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Since its first definition, back in 1990, the electron localization function (ELF) has settled as one of the most commonly employed techniques to characterize the nature of the chemical bond in real space. Although most of the work using the ELF has focused on the study of ground-state chemical reactivity, a growing interest has blossomed to apply these techniques to the nearly unexplored realm of excited states and photochemistry. Since accurate excited electronic states usually require to account appropriately for electron correlation, the standard single-determinant ELF formulation cannot be blindly applied to them, and it is necessary to turn to correlated ELF descriptions based on the two-particle density matrix (2-PDM). The latter requires costly wavefunction approaches, unaffordable for most of the systems of current photochemical interest. Here, we compare the exact, 2-PDM-based ELF results with those of approximate 2-PDM reconstructions taken from reduced density matrix functional theory. Our approach is put to the test in a wide variety of representative scenarios, such as those provided by the lowest-lying excited electronic states of simple diatomic and polyatomic molecules. Altogether, our results suggest that even approximate 2-PDMs are able to accurately reproduce, on a general basis, the topological and statistical features of the ELF scalar field, paving the way toward the application of cost-effective methodologies, such as time-dependent-Hartree-Fock or time-dependent density functional theory, in the accurate description of the chemical bonding in excited states of photochemical relevance.
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Partitions of the electronic energy such as that provided by the Interacting Quantum Atoms (IQA) approach have given valuable insights for numerous chemical systems and processes. Unfortunately, this kind of analysis may involve the integration of scalar fields over very irregular volumes, a condition which leads to a large and often prohibitive computational effort. These circumstances have limited the use of these energy partitions to systems comprising a few tens of atoms at most. On the other hand, semiempirical methods have proved useful in the study of systems of several thousands of atoms. Therefore, the goal of this work is to carry out partitions of the semiempirical method PM7 in compliance with the IQA approach. For this purpose, we computed one- and two-atomic energetic contributions whose sum equals the PM7 electronic energy. We illustrate how one might exploit the partition of electronic energies computed via the PM7 method by considering small organic and inorganic molecules and the energetics of individual hydrogen bond interactions within several water clusters which include (H2O)30, (H2O)50 and (H2O)100. We also considered the solvation of the amphiphilic caprylate anion to exemplify how to exploit the energy partition proposed in this paper. Overall, this investigation shows how the approach put forward herein might give further insights of the interactions occurring within complex systems in physical and biological chemistry.
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Resonance-assisted hydrogen bonds (RAHB) are intramolecular contacts that are characterised by being particularly energetic. This fact is often attributed to the delocalisation of π electrons in the system. In the present article, we assess this thesis via the examination of the effect of electron-withdrawing and electron-donating groups, namely -F, -Cl, -Br, -CF3, -N(CH3)2, -OCH3, -NHCOCH3 on the strength of the RAHB in malondialdehyde by using the Quantum Theory of Atoms in Molecules (QTAIM) and the Interacting Quantum Atoms (IQA) analyses. We show that the influence of the investigated substituents on the strength of the investigated RAHBs depends largely on its position within the π skeleton. We also examine the relationship between the formation energy of the RAHB and the hydrogen bond interaction energy as defined by the IQA method of wave function analysis. We demonstrate that these substituents can have different effects on the formation and interaction energies, casting doubts regarding the use of different parameters as indicators of the RAHB formation energies. Finally, we also demonstrate how the energy density can offer an estimation of the IQA interaction energy, and therefore of the HB strength, at a reduced computational cost for these important interactions. We expected that the results reported herein will provide a valuable understanding in the assessment of the energetics of RAHB and other intramolecular interactions.
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The analysis of the reaction force and its topology has provided a wide range of fruitful concepts in the theory of chemical reactivity over the years, allowing to identify chemically relevant regions along a reaction profile. The reaction force (RF), a projection of the Hellmann-Feynman forces acting on the nuclei of a molecular system onto a suitable reaction coordinate, is partitioned using the interacting quantum atoms approach (IQA). The exact IQA molecular energy decomposition is now shown to open a unique window to identify and quantify the chemical entities that drive or retard a chemical reaction. The RF/IQA coupling offers an extraordinarily detailed view of the type and number of elementary processes that take reactants into products, as tested on two sets of simple reactions.
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We explore herein the supramolecular interactions that control the crystalline packing in a series of fluorothiolate triphenylphosphine gold(I) compounds with the general formula [Au(SRF)(Ph3P)] in which Ph3P = triphenylphosphine and SRF = SC6F5, SC6HF4-4, SC6F4(CF3)-4, SC6H3F2-2,4, SC6H3F2-3,4, SC6H3F2-3,5, SC6H4(CF3)-2, SC6H4F-2, SC6H4F-3, SC6H4F-4, SCF3, and SCH2CF3. We use for this purpose (i) DFT electronic structure calculations and (ii) the quantum theory of atoms in molecules and the non-covalent interactions index methods of wave function analyses. Our combined experimental and computational approach yields a general understanding of the effects of ligand fluorination in the crystalline self-assembly of the examined systems, in particular, about the relative force of aurophilic contacts compared with other supramolecular interactions. We expect this information to be useful in the design of materials based on gold coordination compounds.
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The kinetic energy is the center of a controversy between two opposite points of view about its role in the formation of a chemical bond. One school states that a lowering of the kinetic energy associated with electron delocalization is the key stabilization mechanism of covalent bonding. In contrast, the opposite school holds that a chemical bond is formed by a decrease in the potential energy due to a concentration of electron density within the binding region. In this work, a topographic analysis of the Hamiltonian Kinetic Energy Density (KED) and its laplacian is presented to gain more insight into the role of the kinetic energy within chemical interactions. This study is focused on atoms, diatomic and organic molecules, along with their dimers. In addition, it is shown that the laplacian of the Hamiltonian KED exhibits a shell structure in atoms and that their outermost shell merge when a molecule is formed. A covalent bond is characterized by a concentration of kinetic energy, potential energy and electron densities along the internuclear axis, whereas a charge-shift bond is characterized by a fusion of external concentration shells and a depletion in the bonding region. In the case of weak intermolecular interactions, the external shell of the molecules merge into each other resulting in an intermolecular surface comparable to that obtained by the Non-covalent interaction (NCI) analysis.
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State-of-the-art chemical bonding analyses show that water clusters have a bifunctional catalytic role in the formation of H2SO4 in acid rain. The embedded H2O monomers mitigate the change in the chemical bonding scenario of the rate-limiting step, reducing thereby the corresponding activation energy in accordance with Hammond's postulate. We expect that the insights given herein will prove useful in the elucidation of the catalytic mechanisms of water in inorganic and organic aqueous chemistry.
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We analyzed non-additive effects in resonance assisted hydrogen bonds (RAHBs) in different ß-enolones, which are archetypal compounds of these types of interactions. For this purpose, we used (i) potential energy curves to compute the formation energy, ΔE, of the RAHBs of interest in different circumstances along with (ii) tools offered by quantum chemical topology, namely, the Quantum Theory of Atoms In Molecules (QTAIM) and the Interacting Quantum Atoms (IQA) electronic energy partition. We established the effect that a given H-bond exerts over ΔE associated with another RAHB, determining in this way the cooperativity or the anticooperativity of these interactions. The mesomeric structures and the QTAIM delocalisation indices are consistent with the determined cooperative or anticooperative character of two given RAHBs. The HB cooperativity and anticooperativity studied herein are directly reflected in the IQA interaction energy E, but they are modulated by the surrounding hydrocarbon chain. The IQA decomposition of ΔEcoop, a measure of the cooperativity between a pair of interacting RAHBs, indicates that the analyzed H-bond cooperative/anticooperative effects are associated with greater/smaller (i) strengthening of the pseudo-bicyclic structure of the compounds of interest and (ii) electron localisations with its corresponding changes in the intra and intermolecular exchange-correlation contributions to ΔE. Overall, we expect that this investigation will provide valuable insights into the interplay among hydrogen bonded atoms and the π system in RAHBs contributing in this way to the understanding of the general features of H-bonds.
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The electronic energy partition established by the Interacting Quantum Atoms (IQA) approach is an important method of wavefunction analyses which has yielded valuable insights about different phenomena in physical chemistry. Most of the IQA applications have relied upon approximations, which do not include either dynamical correlation (DC) such as Hartree-Fock (HF) or external DC like CASSCF theory. Recently, DC was included in the IQA method by means of HF/Coupled-Cluster (CC) transition densities (Chávez-Calvillo et al., Comput. Theory Chem. 2015, 1053, 90). Despite the potential utility of this approach, it has a few drawbacks, for example, it is not consistent with the calculation of CC properties different from the total electronic energy. To improve this situation, we have implemented the IQA energy partition based on CC Lagrangian one- and two-electron orbital density matrices. The development presented in this article is tested and illustrated with the H2 , LiH, H2 O, H2 S, N2 , and CO molecules for which the IQA results obtained under the consideration of (i) the CC Lagrangian, (ii) HF/CC transition densities, and (iii) HF are critically analyzed and compared. Additionally, the effect of the DC in the different components of the electronic energy in the formation of the T-shaped (H2 )2 van der Waals cluster and the bimolecular nucleophilic substitution between F(-) and CH3 F is examined. We anticipate that the approach put forward in this article will provide new understandings on subjects in physical chemistry wherein DC plays a crucial role like molecular interactions along with chemical bonding and reactivity. © 2016 Wiley Periodicals, Inc.