RESUMEN

Although real space regions have been widely used in theoretical chemistry, not much effort has been devoted to treat them as open quantum systems. We embrace this task here, finding closed expressions for the density operator of a quantum subsystem in real space by tracing out the degrees of freedom in its complementary region. Our results are then linked to previous knowledge. For single-determinant descriptions it is shown that the entanglement orbitals coincide with Ponec's domain natural orbitals. In general, the subsystem density operator is written as a direct sum of a fixed number of electron sectors, with weights that turn out to be equal to those found within the theory of electron distribution functions. As a computational application we show how to obtain the global first order density matrix of a subsystem and its eigensolution in a couple of toy systems. In the multideterminant wave function case, the domain natural orbitals defined through this open system approach do not coincide with those of Ponec and, contrary to the latter, have always strictly positive occupations.

RESUMEN

A force field that accounts for the quantum chemical reality of interacting atoms must include Coulomb interactions between bonded atoms. The short-range nature of such 1,2 interactions necessitates atomic multipole moments in addition to point charges. However, the close proximity of bonded atoms would normally lead to a divergent multipolar expansion. A special algorithm presented here, within the scope of the previously presented multipole shifting method [M. Rafat and P. L. A. Popelier, J. Chem. Phys. 124, 144102 (2006)], shows that convergence can nevertheless be achieved by a suitable selection of multipole displacements. The algorithm is applied to improve the convergence of the multipolar expansion within the quantum theory of atoms in molecules approach.

Asunto(s)

RESUMEN

A general strategy to extend the interacting quantum atoms (IQA) approach to pseudopotential or effective core potential electronic structure calculations is presented. With the protocol proposed here, the scope of IQA thinking opens to chemical bonding problems in heavy-atom systems, as well as to larger molecules than those presently allowed by computational limitations. We show that, provided that interatomic surfaces are computed from core-reconstructed densities, reasonable results are obtained by integrating reduced density matrices built from the pseudowave functions. Comparison with all-electron results in a few test systems shows that exchange-correlation energies are better reproduced than Coulombic contributions, an effect which is traced to inadequate atomic populations and leakage of the core population into the surrounding quantum atoms.

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We present a novel computational procedure, general, automated, and robust, for the analysis of local and global properties of the electron localization function (ELF) in crystalline solids. Our algorithm successfully faces the two main shortcomings of the ELF analysis in crystals: (i) the automated identification and characterization of the ELF induced topology in periodic systems, which is impeded by the great number and concentration of critical points in crystalline cells, and (ii) the localization of the zero flux surfaces and subsequent integration of basins, whose difficulty is due to the diverse (in many occasions very flat or very steep) ELF profiles connecting the set of critical points. Application of the new code to representative crystals exhibiting different bonding patterns is carried out in order to show the performance of the algorithm and the conceptual possibilities offered by the complete characterization of the ELF topology in solids.

RESUMEN

Widely used chemical concepts like Pauli repulsion or hyperconjugation, and their role in determining rotation barriers or stereoelectronic effects, are analyzed from the real space perspective of the interacting quantum atoms approach (IQA). IQA emerges from the quantum theory of atoms in molecules (QTAIM), but is free from the equilibrium geometry constraint of the former. A framework with both electronically unrelaxed and relaxed wavefunctions is presented that leads to an approximate correspondence between the IQA concepts and those used in the EDA (energy decomposition analysis) or NBO (natural bond orbital) procedures. We show that no net force acts upon the electrons in an electronically relaxed system, so that any reasonable definition of Pauli repulsion must involve unrelaxed state functions. Using antisymmetrized fragments clarifies that Pauli repulsions are energetically connected to the IQA deformation energies, leaving footprints in the finally relaxed states. Similarly, EDA or NBO hyperconjugative stabilizations are found to be naturally related to the IQA electron delocalization patterns. Applications to the rotation barrier of ethane and other simple systems are presented, and the very often forgotten role of electrostatic contributions in determining preferred conformations is highlighted.

RESUMEN

Advantages of the analysis of the topology of the electron localization function (ELF) in the characterization of the chemical bonding in solids are illustrated in the study of the zinc blende --> rock salt transformation in BeO. The 4-fold to 6-fold coordination change is described as a two-step process: first, a catastrophic-like emergence of two new Be-O bonds reveals the onset of the rock salt structure, and second, the new interactions gradationally evolve to achieve the bonding network of the high-pressure phase. The increase in coordination, the volume collapse and the enhancement in the bulk modulus across the transition pathway are qualitatively and quantitatively traced back to the oxygen's valence shell. Although several ELF indexes point toward the expected greater bond polarity in the B3 than in the B1 structure, it can be concluded that there is no substantial modification in the nature of the crystal interactions induced by the phase transformation.

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Evidence that the bond paths of the quantum theory of atoms-in-molecules (QTAIM) signal preferred quantum-mechanical exchange channels is presented. We show how bond paths between an atom A and the atoms B in its environment appear to be determined by competition among the A-B exchange-correlation energies that always contribute to stabilize the A-B interactions. These pairwise additive stabilizations depend neither on the attractive or repulsive nature of the classical electrostatic interaction between the atoms' charge densities, nor on the change in the self energies of the atoms involved. These other terms may well cause an overall molecular-energy increase in spite of a possibly large A-B exchange-correlation stabilization. After our proposal, bond paths, both at and out of equilibrium geometries, are endowed with a specific energetic meaning that should contribute to reconcile the orthodox QTAIM interpretation with other widely accepted views, and to settle recent controversies questioning the meaning of hydrogen-hydrogen bonding and the nature of the so-called "steric interactions", the role of bond paths in endohedral complexes, and the generality of the results provided by the QTAIM. Implications for the nature of more general closed-shell interactions are also briefly discussed.

RESUMEN

We analyze the response of a quantum group within a molecule to charge transfer by using the interacting quantum atoms approach (IQA), an energy partitioning scheme within the quantum theory of atoms in molecules (QTAM). It is shown that this response lies at the core of the concept of the functional group. The manipulation of fractional electron populations is carried out by using distribution functions for the electron number within the quantum basins. Several test systems are studied to show that similar chemical potential groups are characterized by similar energetic behavior upon interaction with other groups. The origin of the empirical additivity rules for group energies in simple hydrocarbons is also investigated. It turns out to rest on the independent saturation of both the self-energies and the interaction energies of the groups as the size of the chain increases. We also show that our results are compatible with the standard group energies of the QTAM.

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A general hierarchy of the coarsed-grained electron probability distributions induced by exhaustive partitions of the physical space is presented. It is argued that when the space is partitioned into atomic regions the consideration of these distributions may provide a first step toward an orbital invariant treatment of resonant structures. We also show that, in this case, the total molecular energy and its components may be partitioned into structure contributions, providing a fruitful extension of the recently developed interacting quantum atoms approach (J. Chem. Theory Comput. 2005, 1, 1096). The above ideas are explored in the hydrogen molecule, where a complete statistical and energetic decomposition into covalent and ionic terms is presented.

RESUMEN

The physical and chemical meaning of real space molecular fragments resulting from arbitrary partitions of the density is reviewed under a common unifying formalism. Both fuzzy (interpenetrating) and non-fuzzy (exhaustive) decompositions are treated on an equal basis. Density decompositions are consistently generalized to compatible density matrix partitions by using Li and Parr's ideas (Li and Parr J Chem Phys 1986, 84, 1704), and these are carried onto an energy partition. It is argued that the merits of a given decomposition should be judged against both the charge and the energetic image it provides. Atomic partitions are used to show how the interacting quantum atoms approach (IQA) allows us to cope with the most important energy cancellations of quantum chemistry. Binding results from a trade-off between atomic (or fragment) energy deformations with respect to a reference and interatomic (interfragment) interactions. Deformation energies are divided into charge transfer and redistribution terms and their relative roles are analyzed. A number of systems are compared against the fuzziness of different density decompositions. The results consistently show that fuzzy partitions tend to give low atomic net charges and enhanced covalency, while exhaustive partitions generate larger net charges and smaller covalencies, across a wide range of bonding regimes.

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Binding energies of first row diatomics are revisited within the interacting quantum atoms (IQA) approach. This is a formalism in chemical bonding theory based upon the quantum theory of atoms in molecules. It is characterized by the preservation of the energetic identity of atoms within molecules. Quantum mechanically computed binding energies are recovered in IQA as a sum of small atomic deformation energies and large pairwise interaction terms. We show how this partition responds faithfully to chemical intuition, and how the different evolution of deformations and interactions accounts in a unified manner for the subtle variations of the binding energy of these molecules.

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We report the results of a theoretical study of AlnNn (n=7-16) clusters that is based on density functional theory. We will focus on the evolution of structural and electronic properties with the cluster size in the stoichiometric AlN clusters considered. The results reveal that the structural and electronic properties tend to evolve toward their respective bulk limits. The rate of evolution is, however, slow due to the hollow globular shape exhibited by the clusters, which introduces large surface effects that dominate the properties studied. We will also discuss the changes induced upon addition of an extra electron to the respective neutral clusters.

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A recent method proposed to compute two-electron integrals over arbitrary regions of space [Martin Pendas, A. et al., J Chem Phys 2004, 120, 4581] is extended to deal with correlated wave functions. To that end, we use a monadic factorization of the second-order reduced density matrix originally proposed by E. R. Davidson [Chem Phys Lett 1995, 246, 209] that achieves a full separation of the interelectronic components into one-electron terms. The final computational effort is equivalent to that found in the integration of a one determinant wave function with as many orbitals as occupied functions in the correlated expansion. Similar strategies to extract the exchange and self-interaction contributions from the two-electron repulsion are also discussed, and several numerical results obtained in a few test systems are summarized.

RESUMEN

A method to compute two-electron integrals over arbitrary regions of space is introduced and particularized to the basins appearing in the quantum theory of atoms in molecules. The procedure generalizes the conventional multipolar approach to account for overlapping densities. We show that the approach is always convergent and computationally efficient, scaling as N(4) in the worst, two-center case. Several numerical results supporting our claims are also presented.

RESUMEN

The electron density of crystals contains all of the information required to complete a classification of their bonding types. We propose here a set of three different indexes, flatness, charge transfer, and molecularity, easily obtained from the experimental or theoretical electron density, which give rise to a classification in close resemblance to the classical van Arkel-Ketelaar diagrams.