Quantum Statistical Method Research Articles

Ortho-Para Conversion for H+ + H2 Collision in Low Temperature: A Fully Close-Coupled Time-Dependent Wave Packet Study.

The collision-induced rate coefficients of ortho-para conversion for the H+ + H2 reaction provide accurate information to probe the lifetime of cold environments in interstellar media. Rotationally resolved reaction probabilities are calculated at the low collision energy regime (0 < Ecol ≤ 0.3 eV) by employing the coupled three-dimensional (3D) time-dependent wave packet (TDWP) formalism in hyperspherical coordinates on a recently constructed ab initio ground adiabatic potential energy surface of H3+ [J. Chem. Phys. 2014, 141, 204306] for the process H+ + H2 (v = 0, j = 0-5) → H+ + H2 (v' = 0, j'). Cross-sections are then computed from the converged reaction probabilities as a function of total angular momentum (J) over the same energy regime and subsequently employed to obtain the rate constants for the ortho-to-para (O-P) and para-to-ortho (P-O) conversions and their ratio. The ratio of ortho-para conversion shows (a) appropriate convergence with the inclusion of a higher number of initial rotational states as well as a reasonable agreement with the results from a quantum statistical method and (b) a peak at lower temperature that could be due to the available collision energy for transitions involving lower rotational states (j = 0 → j' = 1).

ТЕРМОДИНАМИКАЛЫҚ ЖҮЙЕДЕГІ ФИЗИКАЛЫҚ ҮДЕРІСТЕРДІ ЗЕРТТЕУ ӘДІСІ

The article uses the thermodynamic method to study the effect of temperature on the Gibbs free energy, the determination of its coefficient and the dependence of the melting temperature of phases on pressure. Nerns's thermal theorem was revised by the method of quantum statistics, and it was discussed in detail and proved that isothermal processes occur without a change in entropy as the temperature approaches T→0, and that changes in free energy (∆G), enthalpy (∆H) are characterized by a tangent parallel to abscissa axis.

Electrical conductivity of hydrogen plasmas: Low-density benchmarks and virial expansion including e–e collisions

An improved virial expansion for the low-density limit of the electrical conductivity σ(T,n) of hydrogen as the simplest ionic plasma is presented. Quantum statistical methods provide exact values for the lowest virial coefficients, which serve as a benchmark for analytical approaches to electrical conductivity as well as for numerical results from density functional theory-based molecular dynamics simulations (DFT-MD) or path-integral Monte Carlo simulations. The correction factor introduced by Reinholz et al. [Phys. Rev. E 91, 043105 (2015)] is applied to describe the inclusion of electron–electron collisions in DFT-based calculations of transport coefficients. As a benchmark, the first virial coefficient is correctly described with this approach. The value of the second virial coefficient is discussed, and questions about its value according to DFT-MD simulations are addressed.

Entropy current and entropy production in relativistic spin hydrodynamics

We use a first-principle quantum-statistical method to derive the expression of the entropy production rate in relativistic spin hydrodynamics. We show that the entropy current is not uniquely defined and can be changed by means of entropy-gauge transformations, similarly as the stress-energy tensor and the spin tensor can be changed with pseudo-gauge transformations. We show that the local thermodynamic relations, which are admittedly educated guesses in relativistic spin hydrodynamics inspired by those at global thermodynamic equilibrium, do not hold in general and they are also non-invariant under entropy-gauge transformations. Notwithstanding, we show that the entropy production rate is independent of those transformations and we provide a universally applicable expression, extending that known in literature, from which the dissipative parts of the energy momentum and spin tensors can be inferred.

Computing the Differences between Asn-X and Gln-X Deamidation and Their Impact on Pharmaceutical and Physiological Proteins: A Theoretical Investigation Using Model Dipeptides

Protein deamidation is a degradation mechanism that significantly impacts both pharmaceutical and physiological proteins. Deamidation impacts two amino acids, Asn and Gln, where the net neutral residues are converted into their acidic forms. While there are multiple similarities between the reaction mechanisms of the two residues, the impact of Gln deamidation has been noted to be most significant on physiological proteins while Asn deamidation has been linked to both pharmaceutical and physiological proteins. For this purpose, we sought to analyze the thermochemical and kinetic properties of the different reactions of Gln deamidation relative to Asn deamidation. In this study, we mapped the deamidation of Gln-X dipeptides into Glu-X dipeptides using density functional theory (DFT). Full network mapping facilitated the prediction of reaction selectivity between the two primary pathways, as well as between the two products of Gln-X deamidation as a function of solvent dielectric. To achieve this analysis, we studied a total of 77 dipeptide reactions per solvent dielectric (308 total reactions). Modeled at a neutral pH and using quantum chemical and statistical thermodynamic methods, we computed the following values: enthalpy of reaction (ΔHRXN), entropy (ΔSRXN), Gibbs free energy of reaction (ΔGRXN), activation energy (EA), and the Arrhenius preexponential factor (log(A)) for each dipeptide. Additionally, using chemical reaction principles, we generated a database of computed rate coefficients for all possible N-terminus Gln-X deamidation reactions at a neutral pH, predicted the most likely deamidation reaction mechanism for each dipeptide reaction, analyzed our results against our prior study on Asn-X deamidation, and matched our results against qualitative trends previously noted by experimental literature.

Global Full-Dimensional Potential Energy Surface for the Reaction 23Na87Rb + 23Na87Rb → 23Na2 + 87Rb2 and the Formation Rate and Lifetime of the 23Na287Rb2 Collision Complex.

A full-dimensional global potential energy surface (PES) for the reaction 23Na87Rb + 23Na87Rb → 23Na2 + 87Rb2 was constructed based on high-level ab initio calculations. The short-range part was expressed as a permutation invariant polynomial-neural network (PIP-NN) fit of 22 003 ab initio points calculated using a coupled cluster method with the one-electron basis 5s5p5d2f plus effective core potentials and core polarizability potentials, while the long-range part was represented in an asymptotically correct form based on multipole expansion. The formation rate of the 23Na287Rb2 complex calculated using a quantum statistical method is in good agreement with experiment, while the estimated 19.20 μs lifetime of the complex from Rice-Ramsperger-Kassel-Marcus (RRKM) theory is significantly shorter than the measured millisecond decay rate, signaling either the inadequacy of RRKM theory or a yet unresolved loss mechanism.

Theoretical investigation of rotationally inelastic collisions of OH(X2Π) with hydrogen atoms.

State-to-state cross sections and rate coefficients for transitions between rotational/fine-structure levels of OH(X2Π) induced by collisions with atomic hydrogen are reported in this work. The scattering calculations take into account the full open-shell character of the OH + H system and include the four potential energy surfaces (1A', 1A″, 3A', 3A″) that correlate with the OH(X2Π) + H(2S) asymptote. Three of these surfaces are repulsive, while the deep H2O well is present on one surface (1A'). The OH + H potential energy curves calculated by Alexander et al. [J. Chem. Phys. 121, 5221 (2004)] are employed in this work. Time independent quantum scattering calculations were performed using the quantum statistical method of Rackham and co-workers [Chem. Phys. Lett. 343, 356 (2001)] because of the presence of the deep H2O well. The computed cross sections include contributions from direct scattering, as well formation and decay of a transient collision complex since the transient HO-H complex is expected to decay nonreactively. Rate coefficients for OH-H inelastic collisions are of interest for astrophysical applications.

The Ionic Product of Water in the Eye of the Quantum Cluster Equilibrium.

The theoretical description of water properties continues to be a challenge. Using quantum cluster equilibrium (QCE) theory, we combine state-of-the-art quantum chemistry and statistical thermodynamic methods with the almost historical Clausius–Clapeyron relation to study water self-dissociation and the thermodynamics of vaporization. We pay particular attention to the treatment of internal rotations and their impact on the investigated properties by employing the modified rigid-rotor–harmonic-oscillator (mRRHO) approach. We also study a novel QCE parameter-optimization procedure. Both the ionic product and the vaporization enthalpy yield an astonishing agreement with experimental reference data. A significant influence of the mRRHO approach is observed for cluster populations and, consequently, for the ionic product. Thermodynamic properties are less affected by the treatment of these low-frequency modes.

Virial expansion of the electrical conductivity of hydrogen plasmas.

The low-density limit of the electrical conductivity σ(n,T) of hydrogen as the simplest ionic plasma is presented as a function of the temperature T and mass density n in the form of a virial expansion of the resistivity. Quantum statistical methods yield exact values for the lowest virial coefficients which serve as a benchmark for analytical approaches to the electrical conductivity as well as for numerical results obtained from density functional theory-based molecular dynamics simulations (DFT-MD) or path-integral Monte Carlo simulations. While these simulations are well suited to calculate σ(n,T) in a wide range of density and temperature, in particular, for the warm dense matter region, they become computationally expensive in the low-density limit, and virial expansions can be utilized to balance this drawback. We present new results of DFT-MD simulations in that regime and discuss the account of electron-electron collisions by comparison with the virial expansion.

QSAR study of unsymmetrical aromatic disulfides as potent avian SARS-CoV main protease inhibitors using quantum chemical descriptors and statistical methods

In silico research was executed on forty unsymmetrical aromatic disulfide derivatives as inhibitors of the SARS Coronavirus (SARS-CoV-1). Density functional theory (DFT) calculation with B3LYP functional employing 6-311 ​+ ​G(d,p) basis set was used to calculate quantum chemical descriptors. Topological, physicochemical and thermodynamic parameters were calculated using ChemOffice software. The dataset was divided randomly into training and test sets consisting of 32 and 8 compounds, respectively. In attempt to explore the structural requirements for bioactives molecules with significant anti-SARS-CoV activity, we have built valid and robust statistics models using QSAR approach. Hundred linear pentavariate and quadrivariate models were established by changing training set compounds and further applied in test set to calculate predicted IC50 values of compounds. Both built models were individually validated internally as well as externally along with Y-Randomization according to the OECD principles for the validation of QSAR model and the model acceptance criteria of Golbraikh and Tropsha’s. Model 34 is chosen with higher values of R2, R2test and Q2cv (R2 ​= ​0.838, R2test ​= ​0.735, Q2cv ​= ​0.757).It is very important to notice that anti-SARS-CoV main protease of these compounds appear to be mainly governed by five descriptors, i.e. highest occupied molecular orbital energy (EHOMO), energy of molecular orbital below HOMO energy (EHOMO-1), Balaban index (BI), bond length between the two sulfur atoms (S1S2) and bond length between sulfur atom and benzene ring (S2Bnz). Here the possible action mechanism of these compounds was analyzed and discussed, in particular, important structural requirements for great SARS-CoV main protease inhibitor will be by substituting disulfides with smaller size electron withdrawing groups. Based on the best proposed QSAR model, some new compounds with higher SARS-CoV inhibitors activities have been designed. Further, in silico prediction studies on ADMET pharmacokinetics properties were conducted.

Prediction of the product channels in the reaction of the methyl radical with fulminic acid

AbstractThe reaction of CH3 + HCNO was theoretically studied by both density functional theory and molecular orbital calculations and analyzed by quantum statistical methods. The potential energy surface was constructed at the UCCSD(T)//B3LYP/6‐311++G(3df,2p) + ZPE level. Four entrance channels are opened relating to the interaction of the CH3 radical with each of the four atoms of the HCNO molecule, giving rise to 18 different product sets. The predicted geometries and heats of reaction are in good agreement with available experimental data. The major pathways involve addition of CH3 to the C atom of HCNO with a small energy barrier of ∼4 kcal/mol forming both Z and E‐HC(CH3)NO (IS1/IS1b) intermediates lying 45 or 44 kcal/mol, respectively, below the reactants. The nascent intermediates can collisionally be deactivated and subsequently decomposed into H + CH3CNO or isomerized prior to decomposition giving other products. Kinetics calculations covering the temperature range of 400‐2500 K, under pressures of 7.6 × 10–1 to 7.6 × 105 Torr for N2, He, and Ar as the third bodies show that at 760 Torr N2, the adducts including both IS1 and IS1b are the major products at temperature below 600 K, whereas H + CH3CNO and CNO + CH4 are the major products at T ≥ 1500 K. The total high‐pressure rate coefficient can well be expressed by the following three‐parameter equation: k(T) = 7.75 × 10–16 T1.69 exp (−1480 K/T) cm3 molecule–1 s–1.

QSAR study of N-substituted oseltamivir derivatives as potent avian influenza virus H5N1 inhibitors using quantum chemical descriptors and statistical methods

In silico modelling studies were executed on thirty two N-substituted oseltamivir derivatives as inhibitors of influenza virus H5N1.

Gate-tunabe gap of heated monolayer graphene on substrates

Temperature effect of energy gap is researched in the presence of the homogeneous magnetic field based on the electrons/holes - surface optical phonons coupling induced by different polar substrates under monolayer graphene. The quantum statistical theory and LLP variational method are used to calculate the energy gap of monolayer graphene on the polar substrate. We found that substrate-induced gap can be tunable in the landau energy level by controlling the temperature T, confinement strength parameter g, polarization strength η of substrate. The energy gap matches with the recent experimental data. These conclusions obtained highlight the vital role of polaron effect in deciding substrate-induced gap and provide a promising way to increase the substrate-induced gap of monolayer graphene.

Application of quantum-statistical methods to studies of thermodynamic and radiative processes in hot dense plasmas

Calculations of thermodynamic and radiative characteristics of hot dense plasmas within different quantum-statistical approaches, such as the use of the Hartree–Fock–Slater model and the ion model, are presented. Calculated equations of state of different substances are used to investigate findings from absolute and relative measurements of the compressibility of solid aluminum samples in strong shock waves. It is shown that our calculated Hugoniot adiabat of aluminum is in a good agreement with experimental data and other theoretical results from first principles. We also present a review of the most important applications of the quantum-statistical approach to the study of radiative properties of hot dense plasmas. It includes the optimization problem of hohlraum wall materials for laser inertial fusion, calculations of the radiative efficiency of complex materials for optically thin plasma in X-pinch, modeling of radiative and gas-dynamic processes in plasma for experiments, where both intense laser and heavy ion beams are used, and temperature diagnostics for X- and Z-pinch plasmas.

Quantum statistical study of the C+ + OH → CO + H+/CO+ + H reaction: Reaction rate and product branching ratio at interstellar temperatures

The C+ + OH reaction is an important process in the interstellar synthesis of the CO molecule and the CO+ ion. This reaction has two possible chemical outcomes, namely, formation of CO + H+ and CO+ + H products. Formation of CO + H+ occurs on the ground 11A′ potential energy surface (PES), while CO+ + H can be formed on the 13A′ and 21A′ PESs. The stationary points on these three PESs have been found in explicitly correlated internally contracted multireference configuration interaction (icMRCI-F12a+Q) calculations. The entrance channel on the 11A′ PES is barrierless, and the barriers on the 13A′ and 21A′ PESs are submerged so that the reaction to form both sets of products can occur at interstellar temperatures. The quantum statistical method of Manolopoulos and co-workers was employed with the three PESs in the reactant channel to compute the total reaction cross section and rate coefficient, as well as the product branching ratio, as a function of temperature. These PESs can be adiabatically accessed by the ground spin-orbit state, C+(2P1/2), and the rate coefficient for the reaction of this state was estimated by invoking the adiabatic approximation.

High-order EXAFS cumulants of diamond crystals based on a classical anharmonic correlated Einstein model

The temperature dependence of high-order cumulants in extended X-ray absorption fine structure (EXAFS) of the diamond crystal structure was calculated and analyzed on the basis of the anharmonic correlated Einstein model and the classical statistical method. Thermodynamic parameters of a system were derived from the high-order anharmonic effective potential, where the Morse potential was used to characterize the interaction between each pair of atoms in expansion up to the fourth order. Analytical expressions for the first four cumulants and their contribution to amplitude reduction and phase shift were obtained in the simple form of the mean-square relative displacement or the correlated Einstein frequency. Numerical results for crystalline germanium were in good agreement with experimental values and values calculated by the quantum statistical method and other methods, especially with the values in the high-temperature range. The analytical results show that this method is useful to reduce measurement and data analysis of experimental EXAFS spectra.

The effect of nonadiabaticity on the C+ + HF reaction.

The chemistry of fluorine in the interstellar medium is particularly simple, with only a few key species and important reactions. Of the latter, the rate of the reaction of C+ ions with HF is not well established but is one of the key reactions that sets the relative abundance of HF and the CF+ ion, the two fluorine-bearing species that have been observed in interstellar clouds. The C+ + HF → CF+ + H reaction proceeds through a deeply bound HCF+ well. In this work, statistical methods, namely, the statistical adiabatic channel method originally developed by Quack and Troe and the quantum statistical method of Manolopoulos and co-workers, are applied to compute the total cross section as a function of energy for this reaction. This reaction proceeds on the ground 12 A' potential energy surface (PES), and there are also two non-reactive PES's, 12 A″ and 22 A', correlating with the C+(2 P 1/2,3/2) + HF reactants. Two sets of scattering calculations were carried out, namely, a single-surface calculation on the 12 A' PES and the one in which all three PES's and the spin-orbit splitting of C+ are included in the description of the entrance channel. In the latter, reactivity of the spin-orbit excited 2 P 3/2 level can be computed, and not just assumed to be zero, as in the single-state adiabatic approximation.

Semiclassical analysis of distinct square partitions

We study the number $P(n)$ of partitions of an integer $n$ into sums of distinct squares and derive an integral representation of the function $P(n)$. Using semi-classical and quantum statistical methods, we determine its asymptotic average part $P_{as}(n)$, deriving higher-order contributions to the known leading-order expression [M. Tran {\it et al.}, Ann.\ Phys.\ (N.Y.) {\bf 311}, 204 (2004)], which yield a faster convergence to the average values of the exact $P(n)$. From the Fourier spectrum of $P(n)$ we obtain hints that integer-valued frequencies belonging to the smallest Pythagorean triples $(m,p,q)$ of integers with $m^2+p^2=q^2$ play an important role in the oscillations of $P(n)$. Finally we analyze the oscillating part $\delta P(n)=P(n)-P_{as}(n)$ in the spirit of semi-classical periodic orbit theory [M. Brack and R. K. Bhaduri: {\it Semiclassical Physics} (Bolder, Westview Press, 2003)]. A semi-classical trace formula is derived which accurately reproduces the exact $\delta P(n)$ for $n > \sim 500$ using 10 pairs of `orbits'. For $n > \sim 4000$ only two pairs of orbits with the frequencies 4 and 5 -- belonging to the lowest Pythagorean triple (3,4,5) -- are relevant and create the prominent beating pattern in the oscillations. For $n > \sim 100,000$ the beat fades away and the oscillations are given by just one pair of orbits with frequency 4.

The entropy of an acoustic black hole in neo-Newtonian theory

In this paper, we consider the metric of a (2[Formula: see text]+[Formula: see text]1)-dimensional rotating acoustic black hole in the neo-Newtonian theory to compute the Hawking temperature, and applying the quantum statistical method, we calculate the statistical entropy using a corrected state density due to the generalized uncertainty principle (GUP). In our calculations, we have shown that the obtained entropy is finite and correction terms are generated. Moreover, the computation of the entropy for this method does not present logarithmic corrections.

Collisional excitation of ArH+ by hydrogen atoms

The rotational excitation of the 36ArH+ ion in collisions with hydrogen atoms is investigated in this work. The potential energy surface (PES) describing the 36ArH+–H interaction, with the ion bond length r fixed at the average of r over the radial v = 0 vibrational state distribution, was obtained with a coupled cluster method that included single, double, and (perturbatively) triple excitations [RCCSD(T)]. A deep minimum (De = 3135 cm−1) in the PES was found in linear H–ArH+ geometry at an ion–atom separation Re = 4.80a0. Energy-dependent cross-sections and rate coefficients as a function of temperature for this collision pair were computed in close-coupling (CC) calculations. Since the PES possesses a deep well, this is a good system to test the performance of the quantum statistical (QS) method developed by Manolopoulos and co-workers as a more efficient method to compute the cross-sections. Good agreement was found between rate coefficients obtained by the CC and QS methods at several temperatures. In a simple application, the excitation of ArH+ is simulated for conditions under which this ion is observed in absorption.