Cyclohexyl radicals are crucial primary intermediates in combustion of fossil and alternative fuels. They would present the inherent conformation feature, i.e. diverse conformers retained in inversion-topomerization pathways, jointly controlled by the varying radical site and specific spatial positions of alkyl side chains on “easy-distortion” cyclic ring. These conformers for one radical have different energies and thermodynamics, and are highly expected to influence their subsequent decomposition reactions in terms of energetics and kinetics. To reveal such impact, all conformational structures and their interconversion mechanisms for trans-1,2-dimethylcyclohexyl isomers were explored by employing quantum chemical calculations coupled with transition state theory. Originated from distinct conformers, all accessible transition states were explicitly identified in different reaction paths for each type of intramolecular H-transfer or β-scission, and then were carefully used in computing rate coefficients. The kinetic predictions demonstrate that the fairly speedy equilibrium among conformers would be established for one isomer via conformation before they proceed the initial decomposition over 300-2500 K. This allows thoroughly evaluating the contribution of various conformers to the kinetics for multiple paths in one reaction regarding to their thermodynamic properties. Moreover, conformational analysis elucidates that H-transfers exhibit strong structure dependence. Note that the most favorable 1,5 H-transfer is only feasible for one twist-boat with radical site in axial side chain accompanied by one isoclinal methyl group. The results for β-scissions are affected by steric energies and substituent effects remained in conformational structures. These findings facilitate to finally suggest the proper kinetic parameters for each decomposition reaction with the aim of their potential implication in kinetic modelling.

We investigate the presence of helical character and chirality using a vector-based charge density perspective instead of energetic or structural measures. The vector-based perspective of the chemical bonding, constructed using the most preferred direction of charge density accumulation, finds the presence of induced symmetry-breaking for α,ω-disubstituted [4]cumulenes as the end groups are torsioned. The stress tensor trajectories Tσ(s) are used to provide the additional symmetry-breaking required to quantify the degree and nature of the chirality and helical character. We find an absence of chirality for [4]cumulene but a very significant degree of axiality as demonstrated by the purely axial form of the Tσ(s) indicating a lack of helical character. The S-1,5-dimethyl-[4]cumulene contains a very low degree of chiral character but significant axiality(helicity) resulting in a weakly helical morphology of the corresponding Tσ(s). The (-)S(-), (+)S(-) and (+)S(+) conformations of S-1,5-diamino-[4]cumulene contain very significant degrees of both chirality and helical character resulting in helical morphology of the corresponding Tσ(s). The chirality assignments are in agreement with the Cahn–Ingold–Prelog (CIP) classifications for the (-)S(-), (+)S(-) and (+)S(+) conformations of S-1,5-diamino-[4]cumulene. We discuss the consequences for the Tσ(s) in locating chiral character in these molecules in future experiment investigations.

Spin projected wave functions are known as generalizations of the Hartree-Fock wave function. Among them, the Half-Projected Hartree-Fock (HPHF) model represents a good compromise between the restricted (RHF) and unrestricted (UHF) Hartree-Fock methods. The HPHF wave function is a nearly pure wave function of spin and recovers a small part of the spin correlation energy. This paper reviews the history of the HPHF theory, not only from the conceptual point of view but also providing a compilation of the publications of this method over the years until now. In addition, the extension of the HPHF method to the calculation of non-orthogonal excited states to the ground state will be treated. The variational collapse during the calculation of singlet excited states with the same symmetry as the ground state is avoided by orthogonalizing the excited orbital to the corresponding occupied orbital. As an example, the potential energy surface of the S0 ground and 1S1(n, π∗) first excited state of the formic acid HCOOH are calculated. Formic acid exhibits complex energy surfaces with respect two large amplitude motions, the torsional rotation of the O-H group and the waving out-of-plane angle of the H atom. In the excited state, the molecule adopts a pyramidal structure. The obtained energy results are fitted to curves that can be used for the calculation of the theoretical spectrum.

Compounds with (NHC)→E coordination bond are being generated and their chemistry is being explored over the past 15 years (NHC= N-heterocyclic carbenes, E = main group elements). Many examples of species with N-heterocyclic olefins (NHOs) are known, which exhibit umpolung chemistry. Increasing number of chemical species, which carry NHC as a functional unit, are being reported. There is a need to understand their electronic structure. Alkylated imidazole oximes (cationic, found useful in medicinal chemistry) ((NHC)-C(H)=N-OH(+)) carry NHC unit as a functional group. Similarly, the corresponding nitroso-N-heterocyclic olefins ((NHC)=C(R)-N=O) also carry NHC as a functional unit. It is important to establish the interaction between the NHC unit and the rest part of the molecule in these species. Density functional (DFT) study has been carried out to explore the electronic structure details of a few oximes and nitroso NHOs. The results indicate that a structure with NHC→C coordination interaction can be considered as one of the resonance structures of these species.

Herein an assessment of several Long Range Corrected (LRC) Density Functional Theory (DFT) methods for the calculation of reduction potentials of the ([Ni(X2C2H2)2]n/[Ni(X2C2H2)2]n-1), and ([Ni(X2C2H2)(N2C2H4)]n/[Ni(X2C2H2)(N2C2H4)]n-1) and (where X= S or Se and n = 0, or -1) redox couples was done. From the results the values of ω that provide best agreement with CCSD(T) for the tested LRC DFT methods are 0.05 bohr-1, 0.15 bohr-1, 0.05 bohr-1, and 0.20 bohr-1 for ω-B97XD, LC-BLYP, CAM-B3LYP, and ω-B97, respectively. With these values the unsigned average in error was 0.12 V with a standard deviation of 0.13 V for ω-B97XD. For LC-BLYP, CAM-B3LYP, and ω-B97 the unsigned averages in relative errors were 0.12 V, 0.11 V, and 0.13 V, respectively, with respective standard deviations of 0.11 V, 0.12 V and 0.13 V.

The relativistic properties of Hydrogen-like atoms (HLAs) are here investigated in the Heisenberg picture for the first time. The relativistic vibrational Hamiltonian (RVH) is first defined as a power series of harmonic oscillator Hamiltonian by using the relativistic energy eigenvalue . By applying the first-order RVH (proportional to ) to the Heisenberg equation, a pair of coupled equations is turned out for the relativistic motion of the electron’s position and linear momentum. A simple comparison of the first-order relativistic and nonrelativistic equations reveals this reality that the natural (fundamental) frequency of HLA (like entropy) is slowly raised by increasing the atomic number from . The second-order RVH (proportional to ) has then been implemented to determine an exact expression for the electron relativistic frequency in the different atomic energy levels. In general, the physical role of RVH is fundamental because it not only specifies the temporal relativistic variations of position, velocity, and linear momentum of the oscillating electron, but also identifies the corresponding relativistic potential, kinetic, and mechanical energies. The results will finally be testified by demonstrating energy conservation.

1,1-diamino-2,2-dinitroethene (FOX-7) is a novel energetic material with high performance and low sensitivity. In order to deeply understand the reaction mechanism in the initiation “hot spots” of FOX-7 and reveal the growth mechanism of these initiation “hot spots” in the explosion process, the detailed mechanisms of bimolecular reaction of NO2 and FOX-7, as well as the subsequent reactions have been investigated by the quantum chemical calculations. The mechanism of NO2 and FOX-7 bimolecular reaction and the catalytic effect of NO2 were revealed by three key dissociation paths. It is demonstrated that the NO2 molecule plays an important role in promoting the decomposition of the FOX-7 molecule, and the main exothermic pathways were the reactions between oxidizing intermediates (NO, NO2), and reducing intermediates (CO, NH3).

A series of 8-hydroxyquinoline derivatives were characterized and tested as potential antennas in a set of designed lanthanide complexes. The molecular structure and ligand localized nature of the excited states were studied in the framework of the multiconfigurational methods CASSCF/NEVPT2 combined with TDDFT- based approaches, which allows applying a fragmentation scheme in the analysis of the most probable sensitization pathway via antenna effect. The photophysical properties of all the complexes and antennas were carefully analyzed, and the most probable energy transfer pathways were elucidated. Rate constants for photophysical processes involved in the mechanism were calculated, showing a significant contribution of the vibronic coupling in all cases and the predominant intersystem-crossing between S1 and T1 states was demonstrated from the analysis of the nature of the wave function of those states. The energy transfer process described herein demonstrates the possibility of Eu(III) and Nd(III) sensitization by the studied ligands. The proposed methodology gives a complete picture of the antenna excited state dynamics.

The Jacobi polynomials $\hat{P}_n^{(\alpha,\beta)}(x)$ conform the canonical family of hypergeometric orthogonal polynomials (HOPs) with the two-parameter weight function $(1-x)^\alpha (1+x)^\beta, \alpha,\beta>-1,$ on the interval $[-1,+1]$. The spreading of its associated probability density (i.e., the Rakhmanov density) over the orthogonality support has been quantified, beyond the dispersion measures (moments around the origin, variance), by the algebraic $\mathfrak{L}_{q}$-norms (Shannon and R\’enyi entropies) and the monotonic complexity-like measures of Cram\’er-Rao, Fisher-Shannon and LMC (L\’opez-Ruiz, Mancini and Calbet) types. These quantities, however, have been often determined in an analytically highbrow, non-handy way; specially when the degree or the parameters $(\alpha,\beta)$ are large. In this work, we determine in a simple, compact form the leading term of the entropic and complexity-like properties of the Jacobi polynomials in the two extreme situations: ($n\rightarrow \infty$; fixed $\alpha,\beta$) and ($\alpha\rightarrow \infty$; fixed $n,\beta$). These two asymptotics are relevant \textit{per se} and because they control the physical entropy and complexity measures of the high energy (Rydberg) and high dimensional (pseudoclassical) states of many exactly, conditional exactly and quasi-exactly solvable quantum-mechanical potentials which model numerous atomic and molecular systems.

The installation of quantum chemistry software packages is commonly done manually and can be a time-consuming and complicated process. An update of the underlying Linux system requires a reinstallation in many cases and can quietly break software installed on the system. In this paper, we present an approach that allows for an easy installation of quantum chemistry software packages, which is also independent of operating system updates. The use of the Nix package manager allows building software in a reproducible manner, which allows for a reconstruction of the software for later reproduction of scientific results. The build recipes that are provided can be readily used by anyone to avoid complex installation procedures.

Population analyses have become an indispensable tool to computational chemists. Yet implementation within popular quantum chemistry software has buried the interesting philosophical choices made when partitioning the electron density into atomic contributions. There is further historical context that has significantly influenced common conceptions of chemical bonding and reactivity. This work reviews select aspects of orbital and spatial decomposition schemes of the density matrix, pointing out essential linear algebraic considerations and associated tools of shared interest to us and Prof. Mayer.

Quantum chemical calculations were carried out to establish the half-sandwich structural behaviour between heavier group-14 elements (Si-Pb) and neutral Be3 ring. The proposed complexes are found to be global minima on the potential energy surface. Quantum chemical investigation revealed that the complexes found possess high bond dissociation energy and also favorable thermodynamics of their formation. The complexes were also found to possess significant aromatic behaviour. In addition, the half-sandwich complexes were found to possess promising chemical properties to be useful for potential H2 storage material under reversible conditions.

Recently, the rovibronic absorption and emission spectra of diatomic molecules dressed by medium-intensity laser fields have been discussed. By computing the total absorption probability as a function of dressing wavelength an asymmetric line shape has been obtained strongly resembling to the well-known Fano line shape. Applying two-state analytical and three-state numerical models the shape of the total absorption probability function is explained. Further confirmation of the model based results is provided by high resolution accurate numerical computations using large number of basis functions.

Phenylenes network is applied in several fields of chemistry sciences due to its advantages compared to other several columnar networks, recently. This paper aims to introduce a kind of networks which obtained by a family of dicyclobutadieno derivative of linear phenylene chain Ln which is made up of n hexagons and (n+1) quadrangles. Let L2n be the strong prism of the dicyclobutadieno derivative of linear phenylenes Ln. By taking full advantage of the knowleges about the normalized Laplacian spectra, we induce the explicit expressions, with respect to the index n, of the multiplicative degree-Kirchhoff index and the number of spanning tree based on the graph L2n.

Organometallic sandwich complexes have been attracting tremendous interest for their potential applications in electronics and spintronics. Here, we systematically studied the structures, electronic and magnetic properties of one dimensional (1D) transition metal (TM)-anthracene (Ant) sandwich molecular wires (SMWs), [TM2Ant]∞ and [TM3Ant]∞ (TM=Ti, V, Cr, Mn), based on density functional theory calculations. Our results showed that all the 1D SMWs display normal sandwich configurations with their binding energies closely related to the choice of TM atoms. Excepting 1D [Mn2Ant]∞ and [Fe3Ant]∞ favoring antiferromagnetic ordering, most 1D [TM2Ant]∞ and [TM3Ant]∞ SMWs display robust ferromagnetic feathers. Particularly, 1D [Cr3Ant]∞ SMW is revealed to be ferromagnetic half-metal with large magnetic moment of 28.0µB per unit cell. Further spintransport calculations double proved that 1D [Cr3Ant]∞ SMW are good spintransport molecular devices. Our findings shed light on the properties of 1D Ant based SMWs and propose a new way to design potential electronic and spintronic devices.

As a continuation of Part I (Int. Journal of Quantum Chem. 2021; 121: qua.26586), dedicated to the ground state of He-like and Li-like isoelectronic sequences for nuclear charges Z ≤ 20, a few ultra-compact wave functions in the form of generalized Hylleraas-Kinoshita functions are constructed, which describe the domain of applicability of the Quantum Mechanics of Coulomb Charges (QMCC) for energies (4-5 significant digits (s.d.)) of two excited states of He-like ions: the spin-singlet (first) excited state 2¹S and for lowest spin-triplet 1³S state. For both states it provides absolute accuracy for energy ∼10−3a.u., exact values for cusp parameters and also for 6 expectation values the relative accuracy ∼10−2. Bressanini-Reynolds observation about the special form of nodal surface of 2¹S state for Helium is confirmed and extended to ions with Z > 2. Critical charges Z = ZB, where ultra-compact trial functions loose their square-integrability, are estimated: ZB(1¹S)≈ZB(2¹S)∼0.905 and ZB(1³S)∼0.902. For both states the Majorana formula - the energy as the second degree polynomial in Z - provides accurately the 4-5 significant digits for Z ≤ 20.

Defect and doping are effective methods to modulate the physical and chemical properties of materials. In this report, we investigated the structural stability, electronic properties and quantum capacitance (Cdiff) of Zr2CO2 by changing the dopants of Si, Ge, Sn, N, B, S and F in the substitutional site. The doping of F, N, and S atoms makes the system undergo the semiconductor-to-conductor transition, while the doping of Si, Ge, and Sn maintains the semiconductor characteristics. The Cdiff of the doped systems are further explored. The B-doped system can be used as cathode materials, while the systems doped by S, F, N, Sn atoms are promising anode materials of asymmetric supercapacitors, especially for the S-doped system. The improved Cdiff mainly originates from Fermi-level shifts and Fermi-Dirac distribution by the introduction of the dopant. The effect of temperature on Cdiff is further explored. The result indicates that the maximum Cdiff of the studied systems gradually decreases with the increasing temperature. Our investigation can provide useful theoretical basis for designing and developing the ideal electrode materials for supercapacitors.

In this paper, in order to study the relationship between structure and performance, four new NFA derivatives were designed based on the two reported NFA molecules BO-4Cl and BTP-S2 by replacing the BT unit with a less-electron deficient BTz unit and inserting another ethylene double bond between the central core and the terminal groups. The DFT and TD--DFT calculations were applied to invstigate linear and nonlinear optical properties, such as electronic structure, electronic absorption, reorganization energy and the second-order NLO properties. The investigation demonstrates that they are all narrow bandgap derivatives, the absorption spectrum extends to the near-infrared region and using two ethylene double bond is the most effective way to reduce the energy gap, redshift the maximum absorption peak and the middle absorption band, enhance hole transport ability and weaken electron transport ability and enhance second-order NLO response. Considering the smaller electron and hole reorganization energy and the larger static first hyperpolarizability value, the studied NFA derivatives have great potential to become ambipolar charge transport materials and large second-order NLO materials.