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 .     

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.     

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.     

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.     

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.     

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.     

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 .     

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.     

The Reaction of Sulfur Dioxide Radical Cation with Hydrogen and its Relevance in Solar Geoengineering Models

SO₂ has been proposed in solar geoengineering as a precursor of H₂SO₄ aerosol, a cooling agent active in the stratosphere to contrast climate change. Atmospheric ionization sources can ionize SO₂ into excited states of , which quickly reacts with trace gases in the stratosphere. In this work we explore the reaction of with excited by tunable synchrotron radiation, leading to ( ), where H contributes to O₃ depletion and OH formation. Density Functional Theory and Variational Transition State Theory have been used to investigate the dynamics of the title barrierless and exothermic reaction. The present results suggest that solar geoengineering models should test the reactivity of with major trace gases in the stratosphere, such as H₂ since this is a relevant channel for the OH formation during the nighttime when there is not OH production by sunlight. OH oxides SO₂, triggering the chemical reactions leading to H₂SO₄ aerosol.     

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.     

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.     

Virial relations in density embedding

The accuracy of charge-transfer excitation energies, solvatochromic shifts, and other environmental effects calculated via various density-embedding techniques depend critically on the approximations employed for the nonadditive noninteracting kinetic energy functional, . Approximating this functional remains an important challenge in electronic-structure theory. To assist in the development and testing of approximations for , we derive two virial relations for fragments in molecules. These establish separate connections between the nonadditive kinetic energies of the noninteracting and interacting systems of electrons, and quantities such as the electron-nuclear attraction forces, the partition (or embedding) energy and potential, and the Kohn-Sham potentials of the system and its parts. We numerically verify both relations on diatomic molecules.     

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.     

Vibrationally Resolved Inner-Shell Photoexcitation of the Molecular Anion C2−

Carbon 1s core-hole excitation of the molecular anion C₂⁻ has been experimentally studied at high resolution by employing the photon-ion merged-beams technique at a synchrotron light source. The experimental cross section for photo–double-detachment shows a pronounced vibrational structure associated with and core excitations of the C₂⁻ ground level and first excited level, respectively. A detailed Franck-Condon analysis reveals a strong contraction of the C₂⁻ molecular anion by 0.2 Å upon this core photoexcitation. The associated change of the molecule's moment of inertia leads to a noticeable rotational broadening of the observed vibrational spectral features. This broadening is accounted for in the present analysis which provides the spectroscopic parameters of the C₂⁻ and core-excited levels.     

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.     

Reaction of Pertechnetate in Highly Alkaline Solution: Synthesis and Characterization of the Nitridotrioxotechnetate Ba[TcO3N]

The preparation of novel technetium oxides, their characterization and the general investigation of technetium chemistry are of significant importance, since fundamental research has so far mainly focused on the group homologues. Whereas the structure chemistry of technetium in strongly oxidizing media is dominated by the anion, our recent investigation yielded the new anion. Brown single crystals of Ba[TcO₃N] were obtained under hydrothermal conditions starting from Ba(OH)₂ ⋅ 8H₂O and NH₄[TcO₄] at 200 °C. crystallizes in the monoclinic crystal system with the space group P2₁/n (a=7.2159(4) Å, b=7.8536(5) Å, c=7.4931(4) Å and β=104.279(2)°). The crystal structure of consists of isolated tetrahedra, which are surrounded by Ba²⁺ cations. XANES measurements complement the oxidation state +VII for technetium and Raman spectroscopic experiments on Ba[TcO₃N] single crystals exhibit characteristic Tc−O and Tc−N vibrational modes.     

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.     

Emergence of Spinmerism for Molecular Spin-Qubits Generation**

Molecular platforms are regarded as promising candidates in the generation of units of information for quantum computing. Herein, a strategy combining spin-crossover metal ions and radical ligands is proposed from a model Hamiltonian first restricted to exchange interactions. Unusual spin states structures emerge from the linkage of a singlet/triplet commutable metal centre with two doublet-radical ligands. The ground state nature is modulated by charge transfers and can exhibit a mixture of triplet and singlet local metal spin states. Besides, the superposition reaches a maximum for , suggesting a necessary competition between the intramolecular and inter-metal-ligand and direct exchange interactions. The results promote spinmerism, an original manifestation of quantum entanglement between the spin states of a metal centre and radical ligands. The study provides insights into spin-coupled compounds and inspiration for the development of molecular spin-qubits.     

Transient electrophoresis of a charged porous particle

The starting electrophoretic motion of a porous, uniformly charged, spherical particle, which models a solvent-permeable and ion-penetrable polyelectrolyte coil or floc of nanoparticles, in an arbitrary electrolyte solution due to the sudden application of an electric field is studied for the first time. The unsteady Stokes/Brinkman equations with the electric force term governing the fluid velocity fields are solved by means of the Laplace transform. An analytical formula for the electrophoretic mobility of the porous sphere is obtained as a function of the dimensionless parameters , , , and , where a is the radius of the particle, κ is the Debye screening parameter, λ is the reciprocal of the square root of the fluid permeability in the particle, ρ_p and ρ are the mass densities of the particle and fluid, respectively, ν is the kinematic viscosity of the fluid, and t is the time. The electrophoretic mobility normalized by its steady-state value increases monotonically with increases in and , but decreases monotonically with an increase in , keeping the other parameters unchanged. In general, a porous particle with a high fluid permeability trails behind an identical porous particle with a lower permeability and a corresponding hard particle in the growth of the normalized electrophoretic mobility The normalized electrophoretic acceleration of the porous sphere decreases monotonically with an increase in the time and increases with an increase in from zero at .