Comparison of classical, semiclassical and quantum methods in hydrogen broadening of acetylene lines

Quantum close coupling (CC) calculations of H₂-broadening coefficients of infrared and isotropic Raman lines of acetylene (C₂H₂) are performed for temperatures between 77 and 2000 K. They are used to test three more approximate methods, the quantum coupled states (CS) theory, the semiclassical Robert-Bonamy (RB) formalism and the full classical (FC) model of Gordon. In order to allow a clear and well founded comparison, all the dynamical calculations were performed employing the same ab initio potential energy surface free of any adjustable parameters. It is shown that below room temperature both the coupled states method and full classical method fail at reproducing the close coupling pressure broadening coefficients while above room temperature they are correct and predict comparable accurate values for temperatures greater than about 1000 K. The values provided by the RB method are clearly not satisfactory even at the highest temperature examined. However, the temperature dependence of the RB results follows the functional form used for interpolating and extrapolating CC, CS and FC pressure broadening coefficients.     

Thermal helium clusters at 3.2 Kelvin in classical and semiclassical simulations

The thermodynamic stability of⁴He_4–13 at 3.2 K is investigated with the classical Monte Carlo method, with the semiclassical path-integral Monte Carlo (PIMC) method, and with the semiclassical all-order many-body method. In the all-order many-body simulation the dipole-dipole approximation including short-range correction is used. The resulting stability plots are discussed and related to recent TOF experiments by Stephens and King. It is found that with classical Monte Carlo of course the characteristics of the measured mass spectrum cannot be resolved. With PIMC, switching on more and more quantum mechanics. by raising the number of virtual time steps results in more structure in the stability plot, but this did not lead to sufficient agreement with the TOF experiment. Only the all-order many-body method resolved the characteristic structures of the measured mass spectrum, including magic numbers. The result shows the influence of quantum statistics and quantum mechanics on the stability of small neutral helium clusters.     

Semiclassical line broadening calculations,using an ab initio potential energy surface,in Q‐branch and S‐branch of N2 perturbed by H2

In order to improve the accuracy of Raman combustion diagnostics, the broadening coefficients of N₂ perturbed by H₂ for Q‐branch and S‐branch have been calculated by the semiclassical Robert–Bonamy model using an ab initio potential energy surface. The calculations have been performed for a large range of temperatures (from 77 to 800 K) and J rotational quantum numbers (from 0 to 60). This paper shows that our results and their temperature dependence are in good agreement with earlier published experimental and theoretical data. Moreover, our results improve the semiclassical calculations made earlier with an adapted analytical potential. The results, obtained at high temperatures and for a large range of rotational quantum numbers, are presented in order to be implemented for optical diagnostics in combustion media. Copyright © 2012 John Wiley & Sons, Ltd.     

Comparison of quantum, semiclassical and classical methods in hydrogen broadening of nitrogen lines

We use an accurate N₂-H₂ab initio potential energy surface (PES) in order to inter-compare various methods commonly employed to calculate pressure broadening coefficients. Close-coupling (CC) calculations of the collisional linewidths of the isotropic Raman lines of N₂ perturbed by H₂ are performed for temperatures between 77 and 2000 K. The CC results compare well with available experimental values. Three less exact methods of calculation are also used: the full classical (FC) model of Gordon, the semiclassical (SC) formalism of Robert and Bonamy and the quantum dynamical coupled states (CS) method. The CS method provides good agreement with CC calculations for all studied temperatures, FC calculations can be considered as accurate above room temperature while the SC method gives overestimated values by about 20-30% in all cases. The temperature dependences of pressure broadening coefficients provided by each method are very similar at elevated (above room) temperatures.     

The Kirkwood-Salsburg integral equation and the virial coefficients of Lennard-Jones molecules

The fifth virial coefficients E_c and E_p are derived for a classical fluid composed of molecules interacting according to the Lennard-Jones potential. The calculations are based on the Kirkwood-Salsburg integral equation and the superposition approximation. It is found that, unlike the systems considered in a previous communication, satisfactory agreement between the present results and the known values is possible only at high temperatures.     

Diffusion coefficient of krypton atoms in helium gas at low and moderate temperatures

In the present work, using the Chapman–Enskog method for dilute gases, the diffusion coefficients of ground krypton atoms in a very weakly ionized helium buffer gas are revisited. The calculations are carried out quantum mechanically in the range of low and moderate temperatures. The ¹ Σ⁺ potential-energy curve via which Kr approaches He is constructed from the most recent ab initio energy points. The reliable data points used in the construction are smoothly connected to adequate long- and short-range forms. The calculations of the classical second virial coefficients and the Boyle temperature of the helium–krypton mixture are also discussed. These coefficients and their variations in terms of temperature are analysed by adopting the constructed HeKr potential and the Lennard–Jones form that fits it. The diffusion and elastic cross sections are also explored and the resonance features they exhibit are closely examined. The variation law of the diffusion coefficients with temperature is determined for typical values of density and pressure. The coefficients show excellent agreement with the available experimental data; the discrepancies do not exceed 5%.     

Ab initio calculation of the refractivity and hyperpolarizability second virial coefficients of neon gas

Second virial coefficients for the density dependence of a number of electric properties are calculated for neon gas. Employing an accurate CCSD(T) potential for the Ne² van der Waals dimer and interaction-induced electric dipole polarizabilities and hyperpolarizabilities obtained from CCSD response theory, we evaluated the dielectric, refractivity, Kerr and ESHG second virial coefficients using both a semiclassical and a quantum statistical approach. The results cover a wide range of temperatures and are expected to be more reliable than the available experimental and empirical data. Quantum effects are found to be important only for temperatures below 100 K. The frequency-dependence of the refractivity virial coefficient is found to be small, but not negligible. For frequencies in the visible region it accounts for a few percent of the final results. For the ESHG virial coefficient of neon, frequency dependence is found to be very important, accounting for 20–25% of the second virial coefficient at the typical frequencies employed in experiments.     

Calculation and analytical representation of self-pressure and air pressure broadening coefficients of ozone spectral lines

The coefficients γ of broadening by self-pressure, and pressure of nitrogen, oxygen, and air are calculated for absorption lines of the rotational band and for the ν₂ band of the ozone molecule for temperatures 296, 252, and 212 K. The calculations are performed by the semiclassical method using rectilinear and exact trajectories for interacting molecules. It is shown that the experimental data obtained for the two bands at T = 296 K can be reconstructed better using different isotropic intermolecular interaction potentials. The experimental and calculated broadening coefficients of ozone absorption lines for the rotational band and for the ν₂ and ν₁ + ν₃ vibrational bands were used to determine the parameters of an analytical model, which permits one to calculate γ in a wide range of rotational quantum numbers, 0 ≤ J ≤ 45, 0 ≤ K _a ≤ 20, and temperatures of 200–296 K.     

Editorial

Using coupled cluster singles and doubles linear response theory and the d-aug-cc-pVTZ basis set extended with a 3s3p2d1f1g set of midbond functions, the interaction induced electric dipole polarisability surface of the CO–Ar van der Waals complex is computed. Combining this surface with accurate intermolecular potential energy and electric dipole surfaces, the pressure and dielectric second virial coefficients of the complex are calculated by a classical statistical approach. Excellent agreement with experimental results (to within the experimental error bars) is obtained for the pressure second virial coefficient over a range of temperatures. No previous experimental or theoretical investigations have been carried out for the dielectric second virial coefficient, B _ε(T), which is estimated to be about 1.9 cm⁶ mol^??1 at room temperature. This value results from a balance of terms due to the interaction induced electric dipole polarisability (predominant at high temperatures) and orientational electric dipole contributions.     

Fluids of general hard triatomic molecules

The second, third, and fourth virial coefficients, B_i , of a fluid of general symmetric hard triatomic molecules (fused hard spheres) have been calculated both numerically and theoretically for a variety of potential parameters. It has been found that: (i) for B₂ a valency angle ω_c exists such that for ω>w_c, B ₂ is independent of ω, (ii) B ₃ is very flat for ω>w_c, and (iii) B ₄ exhibits a maximum at ω～π/2. Theoretical calculations employing an assigned convex body fit very well the second and fairly well the third virial coefficients, but fail for the fourth except in the case of a linear molecule.     

Virial expansion for the radial distribution function of a fluid using the 6 : 12 potential

The radial distribution function can be expressed in a virial expansion. Using the 6 : 12 potential the second-order density coefficient, g ₂(r), is numerically calculated for a wide range of temperatures and intermolecular separations. These results are used to calculate the second-order density coefficient, c ₂(r), in the expansion of the direct correlation function and to calculate the fourth virial coefficient, B ₄. In addition, approximate results for g ₂(r), c ₂(r), and B ₄ are calculated on the basis of the Percus-Yevick, hypernetted chain, and the self-consistent approximations of Hurst and Rowlinson. These approximate results are compared with the exact results. The Percus-Yevick theory is in good agreement with the exact results at high temperatures but is unsatisfactory at low temperatures. The hyper-netted-chain approximation is in fair agreement with the exact results at high temperatures, is in poor agreement at intermediate temperatures, but is in good agreement at low temperatures. The self-consistent approximations are in reasonably good agreement with the exact calculations at all temperatures.     

Theoretical and experimental analysis of N2–H2 stimulated Raman spectra

The paper reports on a detailed study of the N₂–H₂ collisional line broadening coefficient. High resolution stimulated Raman spectra of nitrogen–hydrogen mixtures have been recorded at liquid nitrogen and room temperatures. Corresponding linewidth calculations have been performed at temperatures between 77 and 500?K using the semiclassical Robert and Bonamy model for J rotational quantum numbers varying between 0 and 11. Comparison between experimental data and calculated results shows good agreement at room temperature using an adjusted value for the kinetic diameter.     

Semiclassical and quasiclassical calculation of reaction probabilities for collinear X + F2→XF + F (X = Mu,H, D,T)

Semiclassical calculations of reaction probabilities have been carried out for the collinear H + F₂ (n = 0, 1) reaction using the best extended LEPS surface No. II of Jonathan et al. Both real and complex valued classical trajectories have been included in the calculations for an energy range where the quasiclassical total reaction probability is unity. Comparison with quantum results shows the semiclassical reaction probabilities are accurate to about ± 0·05 provided only two real or complex stationary phase points make an important contribution to the S matrix element, so that the uniform Airy or integer Bessel approximations are valid. Real semiclassical calculations are also reported for the collinear Mu, D, T + F₂ (n = 0) reactions. For the D and T reactions, the semiclassical reaction probabilities are estimated to be accurate to ± 0·05, except close to the reaction threshold, but for the Mu reaction the estimated errors are much larger. In addition, quasiclassical calculations for the reaction probabilities have been carried out using half integer boxing and smooth sampling methods to quantize the product distributions. For the H + F₂ reaction, there are usually systematic deviations from the quantum reaction probabilities and the same is expected to be true for the Mu, D and T reactions.     

Overlap graph representation of B6 and B7

The virial coefficients B_n of the pressure of a thermodynamic system can be represented in terms of graphs. The recently defined overlap graphs are studied in detail. Furthermore, the overlap graph representation of the sixth and seventh virial coefficientsB ₆ andB ₇) is determined.     

On the accuracy of classical, semiclassical and quantum methods in collision line broadening calculations: Comparative analysis for C2H2-Ar, He systems

Accuracies of classical, semiclassical and quantum methods are comprehensively examined in calculations of impact line widths of C₂H₂ molecules perturbed by Ar and He. The field of comparative study covers both infrared absorption and Raman scattering lines of acetylene having rotational quantum number J=0-30 at temperatures 173 and 296 K. Calculations have been made by fully classical method and by three basic least approximate semiclassical methods, namely, Neilsen-Gordon (NG) method, peaking approximation (PA) and Smith-Giraud-Cooper (SGC) method. Most accurate ab initio potential energy surfaces (PES) of Yang et al. (1996) [21] and Mozsynski et al. (1995) [22] have been applied to model C₂H₂-Ar and C₂H₂-He interactions. The comparison has been made also with available experimental data and with the results of rigorous fully quantum-mechanical calculations within close coupling and coupled states approaches in identical conditions. Semiclassical methods are proved to be not so much accurate as it is generally believed since all they gave in the cases considered seriously underestimated results. The fundamental issue of the adequacy of simplified trajectories in collision broadening calculations is finally reasonably solved. In cases of C₂H₂-Ar and C₂H₂-He systems the use of the “exact” isotropic trajectories (i.e. driven only by the isotropic part of PES) is the main reason of failing of NG, PA and SGC methods. Thus the neglecting of back-influence of the RT exchange on the classical path is a principal defect of semiclassical methods. Finally, the application of simplified trajectories is recognized as inadequate and risky in broadening calculations for molecules having relatively small rotational constants when accurate ab initio PES are applied.     

Comparison of quantum,semi-classical and classical methods in the calculation of nitrogen self-broadened linewidths

We perform dynamical calculations on two robust N₂–N₂ potential energy surfaces in order to intercompare pressure broadening coefficients derived from close coupling and coupled states quantum dynamical methods, the semi-classical model of Robert and Bonamy and a full classical method. The coupled states and full classical results compare well with the experimental results or with close coupling values when available. This study confirms that the classical method is a good alternative at room and high temperatures to quantum dynamical methods. The results obtained using the semi-classical method however deviate from the other sets of data at all temperatures considered here (77–2400 K).     

Ground state and excited state properties of ethylene isomers studied by a combined Feynman path integral-ab initio approach

Ground state and excited state properties of ethylene, C₂H₄, and several ethylene isomers have been studied by Feynman path integral Monte Carlo (PIMC) simulations. The PIMC treatment of the atomic nuclei has been combined with different electronic Hamiltonians in order to analyse the influence of the nuclear degrees of freedom on electronic quantities. Electronic expectation values at the minimum of the potential energy surface (PES) have been compared with PIMC based ensemble averaged values. Ensemble averaged quantities have been derived by Hamiltonians of the ab initio type and a tight-binding (TB) one-electron model. The combined influence of anharmonicities in the interatomic potential and the quantum fluctuations of the atomic nuclei lead to ensemble averaged bondlengths r _g which are significantly larger than the parameters r _e, at the minimum of the PES. The implications of this bond length elongation for the electronic properties of ethylene are discussed. The occupied canonical molecular orbitals (CMOs) of ethylene are destabilized under the influence of the nuclear degrees of freedom while virtual CMOs are stabilized. These shifts of one-electron energies suggest a comparison of electronic excitation energies at the minimum of the PES with PIMC based ensemble averages. The quantum fluctuations of the nuclei cause a strong redistribution in the intensities of electronic transitions. Transitions, which are dipole allowed in the planar D_2h geometry of ethylene, lose intensity under the influence of nuclear quantum effects, and vice versa for electronic excitations that are dipole forbidden under D_2h symmetry. This ‘vibrational borrowing’ is enhanced with decreasing atomic masses. The Feynman centroid density has been used to calculate the anharmonic vibrational wavenumbers of C₂H₄ and C₂D₄. The results of the present PIMC simulations have been employed to emphasize general problems of electronic structure calculations based on a single nuclear configuration (i.e. the configuration at the minimum of the PES).     

The influence of intermolecular interactions on the Kerr effect in gases

Expressions are derived for the second and third Kerr virial coefficients, B _K and C _K, of spherical top molecules in terms of irreducible cluster polarizabilities, and values are calculated using the dipole-induced dipole model for argon, krypton, xenon, methane, tetrafluoromethane, neopentane and sulphur hexafluoride. For mixtures of rare gases it is shown that the collision-induced dipole moment makes a negligible contribution to B _K. The effect of the choice of intermolecular potential function on the calculated second Kerr virial coefficients is also demonstrated. It is found that the predominant contributions to C _K arise from the pair polarizability, and that the triplet polarizability is only of minor importance.     

On the second-order virial coefficient and the relationships between quantum and classical statistics and scattering

We clarify some aspects of the relationship between quantum statistical mechanics and scattering theory, which show up in their simplest form in the behaviour of the second-order virial coefficient b₂. For this purpose we derive a new representation for b₂. The relationship with classical statistical mechanics is also illuminated by a recently obtained formula for the difference between the classical and quantum second order virial coefficients which allows the determination of the leading quantum correction to b₂. The several approaches represent alternative ways of implementing the cancellation of divergences in b₂.     

Equations of state for the hard disk fluids

By using the published accurate new virial coefficients B₁₁～B₁₄ for the hard disk fluids [C. Zhang and B.M. Pettitt, Mol. Phys., 2014, 112, 1427], we here propose a new updated version of Tian-Gui-Mulero equation of state [J.X. Tian, Y.X. Gui and A. Mulero, Phys. Chem. Chem. Phys., 2010, 12, 13597]. Compared with other proposals, the new version stands strongly to be the only which can reproduce the known virial coefficients B₂～B₁₃ at the same time that can describe the relation of the compressibility factor versus the packing fraction for the hard disk fluids with high accuracy.