Relativistic (SR‐ZORA) quantum theory of atoms in molecules properties

The Quantum Theory of Atoms in Molecules (QTAIM) is used to elucidate the effects of relativity on chemical systems. To do this, molecules are studied using density‐functional theory at both the nonrelativistic level and using the scalar relativistic zeroth‐order regular approximation. Relativistic effects on the QTAIM properties and topology of the electron density can be significant for chemical systems with heavy atoms. It is important, therefore, to use the appropriate relativistic treatment of QTAIM (Anderson and Ayers, J. Phys. Chem. 2009, 115, 13001) when treating systems with heavy atoms. © 2016 Wiley Periodicals, Inc.     

Critical charges of simple coulomb molecular systems: One‐two electron case

We consider some Coulomb systems with several infinitely massive centers of charge Z and one or two electrons: (Z,e), (2Z,e), (3Z,e), (4Z,e), (2Z,e,e), and (3Z,e,e). It is shown that the physical, integer charges Z = 1,2,… do not play a distinguished role for the total energy and for the equilibrium configuration of a system, giving no indication of a charge quantization. By definition, a critical charge Z_cr for a given Coulomb system (nZ,e) or (nZ,e,e) is a charge which separates the domain of the existence of bound states from the domain of unbound states (the domain of stability), the continuum (the domain of instability). For all the above‐mentioned systems critical charges Z_cr as well as equilibrium geometrical configurations are found. Furthermore, an indication to a branch point singularity at Z = Z_cr with exponent 3/2 was obtained. It is demonstrated that in the domain of the existence the optimal geometrical configuration for both (nZ,e) at n = 2,3,4 and (nZ,e,e) at n = 2,3 corresponds to the Platonic body. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Theoretical study of one‐electron bonds in a series of high‐spin lithium–beryllium–hydrogen clusters: “Valence shell single‐electron repulsion” rule and electron localization function analysis

A series of high‐spin clusters containing Li, H, and Be in which the valence shell molecular orbitals (MOs) are occupied by a single electron has been characterized using ab initio and density functional theory (DFT) calculations. A first type (⁵Li₂, ⁿ⁺¹LiH_n+ (n = 2–5), ⁸Li₂H) possesses only one electron pair in the lowest MO, with bond energies of ～3 kcal/mol. In a second type, all the MOs are singly occupied, which results in highly excited species that nevertheless constitute a marked minimum on their potential energy surface (PES). Thus, it is possible to design a larger panel of structures (⁸LiBe, ⁷Li₂, ⁸Li, ⁴LiH⁺, ⁶BeH, ⁿ⁺³LiH (n = 3, 4), ⁿ⁺²LiH (n = 4–6), ⁸Li₂H, ⁹Li₂H, ²²Li₃Be₃ and ²²Li₆H), single‐electron equivalent to doublet “classical” molecules ranging from CO to C₆H₆. The geometrical structure is studied in relation to the valence shell single‐electron repulsion (VSEPR) theory and the electron localization function (ELF) is analyzed, revealing a striking similarity with the corresponding structure having paired electrons. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

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.     

Electron correlation in the interacting quantum atoms partition via coupled‐cluster lagrangian densities

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, H₂O, H₂S, 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 CH₃F 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.     

Tetravalent Oxygen and Sulphur Centres Mediated by Carborane Superacid: Theoretical Analysis

The tetravalent oxygen or sulphur centres, especially in H₄O²⁺ and H₄S²⁺ dications, were analysed experimentally and theoretically in various studies. Herein, we discuss stabilities of such centres in related H(CH₃)₃O²⁺ and H(CH₃)₃S²⁺ dications mediated by carborane superacid. The ωB97X-D/6-311++G(d,p) calculations were performed for a gas phase and for different solvents characterized by a wide range of dielectric constants for complexes of these dications with the conjugated base of H(CHB₁₁F₁₁) carborane superacid, CHB₁₁F₁₁⁻, which indicate that these complexes are linked by hydrogen bonds. The Quantum Theory of ‘Atoms in Molecules’ (QTAIM) approach is applied to characterize these interactions. DFT results show that tetravalent oxygen and sulphur structures are additionally stabilized by polar solvents.     

One‐, two‐, and three‐electron bonding: An “in vitro” theoretical study using noninteger nuclear charges evidences the crucial role of electronegativity in the strength of symmetrical bonds

Fictitious hydrogen atoms H*_A of variable nuclear charge 0.5 ≤ Z_A ≤ 2 (and thus of variable electronegativity) are used to study the intrinsic dependency of chemical bonding on electronegativity. Dissociation energy and equilibrium distance are reported for symmetrical 1‐, 2‐ and 3‐electron H*_AH*_A systems and 2‐electron dissymmetrical H*_A‐H ones. Dealing with symmetrical systems, the strongest two‐electron bonds are found for Z_A ≈ 1.2. Oneelectron and three‐electron strongest bonds occur respectively with low (ca. 0.7) and high (ca. 1.7) Z_A values and can become stronger than the corresponding 2‐electron system. Comparison with data on real systems leads to conclude that electronegativity is a prevailing atomic property in the control of the dissociation energy of symmetrical 1‐, 2‐ and 3‐electron bonds. A simplified mathematical model at Hartree‐Fock or Heitler‐London level with a minimal basis set reproduces these trends semi‐quantitatively and provides the overall shape of the dissociation curves. Finally some points are qualitatively discussed from MO analysis, which emphasize the dependence of the bonding/antibonding properties on the nucleus charge Z_A and their occupancy number. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

On the relationship between the one‐electron and Bohm's quantum potential

The one‐electron potential, derived from the electron density, is a three‐dimensional function, whereas Bohm's quantum potential depends on the spatial coordinates of all involved electrons. To analyze the relationship between the two potentials in the many‐electron case, first the dimensionality of the quantum potential needs to be reduced to match that of the one‐electron potential. A possible approach for such dimensionality reduction by calculating the expectation value of the quantum potential over all but one electron, using the factorization of the real part of the wave function into a marginal and conditional function is presented, and a relation between such three‐dimensional local quantum potential and the one‐electron potential is given. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Occupation numbers for atomic shells in direct space bounded by the maxima of the one‐electron potential

Atomic shells defined as wells of the one‐electron potential $\nabla^{2}\sqrt{\rho}/2\sqrt{\rho}$ bounded by successive maxima of this electron density function give reasonable electron numbers for the occupation of shells with empty d orbitals. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 83: 324–331, 2001     

A mechanism of the 1,3‐dipolar cycloaddition between the hydrogen nitryl HNO2 and acetylene HCCH: The electron localization function study on evolution of the chemical bonds

The reaction between the simplest nitro compound HNO₂ (hydrogen nitryl) and acetylene HCCH ‐ formally proceeding via 1,3‐dipolar cycloaddition ‐ has been studied by means of the B3LYP, MPW1K and MP2 methods. The energy barrier of 20.74 ÷ 32.91 kcal/mol is similar to ΔE_a of the NNO + HCCH process but is essentially larger than computed for the reactions of HCCH with fulminic acid (HCNO) and NNCH₂. Whole process is exothermic with the reaction energy: ?10.87 ÷ ?17.94 kcal/mol. An evolution of the chemical bonding has been analyzed by means of the Bonding Evolution Theory (BET) at the B3LYP/6‐31+G(d) and B3LYP/cc‐pVTZ levels. Two approximations of the reaction path have been considered, namely: the IRC and pseudo‐reaction paths. The reaction requires five steps and seven catastrophes of the fold and cusp type. A different effect of first fold catastrophe has been noticed. At the B3LYP/6‐31+G(d) level one of two nonbonding V_i=1,2(N) attractors is annihilated (F), meanwhile at B3LYP/cc‐pVTZ new V(N) attractor is created (F^?). The chemical bonds are not formed/broken in TS. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

The Role of One‐Electron Reduction of Lipid Hydroperoxides in Causing DNA Damage

The in vivo metabolism of plasma lipids generates lipid hydroperoxides that, upon one‐electron reduction, give rise to a wide spectrum of genotoxic unsaturated aldehydes and epoxides. These metabolites react with cellular DNA to form a variety of pre‐mutagenic DNA lesions. The mechanisms of action of the radical precursors of these genotoxic electrophiles are poorly understood. In this work we investigated the nature of DNA products formed by a one‐electron reduction of (13S)‐hydroperoxy‐(9Z,11E)‐octadecadienoic acid (13S‐HPODE), a typical lipid molecule, and the reactions of the free radicals thus generated with neutral guanine radicals, G(?H)^.. A novel approach was devised to generate these intermediates in solution. The two‐photon‐induced ionization of 2‐aminopurine (2AP) within the 2′‐deoxyoligonucleotide 5′‐d(CC[2AP]TCGCTACC) by intense nanosecond 308 nm excimer laser pulses was employed to simultaneously generate hydrated electrons and radical cations 2AP^.+. The latter radicals either in cationic or neutral forms, rapidly oxidize the nearby G base to form G(?H)^.. In deoxygenated buffer solutions (pH 7.5), the hydrated electrons rapidly reduce 13S‐HPODE and the highly unstable alkoxyl radicals formed undergo a prompt β‐scission to pentyl radicals that readily combine with G(?H)^.. Two novel guanine products in these oligonucleotides, 8‐pentyl‐ and N²‐pentylguanine, were identified. It is shown that the DNA secondary structure significantly affects the ratio of 8‐pentyl‐ and N²‐pentylguanine lesions that changes from 0.9:1 in single‐stranded, to 1:0.2 in double‐stranded oligonucleotides. The alkylation of guanine by alkyl radicals derived from lipid hydroperoxides might contribute to the genotoxic modification of cellular DNA under hypoxic conditions. Thus, further research is warranted on the detection of pentylguanine lesions and other alkylguanines in vivo.     

Formation of o‐Phenylenediamine Oligomers and their Self‐Assembly into One‐Dimensional Structures in Aqueous Medium

Summary: Uniform one‐dimensional (1D) structures of o‐phenylenediamine (oPD) oligomers are obtained by direct mix of AgNO₃ and oPD aqueous solutions at room temperature. The formation of the 1D structures involves two stages: (1) oxidation of oPD by AgNO₃, yielding individual oPD oligomers; and (2) self‐assembly of the oligomers, forming the 1D structures. Upon decreasing medium pH, the 1D structures can break‐apart to form individual oligomers, or vice versa. It is also found that both the concentration and molar ratio of reactants can influence the morphology of the structures thus formed.

Schematic illustration of the formation mechanism of 1D structures from oPD and AgNO₃, and energy‐dispersed spectrum of the precipitate.     

Simultaneous evaluation of one‐electron reducing systems and radical reactions in cells by nitroxyl biradical as probe

In the present study, a novel probe for the simultaneous evaluation of one‐electron reducing systems (electron transport chain) and one‐electron oxidizing systems (free radical reactions) in cells by electron chemical detection was developed. Six‐membered cyclic nitroxyl radicals (2,2,6,6‐tetramethylpiperidine‐1‐oxyl; TEMPO series) are sensitive to one‐electron redox systems, generating the hydroxylamine form [TEMPO(H)] via one‐electron reduction, and the secondary amine form [TEMPO(N)] via one‐electron oxidation in the presence of thiols. In contrast, the sensitivities of five‐membered cyclic nitroxyl radicals (2,2,5,5‐tetramethylpyrrolidine‐1‐oxyl; PROXYL series) to the one‐electron redox systems are comparatively low. The electron chemical detector can detect 2,2,6,6‐tetramethylpiperidine‐1‐oxyl (TEMPO), TEMPO(H) and PROXYL but not TEMPO(N). Therefore, nitroxyl biradical, TEMPO‐PROXYL, as a probe for the evaluation of one‐electron redox systems was employed. TEMPO‐PROXYL was synthesized by the conjunction of 4‐amino‐TEMPO with 3‐carboxyl‐PROXYL via the conventional dicyclohexyl carbodiimide reaction. TEMPO‐PROXYL, TEMPO(H)‐PROXYL and TEMPO(N)‐PROXYL were simultaneously quantified by HPLC with Coularray detection. Calibration curves for the quantification of TEMPO‐PROXYL, TEMPO(H)‐PROXYL and TEMPO(N)‐PROXYL were linear in the range from 80 nm to 80 μm , and the lowest quantification limit of each molecule was estimated to be <80 nm . The relative standard deviations at 0.8 and 80 μm were within 10% (n = 5). Copyright © 2015 John Wiley & Sons, Ltd.     

Energy decomposition in the topological theory of atoms in molecules and in the linear combination of atomic orbitals formalism: a note

 It is shown that the molecular energy calculated at the self-consistent-field level can be strictly expressed as a sum of one- and two-atom energy components in the framework of Bader's topological theory of atoms in molecules (AIM). The expressions of our recent “chemical energy component analysis” can be obtained from the AIM ones as some linear combination of atomic orbitals mappings of the integrations over the atomic basins. Received: 15 June 2000 / Accepted: 4 October 2000 / Published online: 19 January 2001     

One‐bond 13C–13C coupling constants in alkyl‐substituted cyclopropenes: experimental and theoretical studies

Measurements of one‐bond carbon–carbon coupling constants, ¹J(C, C), were performed for two series of compounds, alkyl‐substituted cyclopropenes and cyclopropanes. The experimental data were complemented by a set of DFT‐calculated J couplings for the parent cyclopropene ( 1 ), its methyl and silyl derivatives and, additionally, for 1‐methylcyclobutene ( 3 ), 1‐methylcyclopentene ( 4 ) and 1‐methylcyclohexene ( 5 ) and good agreement was observed between the experimental and the calculated data; all the trends are perfectly maintained, including a dramatic decrease in the couplings across endocyclic single bonds in cyclopropene and its derivatives, and a significant decrease in the corresponding couplings in cyclobutene. Using the data obtained, the s characters of the carbon hybrid orbitals involved in the formation of the cyclopropene were calculated. The results clearly show that the ring closure and the related strain exerted upon the cyclopropene molecule only slightly disturb the electron structure of the double bond. The s character of the corresponding carbon orbital is 0.314 in cyclopropene vs the theoretical value of 0.333 in ethene. This is at variance with the endo‐ and exocyclic single bonds, where the s characters of the orbitals forming the endocyclic single bonds are much smaller than those of the bonds in the open‐chain compounds, i.e. 0.229 (C‐1 and/or C‐2) and 0.166 (C‐3). The s values calculated for the exocyclic CH bonds are 0.334 for C‐3 and 0.456 for C‐1 and/or C‐2. Copyright © 2002 John Wiley & Sons, Ltd.     

Electronic fluxes during diels‐alder reactions involving 1,2‐benzoquinones: mechanistic insights from the analysis of electron localization function and catastrophe theory

By means of the joint use of electron localization function (ELF) and Thom's catastrophe theory, a theoretical analysis of the energy profile for the hetero‐Diels‐Alder reaction of 4‐methoxy‐1,2‐benzoquinone 1 and methoxyethylene 2 has been carried out. The 12 different structural stability domains obtained by the bonding evolution theory have been identified as well as the bifurcation catastrophes (fold and cusp) responsible for the changes in the topology of the system. This analysis permits finding a relationship between the ELF topology and the evolution of the bond breaking/forming processes and electron pair rearrangements through the reaction progress in terms of the different ways of pairing up the electrons. The reaction mechanism corresponds to an asynchronous electronic flux; first, the O1? C5 bond is formed by the nucleophilic attack of the C5 carbon of the electron rich ethylene 2 on the most electrophilically activated carbonyl O1 oxygen of 1 , and once the σ bond has been completed, the formation process of the second O4? C6 bond takes place. In addition, the values of the local electrophilicity and local nucleophilcity indices in the framework of conceptual density functional theory accounts for the asychronicity of the process as well as for the observed regioselectivity. © 2012 Wiley Periodicals, Inc.