from two adult males with tunica vaginal hydrocele revealed some protrusions from the basal lamina to the germinal epithelium in the seminiferous tubule. The protrusions were of three types: some between the spermatogonia and Sertoli cells, some directly within the Sertoli cell cytoplasm and others inside the spermatogonia. The protrusions inside the spermatogonia were only 0.5 μm deep whereas the other types were from 1–11 μm deep. Occasionally some cut off portions of these protrusions were seen inside the ground cytoplasm of the Sertoli cell without an apparent connection with the original stalk. The matrix of the protrusions contained a homogenous component (composed of a fine filamentous element) and granular and membranous components. These components closely resemble the materials found in the basal lamina of the seminiferous tubule. It has been suggested that under mild pathological conditions, i.e., hydrocele, the junctions between the seminiferous tubule epithelium and the basal lamina become somewhat more flexible. As a result, the protrusions become longer and a passage might be formed to allow the flow of raw materials in or out of the seminiferous tubule.

Notes: Summary The structure of the nongranulated cells in the sea lamprey adenohypophysis and similar cells of the rostral pars distalis in a number of actinopterygian fishes was examined with the aim of determining the role(s) of these cells in pituitary function. A number of possible roles are proposed for the nongranulated cells. In salmonids and Amia calva the cells may be involved in the active movement of material into or from the follicle lumina. The structure of the nongranulated cells in in vitro cultured and in in vivo transplanted trout rostral pars distalis also suggests a phagocytotic role for these cells. In teleosts with a non-follicular rostral pars distalis the nongranulated cells appear to play roles in the release of granules from the prolactin cells and in the subsequent dispersal of the hormone (and/or carrier substance) into the peripheral circulation.

Notes: Summary The problem of the direct retinohypothalamic projection in mammals (Moore, 1973) was reinvestigated in the laboratory mouse by electron microscopy and cobalt chloride-iontophoresis. The time-course of the axonal degeneration in the suprachiasmatic nucleus was studied 3, 6 and 12 h, 1, 2, 4, 6, 9 and 12 days after unilateral retinectomy. Specificity of the degenerative changes was controlled by investigation of the superficial layers of the superior colliculus. The ratio of crossed to uncrossed optic fibers could be determined by counting degenerating structures (axons and terminals) in the optic chiasma and the ipsilateral and contralateral areas of the optic tract, the suprachiasmatic nucleus, and the superior colliculus. The number of degenerating axons in the suprachiasmatic nucleus showed a maximum one day after unilateral retinectomy and was, at all stages studied, two to three times higher in the contralateral than in the ipsilateral nuclear area. In the optic tract and in the superior colliculus the number of degenerating profiles was three times higher in the contralateral than in the ipsilateral area. Retinohypothalamic connections and crossing pattern of retinal fibers were studied light microscopically using impregnation with cobalt sulfide in whole mounts of brains. Most of the optic fibers in the laboratory mouse are crossed (70–80%). A bundle of predominantly crossed optic fibers runs to the suprachiasmatic nucleus.

Notes: Summary Tissue from the digitiform rectal gland of the spiny dogfish, Squalus acanthias, was fixed briefly by formaldehyde perfusion and studied for the specificity and localization of p-nitrophenyl phosphatase (NPP'ase) activity. The enzymatic activity was K+-dependent (56%) and ouabain-sensitive (67% inhibition). The electron-dense reaction product (SrPO4) of the cytochemical reaction (Ernst, 1972b) was localized along the inner surfaces of the basolateral membranes of the secretory cells. It was absent from mitochondria, nuclei, vesicles, and other organelles. The luminal surface of the secretory cells was slightly reactive. On the basis of (1) this pattern of localization for the sodium transport system, (2) the presence of extensive intercellular labyrinthine channels (Bulger, 1963) that would facilitate “standing gradients” (Diamond and Bossert, 1968), and (3) the specific distribution of the energy-providing mitochondria, we conclude that the concentration and electrochemical gradients recorded from the secreting gland (Hayslett et al., 1974) are maintained across the domains of the basolateral surfaces of the secretory cells.

Notes: Summary The ultrastructure of human placental capillaries was investigated using perfusion fixation and the freeze-fracturing technique. The capillaries have a continuous endothelium especially rich in microfilaments, whereas micropinocytotic vesicles are exceedingly scarce. The endothelial cells are connected by three types of junctions: (1) zonulae occludentes characterized by 2 to 4 focal regions of membrane contact in thin-sectioned specimens and an equal number of ridges on the membrane E-face in freeze-fractured specimens; (2) small gap junctions associated with the zonula occludens. (3) attachment plaques resembling zonulae adhaerentes in their fine structure. Endothelial cells are provided with long, circularly oriented pseudopodial extensions, which may be responsible for intermittent constrictions of the vessel lumen. These findings indicate that diaplacental transport at the level of the fetal capillary is controlled by the cytoplasm of the endothelial cells and probably occurs only to a very limited extent by way of micropinocytotic vesicles.

Notes: Summary In the rat superior cervical and coeliac-mesenteric ganglia we have observed three types of small granulated (SG) cell: Type I cells are characterised by membrane-bounded cytoplasmic granules with a core of variable, moderate to low electron-density, whose limiting membranes are rounded in profile ranging from 50–150 nm in diameter. Type II SG cells contain numerous highly electron-dense, polymorphic cytoplasmic granules ranging from 100–300 nm in diameter. The haloes of Type II cell granules are variable in shape, and the core is often eccentrically located or fragmented. Type III SG cells contain membrane-bounded granules with a core of variable moderate to low electron-density. In profile these granules appear oblong or circular with average dimensions of 170 × 50 nm. All three SG cell types receive cholinergic-type pre-ganglionic terminals whose afferent nature is confirmed by their degeneration following pre-ganglionic neurectomy. Only Type I cells have been observed to donate efferent synapses to dendrites of principal ganglionic neurones and are thus interneuronal.

Notes: Summary The sinu-atrial node in the heart of the mole, Mogera wogera, contains myocytes which are devoid of atrial specific granules and which may be classified into two types: electron-lucent (majority) and dark (minority). Numerous unmyelinated axon terminals, containing synaptic vesicles, face the nodal myocyte surface with interspaces of less than 300 nm. There are about 6 terminals per myocyte profile and about 10 per profile at nuclear levels. Of a total of 2717 of these terminals 85.2% are 50–200 nm from the nodal myocytes, and 9.6% form closer neuromuscular junctions, with less than 50 nm interspace and some membrane specialization. Such specializations are almost exclusively found in relation to the dark, minority-type of nodal myocyte. Myelinated nerve fibers are also numerous within the mole SA node, and may terminate almost directly on a nodal myocyte. A few nerve fibers contain many mitochondria and may represent afferent endings. Nodal capillaries are smaller and fewer than capillaries in the juxtanodal myocardium, probably indicating a lesser blood supply to the SA node than to the ordinary myocardium.

Notes: Summary The duodenum of 16-day Black Australorp chick embryos, and the duodenum, ileum, large intestine and caeca of 18-day embryos and of chicks within 30 h of hatching, have been studied by electron microscopy. Cells were found with secretory granules resembling those in mammalian EC, S, A-like, EG and D cells (terminology of Solcia et al., 1973), and were on this basis tentatively identified accordingly. The distribution and frequency of the chick cells in different parts of the tract correspond well to the situation in mammals.

Notes: Summary The proventriculus, gizzard and pyloric antrum (region between the gizzard and the duodenum) of 18-day Black Australorp chick embryos and of chicks within 30 h of hatching have been studied by electron microscopy. D and EC cells, and putative G, D1 and A-like cells were identified (terminology of Solcia et al., 1973) but no ECL cells. No endocrine cells of any kind were revealed in the gizzard.

Notes: Summary Reflecting chromatophores in the integument of the guppy, Lebistes reticulatus Peters, are of two distinct types, iridophores and leucophores. The iridophores are smaller and fixed, producing a metallic iridescent color. The cytoplasmic organelles involved in the coloration of iridophores are the reflecting platelets, as in the iridophores of other fish and amphibian species on which earlier reports have been made. Spherical granules of pleiomorphic internal structure, quite variable in size but generally 0.2 μm to 1.0 μm in diameter, are also numerous in the iridophores. The nature of these granules remains unknown. The leucophores are larger, and highly dendritic; their pigment granules are migratory and they exhibit a dull whitish color. Pigment granules of the leucophores are spherical in form, varying from 0.5–0.8 μm in diameter, with a double membrane enclosing the internal fibrous materials. Melamine-treatment of the fish caused degenerative changes in the pigment granules and also the other cytoplasmic organelles of the leucophores, whereas the other kinds of chromatophores, including the iridiophores, remained intact. Some problems in general characterization and classification between these two types of chromatophores were discussed.

Notes: Summary Neither the concept of the Reticulo-Endothelial-System (RES) Aschoff's (1924) nor that of the Reticulo-Histiocyte-System (RHS) provides a satisfactory framework into which the present knowledge of the phagocytic mononuclear cells can be fitted. Current knowledge concerning morphology, histochemistry (peroxydase and esterase activity), immunology (specific surface antigens, receptors on the cell membranes), function (immune phagocytosis, pinocytosis), kinetics (3H-thymidine labelling) and culture makes it possible to place all highly phagocytic mononuclear cells and their precursors in one system, which is called the Mononuclear-Phagocytic-System (MPS) (Langevoort, Conn, Hirsch, Humphrey, Spector, van Furth, 1969). Kinetic studies with labelled cells have shown, that mononuclear phagocytes originate from precursor cells in the bone marrow (stem cell → monoblasts → promonocytes), than are circulating in the peripheral blood as monocytes and are transformed to tissue macrophages entering tissues. The MPS comprises following cells in following organs: connective tissue (histiocytes resp. macrophages); liver (Kupffer-cells); lung (alveolar macrophages); lymph nodes (free and fixed macrophages); bone marrow (macrophages); serous cavities (pleural and peritoneal macrophages); bone tissue (osteoclasts?); nervous system (microglial cells) (see Table 1). The reticular cells, endothelial cells and fibroblasts (fibrocytes) can therefore not be included in the MPS. Besides differences in morphology, histochemistry and function, they derive from mesenchymal cells and not from the bone marrow as the MPS. The present investigation demonstrates the structure and significance of the MPS in various kinds of chronic-specific and non-specific rhinosinusitis. On semithin sections two kinds of macrophages can be distinguished light-microscopically: 1. Larger macrophages with many phagosomes (storage cells) (Fig. 1A), which can exhibit sometimes a ring-shape on sections embracing greater parts of the interstitium (Fig. 1B). Such forms are mainly found in chronic (maxillary) sinusitis and are interpretated as “scavenger” macrophages. 2. The second type consists of smaller macrophages with extremely ruffling of the cell surface, wich is interpretated as an expression of highly (specific?) stimulated states. These later macrophages can be seen mainly in edematous nasal polyps, which might be caused by allergic reactions of the anaphylactic type. The fine structure of the phagocytes is to some extend dependent on the actual development and functional state: there are “immature” macrophages, which are practically indistinguishable from blood monocytes (Fig. 2A); some of them can be stimulated and can therefore show many surface foldings and projections (Fig. 2B). The “mature” macrophage shows a well developped Golgi-area and many secondary lysosomes (Fig. 3). The storage type of the macrophages, which can predominate in some cases of chronic maxillary sinusitis, is characterized by many electron-lucent vacuoles (Fig. 4). The macrophages can transform unspecifically to epitheloid- and giant-cells, as it is shown in foreign bodys- and cholesterol-granulomas in maxillary sinusitis (Fig. 5A and 5B). This tranformation to epitheloid and giant-cells might also be induced specifically by stimulated T-lymphocytes in immunological reaction of the delayed type, for example in sarcoidosis (Fig. 6A) and tuberculosis (Fig. 6B) of the nose. The macrophage is not only of great importance as the carrier of the cellular immunity in the sense of Metschnikoff (1905), but he is also involved in the initiation and regulation of the specific humoral and cellular immune responses. These facts and the phagocytic and synthetic properties of the macrophages are discussed in regard to their significance for the etiology and course of chronic rhinosinusitis.

Notes: Inverses and inverse square roots of overlap matrices are approximated by polynomials constructed on the basis of an integral transform of the metric resolvent and Kublanovskaya's conformal mapping technique. Given reasonable upper and lower bounds for the support of the overlap matrix spectral distribution, the described expansions have significantly better convergence properties than the well known power series methods, yet retain the simplicity of these schemes.

Notes: The algebra of the representation of the special unitary group SU(2), the universal covering of the proper rotation group SO(3), is studied in a nonstandard basis. We are using a basis adapted to a chain of type SU(2) ⊃ … ⊃ G″ ⊃ G′ ⊃ G. The introduction of such a chain enables us to label, at least partially, the elements of the irreducible tensorial sets under SU(2) with irreducible representations of G, G″ G″, …. We are thus led to introduce the restriction SU(2) → … → G″ → G′ → G in the Wigner-Racah algebra of the group SU(2). The physical interest of this machinery lies in the fact that the double group of any point symmetry group belongs, up to an isomorphism, to the considered chain. The formalism described in this paper thus appears to be useful in molecular and solid-state calculations. It is particularly efficient in the fields of vibrational-rotational and electronic spectroscopy of molecules. In Appendix A the master formulae, principally the Wigner-Eckart-Racah theorem, for the Wigner-Racah algebra of a chain of compact topological groups (discrete or continuous) are briefly discussed. Lastly, a programme for computing Clebsch-Gordan coefficients for a chain SU(2) ⊃ … ⊃ G″ ⊃ G′ ⊃ G and numerical results for chains isomorphic to SU(2) ⊃ O′ ⊃ D′4 ⊃ D′2 are described in Appendix B.

Notes: The space correlation factor is studied in LiH and Li2 molecules, using MCSCF wave-functions. The shape of the Fermi hole is related to the localization of molecular space orbitals, while the Coulomb hole study indicates the importance of symmetry properties of the molecular orbitals involved in excited configurations for the representation of the electronic correlation inside the chemical bond.

Notes: The influence of various correlation functions, multiplying the monoelectronic space function, is studied and applied to the Helium atom and its isoelectronic series. We used Slater-type basis orbitals and the ground and first excited states have been studied, taking into account the virial and cusp conditions. In the ground state, a very good value for the correlation energy is obtained, using a function of the type \documentclass{article}\pagestyle{empty}\begin{document}$$ 1 - \frac{1}{{1 + 2\alpha }}e^{ - \alpha r_{12} } $$\end{document}For the excited states, this type of function overestimates the assumed value of the correlation energy.

Notes: A method is given for generating the Yamanouchi-Kotani genealogical spin eigenfunctions which requires neither storage of eigenfunctions for smaller numbers of electrons, nor summations of large order, nor explicit use of results from the theory of representations of the symmetric group. An explicit formula is given for the coefficients of expansion in terms of spin products.

Notes: Accurate variational energies have been calculated for three lowest sigma states of the HeH+ ion. This includes the ground state (5 ≤ R ≤ 9 a.u.) which dissociates into He + H+, as well as the A 1Σ+ state (4 ≤ R ≤ 10) and the a 3Σ+ state (3 ≤ R ≤ 10) which both dissociate into He+ + H. The variational results are compared with those obtained using a perturbation theory expansion.

Notes: Semiorthogonalized orbitals are introduced as a basis of approximate ab initio molecular calculations. The semiorthogonalized orbitals are obtained from the usual overlapping atomic orbitals by means of a generalized Löwdin transformation. The new orbitals are characterized by two features: many overlaps between them are zero, and they are close to their corresponding initial atomic orbitals. On the basis of the semiorthogonalized orbitals, a scheme of integral approximations is proposed which allows one to carry out approximate ab initio calculations with less computational efforts and thus offers a possibility to perform calculations on much bigger molecules with limited computational facilities. Results are presented for model calculations on the anthracene π-electron system. Orbital energies and electron distribution are quite close to the rigorously calculated values.

Notes: The representation of an N-electron Schrödinger Hamiltonian on an orthonormal, spin-free (freon) orbital product space is exactly modeled by a second-degree polynomial in the infinitesimal generators of the unitary group. Symmetry adaptation of the orbital product space with respect to the symmetric group yields Gel'fand states which provide base for irreducible represntations of the unitary group. These exist in closed form as, in consequence, does the representation of the model Hamiltonian in this same basis. We retain as physical only those states characterized by tableaux with no more than two columns for which the spin labelling is one-half the difference in the lengths of the two columns. The unitary group formulation is equivalent to standard, number-conserving, second-quantized, many-body theory.

Notes: Quantum chemical CNDO/2 calculations for the conformational preference of the side chain of thioridazine as a function of angle indicated the crystallographically determined structure gave the lowest energy. There is also a small region of conformational flexibility within the first 90° of rotation of the side chain. This is commensurate with the results which we had obtained previously for our similar calculations for promazine and its Cl and CF3 derivatives, perazine and its Cl and CF3 derivatives, and for the hypothetical hitherto unknown N-piperidinopromazine and its Cl and CF3 derivatives. The conformational profile of thioridazine resembles that of the perazines. The calculated gross atomic populations on the alkyl nitrogen in thioridazine was within the range we had previously found necessary for neuroleptic activity.

Notes: The methodology developed in earlier papers is used to compute the 6j symbols and 3jm factors that arise in the group chain SO3 ⊃ T ⊃ C1. The relevant character theory is given and the 2j and 3j symbols calculated. Selection rules are used to predict which j symbols or jm factors are necessarily zero, and then a set of 6j fundamentals computed for T. The complete set of primitive 6j symbols are then computed by application of the orthogonality and Racah backcoupling relations. Primitive 3jm factors are calculated for SO3 ⊃ T and T ⊃ C3 and, from these, all the 3jm factors for T ⊃ C3 and some of those for SO3 ⊃ T computed. A complete table of non-equivalent 6j symbols for T and 3jm factors for T ⊃ C3 is given, together with a table for SO3 ⊃ T of all 3jm factors with j ≤ 2.

Notes: In this paper an iterative generalization of the minimum principle proposed for electronic systems by Hall, Hyslop, and Rees is investigated. It is shown that this generalization still retains the advantage of using members of a larger class of trial wave-functions, for example those with discontinuities, as initial approximations to the wave-functions. This scheme has the advantage that, at each stage of iteration, an upper bound is obtained which is at least as good as that obtained previously.The theory is first applied to the hydrogen atom. It is then adapted to estimate the Hartree-Fock energy of the helium atom, the Hartree-Fock limit being obtained after a relatively small number of iterations.

Notes: A method is proposed for characterizing pairs of finite dimensional subspaces of the Hilbert space. The method might be helpful for the proper selection of coordinate and projective spaces leading to reliable realizations of the Galerkin-Petrov method for use in quantum chemistry. In order to illustrate the method some numerical results are presented.

Notes: A new effective semiempirical method of optimization of one-electron wave-functions has been proposed without a necessity to determine any exact many-electron wave-function. The method designed for LCAO MO calculations is based on a concept of interacting quasi-particles and on nonorthogonal spin-orbitals. “Mixing” of the pure single-particle wave-functions is optimized by means of the procedure which requires only one empirical parameter for each considered state of a whole system. The procedure results in optimal distribution of total electron charge between the individual spin-orbitals. The general method has been illustrated with calculations for the ground state of lithium atom.

Notes: Coupled and uncoupled Hartree-Fock theories are used to compute the electric dipole polarizability of water, ammonia, and methane with three different GTO basis sets. Bounds for the geometric approximation to uncoupled polarizabilities are also computed to examine the accuracy of calculated values. The results are compared with those obtained by a variational-perturbation method proposed by Rebane. The numerical tests provide some information on the correlation terms affecting total computed polarizabilities. The computed values are shown to be in fair or good agreement with experimental data for the largest basis sets. The reliability of Rebane's method with respect to coupled HF procedure is also discussed.

Notes: The orthogonalized plane wave (OPW) method of calculating electronic continuum wave-functions is tested by the computation of photodetachment cross-sections and angular distributions for gaseous halide anions. The results are compared to those obtained by a related augmented plane wave (APW) method involving the exact solution of a single-particle Schrödinger equation containing a piecewise Coulombic potential energy. These comparisons, as well as other involving experimental and theoretical cross-sections from the literature, indicate that OPW cross-sections are, at best, only semi-quantitatively reliable for describing photodetachment even at low photon energies, and that OPW cross-sections should be calculated using the dipole length operator rather than the dipole velocity operator.

Notes: A computation scheme is proposed to determine the wave-functions of molecular systems within the framework of the CMC SCF theory and the APSG SCF approach. The orbital optimization is carried out by the refined first-order one-electron Hamiltonian method. Explicit expressions of the first and second energy derivatives are obtained. In the suggested scheme all the calculations are based on using the matrices of the “partial” Coulomb and the exchange operators constructed over the orbitals at the current iteration cycle.

Notes: The spatial angular correlation of electrons in the ground state of the helium atom has been examined using configuration interaction and Hylleraas wave-functions. It was found that, in general, the average angle between the electrons is not a maximum when the two electrons are at the same distance from the nucleus. For configuration interaction wave-functions there is a position of the electrons for which the average value of the angle between the electrons is a maximum. Hylleraas wave-functions do not show this behavior.

Notes: Interrelations between the local and the global aspects of the stability, continuity, and symmetry properties of variational wave-functions are discussed. The spherical limit of one-electron diatomic molecules and the Hartree-Fock approximation of the ground state of the two-electron atom are shown to exhibit the various concepts involved in an ab initio, yet sufficiently simple, manner.

Notes: The energy of the π-electron system in benzene has been obtained by means of valence bond calculations using orthogonal and nonorthogonal basis orbitals at different levels of configuration interaction, which shows the influence of the orthogonalization procedures.

Notes: Another possible application of a previously reported approximation theory for electron repulsion integrals using rigorous error bounds is considered by incorporating the electron density matrix in the approximation scheme. Error bounds are set on the contribution of a given integral to the total energy for a given molecular wave-function; the wave-function is then refined cyclically and additional integrals are computed exactly if necessary until convergence is achieved.

Notes: Matrix elements of the Runge-Lenz vector A are presented for those linear combinations of degenerate hydrogenic functions often referred to as hybrid orbitals. The uncertainties in the components of A for each type of wave-function are related to the distribution of classical Kepler orbits corresponding to each function. Matrix elements of A with respect to radially nodeless Slater functions are presented, as these functions are often used as a basis set in atomic and molecular calculations. The properties of A for a piecewise Coulombic central field are discussed in relation to the description of penetrating orbits in the old quantum theory. Simultaneous eigenfunctions of A and the Hamiltonian cannot be chosen for the piecewise Coulombic field because of a discontinuity in the radial derivative of the potential energy.

Notes: The PCILO method is used for the study of molecular systems with translational symmetry in a two-dimensional lattice. The calculation for the whole crystal is reduced to the calculation of unit cell pairs. By using the translational symmetry and the first-neighbour approximation, one shows that only four unit cell pairs have to be considered. The procedure described yields the ground-state energy and the charge distribution of the unit cell.

Notes: The instabilities, especially the singlet instabilities, of the conventional Hartree-Fock (HF) solutions for a variety of alternant and nonalternant hydrocarbons, some of which have been known to show lattice instabilities (bond-length alterations), are examined. The HF solutions for nonalternant hydrocarbons in the pentalene series larger than heptalene and [4n + 2]-annulenes larger than C22H22 are found to be singlet unstable and there appear new solutions lower in energy than the conventional HF solutions and characterized by charge-density waves exhibiting bond-order alterations. It is found that such symmetry-breaking solutions are energetically further stabilized by distorting the nuclear framework so that it may match up with the distribution of bond-order matrix elements of the charge-density wave, which means that in conjugated systems the singlet instability of the HF solution is always accompanied with the lattice instability. Further, it is shown that in conjugated systems, even when the HF solution is singlet stable, if it is not sufficiently stable as, for example, in pentalene and heptalene, there is every possibility for the occurrence of lattice instability. It is also shown that the singlet instability as well as the lattice instability arises from the existence of a sufficiently low-lying singlet excited state.

Notes: We have performed RHF, UHF, UHF with subsequent spin projection, and EHF calculations for the π-electrons of some polyene chains of different lengths in order to investigate the relations among these methods when the number of electrons increases. Special attention is paid to the importance of spin projection for different energetic quantities.

Notes: The densities of states and Fermi energies were accurately calculated from E(k) data obtained by the self-consistent-band Augmented Plane Wave (APW) method, using a quadratic energy expansion. The reliability of the Monte Carlo integration was investigated. It was sufficiently good to determine the anisotropy of the Fermi surface of lithium, sodium, and potassium.

Notes: A new method is proposed for the analysis of components of molecular interaction energy within the Hartree-Fock approximation. The Hartree-Fock molecular orbitals of the isolated molecules are used as the basis for the construction of Fock matrix of the supermolecule. Then certain blocks of this matrix are set to zero subject to specify boundary conditions of the supermolecule molecular orbitals, and the resultant matrix is diagonalized iteratively to obtain the desired energy components. This method can be considered as an extension of our previous method, but has an advantage in the explicit definition of the charge transfer energy, placing it on an equal footing with the exchange and polarization terms. The new method is compared with existing perturbation methods, and is also applied to the energy and electron density decomposition of (H2O)2.

Notes: The canonical orthornormalisation procedure is derived through an integral equation with a finite rank kernel. Its optimal properties in connection with the problem of approximate linear dependence are established.

Notes: Single-exponential Slater type orbitals of the form ψ1 = (1 + L1(r, θ) + L2(r, θ) +…+ Ln(r, θ)) exp (- αr) are examined for their potential use as one-center molecular orbitals. These are then to be used as molecular fragments in a LCMO study. The system examined is HeH+ + with calculated energies and dipole moments being compared to the exact values. These functions behave best in the region of chemical interest (the bonding region) and thus demonstrate a possible usefulness in LCMO calculations and in the field of one-electron diatomics.

Notes: The ground-state energy of the beryllium atom is calculated using a variational procedure in which the elements of the two-body reduced density matrix (particle-particle matrix) are the variational parameters. It is shown that, for this problem and with the limited number of spin-orbitals used, the trace condition and the simultaneous nonnegativity conditions on the particle-particle, the particle-hole, and the hole-hole matrices form a complete solution to the N-representability problem.The energy obtained is - 14.61425 a.u., practically identical to the value given by a configuration interaction calculation which uses the same states. The effects of weakening the nonnegativity conditions on each of the matrices in turn were also explored.

Notes: Inelastic collisions leading to rotationally excited molecular targets and involving protons as projectiles are theoretically examined from the point of view of both the scattering equations in the close coupling formalism and the interaction potentials between the partners.A phenomenological approach is suggested for constructing such interactions and computational results are reported for simple diatomic targets. The inadequacy of more traditional ‘static’ approaches, when called for explaining dynamic couplings with open channels and centrifugal effects, is also discussed.

Notes: This paper contains a discussion of asymptotic properties of inverses of cyclic overlap matrices relevant to LCAO theory based on localized orbitals. For inverse metric elements, Δlαl′β-1, and for large distances, R, between centres of localized orbital α in cell l and localized orbital β in cell l′, it is shown that: one-dimensional case: \documentclass{article}\pagestyle{empty}\begin{document}$$ \Delta _{l\alpha l\prime\beta }^{- 1} \sim{\rm const}{\rm .}\,{\rm exp}\,{\rm (} -{\rm const}{\rm . \times }R{\rm )} $$\end{document} two-dimentional case: \documentclass{article}\pagestyle{empty}\begin{document}$$ \Delta _{l\alpha l\prime\beta }^{ - 1} \sim{\rm const}{\rm .}\,\,R^{ - _2^1 } \,{\rm exp}\,{\rm (} - {\rm const}{\rm . \times }R{\rm )} $$\end{document} three-dimentional case: \documentclass{article}\pagestyle{empty}\begin{document}$$ \Delta _{l\alpha l\prime\beta }^{ - 1} \sim{\rm const}{\rm .}\,\,R^{ - 1} \,{\rm exp}\,{\rm (} - {\rm const}{\rm . \times }R{\rm )} $$\end{document}These results are quite general and do not presuppose any restrictions as to symmetry (apart from the cyclic one), number of orbitals per unit cell, or vanishing of overlap integrals associated with neighbours beyond a fixed order. By way of illustration, explicit applications to one-, two-, and three-dimensional, simple, mono-orbitalic lattices with first-neighbour overlap only are included.

Notes: The half-projected Hartree-Fock function for singlet states (HPHF) is analysed in terms of natural electronic configurations. For this purpose the HPHF spinless density matrix and its natural orbitals are first deduced.It is found that the HPHF function does not contain any contribution from odd-times excited configurations. It is seen in addition, in the case of the singlet ground states, this function is approximately equivalent to two closed-shell configurations, although the nature of the excited one depends on the nuclear geometry. An example is given in the case of the LiH ground state. Finally, the application of this model for studying systems of more that two atoms is criticized.

Notes: A simple proof of the theorem that completely filled shells of fermions do not contain any symmetry component other than the totally symmetric representation is given.

Notes: The introduction of symmetry-adapted hybrid atomic orbitals on the metallic atoms allows us to divide the crystal into elementary cells which contain 8 valence electrons each. These cells are described by linear combinations of the halogen valence shell s and p orbitals and the hybrid orbitals of the nearest metallic atoms which point to the halogen. The electronic delocalization of the halogen ions is very weak (≤0.02) for: LiF, NaF, KF, LiCl, NaCI, and KCI. The cell energy in the crystal is obtained by using a first-order perturbative treatment. In agreement with experiment, the f.c.c. type is found more stable than the b.c.c. or the blende type.

Notes: Ab initio LCAO-MO-SCF Gaussian basis function calculations have been performed for chlorpromazine and promazine. By prescreening for the size of the integrals before calculation, it was only necessary to calculate 12 million out of the possible 38.5 million integrals for chlorpromazine. By a novel procedure of processing the integral tapes for the SCF it was possible to cut down significantly on the amount of time for the SCF. The SCF calculations converged smoothly for both promazine and chlorpromazine. There is a sizeable energy gap between the energy of the highest occupied molecular orbitals in these molecules (which is of the order of -0.3 a.u.) and the lowest unoccupied molecular orbital (which is of the order of + 0.15 a.u.). The gross atomic populations of chlorpromazine and promazine resemble each other and differ only somewhat on the carbon atom to which the substituent is attached and the carbons and their hydrogens adjacent to it.

Notes: A variant of the transcorrelated method of Boys and Handy employing finite differences is presented. It is based upon the following two properties of the transcorrelated Hamiltonian operator C-1HC: (1) C-1HC possesses an energy eigenvalue spectrum which is identical to that associated with H itself; and (2) if \documentclass{article}\pagestyle{empty}\begin{document}$$ C \equiv \begin{array}{*{20}c} \pi & {e^{r_{ij} /2} } \\ {i 〉 j} & {} \\ \end{array} $$\end{document} then C-1HC is free of the singularities of H at the points where the interelectron separation rij is zero. A bivariational principle for approximating the eigenvalues and the left and right eigenfunctions of C-1HC is introduced and the resulting set of coupled integro-differential equations are solved in finite-difference form by means of a coupled self-consistent field, Newton Raphson algorithm. As a preliminary test of the method, a calculation of the ground-state energy of the helium atom is presented.

Notes: The effectiveness of the recently developed method for optimization of one-electron wave-functions is directly examined by means of a simple procedure. By means of the same procedure the dependence of electron correlation on the nuclear charge and on the number of electrons is also investigated.

Notes: A molecular one-electron Dirac equation is derived by variation of a total energy density functional, whereby the one-electron energies are ascribed a physical meaning. The multiple scattering formalism for molecular systems is relativistically generalized for the determination of molecular four-component spinors. Optimal spinors and one-electron energies for a finite basis set are derived by variation of a functional. The form of the secular equation is very similar to the nonrelativistic form. Using scattering theory, the quantities appearing in the secular equation are interpreted.

Notes: We investigated various nonstandard 1s basis functions (generalized Slater-Gaussian, ellipsoidal Gaussian, floating spherical and ellipsoidal Gaussian, rational function, Hulthén approximation, two-Slater-type orbital, generalized Guillemin-Zener function, and various noninteger-n elliptical orbitals) for approximating the 1Σg+ ground state of H2 and He2++. A CI trial wave-function including Σg-type MO's is adopted and molecular integrals are evaluated numerically. The energy improvement on the 1s STO is small except for noninteger-n orbitals which closely approach the “SCF limit”.

Notes: The relation of the straightforward Rayleigh-Schrödinger perturbation theory for the interaction of two atoms to the asymptotic exchange theory is described. The one-electron case of a hydrogen atom perturbed by a nucleus is examined in detail. It is shown that the asymptotic theory contains an infinite summation of terms in the Rayleigh-Schrödinger series. The nature of the branching between states and its implications for convergence is elucidated.

Notes: The optimization scheme of the “multiconfiguration method based on the generalized Brillouin theorem” (MCGBT) has been analysed and found to converge quadratically. Its rate of convergence has been compared with that of other optimization methods such as the first-order Rayleigh-Schrödinger perturbation, the steepest descent, the single vector diagonalization, the Newton-Raphson, and the conventional SCF method. The convergence of the MCGBT scheme has been found to be superior to the convergence of the above mentioned schemes.

Notes: A direct method to optimize parameters in nonorthogonal basis orbitals is discussed. The partial derivatives of the energy of the state of interest, not necessarily the ground state, with respect to the orbital parameters are calculated analytically. The required cofactors up to third order of the overlap matrices over spin-space orbitals in pairs of Slater determinants are calculated by biorthogonalization. All parameters are varied simultaneiously in the direction of the negative gradient (steepest descent). A search logic with dynamically adjusted step-size is shown, in the example of the minimum basis Ne ground state, to find the energy minimum in an efficient manner.

Notes: Assuming a determinantal form for the wave-functions of free molecules, explicit formula for the first-order interaction energy of many closed-shell molecules has been derived. Provided that the determinants describing the free molecules are constructed from the Hartree-Fock orbitals, the two-, three-, and four-body effects predicted by the first-order perturbation theory are closely related to those which one obtains in the framework of the Löwdin LCAO MO-type approach. The results are illustrated by numerical calculations for the system of three ground-state helium atoms.

Notes: It is proposed to calculate electronic structure of atoms and molecules by combining the Thomas-Fermi-Dirac (TFD) theory and a correct quantum mechanical treatment. The potential generated from the TFD treatment of the positively charged cores contains no adjustable parameters and requires no modification for proper asymptotic behavior. To take the exclusion principle into account, the valence electron wave-function is constructed from the n + 1st, n + 2nd, etc. solutions to the one-electron Schrödinger equation using the core potential, where n is the number of core electrons. For the potassium atom, the simple calculations give excellent agreement with experiment for ionization potential, transition frequencies and intensities, magnetic susceptibility, and electric polarizability. From a two-electron configuration interaction wave-function for K-, a value for the electron affinity of K is obtained which agrees with experimental values.

Notes: The evaluation of interatomic interactions at large separations (R) typically involves neglecting electron exchange, treating the Coulomb interaction between atoms as a perturbation, neglecting third- and higher-order energy contributions, and approximating the Coulomb interaction by a short expansion in spherical harmonics and, usually, powers of R-1. This last approximation, using an approximate perturbing Hamiltonian to evaluate a second-order perturbed energy, is examined here; error bounds and a simple correction are introduced. Three illustrative applications to the H—H+ interaction are given: the error incurred by truncating the spherical-harmonic expansion is bounded, the R-1 expansion is corrected for the overlap of the “atomic” charge distributions, and the R-1 expansion is analyzed to see why it works as well as it does.

Notes: We have developed a many-body version of Woodward-Hoffmann theory which is capable of rapid computation of π-electronic surfaces. This theory, called the Hückel-Hubbard theory, employs Hückel parameters as reaction coordinates and the Hubbard parameter for electron repulsion. We apply it to the cis-trans isomerization of ethylene and to several pericyclic reactions.

Notes: The various orthogonality and sum rules which the 6j and 3jm symbols satisfy are sufficient to obtain the algebraic formulas for these symbols for SO3 ⊃ SO2. Character theory enters in that the j's and m's occurring in the various sums are given by the triangle rule \documentclass{article}\pagestyle{empty}\begin{document}$$ j_1 \times j_2 = \left| {j_1 - j_2 } \right| \oplus \ldots \oplus \left( {j_1 + j_2 } \right) $$\end{document} together with information on the symmetrized product and the branching, SO3 ⊃ SO2, \documentclass{article}\pagestyle{empty}\begin{document}$$ j \to \left( { - j} \right) \oplus \ldots \oplus \left( j \right) $$\end{document} The resulting calculation is somewhat simpler, algebraically speaking, than previous calculations and has the pedagogical advantage that only the concept of an irreducible representation of a group is required, instead of the more elaborate concept of ladder operators.

Notes: Singlet-triplet spin-orbit matrix elements, which govern the lowest 3B1u ← 1Ag transition in typical aromatic molecules like naphtalene and anthracene, are calculated with INDO molecular orbitals and the conventional spin-orbit one-electron hamiltonian. The correct order of magnitude of the triplet radiative lifetimes is obtained for the two molecules, when INDO MO coefficients are referred to a symmetrically orthogonalized basis. The possibility of using the semiempirical Hamiltonian is explored using ab initio wave-functions for a few test cases. Reasonably accurate doublet-doublet and singlet-triplet matrix elements have been computed.

Notes: A method is developed for determining the allowed states of a many-particle system at definite states of the subsystems (impurity ion complexes in crystals, nucleon clusters in nuclei, polyatomic molecules). The advantage of the method proposed here over those previously developed is that the present one is independent of the number of particles in the subsystems. Depending on the value of spin Sa the subsystems are considered either as bosons or fermions. The representation character expression whose expansion gives all the terms 2s+1Γ(α) with a definite value of total spin of the system is written as the product of permutation and orbital factors. The orbital factor is defined in terms of characters of the local point group representations. Some alternative ways of calculating the permutation factor are discussed: a) with the use of tables of reduction of the unitary transformation group U2Sa+1 in a three-dimensional rotation group; b) through the plethysm coefficients; and c) in terms of 3nj-symbols of three-dimensional rotation group. Some examples of application of the method to various systems are presented.

Notes: A study of selected electronic properties for isoelectronic series of Li, Be, B, and C has been presented. The study is based on the recently developed procedure of optimization of atomic spin-orbitals.

Notes: A general model for the vibrational interactions of the hydrogen bonds in molecular crystals is presented. The energy and the intensity distributions of the IR spectra of the 1-methylthymine and uracil crystals are correctly reproduced.