Mulliken crystals

Mulliken symbols The designators, arising from group theory, of the electronic states of an ion in a crystal field. A and B are singly degenerate, E doubly degenerate, T triply degenerate states. Thus a D state of a free ion shows E and Tj states in an octahedral field. 

Crystal can compute a number of properties, such as Mulliken population analysis, electron density, multipoles. X-ray structure factors, electrostatic potential, band structures, Fermi contact densities, hyperfine tensors, DOS, electron momentum distribution, and Compton profiles. 

The nitrosonium cation bears a formal relationship to the well-studied halogens (i.e. X2 = I2, Br2, and Cl2), with both classes of structurally simple diatomic electron acceptors forming an extensive series of intermolecular electron donor-acceptor (EDA) complexes that show well-defined charge-transfer absorption bands in the UV-visible spectral region. Mulliken (1952a,b 1964 Mulliken and Person, 1969) originally identified the three possible nonbonded structures of the halogen complexes as in Chart 7, and the subsequent X-ray studies established the axial form II to be extant in the crystals of the benzene complexes with Cl2 and Br2 (Hassel and Stromme, 1958, 1959). In these 1 1 molecular complexes, the closest approach of the... 

At the end of Section 10.1 the Mulliken overlap population is mentioned as a quantity related to the bond order. A corresponding quantity for solids was introduced by R. Hoffmann the crystal orbital overlap population (COOP). It is a function that specifies the bond strength in a crystal, all states being taken into account by the Mulliken overlap populations Its calculation requires a powerful computer however, it can... 

The lowest crystal-field multiplets IR-Bethe(Mulliken) x degeneracy, energy (Zeeman coefficient gzMj) ... 

The crystal-field multiplets are classified according to the irreducible representations of the respective double-group where both, the Bethe and the Mulliken (in parentheses) notations are written. DsH means the spin-Hamiltonian D-value accounting for all excitations AmIi - the lowest energy levels difference using the model-Hamiltonian in the first iteration Affl - the... 

Here we note that only a single polarizability or susceptibility exists for any system. The reconstruction from local contributions is in fact an abstraction, the result of which depends on the detail wanted macroscopic with local susceptibilities or microscopic with local polarizabilities and—more importantly—on the partitioning of such properties. However, experimental chemists are used to such procedures from well-chosen series of compounds they derive bond energies as local contributions to heats of formation and ionic radii from crystal structures. Theoretical chemists obtain atomic charges from, e.g., a Mulliken analysis of their wave functions. We are able, following similar reasoning, to construct molecular polarizabilities from atomic ones [38,60], although there is formally no connection between them. In an opposite direction we can decompose a molecular polarizability into a many-center... 

The Mulliken arguments may be extended to charge-transfer crystals. The first solid charge-transfer crystals studied were colored, but had low thermodynamic stability relative to the separate neutral donor and acceptor crystals. However, if the donor D had low ID and if the acceptor had high Aa ... 

In order to study the electronic properties of the metal-organic frameworks we have analyzed their MulUken charges as well as the densities of states in the periodic crystals and the free building blocks. The calculated atomic Mulliken charges of different MOF systems show an almost unchanged charge distribution compared to the smallest in the series IRMOF-1. Moreover, the... 

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