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Kassman's path deletion procedure for the determination of eigenvector polynomials (EPs) and hence the eigenvector or molecular orbital (MO) coefficients of a molecular graph is revisited with required proofs and illustrations. As EPs vanish for n-fold degenerate eigenvalues, the calculation of eigenvector (MO) coefficients for such an eigenvalue requires (n-1)-th derivative of each EP. The eigenvector coefficients for other degenerate eigenvalues are then obtained by exploiting the inherent symmetry of the molecular graph. The method of symmetry-factorisation followed by the path deletion procedure makes such calculations straightforward and simple as symmetry-factorisation distributes the degenerate eigenvalues (if there are any) in the fragmented graphs and the problem of degeneracy is thus avoided in calculating the MO coefficients for the individual fragments. The procedure is illustrated with the molecular graphs having non-degenerate and degenerate eigenvalues. [ABSTRACT FROM AUTHOR]

The performance of the recently suggested projected atomic orbitals (PAO) approach as the virtual space in excited state projection-based embedding applications is analysed. The role of the parameters in the PAO generation is discussed and the impact of different choices is evaluated on the ground state of the stacked formaldehyde and pyrrole dimers. A comparison of excitation energies obtained with PAOs and localised virtual orbitals is given and the role of diffuse basis functions is discussed using a benchmark set from previous studies. [ABSTRACT FROM AUTHOR]

Amino acids are essential for Earth-like life and are hypothesised to have originated in interstellar space, potentially being transported to Earth via meteorite impacts. Detecting amino acids in interstellar environments and understanding their formation mechanisms through laboratory experiments are crucial for supporting this hypothesis and unravelling the origins of life. In this study, the formation of serine ( $ {\rm NH}_2{\rm CH}({\rm CH}_2{\rm OH}){\rm COOH}) $ NH 2 CH (CH 2 OH) COOH) from α-glycyl ( $ {\rm NH}_2{\rm C}{\cdot }{\rm HCOOH} $ NH 2 C ⋅ HCOOH ) and hydroxymethyl ( $ {\cdot } {\rm CH}_2{\rm OH} $ ⋅ CH 2 OH ) radicals was investigated using quantum chemical computations. It was found that the anticipated recombination reaction, along with analogous formation pathways of other natural amino acids, is accompanied by competing reactions yielding alternative products, potentially diminishing serine formation. Alternative interstellar formation pathways for serine are proposed, which could be experimentally tested by future laboratory studies. [ABSTRACT FROM AUTHOR]

In recent decades, the de Broglie-Bohm or 'pilot wave' interpretation of quantum mechanics–especially its concept of the 'quantum trajectory'–has inspired a plethora of computational methods in molecular and chemical physics. One particularly promising subclass of such methods are the 'interacting quantum trajectory' (IQT) methods, for which an ensemble of trajectories is propagated independently of–and without any recourse to–an underlying wavefunction. In this work, an IQT version of the Pauli equation is developed–enabling spin to be incorporated into IQT theories for the first time, to the authors' knowledge. The new trajectory-based dynamical equations are then used to solve two iconic quantum problems involving spin: the 'quantum spin flipper', and the Stern-Gerlach experiment. [ABSTRACT FROM AUTHOR]

The predicted rotation-vibration absorption spectrum of the radioactive isotopically substituted water molecule, H214O, is presented. Variational nuclear-motion calculations are performed using the DVR3D software package based on the use of a high-precision potential energy function and an accurate dipole moment surface. Line centres, intensity and Einstein coefficients are calculated, and air pressure broadening coefficients are estimated. The calculation was carried out over a wide wavenumber range from 0 to 25000 cm $ {}^{-1} $ − 1 and total angular momentum up to J = 20. Isotopologue extrapolation rules based on experimental data on the energy levels of the stable isotopologues H216O, H $ {}_{2}^{16} $ 2 16 O H217O and H218O were also used to improve the predicted line positions. Spectral ranges best suited to the detection of H214O are identified. [ABSTRACT FROM AUTHOR]

A commonly used quantum mechanical formulation of the mean square displacement $ \delta _x^2(t) $ δ x 2 (t) is based on the quantum correlation function of the position operator. While this quantity yields the classically expected result $ \delta _x^2(t)\propto t^2 $ δ x 2 (t) ∝ t 2 for a ballistic particle in the interval topology, it is found here to diverge at essentially all times, when evaluated on infinitely large rings. A somewhat different formulation of the mean square displacement in quantum mechanics was proposed in a previous work (R. Marquardt, Mol. Phys. 119, e1971315 (2021)) and yielded the result $ \delta _x^2(t)\propto t $ δ x 2 (t) ∝ t for the ballistic particle on an infinitely large ring. Here, it is shown analytically that that formulation yields $ \delta _x^2(t)\equiv 0 $ δ x 2 (t) ≡ 0 for the ballistic particle on an infinitely long interval. The two formulations define two different, topology dependent quantities that have the dimension of an area and that could in principle be determined from the same experiment, following a measurement idea proposed in the aforementioned work. That idea is critically reviewed here. [ABSTRACT FROM AUTHOR]

Lead is heavily utilised in industry, but it bears potential harm due to its toxic nature. Identifying lead is important in diagnosing and preventing lead poisoning. Hydride generation via inductively-coupled plasma mass spectrometer (HG-ICP-MS) can detect small amounts of lead with high accuracy. Here we investigate seven structures of Pb $ _2 $ 2 H $ _2^+ $ 2 + . The geometries of each structure were optimised using coupled cluster with single, double, and perturbative triple excitations [CCSD(T)] method with the cc-pwCVQZ-PP basis set for lead and the cc-pVQZ basis set for hydrogen. Likewise, harmonic vibrational frequencies were obtained using the same method. Anharmonic frequencies were determined using CCSD(T) with cc-pwCVTZ-PP and cc-pVTZ basis sets for lead and hydrogen, respectively. The focal point approach (FPA), including CCSDT and CCSDT(Q) computations, was applied to the seven structures to find the relative energies with respect to the global minimum butterfly structure. Relative to the global minimum butterfly structure, the energies for the planar transition state, monobridged, vinylidene-like, trans, cis, and linear structures are: 1.1, 18.3, 26.5, 27.8, 28.8, and 93.7 kcal mol $ ^{-1} $ − 1 , respectively. Natural bond orders and dipole moments are reported as well. The predicted vibrational frequencies should be helpful in guiding the laboratory observation of Pb $ _2 $ 2 H $ _2^+ $ 2 + . [ABSTRACT FROM AUTHOR]

A reduced-cost explicitly correlated second-order Møller–Plesset (MP2-F12) approach is presented. Based on our recent reduced-cost explicitly correlated coupled-cluster method [J. Chem. Theory Comput., 19, 174 (2023)], the frozen natural orbital, the natural auxiliary basis, and the natural auxiliary function approximations are utilised to decrease the size of the molecular orbital basis and the auxiliary basis sets required for the density fitting and for the expansion of the explicitly correlated geminals. The necessary modifications of the above approximations for MP2-F12 are discussed. The performance of the new method is tested for atomisation and reaction energies. Our results demonstrate that speedups of 1.5–4 can be achieved in the calculation of MP2-F12 correlation energies with a moderate loss of accuracy. [ABSTRACT FROM AUTHOR]

Isotope shifts in the transition energies between several lowest $ ^3 P^{e} $ 3 P e states of the carbon atom are calculated at the nonrelativistic level of theory. We considered the $ ^{12} $ 12 C, $ ^{13} $ 13 C, and $ ^{14} $ 14 C isotopes, for which we performed variational calculations by expanding the wave functions of the atomic states in terms of all-electron explicitly correlated Gaussian functions. The Born–Oppenheimer approximation was not assumed in the calculations. By combining the computed isotope shifts with the experimentally derived Ritz wavelengths for the natural mixture of the isotopes we make predictions of the positions of the spectral lines for specific carbon isotopes. These predictions may be useful for guiding future experimental measurements of these lines using high-resolution spectroscopy. [ABSTRACT FROM AUTHOR]

The rovibrational spectrum of the molecular ion H $ _2 $ 2 CCCH $ ^+ $ + was investigated in a 4 K cryogenic ion trap instrument employing the leak-out spectroscopy method. Transitions within the fundamental $ \nu _1 $ ν 1 (C–H stretch) and the combination band $ \nu _3 $ ν 3 + $ \nu _5 $ ν 5 (C–C stretches) were detected, the search aided by high level quantum chemical calculations. The analysis of the rovibrational measurements enabled us to predict the rotational structure of the ground state. Using a rotational-vibrational double-resonance scheme, 14 pure rotational transitions were measured. This, in turn, led to the radio astronomical detection of H $ _2 $ 2 CCCH $ ^+ $ + in the interstellar medium, as recently reported (Silva et al., Astron. Astrophys. 676, L1, 2023). [ABSTRACT FROM AUTHOR]

A basic fact, having fundamental significance in quantum mechanics, is that hermitian (or self-adjoint) operators have only real eigenvalues. However, in certain applications in molecular physics, one deals with non-hermitian operators. We discuss a condition for non-hermitian operators to have real eigenvalues, proving that it is the case if and only if it can be decomposed as a product of two, generally non-commuting hermitian operators, one of which is positive definite. The theorem is illustrated on the example of non-hermitian effective Hamiltonians occurring in the non-perturbative form of the Bloch equation. [ABSTRACT FROM AUTHOR]

The reactions between ground state H 2 + (X 2 Σ g + (v = 0 , J = 0)) and D 2 forming HD 2 + + H and H 2 D + + D were investigated in the range of collision energies E coll between E coll / k B = 0 and 10 K using a merged-beam approach. The reaction rates measured experimentally are compared to those obtained for the reaction between H 2 + and H 2 forming H 3 + + H under similar experimental conditions. Below 1 K, a clear enhancement of the reaction rate coefficient compared to the Langevin rate measured at higher collision energies was observed in both reaction systems. This enhancement is interpreted as originating from the interaction between the charge of H 2 + and the quadrupole of para D 2 and ortho H 2 molecules in the J = 1 rotational level. The enhancement of the reaction with D 2 was found to be significantly less than that of the reaction with H 2 , reflecting the relative population of the J = 1 rotational level of H 2 (75%) and D 2 (33%) in natural samples at low temperatures. Simulations of the experimental results based on the theoretical predictions of the reaction cross sections by Dashevskaya et al. [J. Chem. Phys. 145, 244315 (2016)] reveal agreement within the experimental uncertainties. The branching ratio η of the reaction involving H 2 + and D 2 and forming H 2 D + and D (η = [ H 2 D + ] [ H 2 D + ] + [ HD 2 + ]) near Ecoll = 0 was determined to be 0.341(15). Time-of-flight measurements of the velocity distributions of the reaction products are compatible with an isotropic product emission with an average total kinetic energy of 0.45(5) eV for both channels, representing about 30% of the total energy released by the reaction. [ABSTRACT FROM AUTHOR]

Phys. i 2021 work was inspired by the fundamental concept of symmetry-breaking transition in a solid-liquid phase transition. Molecular modelling of crystallization has been an active area of research for a long time, and with the advancement of new simulation methods and computer resources, it is feasible to study crystallization of complex molecular as well as biomolecular systems. Subsequently, we used this NN collective variable in the on-the-fly probability-based enhanced sampling (OPES) method (the latest enhanced sampling method) which samples the solid-liquid phase transitions (see Figures 2 and 3 of our I Mol. [Extracted from the article]

In this paper, the vacancy formation at the interface between different grains (Ag3Sn and βSn) induced by electromigration was investigated from the perspective of atom diffusion. To explain the micro-mechanism of void formation near the interface, the diffusion coefficient was specifically studied here via molecular dynamics (MD) simulation. By comparing the atom diffusion rates of atoms in βSn and Ag3Sn, a significant difference could be observed when the temperature is up to 400 K. The Sn atoms in βSn have a higher diffusion coefficient (8E − 9 cm2/s) than atoms in Ag3Sn (4E − 9 cm2/s), which indicated that the void would be prone to appear in βSn near the interface. Moreover, the effect of grain size and pressure on atom diffusivity was studied. Results show that the atom diffusivity depends heavily on the grain size of Ag3Sn. When the thickness of Ag3Sn is increased from 4 to 12 nm, this difference is significant when the temperature is only 375 K. On the other hand, the atom diffusion character of Ag3Sn and βSn changes substantially under constant pressure. The difference of the atom diffusion rate would be inhibited by pressure perpendicular to the interface, which indicated voids have less possibility to appear herein. [ABSTRACT FROM PUBLISHER]

A combination of Hamilton–Jacobi equation and fast marching algorithm can be used to study reaction dynamics by converting the potential energy surface to a reaction action surface. The reaction action surface has been found to be an important tool in theoretical chemistry, allowing us to provide a different force-based perspective of chemical reactions. Several properties such as reaction force, reaction force surface, reaction path force and reaction path force constant have been defined and calculated by using the reaction action surface. This paper investigates these newly defined properties in order to understand the role they play in chemical reaction with reference to a model 4-well potential energy surface. [ABSTRACT FROM PUBLISHER]

In this paper, the spin-Hamiltonian parameters (gfactorsgx,gy,gzand hyperfine structure constantsAAx,Ay,Az) and the absorption spectrum of K2CrO4: Mn6 +crystal are theoretically explained by using the high-order perturbation theory, the double-spin-orbit-coupling model theory and the double-mechanism theory (the crystal field mechanism and the charge-transfer (CT) mechanism). The calculation results show that the contribution of the CT mechanism cannot be neglected for Mn6 +ions in orthorhombic clusters with the ground state. [ABSTRACT FROM PUBLISHER]

In this paper, density functional theory method was employed to study the electronic absorption spectrum and electronic static second hyperpolarisability of X-shaped pyrazine derivatives with two-dimensional charge-transfer structures. Computational results show that the push–pull electron abilities of the substituent groups and the length of the conjugated chains affect the electronic spectrum and static second hyperpolarisability of the pyrazine derivatives. As the push–pull electron abilities of the substituent groups or the length of the conjugated chains increases, the frontier molecular orbital energy gap decreases, resulting in increased second hyperpolarisability and redshift of the electronic absorption bands. The electronic absorption spectra of the pyrazine derivatives maintain good transparency in the blue light band. The electronic static second hyperpolarisability exhibits a linear relationship to the frontier molecular orbital energy gap. Particularly, increasing/decreasing the push–pull electron abilities of the substituent groups considerably affect the static second hyperpolarisability in long conjugated systems, which is important to the modulation of molecular organic nonlinear optical (NLO) properties. The studied pyrazine derivatives show large third-order NLO response and good transparency in the blue light band and are thus promising candidates as NLO materials for photonics applications. [ABSTRACT FROM PUBLISHER]

The coupled-cluster (CC) method is one of the most efficient approaches to describe electron correlation effects in atoms and molecules. The method can be related to other earlier and more conventional methods for an approximate evaluation of the correlation energy like perturbation theory or configuration interaction method. The relations are usually used to suggest possible ways of solving the CC equations. The most popular iterative schemes for obtaining the cluster amplitudes are based on perturbative Jacobi-type procedures but also other algorithms are known from the literature. All of them are characterised by different convergence properties. In the paper, we try to study the efficiency of the basic iterative schemes used in the CC calculations. [ABSTRACT FROM PUBLISHER]

In this paper, we investigate the electronic and magnetic properties of Cu-doped nickel clusters by means of density functional theory. The stabilities of these clusters have also been studied in terms of the binding energies, second-order difference of energies, fragmentation energies and HOMO--LUMO energy gaps. The obtained results reveal that the N4Cu, N5Cu and Ni7Cu clusters are found to be more stable that than all other clusters. Higher HOMO--LUMO gap was observed for Ni5Cu cluster (2.265 eV), indicating its higher chemical stability. A half-metallic behaviour has also been observed for the NinCu clusters, which suggests that these clusters can be employed as nanocatalysts for several catalytic processes, particularly for hydrogenation and dehydrogenation reactions. The magnetism calculations show that the magnetic moment is mostly located on the Ni atoms, and the contribution of the Cu atom to the total magnetic moment in the NinCu clusters is very small. Furthermore, partial density of states analysis indicates that the 3d orbitals in Ni atoms are mostly responsible for the magnetic behaviour of these clusters, and the s orbitals have a very little contribution to the total magnetic moment. [ABSTRACT FROM AUTHOR]

Fragment embedding approaches offer the possibility of accurate description of strongly correlated systems with low-scaling computational expense. In particular, wave function embedding approaches have demonstrated the ability to subdivide systems across highly entangled regions, promising wide applicability for a number of challenging systems. In this paper, we focus on the wave function embedding method Bootstrap Embedding, extending it to the Pariser–Parr–Pople and 2D Hubbard models in order to evaluate the behaviour of the method in systems that are less amenable to local fragment embedding. We find that Bootstrap Embedding remains accurate for these systems, and we investigate how fragment size, shape, and choice of matching conditions affect the results. We also evaluate the properties of Bootstrap Embedding that lead to the method's favourable convergence properties. [ABSTRACT FROM AUTHOR]

Coherent dynamics of localised π-electron rotations in an aromatic ring molecule may play an important role in designing next generation photo-induced organic molecular devices. In this paper, we present a theoretical study of laser control of localised π-electron rotations in a low symmetry aromatic ring molecule, which are created by the coherence of two or more electronic excited states. The control scenario is to manipulate energy spacings between two electronic states by utilising AC Stark shift induced by strong non-resonant ultraviolet (UV) laser. We set three targets for laser manipulation of localised electron rotational dynamics for (P)-2,2′-biphenol with two aromatic rings. The first target is flipping of the direction of the localised π-electron rotation on the same ring, the second one is the transfer of the π-electron rotation localisation from one aromatic ring to the other, and the third one is freezing the unidirectional π-electron rotation localised on one aromatic ring. We propose the fundamental principle of laser manipulation of localised π-electron rotation utilising AC Stark shift. Expectation values of the localised electron angular momentum are calculated numerically to demonstrate our idea of laser manipulation. Effects of laser-field intensity on localised electron rotation dynamics are briefly discussed. [ABSTRACT FROM AUTHOR]

Thermal diffusion factors play key roles in the analysis of composition variation of the mixture components in hydrocarbon reservoirs and to ensure reliable formation fluid evaluation. This paper presents the statistical thermodynamics of thermal diffusion factors of binary hydrocarbon systems using the modified theory of linear transport. The theory is revised to include the effect of pressure and unlike interaction parameters in calculating the unlike collision integrals and account for the explicit effects of the intermolecular interactions, molecular mass, energy and size parameters. The dependence of the diffusion factors on temperature, pressure and composition of the mixtures is investigated in a systematic way. Comparisons of calculated results with experimental data show that the revised theory could predict the thermal diffusion factors of binary nonhydrocarbon gas mixtures and liquid hydrocarbon mixtures very well over a range of temperature and pressure including the reservoir conditions. [ABSTRACT FROM PUBLISHER]

This paper presents a review of the BACKONE equation of state (EOS) and its various applications in the study of pure fluid and mixtures as refrigerants, working fluids, natural gases and the study of heat pumps, refrigeration cycles, organic Rankine cycles, trilateral cycles and power flash cycles. It also presents an accurate parameterisation of the BACKONE EOS for the low global warming potential working fluid 3,3,3-trifluoropropene (HFO-1243zf). The average absolute deviations (AAD) between experimental vapour pressure and saturated liquid density data from those of the BACKONE EOS are 0.12% and 0.08%, respectively. The BACKONE EOS for HFO-1243zf also predicts thermodynamic data accurately. The AAD between the BACKONE predicted values and experimental data are 0.20% for sub-cooled liquid density and 0.56% for gaseous pressure. [ABSTRACT FROM PUBLISHER]

Atmospheric oxygenation and evolution of aerobic life on our earth are a result of water oxidation by oxygenic photosynthesis in photosystem II (PSII) of plants, algae and cyanobacteria. The water oxidation in the oxygen-evolving complex (OEC) in PSII is expected to proceed through five oxidation states, known as the Si(i= 0, 1, 2, 3 and 4) states in the Kok cycle, with the S1being the most stable state in the dark. The OEC in PSII involves the active catalytic site made of four Mn ions and one Ca ion, namely the CaMn4O5cluster. Past decades, molecular structures of the CaMn4O5cluster in OEC in PSII have been investigated by the extended X-ray absorption fine structure (EXAFS). The magneto-structural correlations were extensively investigated by electron paramagnetic resonance (EPR) spectroscopy. Recently, Kamiya and Shen groups made great breakthrough for determination of the S1structure of OEC of PSII by the X-ray diffraction (XRD) and X-ray free-electron laser (XFEL) experiments, providing structural foundations that are crucial for theoretical investigations of the CaMn4O5cluster. Large-scale quantum mechanics/molecular mechanics calculations starting from the XRD structures elucidated geometrical, electronic and spin structures of the CaMn4O5cluster, indicating an important role of the Jahn–Teller (JT) effect of Mn(III) ions. This paper presents theoretical formulas for estimation of the JT deformations of the CaMn4O5cluster in OEC of PSII. Scope and applicability of the formulas are examined in relation to several different structures of the CaMn4O5cluster proposed by XRD, XFEL, EXAFS and other experiments. Implications of the computational results are discussed for further refinements of geometrical parameters of the CaMn4O5cluster. [ABSTRACT FROM PUBLISHER]

The effects of bend angle on the stability, electronic structure and optical properties of Li-absorbed borophene system are studied by using density functional theory based on the first principles. The structure of borophene did not change significantly after adsorption of a Li atom, and the planar structure of borophene was not destroyed. Bending deformation affects the stability of the adsorption system and reduces the binding energy of the adsorption system. The adsorption of Li atoms obviously changes the energy band structure of borophene, and more impurity levels appear in the conduction band. The 2s orbital of Li and the 3p orbital of B are obviously hybridised. A charge transfer occurs between Li atoms and borophene. As the deformation increases, the amount of charge transfer increases. The bending angle affects the size of the absorption peak and reflection peak of the adsorption system. [ABSTRACT FROM AUTHOR]

In this study, the interplay between aromaticity and intermolecular hydrogen bonding was investigated in some heterocyclic compounds using quantum mechanical calculations. The NH ... O intermolecular hydrogen bonds between formamide and NH and CO functional groups of the selected compounds enhance the delocalisation of the six-membered ring electron cloud, resulting in an increase in the aromaticity of the ring. The contribution of various factors to the binding energy, including the stabilisation energy of the interplay between aromaticity and H-bonding, was estimated using two model systems. The relative binding energies and the estimated stabilisation energies of the aforementioned interplay can be explained by the weights of resonance structures calculated using the natural resonance theory (NRT) analysis with the natural bond orbitals (NBO) method. These weights reflect the tendency of ring nitrogen lone pairs to contribute to the π electron cloud of the ring. The results of the topological analysis of electron charge densities using the atoms in molecules (AIM) method were used to estimate the aromaticity of the ring. Aromaticity indices, particularly nucleus-independent chemical shifts (NICS) calculated one angstrom above the ring plane, are in good linear correlation with the estimated stabilisation energies and electron density at the H-bond critical points. The sum of the total nuclear spin–spin coupling 1J of adjacent atoms of the ring (Σ1J), and the J values of H-bond donor and H-bond acceptor atoms, 1HJNO, which are in good agreement with the energy data and aromaticity indices, can be used as measures of the interplay between aromaticity and H-bonding. The interplay between H-bonding and the aromaticity of the ring is clearly evident from the changes in the pattern of the molecular electrostatic potential (MEP) contour maps at 1.7 Å above the plane of the molecule upon H-bond complexation. [ABSTRACT FROM AUTHOR]

In this study, we define Szeged-like topological coindices in which formulas are constructed by a complement of a given graph. We introduce two new co-polynomials of two variables, denoted by $ \overline {SMP} ({x,y}) $ SMP ¯ (x , y) and $ \overline {SM{P_e}} ({x,y}) $ SM P e ¯ (x , y) briefly, to compute modifications and edge versions of these molecular descriptors. In order to the perform the effect of the topological descriptors, firstly we obtain the graph structures of five novel diamide derivatives which are considered potential agents for Alzheimer's disease. After completing the computation process of each index from some modifications of the polynomials mentioned above, we correlate the coindices values with the pMIC values of the compounds against three Gram-negative bacteria E. coli, P. aeruginosa, K. pneumoniae, and three Gram-positive bacteria E. faecalis, B. cereus, S. aeurus to predict the bioactivity properties. As a result of the QSAR analysis, we get good correlations among the bioactivity data and topologic values which shows the effectiveness of our newly created coindices. Also we give mathematical equations giving the best approach to predict the relation between the topological coindices and bioactivity properties obtained by exponential regression analysis. [ABSTRACT FROM AUTHOR]

Analytical expressions for radial distribution function (RDF) are of critical importance for various applications, such as development of the perturbation theories. Theoretically, RDF expressions for odd-dimensional fluids can be obtained by solving the Percus-Yevick integral equations. But for even-dimensional cases, such as the hard disk (2D) fluid, analytical expressions are infeasible. The only 2D RDF is a heuristic expression which provides acceptable estimations for an intermediate and low density range. In this work, we employ a simple and empirical expression for the 2D RDF and the 3D RDF based on an approach proposed for the 3D RDF. The parameters are determined in such a way that the final RDF expressions are thermodynamically consistent, namely the pressure and the isothermal compressibility constraints are both satisfied. The new RDFs for the 2D and 3D hard spheres are highly accurate for the entire density range up to the first-order phase transition points. The predictions of the first coordination numbers are consistent with simulation results for the 3D fluid. Finally, by using the 2D RDF with a primitive second-order perturbation theory, the pressure-volume-temperature relation and vapor-liquid equilibrium are calculated for the 2D Lennard-Jones fluid. Comparisons with the simulation data show promising results. [ABSTRACT FROM AUTHOR]

To screen efficient organic dyes, six novel XY1b-based molecules are designed by modifying electron-assisted acceptors, and their electronic structure, optical properties and photovoltaic performances are evaluated in detail with density functional theory (DFT) and time-dependent DFT (TD-DFT) calculations coupled with the incoherent charge transfer model. Results show that benzoselenadiazole (BSD) and diketopyrrolopyrrole (DPP) are two best electron-assisted acceptors and replacing benzothiadiazole (BTD) with the BSD/DPP unit can redshift the maximum absorption peak by 13/67 nm. According to our estimation, the overall photoelectric conversion efficiency (PCE) of XY1b is as high as 13.09% with a Jsc of 16.261 mA·cm−2, Voc of 1.047 V and FF of 0.769, in good agreement with its measured value of 11.8 ± 0.2% (Jsc = 15.26 ± 0.18 mA·cm−2, Voc = 1.01 ± 0.003 V and FF = 76.3 ± 0.2%), verifying that the scheme proposed by us is reliable. With the same procedure, the predicted PCE values for dyes 1, 2 and 5 reach up to 18.00%, 15.95% and 27.37% respectively, indicating that these three dyes are potential efficient sensitisers and are worthy of further study by experiments. [ABSTRACT FROM AUTHOR]

The critical points were calculated using the Dirac equation and real optical potential model, in addition to calculating differential, integrated elastic, transfer momentum and viscosity cross sections, and Sherman function for elastic scattering of Potassium atoms at the range 4 to 150 eV and in the angular range θ = 0–180°. We obtained two critical positions (38.1 eV, 141.1°) and (128.1 eV, 120.2°) at these positions we obtained the highest polarisation of spin, and the amplitude of the spin–flip is greater than the amplitude of the direct scattering. This study is considered the first calculation of the critical points in the differential cross sections for electron scattering by potassium atom. [ABSTRACT FROM AUTHOR]

In the present study, we elucidate the behaviour of a suspension composed of magnetic disk-like particles that flow in a Hagen-Poiseuille flow in a gradient magnetic field and the trapping characteristics of the magnetic particles. To this end, we utilise multiple pairs of magnetic poles located outside the cylindrical system. Brownian dynamics simulations were performed in order to clarify the dependence of these characteristics on a variety of factors. It is seen that an increase in the magnetic field strength improves the trapping characteristics of disk-like particles if the influence of an applied magnetic field is sufficiently more dominant than that of a flow field and that of the magnetic particle-particle interaction. In the case of a strong magnetic particle-particle interaction, thin chain-like clusters are formed from an anchored particle trapped around a magnetic pole. If the two poles are sufficiently close to each other, an arch-type cluster is formed between them. We expect that this arch-type cluster may give rise to good trapping performance even in the presence of a strong flow field if the formation arises at a sufficiently large separation distance between the pair of magnetic poles. Highlights We have performed Brownian dynamics simulations for a magnetic disk-like particle suspension in a Hagen-Poiseuille flow. If the magnetic particle-particle interaction is sufficiently more dominant than the flow field, thin chain-like clusters are formed from an anchored particle. As the pole separation distance decreases, an arch-type configuration tends to be formed along the surface of the wall. This arch-type cluster that is formed between the pair of magnetic poles may be expected to improve the trapping characteristics depending on the pole separation distance. [ABSTRACT FROM AUTHOR]

Inspired by the remarkable photochemical and photophysical properties of novel 2-(2'-hydroxyphenyl)benzothiazole (HBT) derivatives that could be potentially applied across various disciplines, in this work, effects of atomic electronegativity of chalcogen elements on excited state hydrogen bond effects and excited state intramolecular proton transfer (ESIPT) reaction of the biphenyl-modified HBT derivatives (i.e. HBT-HH-O, HBT-HH-S and HBT-HH-Se) are focused. By comparing the structural changes and infrared (IR) vibrational spectra of the HBT-HH fluorophores in toluene solvent, combined with the preliminary detection of hydrogen bond interaction by core-valence bifurcation (CVB) index, we can conclude that the hydrogen bond could be strengthened in S1 state, which is favourable for the occurrence of ESIPT reactions. The charge recombination behaviour of hydrogen bond induced by photoexcitation also further illustrates this point. Via constructing potential energy curves (PECs) based on restrictive optimisation and searching transition state (TS) form, we confirm the variations of atomic electronegativity of chalcogen have the regulatory effect on the ESIPT behaviour for HBT-HH derivatives, that is, the lower the atomic electronegativity is more conducive to the ESIPT reaction. [ABSTRACT FROM AUTHOR]

A semiempirical molecular-orbital approach has been developed to calculate the dissociation energies of 57 second-row neutral and charged diatomic molecules. One-electron energies and wave functions were used. The 2s and 2p electrons have separate energies and separate values of Z2S and Z2P. Calculations were made with a CNDO/INDO FORTRAN programme modified to a level of approximation that is more similar to extended Hückel calculations than to either CNDO or INDO. The correlation between calculated and experimental dissociation energies was favourable with a relative standard deviation of 15%. Additionally, dipole moments for the molecules were calculated concurrently with the same parameters. The correlation between calculated and experimental dipole moments was favourable for seventeen molecules with a relative standard deviation of 19%. The correlation between calculated and experimental ionisation potentials for fourteen molecules was also favourable with a relative standard deviation of 11%. Also, a repulsion work function was formulated and used in this work between pairs of atoms. For 90% of the molecules studied, the maximum calculated dissociation energy occurred within ±0.1 Å of the experimental bond distance. The semiempirical methods used in the present work could be used for future studies of larger molecules, including organic molecules. [ABSTRACT FROM AUTHOR]

Recently, more and more researchers have committed to designing higher-performance materials to improve the power conversion efficiencies (PCEs) of OSCs. However, the inherent laws of synthesising high-quality organic materials are still ambiguous. It is important to explore the structural effect on the photoelectric properties of the synthesised organic. In 2023, the Zou group designed two electron donors, 2DTBDT and 2DTBDT-2T, which are respectively without and with bithiophene in the molecular skeleton. The introduction of bithiophene into 2DTBDT-2T made the PCE of 2DTBDT-2T:Y6 heterojunction triple the 2DTBDT counterpart. Based on this, we selected eco-friendly electron acceptors, CBM, FBR, O-IDFBR and O-IDTBR, to compose the heterojunction with 2DTBDT and 2DTBDT-2T. The ionisation energies (IEs) and absorption spectra of all independent molecules and the excitation energy transfer (EET) couplings of heterojunction are accurately investigated from many-body Green's function theory (MBGFT). We found that the electronic structure and excitation are sensitive to the resonance-antiresonance transitions and the electron–hole interactions. The thienyl group makes the molecule lower CT energy and the stronger EET coupling of heterojunctions, to promote the efficiency of relevant OSCs. The Dexter and overlap types couplings are very important to the study on the EET of organic heterojunctions. [ABSTRACT FROM AUTHOR]

The nitro groups are introduced into 4-(1H-1,2,4-triazol-1-yl) pyrimidine to substitute the hydrogen atoms successively, through which a total of 31 derivatives are constructed to look for high energy density compounds (HEDCs). To probe the thermal stabilities, the heats of formation (HOFs) are calculated by using the G3MP2 method. To explore the dynamic stability, the natural bond orbital (NBO) analysis is performed to confirm the trigger bond, for which the bond dissociation energy is calculated using the B3PW91 method with the 6-311 + G(d,p) basis set. Furthermore, the detonation velocity (D), the detonation pressure (P), the molecular density (ρ), the explosive heat (Q), and character height (H50) are also predicted. Based on our calculation, it is confirmed that D1, D2, D5, and E are potential high-energy-density compounds with sufficient stability and excellent detonation performance. [ABSTRACT FROM AUTHOR]

It is crucial to identify an efficient system for the sensing of formaldehyde (FD). The feasibility of utilising a B3S monolayer (B3SML) detector of FD was evaluated by analysing the adsorption, optical properties, gas-sensing behaviour, and electronic properties of FD and other gas molecules on the B3SML under density functional theory (DFT). The pristine B3SML was found to have satisfactory sensing toward FD molecules. The analysis of the adsorption mechanisms, geometric systems, adsorption energy, electronic and optical properties, charge transfer, and electron density differences revealed that the B3SML could potentially serve as an FD detector. It can be said that the B3SML is a promising sensor for detecting FD molecules. The present study contributes to the existing knowledge of gas-surface interactions and helps develop 2D sensor structures to detect FD gas molecules. [ABSTRACT FROM AUTHOR]

In this article, the adsorption process of transition metal Fe-doped ZIF-67 material on characteristic gases in oil was investigated based on the first principles. The geometry optimisation model, adsorption parameters, energy band structure, TDOS and PDOS of each adsorption system were analysed and compared. The results showed that Fe-ZIF-67 chemically adsorbed all four characteristic gases in oil. And after doping, the adsorption energy of ZIF-67 material to CO gas can be greatly improved, but the adsorption energy to C2H2 gas is reduced. The adsorption performance ranking is CO > C2H2 > C2H4 > C2H6. This result shows that the addition of Fe enhances the selective absorption of characteristic gases in oil by ZIF-67 materials. The addition of Fe enhances the selective absorption of characteristic gases in oil by the ZIF-67 material. This article offers part of the theoretical evidence for the selective detectability and gas adsorption of characteristic gases in oil by ZIF-67 material. [ABSTRACT FROM AUTHOR]

This study offers the impacts of MHD Jeffery fluid research on a stretching cylinder. The Cattaneo–Christov heat model is acquired instead of the Fourier law of heat conduction to construct the energy equation. The order analysis of a fluid model is performed using the boundary layer theory. On differential equations, appropriate similarity transformations are used to attain the differential equations. The following nonlinear equations were then mathematically solved utilising the shooting method. The visual inspection of the conclusions of the velocity, thermal and concentration profiles is completed for several important thermophysical parameters. For numerous thermos physical variables, the numerical variation in the valuations of the mass transport rate, coefficient of skin friction and heat rate transfer has been assessed and provided in a table. The main conclusions of the study show that temperature, concentration distribution and flow speed all decrease as the curvature parameter increases. It has also been deduced in this investigation that the higher values of the Lewis number higher the mass transfer rate and lower the heat flux at the surface of the cylinder. These results exhibit a more favourable agreement across all findings when compared to previous findings. [ABSTRACT FROM AUTHOR]

Inspired by the brilliant photophysical properties of novel organic molecules containing chalcogenide substitution, in this work, effects of atomic electronegativity of chalcogen (O, S and Se) on hydrogen bond interactions and proton transfer (PT) reaction are focused. We present the characteristic CN-BTN is the main objective to explore the influence of atomic electronegativity on the hydrogen bond interaction and excited state intramolecular proton transfer (ESIPT) behaviour by photoexcitation. By comparing the structural changes and infrared (IR) vibrational spectra of the CN-BTN derivatives (CN-BTN-O, CN-BTN-S and CN-BTN-Se) fluorophores in S0 and S1 states, combined with the preliminary detection of hydrogen bond interaction by core-valence bifurcation (CVB) index, we can conclude that hydrogen bond is strengthened in S1 state, which is favourable for the occurrence of ESIPT reaction. The charge recombination behaviour of hydrogen bond induced by photoexcitation also further illustrates this point. Via constructing potential energy curves (PECs) based on restrictive optimisation and searching transition state (TS) configuration, we finally clarify the ESIPT mechanism for CN-BTN derivatives. Specially, we confirm change of atomic electronegativity has a regulatory effect on the ESIPT behaviour of CN-BTN derivatives, that is, the lower the atomic electronegativity is more conducive to the ESIPT reaction. [ABSTRACT FROM AUTHOR]

In this study, we present a glucose sensor that utilises photonic crystal fibre. The proposed sensor was analysed and demonstrated numerically. A unique structure was infiltrated into the first ring of holes with glucose, serving as the test analyte. We achieved an exceptionally high average spectral sensitivity. Three different wavelengths, 1.1, 1.3 and 1.55 µm, were selected for this investigation. Notably, while the reported sensitivity was already high when the remaining gaps within the structure were filled with air, it was significantly higher when the holes were infiltrated with water at a wavelength of 1.55 µm, calculated to be 0.11493 ps/(nm·km)/(g/l). We anticipate that this sensor will prove to be a valuable tool for glucose sensing and could contribute to further advancements in non-invasive glucose measurement. [ABSTRACT FROM AUTHOR]

It is shown by tiling that only three out of the thirteen title molecules are planar. Using our recent concept of quasi-molecule ('tile') or its generalisation, all participating tiles have been here optimised in a few spin-states both at the DFT level with the B3LYP and M06-2X functionals, and using the CCSD(T) method. While borazine ( $ 1,4,6-{\rm B}_3{\rm N}_3{\rm H}_6 $ 1 , 4 , 6 − B 3 N 3 H 6 ) was synthesised in the forties of the past century, its next up-lying planar isomer ( $ 1,3,4-{\rm B}_3{\rm N}_3{\rm H}_6 $ 1 , 3 , 4 − B 3 N 3 H 6 or $ {\rm BHNHNHBHBHNH} $ BHNHNHBHBHNH ) was not. Quasi-tetratomic tiles are then shown to be shape-determining while 5-body terms and beyond are shape-preserving. The need to bring the notion of planarity as a probabilistic outcome is also examined, and the concept of planarity likelihood ratio (index) introduced. As for the above borazine isomers, this index is also predicted to be unit for $ 1,4-{\rm B}_4{\rm N}_2{\rm H}_6 $ 1 , 4 − B 4 N 2 H 6 , a result that is corroborated upon its optimisation at DFT/B3LYP/AVTZ level but not with M06-2X by which it is predicted as quasi-planar. Nevertheless, recent work with a derivative of diazatetraborinine where all atoms are bonded to substituent atoms or groups of atoms confirms the planarity of the $ {\rm B}_4{\rm N}_2 $ B 4 N 2 ring. Such a result is further corroborated at the gold-standard CCSD(T) level. Although planarity is also predicted for $ {\rm B}_6{\rm H}_6 $ B 6 H 6 , DFT and CCSD(T) frequency calculations suggest it to be likely a saddle point. [ABSTRACT FROM AUTHOR]

New diabatic potential energy surfaces (PESs) for the KH2 system, related to both ground and first excited states, were constructed using only adiabatic electronic energies. The elements of the diabatic potential energy matrix were determined using neural network (NN) method. Prior to calculation, the symmetry constraints of the coupling term were incorporated into the NN code. A comprehensive comparison was undertaken between the topographic characteristics of the newly constructed diabatic PESs and those previously developed using the molecular properties method. To validate the accuracy of the new diabatic PESs, the dynamics calculations of K(4p2P) + H2 (v0 = 1, j0 = 0) reaction were performed based on both new and old diabatic PESs with same parameters. The results indicate that the values based on the new diabatic PESs generally agree well with those from the old ones. In addition, compared with the previous diabatic PESs, the new diabatic PESs can accurately describe the geometric phase effect. [ABSTRACT FROM AUTHOR]

Herein, the molecular structures of amide ↔ imide tautomers of articaine (ART) were computationally investigated at the DFT/B3LYP/6–311++G (d,p) methodology. Experimental FT-IR and UV-Vis characterisation results of ART were compared with the theoretical results of amide (ART-A) and imide (ART-I) forms. Thermodynamic parameters computed for each phase revealed that the amide tautomer of ART was preferred with energy values in the range of 11.9–13.8 kcal/mol. The modification in surface properties as a function of prototropic tautomerism in the ART molecule was studied by electrostatic surface properties (ESP) analysis. Frontier molecular orbital (FMO), natural bond orbital (NBO), and nonlinear optical (NLO) analyses were performed. It is revealed that energy gap values of the ART-I (4.670–4.738 eV) for each phase are slightly higher than those of the corresponding phases in the ART-A (4.515–4.586 eV). Therefore, it can be concluded that the imide form exhibits lower chemical reactivity compared to the amide form. Regarding NLO characteristics, dipole moment (μtot), mean polarisability (αtot), and mean first-order hyperpolarisability (βtot) values of tautomers have been reported. It was determined that the βtot values computed for ART-A (0.653 × 10−30 esu) and ART-I (0.710 × 10−30 esu) were approximately twice the value of the standard urea. [ABSTRACT FROM AUTHOR]

Lately, the significance of employing nanostructured materials for extracting organic solvents from various mediums has grown in different industries. This includes the development of innovative and versatile nano adsorbents. Computational methods, particularly those utilising dispersion corrected DFT approach, have proven to be powerful tools for investigating the nature of interactions and exploring molecular systems at the atomic level. In order to thoroughly investigate how Eriochrome Black T molecules cling to an o-B2N2 monolayer, we used the dispersion corrected DFT approach in this study. As part of our research, we looked at the fundamental causes of molecular scale experimental results. We used techniques including charge transfer, density of states, and molecular orbitals to investigate a variety of aspects, including energy and electrical elements. We also investigated the relationship between the sensor response (R) and the HOMO-LUMO energy gap. Particularly noteworthy were the o-B2N2 monolayer and EBT, both of which demonstrated significant chemisorption with an adsorption energy (Ead) of −1.11 eV. The conductivity of these devices significantly increased as EBT adsorption neared completion, demonstrating the potential of the o-B2N2 monolayer as a reliable electrical EBT sensor. Moreover, at 698 K, the projected recovery time for the sensor stands at 580 s. [ABSTRACT FROM AUTHOR]

In this study, twelve drugs used to treat Parkinson's disease were analyzed. To simplify calculations and data analysis, a computer-based computing technique along with the algorithm has been employed. The M-polynomial and their degree-based topological indices derived from the M-polynomial were calculated using MATLAB coding. Linear, quadratic, cubic, logarithmic, inverse, power, compound, s-curve, growth, and exponential regression model analyses were utilized to create QSPR models between the topological indices and eight the Physicochemical properties of the drugs to determine their effectiveness. Confidence intervals at a 95% level were computed for both the slope and intercept of the linear regression models. Also, based on the maximum $ R^{2} $ R 2 , optimal equations for estimating the Boiling point, Enthalpy of vaporization, Molar refractivity, Polarizability, and Molar volume using different indices have been determined, and linear, quadratic, and cubic equations have been specified. Calculated feature values are strongly correlated with actual values, indicating reliable predictive capabilities of the indices. For statistical analysis and to determine if there is a significant difference between the averages of the two groups, we used either an independent T-test or Welch's T-test. The results show that the p-value is less than 0.05, which indicates that the mean difference between the samples is statistically significant. [ABSTRACT FROM AUTHOR]

Density functional theory (DFT)-based calculations were performed for 36, 72 and 108 water molecules forming twisted ribbon-like nano-ring structures of diameter 1.54, 3.10 and 4.56 nm, respectively. We explore the electric field evolution of the structure, energetics and stability of the water nano-ring structures that are essentially symmetric and non-polar, or less-symmetric and polar, hydrogen-bonded clusters. The results suggest that for fields applied perpendicular to the ring, larger rings are more susceptible to the field influence, while fields applied parallel to the ring quickly transform the ring structures into arbitrary ones, regardless of the ring size. Infrared and Raman spectral analysis of local modes demonstrate the typical vibrational response of water molecules to various H-bonding environments and applied fields, providing a spectroscopic signature that can be used to identify the manifestation of such H-bonded ring networks. Our study underscores the implications of the nano-sized ring water clusters, which have the potential to be exploited in a variety of device applications. [ABSTRACT FROM AUTHOR]

The now classic Foldy–Wouthuysen transformation (FWT) was introduced as successive unitary transformations. This fundamental idea has become the standard in later developments such as the Douglas–Kroll transformation (DKT) – but it is not the only possibility. FWT can be seen as a simple special case of the general Van Vleck transformation (VVT) which besides thesuccessiveversion has another, known as thecanonicalbecause of a series of nice mathematical properties discovered gradually over time. The aim of the present paper is to compare the two approaches – which give identical results in the lower orders, but not in the higher. After having recapitalised both, we apply them to Dirac's Hamiltonian for the electron in a constant electromagnetic field, written with so few assumptions about the operators that the mathematical techniques stand out separated from the terminology of relativistic quantum mechanics. FWT for a free particle is dealt with by a recent geometric approach to VVT. The original FWT is continued through the next non-zero orders. DKT is considered with special weight on equivalent formulations of the generalised and the optimised forms introduced by Wolf, Reiher and Hess. [ABSTRACT FROM AUTHOR]

Approaches and programs for calculations of the EPRg-tensor in the framework of the two- and four-component methods are still very rare. There are three main reasons for this: the wider community's unawareness of the importance of second- and higher order spin–orbit effects on theg-tensor, the methodological problems associated with performing such calculations and the lack of understanding of these problems. This paper reports on the implementation of a method for calculation of theg-tensor in the framework of the relativistic unrestricted two- and four-component Hartree–Fock and density functional theory approaches based on the Kramers pair formalism. This implementation allows us to analyse problems which arise when theg-tensor is calculated via Kramers pairs in the unrestricted framework. [ABSTRACT FROM AUTHOR]

The detailed structure and clustering free energy of aerosol particles are important for understanding of new particle formation from molecules and ions in the atmosphere. In this paper, configurations of the H2SO4·HSO−4dimer were sampled with meta-dynamics aidedab initiomolecular dynamics (MTD-AIMD) simulations. Based on the rigid rotor harmonic oscillator (RRHO) approximation and the law of mass action, the binding free energies (ΔG) of the dimer in the most stable configuration were calculated for three atmospheric circumstances, i.e. at the ground level and in the middle and upper troposphere. The results show that, the most stable H2SO4·HSO−4dimer is combined via triple O–H⋅⋅⋅O hydrogen bonds. It can be generated efficiently in both the middle and upper troposphere, but not at the ground level. All our simulations were carried out at the level of hybrid density functional theory (PBE0, hybrid-DFT), which is more accurate than DFT only. [ABSTRACT FROM AUTHOR]

Periplasmic binding protein-dependent maltose transport system (MBP-MalFGK2) ofEscherichia coli, an important member of the Adenosine triphosphate-binding cassette transporter superfamily, is in charge of the transportation of maltoses across cellular membrane. Studies have shown that this transport processes are activated by the binding of maltose and are accompanied by large-scale cooperative movements between different domains which are mediated by a network of important residues related to signal transduction and allosteric regulation. In this paper, the functionally crucial residues and long-range allosteric pathway of the regulation of the system by substrate were identified by utilising a coarse-grained thermodynamic method proposed by our group. The residues whose perturbations markedly change the binding free energy between maltoses and MBP-MalFGK2were considered to be key residues. In result, the key residues in 62 clusters distributed in different subdomains were identified successfully, and the results from our calculation are highly consistent with experimental and theoretical observations. Furthermore, we explored the long-range cooperation within the transporter. These studies will help us better understand the physical mechanism of the effects of the maltose on MBP-MalFGK2by long-range allosteric modulation. [ABSTRACT FROM PUBLISHER]