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Quantum crystallography (QCr) is a branch of crystallography aimed at obtaining the complete quantum mechanics of a crystal given its X-ray scattering data. The fundamental value of obtaining an electron density matrix that is N-representable is that it ensures consistency with an underlying properly antisymmetrized wavefunction, a requirement of quantum mechanical validity. However, X-ray crystallography has progressed in an impressive way for decades based only upon the electron density obtained from the X-ray scattering data without the imposition of the mathematical structure of quantum mechanics. Therefore, one may perhaps ask regarding N-representability 'why bother?' It is the purpose of this article to answer such a question by succinctly describing the advantage that is opened by QCr. Key words: momentum density, density matrices, Clinton equations, N-representability, Bader's quantum theory of atoms in molecules (QTAIM), interacting quantum atom (IQA). La cristallographie quantique (QCr) est une branche de la cristallographie ayant pour but de fournir la description quantique complete d'un cristal a partir de ses donnees de diffraction des rayons X. La valeur fondamentale de l'obtention d'une matrice de densite electronique qui est N-representable est l'assurance de sa coherence avec une fonction d'onde sous-jacente correctement anti-symetrisee comme l'exige la mecanique quantique. Mais la cristallographie aux rayons X a progresse de façon impressionnante pendant des decennies en ne se basant essentiellement que sur la densite electronique obtenue a partir des donnees cristallographiques experimentales, sans l'imposition de la structure mathematique de la mecanique quantique. Par consequent, on pourrait se demander a propos de la N-representabilite : << pourquoi s'en soucier? >> Cet article a pour but de repondre a cette question en decrivant brievement l'avantage que presente la cristallographie quantique. Mots-cles: densite de quantite de mouvement, matrices de densite, equations de Clinton, N-representabilite, theorie quantique des atomes dans les molecules (QTAIM) de Bader, atomes quantiques en interaction (IQA)., Introduction Quantum crystallography (QCr) (1-8) is a branch of crystallography bringing diffraction experiments within the purview of quantum mechanics. X-ray scattering data analyzed with a strictly quantum mechanical formalism closely [...]

The fate of dimensions of dimensioned quantities that are inserted into the argument of transcendental functions such as logarithms, exponentiation, trigonometric, and hyperbolic functions is discussed. Emphasis is placed on common misconceptions that are not often systematically examined in undergraduate courses of physical sciences. The argument of dimensional inhomogeneity of the terms of a Taylor expansion of a transcendental function presented in some nonpeer-reviewed popular Internet sites is shown to be false.

The properties of metal-metal bonding for transition metal homonuclear diatomics from groups 10, 11 and 12 are studied within the framework of the quantum theory of atoms in molecules (QTAIM) at the coupled cluster CCSD and CCSD(T) levels of theory. A novel approximate method developed by Keith and Frisch is used to augment electron densities calculated with pseudopotentials with the missing relativistic core densities to obtain approximations to the total densities of the dimers. The calculated delocalization indices for group 10 dimers are: [Ni.sub.2] (1.6), [Pd.sub.2] (0.44, an outlier in the group), and [Pt.sub.2] (1.8); for group 11 dimers: [Cu.sub.2] and [Ag.sub.2] (1.01), and [Au.sub.2] (1.13), all covalent bonds; for group 12: [Zn.sub.2] (0.06), [Cd.sub.2] (0.08), and [Hg.sub.2] (0.09), all consistent with weak van der Waals complexes. The picture of bonding obtained by examining the values of the electron density at the bond critical points is consistent with the one obtained on the basis of these delocalization indices. A curious linear (instead of exponential) dependence of the delocalization index on the electron density at the bond critical point is presented here as an observation and will be investigated in more depth in later work. Several correlations between bond properties and bond dissociation energies are also explored. It is found that, with the exception of the [Ni.sub.2] dimer that exhibits considerable multi-reference character, there are correlations between the calculated bond dissociation energies of the studied diatomics and several bond critical point properties. These correlations are novel as they span a set of bonds between different pairs of elements, while traditionally these correlations were reported for bonds between the same pair or elements but with different substituents. Key words: topology of the electron density, chemical bonding in transition metals, quantum theory of atoms in molecules, QTAIM, metal-metal bonding. Resume : Les proprietes des liaisons metal-metal pour les dimeres homonucleaires des metaux de transition des groupes 10,11 et 12 sont etudies dans le cadre de la theorie quantique des atomes-dans-les-molecules (QTAIM) en faisant appel aux niveaux de theorie CCSD et CCSD (T). Une nouvelle methode developpee par Keith et Frisch est utilisee pour augmenter des densites electroniques calculees a l'entremise de pseudo potentiels avec les densites de cceur relativistes manquantes pour obtenir des approximations aux densites totales des dimeres. Les indices de delocalisation calcules pour les dimeres du groupe 10 : [Ni.sub.2] (1.6), [Pd.sub.2] (0.44, qui est en ecart du reste du groupe) et [Pt.sub.2] (1.8); pour les dimeres du groupe 11: [Cu.sub.2] et [Ag.sub.2] (1.01) et [Au.sub.2] (1.13), toutes les liaisons etant covalentes; et pour le groupe 12 : [Zn.sub.2] (0.06), [Cd.sub.2] (0.08) et [Hg.sub.2] (0.09) indiquant de faibles liaisons du type van der Waals. L'image qui emerge a propos de la nature de la liaison chimique obtenu en examinant les valeurs de la densite electronique aux points critiques est completement en accord avec celle obtenue sur la base des indices de delocalisation. Une curieuse dependance lineaire (au lieu d'exponentielle) de l'indice de delocalisation sur la densite electronique au point critique est presente ici comme une observation et sera enquete en plus de profondeur dans un travail future. Plusieurs correlations entre les proprietes des liaisons chimiques et les energies de leur dissociation sont aussi explorees. Il est constate que, a l'exception du dimer de [Ni.sub.2], dote d'un caractere multireferenciel considerable, il existe des correlations entre les energies de dissociation des dimeres etudies et plusieurs des proprietes de leur point critiques de liaisons. Ces correlations sont nouvelles car ils s'etendent sur un ensemble de liaisons entre de paires d'elements differentes, quand traditionnellement ces correlations ont ete trouvees pour les liaisons entre une meme paire d'element, mais avec des substituents differents. Mots-cles: la topologie de la densite electronique, la liaison chimique des metaux de transition, la theorie quantique des atomes dans les molecules (QTAIM/TQADM), la liaison metal-metal., Introduction Transition metal dimers have been studied for a number of years (1) and continue to provide challenges for ab initio methods. As noted by Yanagisawa, Tsuneda, and Hirao, nonhybrid [...]

The basic principles underlying the remote electronic effects of [Mg.sup.2} on the strength of a simple model of the P-O bond are explored. The results have shown that an individual bond might be strengthened by complex formation but the dissociation is globally more favorable due to other more dominant driving forces.