The realization of fractional quantum chemistry is presented. Adopting the integro-differential operators of the calculus of arbitrary-order, we develop a general framework for the description of quantum nonlocal effects in the complex electronic environments. After a brief overview of the historical and fundamental aspects of the calculus of arbitrary-order, various classes of fractional Schr\"odinger equations are discussed and pertinent controversies and open problems around their applications to model systems are detailed. We provide a unified approach toward fractional generalization of the quantum chemical models such as Hartree-Fock and Kohn-Sham density functional theory and develop fractional variants of the fundamental molecular integrals and correlation energy . Furthermore, we offer various strategies for modeling static- and dynamic-order quantum nonlocal effects through constant- and variable-order fractional operators, respectively. Possible directions for future developments of fractional quantum chemistry are also outlined..

Hexagonal chains are a special class of catacondensed benzenoid system and phenylene chains are a class of polycyclic aromatic compounds. Recently, A family of Sombor indices was introduced by Gutman in the chemical graph theory. It had been examined that these indices may be successfully applied on modeling thermodynamic properties of compounds. In this paper, we study the expected values of the Sombor indices in random hexagonal chains, phenylene chains, and consider the Sombor indices of some chemical graphs such as graphene, coronoid systems and carbon nanocones.

We present the derivation of a new response method termed rst order po- larization propagator approximation. The electronic structure is given by a density functional representation. We provide a detailed derivation of the method along with explicit expressions for the relevant integrals and matrix elements.

Nuclear Magnetic Resonance (NMR) shielding constants of transition metals in solvated complexes are computed at the relativistic density functional theory (DFT) level. The solvent effects evaluated with subsystem-DFT approaches are compared with the reference solvent shifts predicted from supermolecular calculations. Two subsystem-DFT approaches are analyzed – in the standard frozen density embedding (FDE) scheme the transition metal complexes are embedded in an environment of solvent molecules whose density is kept frozen, in the second approach the densities of the complex and of its environment are relaxed in the “freeze-and-thaw” procedure. The latter approach improves the description of the solvent effects in most cases, nevertheless the FDE deficiencies are rather large in some cases. KEYWORDS — Frozen Density Embedding, NMR shielding constant, solvent shifts, transition-metal complexes

A Majorana fermion is the single fermionic particle that is its own antiparticle. Its dynamics is determined by the Majorana equation, where the spinor field is by definition equal to its charge-conjugate field. In this paper, we investigated Shannon’s entropy of linear Majorana fermions to understand how this quantity is modified due to an external potential of the linear type linear. Subsequently, we turn our attention to the construction of an ensemble of these Majorana particles to study the thermodynamic properties of the model. Finally, we show how Shannon’s entropy and thermodynamic properties are modified under the linear potential action. KEYWORDS: Majorana Fermions; Thermodynamic properties; Shannon’s Entropy.

Abstract: In the present work, the geometric structures, the frontier molecular orbitals and the enthalpy of formation (HOF) of thirty six 1, 2, 4, 5-tetrazine derivatives (FTT) were systematically studied by using the B3LYP/6-311+G* method of density functional theory. Meanwhile, we also predicted the stability, detonation properties and thermodynamic properties of all FTT compounds. Results showed that all compounds have superior enthalpy of formation far exceeding that of common explosives RDX and HMX, ranging from 859kJ·mol-1-1532kJ·mol-1. In addition, the detonation performance (Q = 1426cal·g-1 -1804cal·g-1; P = 29.54GPa - 41.84GPa; D = 8.02km·s-1 - 9.53km·s-1), which is superior to TATB and TNT. It is also concluded that the introduction of coordination oxygen on the tetrazine ring can improve the HOF, density and detonation performance of the title compound, and -NH-NH- bridge and -NHNO2 group are also the perfect combination to increase these values. In view of stability, because of the fascinating performance of D3 (ρ =1.89g·cm-3; D = 9.38km·s-1; P = 40.13GPa)，E3(ρ = 1.87g·cm-3; D = 9.19km·s-1; P = 38.35GPa), F1 (ρ = 1.87g·cm-3; D = 9.42km·s-1; P = 40.23GPa) and F3 (ρ= 1.92g·cm-3; D = 9.53km·s-1; P = 41.84GPa), makes them very attractive to be chosen as HEDMs.

We have reported the electronic, magnetic, and optical properties of the top layer carbon-doped hexagonal Boron Nitride(h-BN) bilayer at B/N-sites using the density functional theory implemented in Quantumwise VNL-ATK package. The calculated structural and electronic properties of the h-BN bilayer are in agreement with the previously reported results. A single carbon doping on B and N sites modifies the large band gap semiconducting behaviour of h-BN bilayer similar to dilute magnetic semi-conducting material with a net magnetic moment of 1.001 μ B and 0.998 μ B , respectively. For double doping at B/N sites net magnetic moment increases to 1.998 μ B and 1.824 μ B , respectively. Whereas for triply carbon doped bilayer system at B/N sites, the system changes to metallic behaviour. Upon carbon doping at N-site, we obtained transition from Non-Magnetic semiconductor(Pristine) → Magnetic semiconductor(1C) → Half-Metal ferromagnetic(2C) → Metal(3C). Whereas, in case of doping at the B-site, we observed transition from Non-Magnetic Semiconductor(Pristine) → Magnetic Semiconductor(1C) → Metal (2C, 3C). Analysis from the PDOS plot of the car- bon doped systems reveals that the net magnetic moments are contributed by the 2p orbitals of carbon and partial contribution from the neighboring nitrogen and boron atoms, respectively. As 1,2C doping at the B-site reduces the energy band gap to 0.81-1.8 eV which falls in the visible spectrum and thus such system further opens up an opportunity to be utilised as a photocatalys material. Our carbon doped systems show a magnetic semiconducting behavior with a nite magnetic moment which is one of the criteria for a spintronic material. So, our system looks promising in this regard. Also, Carbon doping can be considered as a simple approach to tune the band gap of the Boron Nitride bilayer system.

To analyze the evolution of a chemical property along the reaction path, we have to extract all the necessary information from a set of electronic structure computations. However, this process is time-consuming and prone to human error. Here we introduce IRC-Analysis, a new extension in Eyringpy, to monitor the evolution of chemical properties along the intrinsic reaction coordinate, including complete reaction force analysis. IRC-Analysis collects the entire data set for each point on the reaction coordinate, eliminating human error in data capture and allowing the study of several chemical reactions in seconds, regardless of the complexity of the systems. Eyringpy has a simple input format, and no programming skills are required. A tracer has been included to visualize the evolution of a given chemical property along the reaction coordinate. Several properties can be analyzed at the same time. This version can analysis the evolution of bond distances and angles, Wiberg bond indices, natural charges, dipole moments, and orbital energies (and related properties).

It has been a challenge in automated analysis of medical and chemical knowledge to extract represent quantitative structure–activity relationship (QSAR) using intelligent computing in drug discovery. One of many domain-specific bottlenecks in drug discovery is robust conformation search in three-dimensional (3D) space for flexible drug candidates. The process involves researchers and machines working together to achieve their own strengths for greater outcome. The present study has been developing a method for conformational sampling conformers in the class of 4-anilinoquinazoline derivatives for epidermal growth factor receptor (EGFR) tyrosine kinases inhibitors (TKIs). We use AG-1478 to demonstrate how the new intelligent computing method helps to quantum mechanically determine 22 target drug conformer clusters and their properties from conformational sampling, based on density functional theory (DFT) method, time-dependent (TD)-DFT in solvents and clustering analysis (CA). The UV-vis spectra of the preferred conformers agree well with earlier experimental measurements in which the conformer dependent UV-Vis spectral shift of AG-1478 can be as large as approximately 15 nm. We are further developing this method to study and design new 4-anilinoquinazoline derivatives of EGFR TKIs.

In this paper, Tetraphenyldipyranylidene (DPPh), a large quinoidal planar π-conjugated heterocyclic, was considered as primary organic molecule in organic field effect transistors (OFETs). Electron-withdrawing atoms such as F, Cl, and Br were attached to the H-atoms of four peripheral phenyl groups of para-positions relative to the O-atoms of DPPh. Density functional theory (DFT) calculations at the M06-2X/6-311G++ (d,p) level were performed. The influences of the different electron-withdrawing atoms such as F, Cl, and Br on the electronic and optical properties, charge transport parameters, and charge carrier mobility were investigated. The absorption and emission spectra of the DPPh and its derivatives were theoretically simulated in OFETs. The simulated spectra show an intense peak in the visible region (400-650 nm), in which the highest adsorption/emission intensity is related to DPPh-Br. Moreover, the charge injection energy barrier of DPPh and its derivatives were calculated by considering Pt as the source electrode. Based on the results, a greater hole transport is predicted than the electron transport. Moreover, the obtained ratio of the hole/electron mobility and the theoretical correlations between the charge transport parameters of monomers and dimers show that the insertion of the electron-withdrawing atoms in the DPPh structure is a promising strategy to have an ambipolar or n-type semiconductor, too. The obtained results show that introducing electron-withdrawing atoms at the para-position of the DPPh improves the hole/electron injection and transport process in the OFET devices. Finally, DPPh-Br shows a great performance in comparison with the substituted F and Cl atoms in the OFETs devices.

Solving numerically a non-Born-Oppenheimer time-dependent Schrödinger equation to study the dissociative-ionization of H2 subjected to strong field six-cycle laser pulses (I = 4 × 1014 W/cm2, λ = 800 nm) leads to newly ultrafast images of electron dynamics in H2+. The electron distribution in H2+ oscillates symmetrically with laser cycle with θ + π periodicity and gets trapped between two protons for about 8 fs by a Coulomb potential well. Nonetheless, this electron symmetrical distribution breaks up for the H2+ internuclear separation larger than 9 a.u. in the field-free region at a time duration of 24 fs as a result of the distortion of Coulomb potential where the ejected electron preferentially localizes in one of the double-well potential separated by the inner Coulomb potential barrier. Moreover, controlling laser carrier-envelope phase θ enables one to generate the highest total asymmetry Aetot of 0.75 and -0.75 at 10○ and 190○, respectively, associated with the electron preferential directionality being ionized to the left or the right paths along the H2+ molecular axis. Thus the laser-controlled electron slightly reorganizes its position accordingly to track the shift in the position of the protons despite much heavier the proton’s mass.

Energetic compounds containing long nitrogen chain, have been a research hotspot. Fused heterocycles are stable due to their aromatic systems. The compound obtained by combining long nitrogen chain and fused ring can not only retain good energetic property, but also ensure better stability. This work designed eight fused heterocycle-based energetic compounds, 3H-tetrazolo[1,5-d]tetrazole (1) and its derivatives (2-8), containing a nitrogen chain with seven nitrogen atoms. The HOF, thermal stability, and energetic properties of these compounds were studied by using the DFT method. The results show that the introduction of -NO2, -N3, -NF2, -ONO2, -NHNO2 groups increased the density, HOF, detonation velocity, and detonation pressure greatly. The densities of 3, 5, 7, and 8 fall within the range designated for high-energy-density materials. The calculated detonation velocity of the compounds 3 and 8 are up to 9.86 km s-1 and 9.78 km s-1, which are superior to that of CL-20. The kinetic study of the thermal decomposition mechanism indicates that the N-R bonds maybe not the weakest bonds of these compounds. The tetrazole ring opening of the heterocycle-based energetic compounds, followed by N2 elimination is predicted to be the primary decomposition channel, whether or not they have substituent groups.

Photochemical reactions of small molecules occur upon irradiation by ultraviolet or visible light, and they are a very important and controversial chemical process in the Earth’s atmosphere because they impact our quality of life and health. Small-unsaturated carbonyl compounds play an important role in the chemistry of the polluted troposphere. The fluorinated aldehydes are very reactive under the sunlight driving to species that trigger more atmospheric reactions. This paper is focused on a theoretical study of the photochemistry of difluoro-crotonaldehyde using static and dynamic calculations by combination of Global Reaction Route mapping (GRRM) and Trajectory Surface Hopping (TSH) approach. The static analysis of the electronic and geometrical structures at the critical points allowed to rationalize the possible pathways that interconnect the stationary and crossing points in order to get a map of the unimolecular photochemical reactions which take place. The time evolution of the electronic states and the degrees of freedom enabled the identification of the requirements to follow the most probable deactivation pathways. This article reports the unimolecular deactivation pathways after the electronic excitation of the trans and cis isomers. In both cases, the excitation energies were calculated and compared with the analogous in the crotonaldehyde in order to elucidate the effect of fluorine atoms on the electronic structure and stabilities. After the initial excitations to the ππ* excited states, the main deactivation channels follow non-adiabatic pathways via S1/S0 conical intersections. Ultrafast processes leading to the early activation of the S1 govern the decay of the difluoro-crotonaldehyde. Depending on the nature of the S1 state before the crossing with the S0, the system can follow several reaction pathways. The main photochemical processes observed were the cis-trans isomerization, the Norrish type I reaction (α-cleavage), Norrish type II reaction (γ-hydrogen abstraction) and fluorine photodissociation. The time scale, the molecular deformations and the electronic states implied for the different photochemical processes, as well as how these compete with the photophysical deactivation are discussed.

The first-order relativistic corrections to the non-relativistic energies of hydrogen-like atom embedded in plasma screening environments are calculated in the framework of direct perturbation theory by using the generalized pseudospectral method. The standard Debye-Hückel potential, exponential cosine screened Coulomb potential, and Hulthén potential are employed to model different screening conditions and their effects on the eigenenergies of hydrogen-like atoms are investigated. The relativistic corrections which include the relativistic mass correction, Darwin term, and the spin-orbit coupling term for both the ground and excited states are reported as functions of screening parameters. Comparison with previous theoretical predictions shows that both the relativistic mass correction and spin-orbit coupling obtained in this work are in good agreement with previous estimations, while significant discrepancy and even opposite trend is found for the Darwin term. The overall relativistic-corrected system energies predicted in this work, however, are in good agreement with the fully relativistic calculations available in the literature. We finally present the scaling law of the first-order relativistic corrections and discuss the validity of the direct perturbation theory with respect to both the nuclear charge and the screening parameter.

In silico search for planar hexacoordinate silicon center has been initiated by global minimum screening with density functional theory and energy refinement using coupled cluster theory. The search resulted in a local minimum of SiAl3Mg3H2+ structure which contains a planar hexacoordinate silicon center (phSi). The phSi structure is 5.8 kcal/mol higher in energy than the global minimum. However, kinetic studies reveal that the local minimum structure has enough stability to be detected experimentally. Born-Oppenheimer molecular dynamics (BOMD) simulations reveal that the phSi structure can be maintained up to 400 K. The formation of multiple bonds between the central silicon atom and framework aluminium atom is the key stabilizing factor for the planar structure.

It is well noticed that hydrogen promotes catalyst activity in Cr/PNP-catalyzed ethylene tetramerization, but the mechanism of this boost is unclear. A density functional theory (DFT) study devoted to exploring this effect was conducted, and conformation changes were carefully taken into consideration to build a clear reaction pathway. Three components in the catalytic cycle was examined in detail: the production of 1-hexene from the metallacycloheptane, the production of 1-octene from metallacyclononane, and the formation of active center on the catalyst. The result indicates that the formation of active center on the catalyst becomes more favorable upon imposition of hydrogen, where hydrogen function as a second ligand. This easing effect could be the key factor leading to the outperformed catalyst activity.

In this paper, an elegant and easy to implement numerical method using matrix mechanics approach is proposed, to solve the time independent Schrodinger equation (TISE) for Morse potential. It is specifically applied to non-homogeneous diatomic molecule HCl to obtain its rotating-vibrator spectrum. While matrix diagonalization technique is utilised for solving TISE, model parameters for Morse potential are optimized using variational Monte-Carlo (VMC) approach by minimizing χ 2 − value. Thus, validation with experimental vibrational frequencies is completely numerical based with no recourse to analytical solutions. The ro-vibrational spectra of HCl molecule obtained using the optimized parameters through VMC have resulted in least χ 2 − value as compared to those determined using best parameters from multiple regression analysis of analytical expressions. Numerical algorithm for solving the Hamiltonian matrix has been implemented utilizing Free Open Source Software (FOSS) Scilab and simulation results are matching well with those obtained using analytical solutions from Nikiforov-Uvarov (NU) method and asymptotic iteration method (AIM).

Finding effective anchoring materials for the immobilization of soluble lithium polysulfides to suppress the shuttling effect has become the key to large-scale application of lithium-sulfur (Li–S) batteries. In this work, the potentials of group-VA two-dimensional (2D) materials including arsenene, antimonene and bismuthene (As, Sb and Bi monolayers) as Li-S battery cathode anchoring materials were systematically investigated by density functional theory (DFT) calculations. The adsorption energies of sulphur (S8) and various lithium polysulfides (Li2Sn, n = 8, 6, 4, 2, 1), as well as the diffusion energy barriers for long-chain Li2S4 and Li2S6 on these three monolayers were studied in detail. The calculated moderate adsorption energies of these monolayers to all polysulfides imply that they can effectively inhibit the shuttling effect. The favorable diffusion barriers for Li2S4 and Li2S6 ensure the efficient diffusion of polysulfides on monolayer surface. In addition, these 2D materials can keep a balance between the binding strength and the structural integrity of polysulfides. The presented merits demonstrate that As, Sb and Bi monolayers can be the promising cathode anchoring materials to improve the performance of Li-S batteries.