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.     

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 .     

Fluxional bonds in quasi-planar and half-sandwich (M = K,Rb, and Cs)

Detailed molecular orbital and bonding analyses reveal the existence of both fluxional σ- and π-bonds in the global minima C_s ( 1 ) and C_s MB₁₈ ( 3 ) and transition states C_s ( 2 ) and C_s ( 4 ) of dianion and monoanions (M = K, Rb, and Cs). It is the fluxional bonds that facilitate the fluxional behaviors of the quasi-planar and half-sandwich which possess energy barriers smaller than the difference of the corresponding zero-point corrections. © 2019 Wiley Periodicals, Inc.     

Dynamical Jahn-Teller effect in the first excited

Jahn-Teller effect of C₆₀ monoanion in the first electronically excited states was theoretically investigated. The orbital vibronic coupling parameters for t_1g next lowest unoccupied molecular orbitals were derived from the Kohn-Sham orbital levels calculated using a frozen phonon approach with both hybrid B3LYP and CAM-B3LYP functionals, which take long-range interaction correction into consideration. With these coupling parameters, the vibronic states of first excited were derived by exactly diagonalizing dynamical Jahn-Teller Hamiltonian. The results showed that dynamical Jahn-Teller effects are more significant in the first excited than those in the ground electronic states. This work also clarified that CAM-B3LYP gives results closer to experimental data than B3LYP.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Cover Feature: How Different are the Diamagnetic and Paramagnetic Contributions to Off-Nucleus Shielding in Aromatic and Antiaromatic Rings? (ChemPhysChem 9/2023)

The spatial variations in the diamagnetic and paramagnetic contributions to the off-nucleus isotropic shielding, , and to the zz component of the off-nucleus shielding tensor, , around benzene (C₆H₆) and cyclobutadiene (C₄H₄) are investigated using complete-active-space self-consistent field wavefunctions. Despite the substantial differences between and around the aromatic C₆H₆ and the antiaromatic C₄H₄, the diamagnetic and paramagnetic contributions to these quantities, and , and and , are found to behave similarly in the two molecules, shielding and deshielding, respectively, each ring and its surroundings. The different signs of the most popular aromaticity criterion, the nucleus-independent chemical shift (NICS), in C₆H₆ and C₄H₄ are shown to follow from a change in the balance between the respective diamagnetic and paramagnetic contributions. Thus, the different NICS values for antiaromatic and antiaromatic molecules cannot be attributed to differences in the ease of access to excited states only; differences in the electron density, which determines the overall bonding picture, also play an important role.     

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.     

An investigation on the structure,spectroscopy, and thermodynamic aspects of clusters: A combined Parallel tempering and DFT based study

The problem of identifying low-energy structures of (n = 1-6) was investigated, and the evaluation of important properties like heat capacity, solvation energy, and vertical detachment energy for each of the clusters was carried out. The problem was handled at two different theoretical levels. First, an adequately chosen empirical potential energy surface was used to account for the major interactions between the constituents of the cluster studied. Once the surface was chosen, the Parallel tempering algorithm was employed to search out the low-energy critical points on this surface, which gave geometries at this level. To refine the structures further, these pre-optimized structures were used as inputs for quantum chemical evaluation to complete the final refinement. To check whether the structures found were reasonable, sensitive properties like heat capacity, solvation energy, and vertical detachment energy were calculated. Then, an effort was made to understand and explain the variations in these properties with change in the cluster size. To understand the process of cluster formation further, thermodynamic aspects like △H (298.15 K), △G (298.15 K), and heat capacity (C_v) changes were also evaluated. Infrared spectroscopic features were also studied to see whether the introduction of the ion caused reasonable shifts compared to a pure water cluster.     

On the Mechanical Properties of Popgraphene-Based Nanotubes: a Reactive Molecular Dynamics Study

Carbon-based tubular materials have sparked a great interest in future electronics and optoelectronics device applications. In this work, we computationally studied the mechanical properties of nanotubes generated from popgraphene (PopNTs). Popgraphene is a 2D carbon allotrope composed of 5-8-5 rings. We carried out fully atomistic reactive (ReaxFF) molecular dynamics for PopNTs of different chiralities ( and ) and/or diameters and at different temperatures (from 300 up to 1200 K). Results showed that the tubes are thermally stable (at least up to 1200 K). All tubes presented stress/strain curves with a quasi-linear behavior followed by an abrupt drop of stress values. Interestingly, armchair-like PopNTs ( ) can stand a higher strain load before fracturing when contrasted to the zigzag-like ones ( ). Moreover, it was obtained that Young's modulus (Y_Mod) (750–900 GPa) and ultimate strength (σ_US) (120–150 GPa) values are similar to the ones reported for conventional armchair and zigzag carbon nanotubes. Y_Mod values obtained for PopNTs are not significantly temperature-dependent. While the σ_US values for the showed a quasi-linear dependence with the temperature, the exhibited no clear trends.     

Indirect Nuclear Spin-Spin Exchange Coupling through Solvated Electron in Small Sizes of Cyclic and Cage-Shaped Perfluoroalkanes

Small perfluorocycloalkanes (hexafluorocyclopropane (c-C₃F₆), octafluorocyclobutane (c-C₄F₈) and decafluorocyclopentane (c-C₅F₁₀) and cage-shaped perfluoroalkanes (perfluoro tetrahedral alkane (C₄F₄), perfluoro prismane (C₆F₆) and perfluoro cubane (C₈F₈)) are better electron scavengers. The captured excess electrons are weakly bound inside their backbone voids or over their backbones, forming the solvated electron ( ) systems (e@c-C_nF_2ns (n=3, 4, 5) and e@C_nF_n (n=4, 6, 8)). There have been many studies on the structures and properties of such systems. However, the effect of on the indirect nuclear spin-spin coupling (J-coupling) is unknown. In this work, we explore how affects ^NeJ-coupling between two coupled F nuclei (^NeJ_FF-coupling) in perfluoroalkane systems through density functional theory calculations. We find unusual trans-^NeJ_FF-couplings (two coupled F nuclei in trans-position) in e@c-C_nF_2n (n=3, 4, 5) and ^NeJ_FF-couplings in e@C_nF_n (n=4, 6, 8). One excess electron not only changes the molecular structures, but also enforces unique distributions and properties, depending on the structural characteristics. We also confirm that such unusual ^NeJ_FF-couplings are realized by through- (T-SE) transmission mechanism, rather than the conventional through-bonds (T−B)/through-space (T−S) ones. The novel transmission mechanism consists of the T-SE coupling path (path 1) and -enhanced T−B T−S coupling path (path 2), and the two paths jointly control ^NeJ_FF through cooperation and competition. Interestingly, the former plays a dominant role for long-range ^NeJ_FF-coupling (N=5), while the latter plays a role in the short-range ^NeJ_FF-coupling (N=3, 4). Path bending angle mainly influences path 1, while path 2 is mainly influenced by the path length. This work not only provides novel insights into the mediating role of in the coupling information exchange, but also proposes a new -based coupling mechanism, possibly opening up potential applications for the -based indirect nuclear spin couplings.     

A Multiconformational Transition State Theory Approach to OH Tropospheric Degradation of Fluorotelomer Aldehydes

Experimental work on the OH-initiated oxidation reactions of fluorotelomer aldehydes (FTALs) strongly suggests that the respective rate coefficients do not depend on the size of the C_xF_2x+1 fluoroalkyl chain. FTALs hence represent a challenging test to our multiconformer transition state theory (MC-TST) protocol based on constrained transition state randomization (CTSR), since the calculated rate coefficients should not show significant variations with increasing values of . In this work we apply the MC-TST/CTSR protocol to the cases and calculate both rate coefficients at 298.15 K with a value of cm³ molecule⁻¹ s⁻¹, practically coincident with the recommended experimental value of k_exp= cm³ molecule⁻¹ s⁻¹. We also show that the use of tunneling corrections based on improved semiclassical TST is critical in obtaining Arrhenius-Kooij curves with a correct behavior at lower temperatures.