Conformational analysis of enantiomerization coupled to internal rotation in triptycyl-n-helicenes.

We present a computational study of a reduced potential energy surface (PES) to describe enantiomerization and internal rotation in three triptycyl-n-helicene molecules, centering the discussion on the issue of a proper reaction coordinate choice. To reflect the full symmetry of both strongly coupled enantiomerization and rotation processes, two non-fixed combinations of dihedral angles must be used, implying serious computational problems that required the development of a complex general algorithm. The characteristic points on each PES are analyzed, the intrinsic reaction coordinates are calculated, and finally they are projected on the reduced PES. Unlike what was previously found for triptycyl-3-helicene, the surfaces for triptycyl-4-helicene and triptycyl-5-helicene contain valley-ridge-inflection (VRI) points. The reaction paths on the reduced surfaces are analyzed to understand the dynamical behaviour of these molecules and to evaluate the possibility of a molecule of this family exhibiting a Brownian ratchet behaviour.

Effects of Temperature on the Shape and Symmetry of Molecules and Solids.

Despite its undeniable problems from a philosophical point of view, the concept of molecular structure, with attributes such as shape and symmetry, directly borrowed from the description of macroscopic objects, is nowadays central to most of the chemical sciences. Descriptions such as "the tetrahedral carbon atom" or "octahedral coordination complexes" are widely used as much in elementary textbooks as in the most up-to-date research articles. The definition of molecular shape is, however, not as simple as it might seem at first sight. Molecules don't behave as macroscopic objects do, and the arrangement of atoms within a molecule changes continuously due to the incessant motion of its constituent particles, nuclei, and electrons. How are molecular shape and symmetry affected by this thermal motion? In this Minireview, we introduce the language of continuous symmetry measures as a new tool to quantitatively describe the effects of temperature on molecular shape and symmetry, enriching in this way the set of molecular descriptors that might be used in the establishment of new empirical structure-property relations, of great interest in concomitant areas such as medicinal chemistry or materials science.

Theoretical evidence for the direct 3MLCT-HS deactivation in the light-induced spin crossover of Fe(ii)-polypyridyl complexes.

Spin-orbit couplings have been calculated in twenty snapshots of a molecular dynamics trajectory of [Fe(bpy)3]2+ to address the importance of geometrical distortions and second-order spin-orbit coupling on the intersystem crossing rate constants in the light-induced spin crossover process. It was found that the effective spin-orbit coupling between the 3MLCT and 5T2 state is much larger than the direct coupling in the symmetric structure, which opens the possibility of a direct 3MLCT-5T2 deactivation without the intervention of triplet metal-centered states. Based on the calculated deactivation times, we conclude that both the direct pathway and the one involving intermediate triplet states are active in the ultrafast population of the metastable HS state, bringing in agreement two experimental observations that advocate for either deactivation mechanism. This resolves a long-standing dispute about the deactivation mechanism of Fe(ii)-polypyridyl complexes in particular, and about light-induced magnetism in transition metal complexes in general.

Electronic Structure and Magnetic Properties of CuFeS2.

Chalcopyrite (CuFeS2) is an antiferromagnetic semiconductor with unusual magnetic and electrical properties, which are still not clearly understood. Neutron diffraction experiments reveal a phase transition at ∼50 K that has been attributed to an unexpected appearance of magnetic moments on Cu ions, having a paramagnetic arrangement down to 50 K and then ordering to an antiferromagnetic state at lower temperatures. In this study we use DFT-based computational methods to investigate the electronic structure and magnetic properties of CuFeS2 in order to obtain a reliable source of information for the interpretation of the observed magnetic behavior, and in particular to shed some light on the magnetic behavior of copper atoms in this compound. We have calculated the electronic structure of the ground and low-energy magnetically excited states and deduced a set of exchange coupling constants that are used afterward in classical Monte Carlo simulations to obtain magnetic susceptibility data, which compare successfully with our experimental results above ∼170 K. From our results it can be inferred that copper atoms remain in a diamagnetic state in this temperature range, although spin delocalization from neighboring iron atoms results in a non-negligible spin density on the copper atoms at high temperatures.

Factors affecting the magnetic coupling in Sr2V3O9 type oxides: As for V substitution in the VO4 tetrahedra and nature of the cation.

A density functional theory study of the magnetic couplings in Sr2V3O9 type magnetic oxides suggests that whereas the intrachain coupling is always weakly ferromagnetic, the interchain coupling may be antiferromagnetic or even weakly ferromagnetic depending on the nature of the central tetrahedral atom (As/V) cations, and, to a lesser extent, structural details.

Structural stability of quaternary ACuFeS2 (A = Li, K) phases: a computational approach.

At ambient conditions, the quaternary sulfides LiCuFeS(2) and KCuFeS(2) present totally different crystal structures: while LiCuFeS(2) crystallizes in a trigonal CaAl(2)Si(2)-type structure, a tetragonal ThCr(2)Si(2)-like structure is found for KCuFeS(2). In this work, we present a computational study describing first the changes in the structural preference of the ACuFe(2) phases as a function of the alkali ion and second, the structural stability of the CuFeS(2) phases obtained by electrochemical removal of the alkali cations from the two ACuFeS(2) compounds. A high copper mobility is found to be responsible for the observed metastability of the layered trigonal CuFeS(2) phase obtained by delithiation of LiCuFeS(2). In contrast, the tetragonal CuFeS(2) structure obtained removing potassium from KCuFeS(2) is predicted to be stable, both from the kinetic and thermodynamic points of view. The possibility of stabilizing mixed Li(x)Cu(1-x)FeS(2) phases with a ThCr(2)Si(2)-type structure and the mobility of lithium in these is also explored.

Electronic structure and spin exchange interactions in Na(2)V(3)O(7): a vanadium(IV) oxide nanotubular phase.

The electronic structure of the inorganic nanotubular phase Na(2)V(3)O(7) has been studied by means of first-principles DFT calculations. The magnetic behavior in this system is relatively complex to study because there are as many as 30 different exchange interactions in the unit cell. The coupling constants are computed directly from the energy differences of several spin configurations. It is found that because of the special geometry of the nanotube, the nearest-neighbor coupling constants are not the only important ones and other next-nearest-neighbor constants cannot be neglected. In contrast with previous studies, it is found that at least 12 different coupling constants must be considered to correctly describe the spin arrangement in this system. However, to get more meaningful values for the smaller constants, a larger set of at least 17 constants must be explicitly taken into account. The lowest-energy collinear spin configuration is found to exhibit ferromagnetic coupling between the rings of the nanotube, whereas the coupling can be ferro- or antiferromagnetic within those rings. This leads to two important spin-frustrated interactions. Use of the so-called dimer approximation (i.e., substituting 16 paramagnetic V(IV) ions of the nanotube by 16 diamagnetic Ti(IV) ions, thus keeping the total charge of the system constant and leaving only two magnetic centers) is found to give invaluable hints concerning the nature of the magnetic interactions. This procedure may be helpful to analyze the magnetic properties of similar non-trivial systems with many paramagnetic centers.

Electronic structure and magnetic properties of potassium ozonide KO(3).

The electronic structure and magnetic properties of potassium ozonide, KO(3), have been investigated by means of periodic spin polarized Hartree-Fock and Density Functional Theory based approaches. These calculations show that KO(3) is a strongly ionic compound with paramagnetic O(3)(-) centers. The most reliable results, provided by the B3LYP hybrid approach, suggest that the system behaves as a magnetic insulator with a gap of approximately 3.0 eV, and with the states around the insulating gap arising mainly from the pi orbitals of the O(3)(-) units while the participation of potassium orbitals in the bands around the band gap is practically negligible. The calculations suggest that, because of the pi character of the magnetic orbitals, the magnetic structure for KO(3) has a significant one-dimensional character, with antiferromagnetically coupled chains along the c axis and a much weaker antiferromagnetic coupling between neighboring chains. This behavior is consistent with available experimental susceptibility data.

Host-guest interactions, uniform vs fragmented linear atom chains and likeliness of Peierls distortions in the (Ca7N4)[M(x)] (M = Ag, Ga, In) phases.

The electronic structure of the recently reported (Ca(7)N(4))[M((x))] (M = Ag, Ga, and In) phases has been studied by means of first principles density functional theory (DFT) calculations. It is shown that under the assumption of very weak host-guest interactions: (a) four calcium atoms per formula unit may be considered as Ca(1.5+), whereas the remaining three may be considered as Ca(2+) so that the guest atoms would be neutral, and (b) the Peierls distortions which could set in the guest linear chains are unlikely. These results are compatible with the experimental information. However, the first principles DFT calculations clearly show that very sizable host-guest interactions occur and drastically modify this situation. As a result, there is a substantial electron transfer from the framework to the guest atoms, and all calcium atoms of the framework are better described as Ca(2+). The stoichiometry and structure of these systems result from a competition between the natural tendency of the bare guest atoms to form uniform linear chains within the reduced space of the channels and the attempt to optimize their positions within the channels through interactions with the calcium atoms. Model calculations suggest that indium has a weaker tendency to form uniform linear chains and interacts in a stronger way with the host. It is shown that, for the (Ca(7)N(4))[M(1.33)] (M = Ag and Ga) phases, a structure built from three repeat units of the Ca(7)N(4) host framework containing uniform linear chains with a repeat unit of four guest metal atoms is compatible with the strong interaction scenario and the lack of correlation between the different linear guest chains. These phases should be metallic conductors, and the carriers have both host and guest character. In contrast, the guest atoms in (Ca(7)N(4))[In(1.0)] prefer to occur as a series of trimeric units. Although this phase is found to have a metallic band structure, the conductivity should be smaller than those of the (Ca(7)N(4))[M(1.33)] (M = Ag and Ga) phases.

Molecules and crystals with both icosahedral and cubic symmetry.

Notwithstanding the apparent incompatibility between octahedral and icosahedral symmetries, fragments with the two types of symmetry coexist in many molecules and crystals, as evidenced by continuous shape and symmetry measures. A geometric analysis of Platonic and Archimedean polyhedra and of a variety of molecular and crystal structures strongly suggests that octahedral symmetry is latent in icosahedral polyhedra and vice versa. In this Feature Article, new concepts and structural data from the literature combine to offer a perspective view of complex molecular and extended structures. Its influence on the common cubic packing of icosahedral molecules is discussed for a variety of examples, including water clathrates, dodecahedrane, Buckminsterfullerene, the Pd145 and Mo132 clusters and several intermetallic phases.

Roles of cations, electronegativity difference, and anionic interlayer interactions in the metallic versus nonmetallic character of Zintl phases related to arsenic.

A first-principles Density Functional Theory study of several layered solids structurally related to rhombohedral arsenic has been carried out. The electronic structures of rhombohedral arsenic, CaSi(2), CaAl(2)Si(2), KSnSb, and SrSn(2)As(2) are discussed in detail, emphasizing on the origins of their metallic or nonmetallic behaviours. It is found that all of these systems are metallic except KSnSb. Electronegativity differences between the elements in the anionic sublattice and/or direct interlayer interactions play the main role in controlling the conductivity behavior. CaSi(2) exhibits a peculiar feature since the cation directly influences the conductivity but is not essential for its appearance. Cation-anion interactions are shown to have an important covalent contribution, but despite this fact and the metallic character found for most of these phases, the Zintl approach still provides a valid approximation to their electronic structure.

Concerning the different roles of cations in metallic Zintl phases: Ba7Ga4Sb9 as a test case.

The question of the different roles of cations in metallic Zintl phases has been examined by taking Ba7Ga4Sb9, an electron-rich phase, as a test case. The electronic structure of this solid has been studied by means of a first-principles density functional theory approach and, indeed, the different Ba atoms are found to play very different roles in determining the structural and transport properties of this phase. It is also found that Ba7Ga4Sb9 should be an anisotropic metal with both one- and three-dimensional contributions to the Fermi surface so that the system could exhibit a potentially very interesting physical behavior while keeping the metallic properties down to very low temperatures. Suggestions in order to modify the band filling and the physical properties are examined. Although isostructural electron-precise phases may be envisioned, it is predicted that they would be essentially three-dimensional metals.

Theoretical determination of multiple exchange couplings and magnetic susceptibility data in inorganic solids: the prototypical case of Cu2(OH)3NO3.

Density functional theory based on hybrid functionals and localized atomic type basis sets is employed to calculate the exchange couplings in the layered three-dimensional compound Cu2(OH)3NO3. We assign accurate values to the six different in-plane exchange couplings. Interlayer exchange interactions through hydrogen bonds are also quantified. The calculated exchange coupling constants are then employed to perform quantum Monte Carlo simulations to yield magnetic susceptibility data, which compare successfully with experiments. Our approach sets the foundations of a viable methodology to extract reliable magnetic susceptibilities from density functional data.

Magnetic properties of cyano-bridged Ln3+-M3+ complexes. Part I: trinuclear complexes (Ln3+ = La, Ce, Pr, Nd, Sm; M3+ = FeLS, Co) with bpy as blocking ligand.

The reaction of Ln(NO3)3(aq) with K3[Fe(CN)6] or K3[Co(CN)6] and 2,2'-bipyridine in water/ethanol led to eight trinuclear complexes: trans-[M(CN)4(mu-CN)2{Ln(H2O)4(bpy)2}2][M(CN)6].8H2O (M = Fe3+ or Co3+, Ln = La3+, Ce3+, Pr3+, Nd3+, and Sm3+). The structures for the eight complexes [La2Fe] (1), [Ce2Fe] (2), [Pr2Fe] (3), [Nd2Fe] (4), [Ce2Co] (5), [Pr2Co] (6), [Nd2Co] (7), and [Sm2Co] (8) have been solved; they crystallize in the triclinic space group P and are isomorphous. They exhibit a supramolecular 3D architecture through hydrogen bonding and pi-pi stacking interactions. A stereochemical study of the nine-vertex polyhedra of the lanthanide ions, based on continuous shape measures, is presented. No significant magnetic interaction was found between the lanthanide(III) and the iron(III) ions.

Electronic structure of the K3Bi2 metallic phase.

The electronic structure of K3Bi2 is discussed on the basis of first-principles DFT calculations. It is shown that the dimers are formally (Bi2)3-, even though this might seem to be in contradiction with the metallic character of the salt. The apparent puzzle is explained by the sizable participation of the K levels in the bonding.

Electronic structure of Li2Ga and Li9Al4, two solids containing infinite and uniform zigzag chains.

The electronic structure of inorganic solids such as Li(2)Ga and Li(9)Al(4) containing infinite zigzag homoatomic chains is discussed. It is shown that Li(2)Ga, a solid for which a Zintl-type electron-counting approach would suggest that a half-filled pi-type band occurs as in trans-polyacetylene, is really a three-dimensional solid with strong covalent interchain connections and small effective charge transfer. The zigzag chains do not play a dominant role as far as the electronic structure near the Fermi level is concerned, and there is no reason for the occurrence of a Peierls distortion despite the possible analogy with trans-polyacetylene. It is suggested that even assuming that a Zintl-type approach is appropriate for electron counting purposes, the infinite zigzag chains in this compound and those in trans-polyacetylene are not isolobal. The bonding in Li(9)Al(4) and Li(2)Ga is very similar, and both phases are predicted to be stable three-dimensional metals.

The rich stereochemistry of eight-vertex polyhedra: a continuous shape measures study.

A stereochemical study of polyhedral eight-vertex structures is presented, based on continuous shape measures (CShM). Reference polyhedra, shape maps, and minimal-distortion interconversion paths are presented for eight-vertex polyhedral and polygonal structures within the CShM framework. The application of these stereochemical tools is analyzed for several families of experimental structures: 1) coordination polyhedra of molecular transition-metal coordination compounds, classified by electron configuration and ligands; 2) edge-bonded polyhedra, including cubane structures, realgar, and metal clusters; 3) octanuclear transition-metal supramolecular architectures; and 4) coordination polyhedra in extended structures in inorganic solids. Structural classification is shown to be greatly facilitated by these tools, and the detection of less common structures, such as the gyrobifastigium, is straightforward.

Minimal distortion pathways in polyhedral rearrangements.

A definition of minimum distortion paths between two polyhedra in terms of continuous shape measures (CShM) is presented. A general analytical expression deduced for such pathways makes use of one parameter, the minimum distortion constant, that can be easily obtained through the CShM methodology and is herein tabulated for pairs of polyhedra having four to eight vertexes. The work presented here also allows us to obtain representative model molecular structures along the interconversion pathways. Several commonly used polytopal rearrangement pathways are shown to be in fact minimum distortion pathways: the spread path leading from the tetrahedron to the square, the Berry pseudorotation that interconverts a square pyramid and a trigonal bipyramid, and the Bailar twist for the interconversion of the octahedron and the trigonal prism. Examples of applications to the analysis of the stereochemistries of several families of metal complexes are presented.