On normalized Laplacians,multiplicative degree-Kirchhoff indices,and spanning trees of the linear [n]phenylenes and their dicyclobutadieno derivatives

Let be the molecular graph of the linear [n] phenylene with n hexagons and n − 1 squares, and let be the graph obtained by attaching four-membered rings to the terminal hexagons of . In this article, the normalized Laplacian spectrum of consisting of the eigenvalues of two symmetric tridiagonal matrices of order 3n is determined. An explicit closed-form formula of the multiplicative degree-Kirchhoff index (respectively the number of spanning trees) of is derived. Similarly, explicit closed-form formulas of the multiplicative degree-Kirchhoff index and the number of spanning trees of are obtained. It is interesting to see that the multiplicative degree-Kirchhoff index of (respectively ) is approximately to one half of its Gutman index.     

On the normalized Laplacian of Möbius phenylene chain and its applications

Let denote a molecular graph of linear [n] phenylene with n hexagons and n squares, and let the Möbius phenylene chain be the graph obtained from the by identifying the opposite lateral edges in reversed way. Utilizing the decomposition theorem of the normalized Laplacian characteristic polynomial, we study the normalized Laplacian spectrum of , which consists of the eigenvalues of two symmetric matrices ℒ _R and ℒ _Q of order 3n. By investigating the relationship between the roots and coefficients of the characteristic polynomials of the two matrices above, we obtain an explicit closed-form formula of the multiplicative degree-Kirchhoff index as well as the number of spanning trees of . Furthermore, we determine the limited value for the quotient of the multiplicative degree-Kirchhoff index and the Gutman index of .     

Is it possible to synthesize bulk salt compounds?

The existence and stability of bulk salt compounds are theoretically investigated in this study. This undertaking is carried out to address the following challenge: synthesizing a bulk salt compound containing a noble gas lighter than Kr. The reliability of theoretical calculations on systems is assessed by benchmark calculations of the well-known salt. In the benchmark calculations, a two-pronged evaluation strategy, including direct and indirect evaluation methods, is used to theoretically investigate the spectroscopic constants of cation and the existence and stability of the salt. The validity of the theoretical calculation methods in the benchmark calculations of salt allows us to adopt a similar methodology to effectively predict the existence and stability of salt compounds. Calculations based on the Born-Haber cycle using estimated lattice energies and some necessary ancillary thermochemical data show that salt compounds can be synthesized, and their upper-limit stable temperatures are estimated to be −237.589, −197.76, and −80.539°C. The salt compound is the most promising candidate. Calculations also show that the salt compounds cannot be stabilized.     

Exponentially correlated Hylleraas-configuration interaction studies of atomic systems. II. Non-relativistic energies of the 1 through 6 states of the Li+ ion

The exponentially correlated Hylleraas-configuration interaction wave function (E-Hy-CI) is a generalization of the Hylleraas-configuration interaction (Hy-CI) in which the single of an Hy-CI wave function is generalized to the generic type . This type of correlation has the right behavior both in the vicinity of the cusp and as goes to infinity; this work shows that wave functions containing both linear and exponential factors converge more rapidly than either one alone for low-lying excited states of ¹S symmetry. E-Hy-CI variational calculations with up to 8568 configurations lead to a nonrelativistic energy of ?7.2799 1341 2669 3059 6491 6759 hartree for the 1 ¹S ground state of the Li+ ion.     

Extremal Wiener and Kirchhoff indices of globular caterpillars

The Wiener and Kirchhoff indices of a graph G are two of the most important topological indices in mathematical chemistry. A graph G is called to be a globular caterpillar if G is obtained from a complete graph K _s with vertex set {v₁,v₂,…, v _s} by attaching n _i pendent edges to each vertex v _i of K _s for some positive integers s and n₁,n₂,…,n _s, denoted by . Let be the set of globular caterpillars with n vertices (). In this article, we characterize the globular caterpillars with the minimal and maximal Wiener and Kirchhoff indices among , respectively.     

DFT and CIS(D) theoretical study on the ground and excited states of pentanitrogen cation

Different isomers of N₅⁺ were modeled at DFT(PBE0)/aug-cc-pV(Q + d)Z, and their ground(transition) state characteristics were assessed through frequency calculations. Single-point energies were accomplished at PBE0/aug-cc-pV(5 + d)Z. Nonlinear optical susceptibilities (NLO) of isomers were accomplished using Firefly, while the linear optical invariant was examined using the finite-field method, Firefly, and modified dipole field tensor in the presence of two different screening factors. The excited states, singlets and triplets, of were modeled at the CIS and CIS(D) and then their optical parameters were estimated at TDFT(PBE0)/aug-cc-pV(Q + d)Z using Firefly. The singlet is found the most stable isomer, with the inversional rate constant larger than that of the Cs isomer and high energy barrier with the triplet counterpart. Isomers 2 , 3 , and 4 are found local minima, while 5 and 6 are saddle points: transition states between equivalent invertomers. Energy calculations of the singlet and triplet isomers were in excellent agreement with the literature. An excellent correlation is found between the average polarizability and the impulse factor. Substantial variations were found between the singlet and triplet excited states in terms of energy, geometry, and optical properties from one side and with from the other side. Reactivity indices showed that N1 and N5 are the optimum nucleophilic and electrophilic reactivity sites.     

Catalytic Reaction Mechanism of Bacterial GH92 α-1,2-Mannosidase: A QM/MM Metadynamics Study

The catalytic mechanism of a -dependent family 92 -mannosidase, which is abundantly present in human gut flora and malfunctions leading to the lysosomal storage disease α-mannosidosis, has been investigated using quantum mechanics/molecular mechanics and metadynamics methods. Computational efforts show that the enzyme follows a conformational itinerary of and the ion serves a dual purpose, as it not only distorts the sugar ring but also plays a crucial role in orchestrating the arrangement of catalytic residues. This orchestration, in turn, contributes to the facilitation of conformers for the ensuing reaction. This mechanistic insight is well-aligned with the experimental predictions of the catalytic pathway, and the computed energies are of the same order of magnitude as the experimental estimations. Hence, our results extend the mechanistic understanding of glycosidases.     

Photoionization Bands of Cyanogen: Multi-Mode Vibronic Coupling and Renner-Teller Effects

Multi-mode vibronic coupling in the , , and electronic states of Cyanogen radical cation (C N ) is investigated with the aid of ab initio quantum chemistry and first principles quantum dynamics methods. The electronic degenerate states of Π symmetry of C N undergo Renner-Teller (RT) splitting along degenerate vibrational modes of π symmetry. The RT split components form symmetry allowed conical intersections with those from nearby RT split states or with non-degenerate electronic states of Σ symmetry. A parameterized vibronic Hamiltonian is constructed using standard vibronic coupling theory in a diabatic electronic basis and symmetry rules. The parameters of the Hamiltonian are derived from ab initio calculated adiabatic electronic energies. The vibronic spectrum is calculated, assigned and compared with the available experimental data. The impact of various electronic coupling on the vibronic structure of the spectrum is discussed.     

Size Evolution of Photoabsorption Spectra of Small Clusters: A Computational Study

Photoabsorption spectra of clusters, N=5–9, have been calculated using a diatomics-in-molecules like electronic structure model and a path-integral Monte Carlo sampling method. A qualitative change in the calculated spectra has been observed at N=9, which has been interpreted in terms of a structural transformation in the clusters consisting in a transition from trimer-like ionic cores observed for N≤7 to dimer-like ionic cores prevailing in through an intermediate state (comparable abundances of both types of ionic cores) observed in . The calculated spectra have been thoroughly compared with an earlier calculation on , , and reported from our group and data available for the same cluster sizes from an experiment.     

Oxidation of methylamine

A detailed chemical kinetic model for oxidation of methylamine has been developed, based on theoretical work and a critical evaluation of data from the literature. The rate coefficients for the reactions of CHNH + O CHNH / CHNH + HO, CHNH + H CH + NH, CHNH CHNH, and CHNH + O CHNH + HO were calculated from ab initio theory. The mechanism was validated against experimental results from batch reactors, flow reactors, shock tubes, and premixed flames. The model predicts satisfactorily explosion limits for CHNH and its oxidation in a flow reactor. However, oxidation in the presence of nitric oxide, which strongly promotes reaction at lower temperatures, is only described qualitatively. Furthermore, calculated flame speeds are higher than reported experimental values; the model does not capture the inhibiting effect of the NH group in CHNH compared to CH. More work is desirable to confirm the products of the CHNH + NO reaction and to look into possible pathways to NH in methylamine oxidation.     

Study on the normalized Laplacian of a penta-graphene with applications

Let L _n denote a linear pentagonal chain with 2n pentagons. The penta-graphene (penta-C), denoted by R _n is the graph obtained from L _n by identifying the opposite lateral edges in an ordered way, whereas the pentagonal Möbius ring is the graph obtained from the L _n by identifying the opposite lateral edges in a reversed way. In this paper, through the decomposition theorem of the normalized Laplacian characteristic polynomial and the relationship between its roots and the coefficients, an explicit closed-form formula of the multiplicative degree-Kirchhoff index (resp. Kemeny's constant, the number of spanning trees) of R _n is obtained. Furthermore, it is interesting to see that the multiplicative degree-Kirchhoff index of R _n is approximately of its Gutman index. Based on our obtained results, all the corresponding results are obtained for .     

Real-Space Interpretation of Interatomic Charge Transfer and Electron Exchange Effects by Combining Static and Kinetic Potentials and Associated Vector Fields**

Intricate behaviour of one-electron potentials from the Euler equation for electron density and corresponding gradient force fields in crystals was studied. Channels of locally enhanced kinetic potential and corresponding saddle Lagrange points were found between chemically bonded atoms. Superposition of electrostatic and kinetic potentials and electron density allowed partitioning any molecules and crystals into atomic - and potential-based -basins; -basins explicitly account for the electron exchange effect, which is missed for -ones. Phenomena of interatomic charge transfer and related electron exchange were explained in terms of space gaps between zero-flux surfaces of - and -basins. The gap between - and -basins represents the charge transfer, while the gap between - and -basins is a real-space manifestation of sharing the transferred electrons caused by the static exchange and kinetic effects as a response against the electron transfer. The regularity describing relative positions of -, -, and - basin boundaries between interacting atoms was proposed. The position of -boundary between - and -ones within an electron occupier atom determines the extent of transferred electron sharing. The stronger an H⋅⋅⋅O hydrogen bond is, the deeper hydrogen atom's -basin penetrates oxygen atom's -basin, while for covalent bonds a -boundary closely approaches a -one indicating almost complete sharing of the transferred electrons. In the case of ionic bonds, the same region corresponds to electron pairing within the -basin of an electron occupier atom.     

Investigating Possible Dipole-Bound States of Cyanopolyynes: the Case for the C5N− Anion Detected in Interstellar Space

We present results of quantum structure calculations aimed at demonstrating the possible existence of dipole-bound states (DBS) for the anion , a species already detected in the Interstellar medium (ISM). The positive demonstration of DBS existence using ab initio studies is an important step toward elucidating possible pathways for the formation of the more tightly bound valence bound states (VBS) in environments where free electrons from starlight ionization processes are known to be available to interact with the radical partner of the title molecule. Our current calculations show that such excited DBS states can exist in , in agreement with what we had previously found for the smallercyanopolyyne in the series: the anion. This system has a very weakly bound anion with binding energies of about 3 and 9 cm⁻¹ for the and DBS, respectively.     

Fluorine Substitution of TCNQ Alters the Redox-Driven Catalytic Pathway for the Ferricyanide-Thiosulfate Reaction

Mechanistic variation in catalysis through substituent-based redox tuning is well established. Fluorination of TCNQ (TCNQ=tetracyanoquinodimethane) provides ~850 mV variation in the redox potentials of the and (n=0, 2, 4) processes. With , catalysis of the kinetically very slow ferrocyanide-thiosulfate redox reaction in aqueous solution occurs via a mechanism in which the catalyst is reduced to when reacting with which is oxidised to . Subsequently, reacts with to form and reform the catalyst, in another thermodynamically favoured process. An analogous mechanism applies with as a catalyst. In contrast, since the reaction of with is thermodynamically unfavourable, an alternative mechanism is required to explain the catalytic activity observed in this non-fluorinated system. Here, upon addition of , reduction of to occurs with concomitant oxidation of to , which then acts as the catalyst for oxidation. Thermodynamic data explain the observed differences in the catalytic mechanisms. (n=0, 4) also act as catalysts for the ferricyanide-thiosulfate reaction in aqueous solution. The present study shows that homogeneous pathways are available following addition of these dissolved materials. Previously, these (n=0, 4) coordination polymers have been regarded as insoluble in water and proposed as heterogeneous catalysts for the ferricyanide-thiosulfate reaction. Details and mechanistic differences were established using UV-visible spectrophotometry and cyclic voltammetry.     

On the accurate estimation of free energies using the jarzynski equality

The Jarzynski equality is one of the most widely celebrated and scrutinized nonequilibrium work theorems, relating free energy to the external work performed in nonequilibrium transitions. In practice, the required ensemble average of the Boltzmann weights of infinite nonequilibrium transitions is estimated as a finite sample average, resulting in the so-called Jarzynski estimator, . Alternatively, the second-order approximation of the Jarzynski equality, though seldom invoked, is exact for Gaussian distributions and gives rise to the Fluctuation-Dissipation estimator . Here we derive the parametric maximum-likelihood estimator (MLE) of the free energy considering unidirectional work distributions belonging to Gaussian or Gamma families, and compare this estimator to . We further consider bidirectional work distributions belonging to the same families, and compare the corresponding bidirectional to the Bennett acceptance ratio () estimator. We show that, for Gaussian unidirectional work distributions, is in fact the parametric MLE of the free energy, and as such, the most efficient estimator for this statistical family. We observe that and perform better than and , for unidirectional and bidirectional distributions, respectively. These results illustrate that the characterization of the underlying work distribution permits an optimal use of the Jarzynski equality. © 2018 Wiley Periodicals, Inc.     

Temperature Dependence of 1H Paramagnetic Chemical Shifts in Actinide Complexes,Beyond Bleaney's Theory: The AnVIO22+–Dipicolinic Acid Complexes (An=Np,Pu) as an Example

Actinide +VI complexes ( = , and ) with dipicolinic acid derivatives were synthesized and characterized by powder XRD, SQUID magnetometry and NMR spectroscopy. In addition, and complexes were described by first principles CAS based and two-component spin-restricted DFT methods. The analysis of the ¹H paramagnetic NMR chemical shifts for all protons of the ligands according to the X-rays structures shows that the Fermi contact contribution is negligible in agreement with spin density determined by unrestricted DFT. The magnetic susceptibility tensor is determined by combining SQUID, pNMR shifts and Evans’ method. The SO-RASPT2 results fit well the experimental magnetic susceptibility and pNMR chemical shifts. The role of the counterions in the solid phase is pointed out; their presence impacts the magnetic properties of the complex. The temperature dependence of the pNMR chemical shifts has a strong contribution, contrarily to Bleaney's theory for lanthanide complexes. The fitting of the temperature dependence of the pNMR chemical shifts and SQUID magnetic susceptibility by a two-Kramers-doublet model for the complex and a non-Kramers-doublet model for the complex allows for the experimental evaluation of energy gaps and magnetic moments of the paramagnetic center.     

The Apparently Unreactive Substrate Facilitates the Electron Transfer for Dioxygen Activation in Rieske Dioxygenases

Rieske dioxygenases belong to the non-heme iron family of oxygenases and catalyze important cis-dihydroxylation as well as O-/N-dealkylation and oxidative cyclization reactions for a wide range of substrates. The lack of substrate coordination at the non-heme ferrous iron center, however, makes it particularly challenging to delineate the role of the substrate for productive activation. Here, we studied the role of the substrate in the key elementary reaction leading to activation from a theoretical perspective by systematically considering (i) the 6-coordinate to 5-coordinate conversion of the non-heme Fe^II upon abstraction of a water ligand, (ii) binding of , and (iii) transfer of an electron from the Rieske cluster. We systematically evaluated the spin-state-dependent reaction energies and structural effects at the active site for all combinations of the three elementary processes in the presence and absence of substrate using naphthalene dioxygenase as a prototypical Rieske dioxygenase. We find that reaction energies for the generation of a coordination vacancy at the non-heme Fe center through thermoneutral H₂O reorientation and exothermic binding prior to Rieske cluster oxidation are largely insensitive to the presence of naphthalene and do not lead to formation of any of the known reactive Fe-oxygen species. By contrast, the role of the substrate becomes evident after Rieske cluster oxidation and exclusively for the 6-coordinate non-heme Fe sites in that the additional electron is found at the substrate instead of at the iron and oxygen atoms. Our results imply an allosteric control of the substrate on Rieske dioxygenase reactivity to happen prior to changes at the non-heme Fe in agreement with a strategy that avoids unproductive activation.     

How does the pH influences the Ru-NO coordination compounds?

The pH influence has important role in the bioavailability of coordination compounds. fac-[Ru(NO)Cl₂(κ³N⁴,N⁸,N¹¹[1-carboxypropyl]cyclam)]⁺, 1 , and the species found at different pHs, 2 - 4 , were investigated. One series of computational methodologies has been used to investigate these compounds. One special highlight is to interacting quantum atoms method, where the total interaction energy, , between two atoms has been used as base to estimate the chemical bonds strength. The deprotonation of -CO₂H, 1 ➔ 2 (pK_a = 3.3), creates a hydrogen bond in the complex 2 , N( 3 )-H⋯ ·OCO⁻, with a more favorable than the presents in 1 , N( 3 )-H⋯ ·OCOH. There are no changes in in Ru-NO bond. The second deprotonation occurs in the N(2) atom of the cyclam group, 2 ➔ 3 (pK_a = 8.0). It promotes an increase in the covalent character of Ru-N( 2 ). In contrast, there is no changes in Ru-N( 5 )O bond. For higher pHs, there is a 3 ➔ 4 equilibrium (pK_a = 11.5) and the conversion of Ru-N( 5 )O for Ru-N( 5 )O₂. The Ru-N( 5 ) of 4 shows a larger ionic character than 3 . Thus, Ru-NO in 1 - 4 has worthy stability about a large pH range, showing potential application as NO scavengers.     

Reversible Metal-Hydride Transformation in Mg-Ti-H Nanoparticles at Remarkably Low Temperatures

We study the kinetics of hydrogen sorption in Mg-Ti-H nanoparticles prepared by gas phase condensation of mixed Mg-Ti vapors under a H₂-containing atmosphere. Four samples with different Ti contents from 14 to 63 at.% Ti are examined in the 100–150 °C range. The hydrogen absorption kinetics coupled with the formation of MgH₂ can be described by a nucleation and growth model. The activation energy is in the range kJ/mol and the rate constant (at 150 °C) increases from s⁻¹ to s⁻¹ with increasing Ti content. Hydrogen desorption is well modeled by a sequence of surface-limited and contracting-volume kinetics, except at the highest Ti content where nucleation and growth is observed. The activation energy of surface-limited kinetics is /mol. The rate constant (at 150 °C) increases from s⁻¹ to s⁻¹ with the Ti content. These results open an unexplored kinetic window for Mg-based reversible hydrogen storage close to ambient temperature.