QTAIM and stress tensor interpretation of the (H2O)5 potential energy surface

Using the quantum theory of atoms in molecules a near complete combined directed spanning quantum topology phase diagram (QTPD) was constructed from the nine (H₂O)₅ reaction‐pathways and five unique Poincaré–Hopf solutions that were found after an extensive search of the MP2 potential energy surface. Two new energy minima that were predicted from earlier work are found and include the first (H₂O)₅ conformer with a 3‐D_QT quantum topology. The stress tensor Poincaré–Hopf relation indicated a preference for 2‐D_QT (H₂O)₅ topologies as well as the presence of coupling between shared‐shell O? H BCPs to the hydrogen‐bond BCPs that share an H NCP. The complexity of the near complete combined QTPD was explained in terms of the O…O bonding interactions that were found in six of the nine (H₂O)₅ reaction‐pathways and for all points of the combined QTPD. The stabilizing role of the O…O bonding interactions from the values of the total local energy density was explored. © 2016 Wiley Periodicals, Inc.     

Quantum topology phase diagrams for the cis‐ and trans‐isomers of the cyclic contryphan‐Sm peptide

Within the quantum theory of atoms in molecules (QTAIM) framework we present a quantum topology phase diagram (QTPD) using the Poincaré–Hopf relation of a total of 17 all new QTAIM topologies of the cis‐ and trans‐isomers of the cyclic contryphan‐Sm peptide. The resultant QTPD consists of separate regions for the cis‐ and trans‐isomers that only overlap for topologies associated with the lowest energy minima of the cis‐ and trans‐isomers. We determine the QTAIM topologies of 29 “missing” isomers. A new, contracted formulation of the QTPD is presented, this contracted formulation includes the interamino acid bond critical points (BCPs) that link together the amino acid units, the disulphide bridge “pivot” BCP and side chain bonding interactions. The seven interamino acid BCPs linking the amino acid units coincide with the so‐called peptide backbone, the conventional qualitative approach to reduce the complexity of the peptide. We expand the interpretation of ellipticity to include the associated eigenvectors and find that higher values of the ellipticity ? are associated with a greater preference to conserve folding states. We quantify previous qualitative findings that suggested the disulfide bond is central to the folding behavior of the cyclic contryphan‐Sm peptide and why the cis‐isomer is the major form of the cyclic contryphan‐Sm peptide. © 2014 Wiley Periodicals, Inc.     

An introduction to analysis of Rényi complexity ratio of quantum states for central potential

Rényi complexity ratio of two density functions is introduced for three and multidimensional quantum systems. Localization property of several density functions are defined and five theorems about near continuous property of Rényi complexity ratio are proved by Lebesgue measure. Some properties of Rényi complexity ratio are demonstrated and investigated for different quantum systems. Exact analytical forms of Rényi entropy, Rényi complexity ratio, statistical complexities based on Rényi entropy for integral order have been presented for solutions of pseudoharmonic and a family of isospectral potentials. Some properties of Rényi complexity ratio are verified for six diatomic molecules (CO, NO, N₂, CH, H₂, and ScH) and for other quantum systems.     

Vibrational–rotational energies of all H2 isotopomers using Monte Carlo methods

Using variational Monte Carlo techniques, we have computed several of the lowest rotational–vibrational energies of all the hydrogen molecule isotopomers (H₂, HD, HT, D₂, DT, and T₂). These calculations do not require the excited states to be explicitly orthogonalized. We have examined both the usual Gaussian wave function form as well as a rapidly convergent Padé form. The high‐quality potential energy surfaces used in these calculations are taken from our earlier work and include the Born–Oppenheimer energy, the diagonal correction to the Born–Oppenheimer approximation, and the lowest‐order relativistic corrections at 24 internuclear points. Our energies are in good agreement with those determined by other methods. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Quantum topological resolution of catalyst proficiency

The purpose of this exploratory investigation is to characterize, contrast, and explain the differences between efficient Ni(π‐allyl)₂ and inefficient Pd(π‐allyl)₂ systems in the catalyzed cross‐coupling of alkanes. Within the framework of the quantum theory of atoms in molecules, we have created quantum topology phase diagrams (QTPDs) for nonisomeric species by the creation of aggregate‐isomers; simple sum rules are introduced to ensure that the Poincaré‐Hopf relation is obeyed. We show that the catalyzed reaction cycles can be represented as a directed QTPD where each species of the main reaction cycle forms a closed loop. The topological position of the unwanted side products relative to the main reaction cycle for each catalyst is also considered. We find the more efficient Ni(π‐allyl)₂ catalyst produces a reaction cycle on the QTPD that contains no “missing” topologies, preferentially proceeding to desired product at 94% yield, while avoiding wasteful side‐product pathways, disconnected from the major pathway by “missing” topologies. The converse is true for the less efficient Pd(π‐allyl)₂ catalyst, whose reaction pathway markedly bifurcates to final yields of 56% and 44% for product and side‐product, respectively. We subsequently used our nearest neighbor ring‐critical point approach to show that the species of the main reaction cycle of the efficient Ni(π‐allyl)₂ catalyst facilitates the desired chemical transformation whilst more effectively barring the formation of unwanted side product, with respect to the inefficient Pd(π‐allyl)₂ catalyst. The findings from the QTPD analysis are in agreement with traditional energetic‐barrier interpretations of reaction pathway preference. © 2015 Wiley Periodicals, Inc.     

A Bond Path and an Attractive Ehrenfest Force Do Not Necessarily Indicate Bonding Interactions: Case Study on M2X2 (M=Li,Na, K; X=H,OH, F,Cl)

Interactions in dimers of model alkali metal derivatives M₂X₂ (M=Li or Na or K; X=H or F, Cl, OH) are studied in the frame of the quantum theory of atoms in molecules (QTAIM) using the interacting quantum atoms approach (IQA). Contrary to opinion prevalent in QTAIM studies, the interaction between two anions linked by a bond path is demonstrated to be strongly repulsive. One may therefore say that a bond path does not necessarily indicate bonding interactions. The interactions between two anions or two cations that are not linked by a bond path are also strongly repulsive. The repulsive anion–anion and cation–cation interactions are outweighed by much stronger attractive anion–cation interactions, and the model molecules are therefore in a stable state. The attractive Ehrenfest forces (calculated in the frame of the QTAIM) acting across interatomic surfaces shared by anions in the dimers do not reflect the repulsive interactions between anions. Probable reasons of this disagreement are discussed. The force exerted on the nucleus and the electrons of a particular atom by the nucleus and the electrons of any another atom in question is proposed. It is assumed that this force unambiguously exposes whether basins of two atoms are attracted or repelled by each other in a polyatomic molecule.     

Embedding scaling relations in Padé approximants: Detours to tame divergent perturbation series

A divergent perturbation series is known to yield very unreliable results for observables even at moderate coupling strengths. One of the most popular techniques in handling such series is to express them as rational functions, but it is often faithful only for small coupling. We outline here how one can gain considerable advantages in the large‐coupling regime by properly embedding known asymptotic scaling relations for selected observables during construction of the aforesaid Padé approximants. Three new bypass routes are explored in this context. The first approach involves a weighted geometric mean of two neighboring PA. The second idea is to consider series for specific ratios of observables. The third strategy is to express observables as functionals of the total energy in the form of series expansions. Symanzik's scaling relation, and the virial and Hellmann–Feynman theorems, are used at appropriate places to aid each of the strategies. Pilot calculations on the ground‐state perturbation series of certain observables for the quartic anharmonic oscillator problem reveal readily the benefit and novelty. © 2012 Wiley Periodicals, Inc.     

On the hydrogen atom beyond the Born–Oppenheimer approximation

Recently a new formulation of quantum mechanics has been suggested which is based on the concept of signed particles, that is, classical objects provided with a position, a momentum and a sign simultaneously. In this article, we comment on the plausibility of simulating atomic systems beyond the Born–Oppenheimer approximation by means of the signed particle formulation of quantum mechanics. First, to show the new perspective offered by this new formalism, we provide an example studying quantum tunnelling through a simple Gaussian barrier in terms of the signed particle formulation. Then, we perform a direct simulation of the hydrogen atom as a full quantum two‐body system, showing that the formalism can be a very promising tool for first‐principle‐only quantum chemistry.     

Metal–organic framework of amine‐MIL‐53(Al) as active and reusable liquid‐phase reaction inductor for multicomponent condensation of Ugi‐type reactions

Metal–organic framework of NH₂‐MIL‐53(Al), with coordinative unsaturated aluminium sites, has been shown to be active in the Groebke–Blackburn–Bienaymé multicomponent coupling reaction based on Ugi‐type amine and aldehyde condensation over isocyanide and then a cyclization process. Interestingly this reaction occurred under solvent‐free conditions with high yield, in which the NH₂‐MIL‐53(Al) could be recovered and reused for five reaction cycles, giving a total turnover number of 455.     

Synthesis,Spectroscopy, Nonlinear Optics,and Theoretical Investigations of Thienylethynyl Octopoles with a Tunable Core

We have synthesized three new molecules that have three thienylethynyl arms substituting a central benzene core and different electron donor/acceptor groups in the three remaining phenyl positions. The absorption, fluorescence, phosphorescence, and transient triplet–triplet spectra are analyzed in the light of the electronic structure of the ground and excited states obtained from quantum‐chemical calculations. From the above, the relevant photophysical data (including quantum yields, lifetimes, and rate constants) could be derived. It was found that the major deactivation pathway is internal conversion, which competes with the fluorescence and intersystem crossing processes. For the three investigated compounds, we provide convincing theoretical support corroborating these findings and further conclusions based on the theoretical information obtained. These molecules are one of the very few cases in which the depolarization ratios, obtained from the NLO optical measurements, clearly reflect the octopolar configuration. Molecular hyperpolarizabilities have been measured and display a typical dependence on the donor–acceptor substitution pattern.     

Bounding the extrapolated correlation energy using Padé approximants

We present a rigorous strategy, based on Stieltjes series and Padé approximants, to obtain suitable bounds for extrapolation of the quantum chemical correlation energy. Computational tests are performed for the second‐order Møller–Plesset (MP2) correlation energy, and the bounds obtained are tight enough for practical calculational purposes: The associated error in most cases is much less than 1 kcal/mol. The bounds presented here are also shown to be rigorous for functional forms that represent a wide variety of methods in quantum chemistry and hence may be used in extrapolating a wide range of expressions, some of them yielding significant computational advantages compared to traditional techniques. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 79: 222–234, 2000     

Theoretical Characterization of Charge Transport in One‐Dimensional Collinear Arrays of Organic Conjugated Molecules

A great deal of interest has recently focused on host–guest systems consisting of one‐dimensional collinear arrays of conjugated molecules encapsulated in the channels of organic or inorganic matrices. Such architectures allow for controlled charge and energy migration processes between the interacting guest molecules and are thus attractive in the field of organic electronics. In this context, we characterize here at a quantum‐chemical level the molecular parameters governing charge transport in the hopping regime in 1D arrays built with different types of molecules. We investigate the influence of several parameters (such as the symmetry of the molecule, the presence of terminal substituents, and the molecular size) and define on that basis the molecular features required to maximize the charge carrier mobility within the channels. In particular, we demonstrate that a strong localization of the molecular orbitals in push–pull compounds is generally detrimental to the charge transport properties.     

Sequence‐Mandated,Distinct Assembly of Giant Molecules

Although controlling the primary structure of synthetic polymers is itself a great challenge, the potential of sequence control for tailoring hierarchical structures remains to be exploited, especially in the creation of new and unconventional phases. A series of model amphiphilic chain‐like giant molecules was designed and synthesized by interconnecting both hydrophobic and hydrophilic molecular nanoparticles in precisely defined sequence and composition to investigate their sequence‐dependent phase structures. Not only compositional variation changed the self‐assembled supramolecular phases, but also specific sequences induce unconventional phase formation, including Frank–Kasper phases. The formation mechanism was attributed to the conformational change driven by the collective hydrogen bonding and the sequence‐mandated topology of the molecules. These results show that sequence control in synthetic polymers can have a dramatic impact on polymer properties and self‐assembly.     

Ion‐Mobility Mass Spectrometry for the Rapid Determination of the Topology of Interlocked and Knotted Molecules

A rapid screening method based on traveling‐wave ion‐mobility spectrometry (TWIMS) combined with tandem mass spectrometry provides insight into the topology of interlocked and knotted molecules, even when they exist in complex mixtures, such as interconverting dynamic combinatorial libraries. A TWIMS characterization of structure‐indicative fragments generated by collision‐induced dissociation (CID) together with a floppiness parameter defined based on parent‐ and fragment‐ion arrival times provide a straightforward topology identification. To demonstrate its broad applicability, this approach is applied here to six Hopf and two Solomon links, a trefoil knot, and a [3]catenate.     

Spectroscopical UV–Vis implications of an intramolecular η2–Mg coordination in bacteriochlorophyll–a from the Fenna–Matthews–Olson complex

Chlorophylls and their related compounds prominently feature a Mg²⁺ ion in the center of a porphyrine, with an intermolecular fifth coordination usually observed to place the ion out of the macrocyclic plane. Herein, we assess the role of a potential intramolecular η²–(C = C)Mg interaction and compare it to the intermolecular coordination from the Hystidine groupt to Mg²⁺ for Bacterichlorophyll–a (Bchl–a), the main photosynthetic pigment in the Fenna–Matthews–Olson complex present in green and purple bacteria. The influence of this fifth coordination on the UV‐Vis spectroscopy (CAM‐B3LYP/cc‐pVDZ), and the concomitant change in geometry around Mg in Bchl–a from planar to pyramidal is assessed by the quantum theory of atoms in molecules based non–covalent interactions scheme and through energetic analysis via natural bond orbital population methods at the M06‐2X/cc‐pVDZ and compared to the reference multi–hapto compound, magnesocene, Cp₂Mg.     

Pillararene Host–Guest Complexation Induced Chirality Amplification: A New Way to Detect Cryptochiral Compounds

The contradiction between the rising demands of optical chirality sensing and the failure in chiral detection of cryptochiral compounds encourages researchers to find new methods for chirality amplification. Inspired by planar chirality and the host–guest recognition of pillararenes, we establish a new concept for amplifying CD signals of cryptochiral molecules by pillararene host–guest complexation induced chirality amplification. The planar chirality of pillararenes is induced and stabilized in the presence of the chiral guest, which makes the cryptochiral molecule detectable by CD spectroscopy. Several chiral guests are selected in these experiments and the mechanism of chiral amplification is studied with a non‐rotatable pillararene derivative and density functional theory calculations. We believe this work affords deeper understanding of chirality and provides a new perspective for chiral sensing.     

Fully polarizable QM/MM calculations: An application to the nonbonded iodine–oxygen interaction in dimethyl‐2‐iodobenzoylphosphonate

The compound dimethyl‐2‐iodobenzoylphosphonate is unusual in that it forms well‐ordered crystals that clearly show short iodine‐oxygen interactions in which both the iodine and the oxygen are in their normal oxidation states. These interactions were studied using a new hybrid quantum mechanical–molecular mechanical approach that employs a polarizable molecular mechanics component. The electric field at the molecular mechanics atoms was calculated from a distributed multipole expansion of the wave function; this induced dipoles on the molecular mechanics atoms. The electrostatic potential in a spherical shell around the induced dipoles was reproduced through induced charges on the atomic center and those bonded to it using an analytical (rather than numerical) procedure. The new atomic charges (induced charges plus permanent charges) were then able to interact with the quantum mechanical entity and polarize the wave function. The procedure was iterated to convergence. The calculations show that the iodine atom becomes more positive in the crystal environment (modeled by a chain of three molecules of dimethyl‐2‐iodobenzoylphosphonate). Thus, while the cooperative effects of the crystal environment may not be the only feature stabilizing this unusual interaction, they do play a significant role in reducing the otherwise unfavourable iodine–oxygen monopole–monopole interaction. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 478–482, 2000     

Local hydrodynamics of solvent near diffusing dendrimers: A test of the new Stokes–Einstein relation

We have reported a new Stokes–Einstein relation (SER) for size determination and tested it by different nanoparticles. We assumed that the breakdown for SER results from local increases in viscosity. Here we investigate hydrodynamics of solvent near dendrimers to further test generality of our new theory. We discuss simulations of dendrimers in comparison to nanoparticles, experimental data on dendrimers from literature, and our theory. Local viscosity and local diffusivity of solvent near dendrimers are estimated by persistence times and exchange times, respectively. We find that the local dynamics of solvent near dendrimers of low density stay almost the same as that of bulk solvent. While the motions of solvent particles slow down near dendrimers of high density. This is similar with changes in local dynamics of solvent near nanoparticles. According to the causes we proposed for the deviation of SER, this is consistent with our findings that the SER works for the dendrimers of low density, while it fails for the dendrimers of high density. The new SER is then tested to predict size of the dendrimers accurately. Taking this together with the results for the nanoparticles, we believe that the new theory is general. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55, 1380–1392