The nature of the hydrogen bond: A synthesis from the interacting quantum atoms picture

The interacting quantum atoms approach [IQA, as presented by Blanco et al., J. Chem. Theory Comput. 1, 1096 (2005)] is applied to standard hydrogen bonded dimers. IQA is an interpretation tool based on a real space energy decomposition scheme fully consistent with the quantum theory of atoms in molecules. It provides a partition of every physical term present in the Hamiltonian into atomic and interatomic contributions. The procedure is orbital-free and self-contained, needing neither external references nor artificial intermediate states. Binding is the result of a competition between the destabilizing deformations suffered by the interacting fragments upon interaction and the stabilizing interaction energy itself. According to IQA, there is no incompatibility between the prevalent electrostatic image of hydrogen bonded systems and that favoring important covalent contributions. Depending on how we gather the different energetic terms, we may recover electrostatic or covalent pictures from the same underlying quantum mechanical description. Our results show that the nonclassical contributions to hydrogen bonding are spatially localized, involving only the H atom and its two nearest neighbors. IQA is well suited as a comparative tool. Its thin energetic decomposition allows us to recover exactly (or to a very good approximation) the quantities of the most widely used energy decomposition schemes. Such a comparison sheds light on the virtues and faults of the different methods and on the origin of the 50 years old debate regarding the covalent/electrostatic nature of the hydrogen bond.

Two-electron integrations in the quantum theory of atoms in molecules

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.

Chemical fragments in real space: definitions, properties, and energetic decompositions

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.

Two-electron integrations in the Quantum Theory of Atoms in Molecules with correlated wave functions

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.

Domain-averaged exchange-correlation energies as a physical underpinning for chemical graphs

A novel solution to the problem of assigning a molecular graph to a collection of nuclei (i.e. how to draw a molecular structure) is presented. Molecules are universally understood as a set of nuclei linked by bonds, but establishing which nuclei are bonded and which are not is still an empirical matter. Our approach borrows techniques from quantum chemical topology, which showed for the first time the construction of chemical graphs from wave functions, shifting the focus on energetics. This new focus resolves issues surrounding previous topological analyses, in which domain-averaged exchange-correlation energies (V(xc)), quantities defined in real space between each possible atom pair, hold the key. Exponential decay of V(xc) in non-metallic systems as the intercenter distance increases guarantees a well-defined hierarchy for all possible V(xc) values in a molecule. Herein, we show that extracting the set of atom pairs that display the largest V(xc) values in the hierarchy is equivalent to retrieving the molecular graph itself. Notably, domain-averaged exchange-correlation energies are transferable, and they can be used to calculate bond strengths. Fine-grained details resulted to be related to simple stereoelectronic effects. These ideas are demonstrated in a set of simple pilot molecules.

Binding Energies of First Row Diatomics in the Light of the Interacting Quantum Atoms Approach

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.

Electron number probability distributions for correlated wave functions

Efficient formulas for computing the probability of finding exactly an integer number of electrons in an arbitrarily chosen volume are only known for single-determinant wave functions [E. Cances et al., Theor. Chem. Acc. 111, 373 (2004)]. In this article, an algebraic method is presented that extends these formulas to the case of multideterminant wave functions and any number of disjoint volumes. The derived expressions are applied to compute the probabilities within the atomic domains derived from the space partitioning based on the quantum theory of atoms in molecules. Results for a series of test molecules are presented, paying particular attention to the effects of electron correlation and of some numerical approximations on the computed probabilities.

An electron number distribution view of chemical bonds in real space

Several key concepts of chemical bonding theory, such as electron pair sharing, polarity, charge transfer, multiple bonding, etc., are shown to be recovered from the statistical properties of multivariate electron number distribution functions. The latter are constructed from the real-space atomic partition provided by the quantum theory of atoms in molecules. We present the basic formalism and several exemplifying calculations.

Evolution of the Properties of AlnNn Clusters with Size

A global optimization of stoichiometric (AlN)(n) clusters (n = 1-25, 30, 35, ..., 95, 100) has been performed using the basin-hopping (BH) method and describing the interactions with simple and yet realistic interatomic potentials. The results for the smaller isomers agree with those of previous electronic structure calculations, thus validating the present scheme. The lowest-energy isomers found can be classified in three different categories according to their structural motifs: (i) small clusters (n = 2-5), with planar ring structures and 2-fold coordination, (ii) medium clusters (n = 6-40), where a competition between stacked rings and globular-like empty cages exists, and (iii) large clusters (n > 40), large enough to mix different elements of the previous stage. All the atoms in small and medium-sized clusters are in the surface, while large clusters start to display interior atoms. Large clusters display a competition between tetrahedral and octahedral-like features: the former lead to a lower energy interior in the cluster, while the latter allow for surface terminations with a lower energy. All of the properties studied present different regimes according to the above classification. It is of particular interest that the local properties of the interior atoms do converge to the bulk limit. The isomers with n = 6 and 12 are specially stable with respect to the gain or loss of AlN molecules.

First Principles Study of Neutral and Anionic (Medium-Size) Aluminum Nitride Clusters: AlnNn,n= 7−16

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.

Charge transfer, chemical potentials, and the nature of functional groups: answers from quantum chemical topology

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.

Pauling Resonant Structures in Real Space through Electron Number Probability Distributions

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.

Performance of the density matrix functional theory in the quantum theory of atoms in molecules

The generalization to arbitrary molecular geometries of the energetic partitioning provided by the atomic virial theorem of the quantum theory of atoms in molecules (QTAIM) leads to an exact and chemically intuitive energy partitioning scheme, the interacting quantum atoms (IQA) approach, that depends on the availability of second-order reduced density matrices (2-RDMs). This work explores the performance of this approach in particular and of the QTAIM in general with approximate 2-RDMs obtained from the density matrix functional theory (DMFT), which rests on the natural expansion (natural orbitals and their corresponding occupation numbers) of the first-order reduced density matrix (1-RDM). A number of these functionals have been implemented in the promolden code and used to perform QTAIM and IQA analyses on several representative molecules and model chemical reactions. Total energies, covalent intra- and interbasin exchange-correlation interactions, as well as localization and delocalization indices have been determined with these functionals from 1-RDMs obtained at different levels of theory. Results are compared to the values computed from the exact 2-RDMs, whenever possible.

Vibrotactile amplitude discrimination capacity parallels magnitude changes in somatosensory cortex and follows Weber's Law

In this study, we investigated the changes in perceptual metrics of amplitude discrimination that were observed in ten healthy human subjects with increasing intensities of stimulation. The ability to perceive differences in vibrotactile amplitude changed systematically with increasing stimulus magnitude (i.e., followed Weber's Law) in a near linear fashion (R (2) = 0.9977), and the linear fit determined by the amplitude discrimination task predicted the subjects' detection thresholds. Additionally, the perceptual metrics correlated well with observations from a previously reported study in which measures of SI cortical activity in non-human primates (squirrel monkeys) evoked by different amplitudes of vibrotactile stimulation were obtained (Simons et al. in BMC Neurosci 6:43, 2005). Stimuli were delivered simultaneously to two different skin sites (D2 and D3), enabling a method for the relatively rapid acquisition of the data. Stability and robustness of the measure, its rapid acquisition, and its apparent relationship with responses previously observed in SI cortex, led to the conclusion that deviations from the baseline values observed in the obtained perceptual metric could provide a useful indicator of cerebral cortical health.