Theoretical treatment of predissociation of the CO (3sσ) B and (3pσ) C1Σ+ Rydberg states based on a rigorous adiabatic representation

Ab initio multireference configuration interaction calculations for adiabatic potential curves, nonadiabatic couplings 〈φ _i (R,r)|d/dR|φ _j (R,r)〉 and 〈φ _i (R,r)|d²/dR ²|φ _j (R,r)〉, and nuclear kinetic energy corrections 〈dφ _i (R,r)/dR|dφ _i (R,r)/dR〉 for the (3sσ) B and (3pσ) C¹Σ⁺ Rydberg states of the CO molecule have been carried out. The energy positions and predissociation linewidths for the observed vibrational levels of these two states have been determined in a rigorous adiabatic representation by the complex scaling method employing a basis of complex scaled harmonic vibrational functions in conjunction with the Gauss-Hermite quadrature method to evaluate the complex Hamiltonian matrix elements. The present treatment correctly reproduces the observed trends in energies and line broadening for vibrational levels of the B¹Σ⁺ state and represents an improvement over the previous treatment in literature. The errors in the determined spacings of the v = 0–4 vibrational levels of the C¹Σ⁺ state are less than 2% compared with measured data. The predissociation linewidths for the v=3,4 levels of the C¹Σ⁺ state are found to be 4.9 and 8.9 cm⁻¹, respectively, in good agreement with the observed values. Received: 23 March 1998 / Accepted: 27 July 1998 / Published online: 9 October 1998     

The role of triplet repulsion in alkyl radical addition to a 7π-C-O bond and alkoxy radical addition to a π-C-C bond

The experimental activation energies of the R^• + O = CR¹R² and RO^• + CH₂ = CHR¹ addition reactions are analyzed within the framework of the parabolic model of the bimolecular addition reaction. The activation energy also depends on the dissociation energy of the forming C-O bond and on the reaction enthalpy: the higher the dissociation energy, the higher the activation energy. The empirical relationshipr _e J..D _e = 0.97 x 10-¹³ m kJ.-¹ mol is found for H^•, Cl^•, Br^{• •} and RO^• radical addition to multiple C=C and C=O bonds (r_e is the distance between the peaks of the intersecting parabolic curves). This is due to the effect of the triplet repulsion on radical addition. The interaction of polar groups and the steric effect also influence the activation energy.     

Long-range molecular interaction coefficients computed from frost-model wave functions

The average long-range interaction energy between two molecules can be written as an inverse asymptotic series in the intermolecular separation distanceR. Using Frost-model wave functions, the dispersion coefficients of the first three (R ^–6,R ^–8,R ^–10 terms in the series are obtained. Coefficients of three- and four-body non-additive interaction energies are also calculated and the form of the dispersion interaction when retardation effects are included is examined.     

Electron correlations in Kohn–Sham exchange‐only theory

We provide an interpretation for the “exchange” energy and potential of Kohn–Sham exchange‐only theory, or equivalently that of the optimized potential method (OPM), which shows that in addition to contribution due to the Pauli exclusion principle, there is a kinetic component to these properties. The interpretation is in terms of a conservative field R ^OPM( r ), which is a sum of two fields, one representative of Pauli electron correlations and the other of kinetic effects. The OPM exchange potential is derived via the differential virial theorem to be the work done to move an electron in the field R ^OPM( r ). The OPM exchange energy is then expressed via the integral virial theorem in terms of this field. A similar interpretation for the energy and potential may also be derived directly from the OPM integral equation. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 71:473–480, 1999     

Effect of the state of h-b-1 hydrogen bond on the character of some atom vibrations in guanine-cytosine pair of the DNA molecule

For the first hydrogen bond of the guanine-cytosine (G-C) pair, the potential function V(r, R) is found for the nonequilibrium bond length R. A new form of the semiempirical potential function, Clementi's calculations for V(r, R₀) and some experimental data are used. New wave functions and energy levels as a function of the H-bond length for the ground and several excited states are obtained. This allows one to obtain frequencies and amplitudes of some vibrations of the G-C pair side groups involved in the formation of the hydrogen bond when the latter is not excited and when it is excited to the first energy level. © 1996 John Wiley & Sons, Inc.     

Chemical bond breaking/forming as a Franck–Condon electronic process

We describe chemical bond changes as Franck–Condon electronic processes within a new theoretical ansatz that we call ‘rigged’ Born–Oppenheimer (R-BO) approach. The notion of the separability of nuclear and electron states implied in the standard Born–Oppenheimer (BO) scheme is retained. However, in the present scheme the electronic wave functions do not depend upon the nuclear coordinate (R-space). The new functions are obtained from an auxiliary Hamiltonian corresponding to the electronic system (r-coordinates) submitted to a Coulomb potential generated by external sources of charges in real space (α-coordinates) instead of massive nuclear objects. A stationary arrangement characterized by the coordinates α_0A, is determined by a particular electronic wave function, ψ(r;α_0A); it is only at this stationary point, where an electronic Schrödinger equation: H_e(r,α_0A)|Ψ(r;α_0A)=E(α_0A)|Ψ(r;α_0A) must hold. This equation permits us to use modern electronic methods based upon analytic first and second derivatives to construct model electronic wave functions and stationary geometry for external sources. If the set of wave functions {Ψ(r;α_0A)} is made orthogonal, the energy functional in α-space, E(α;α_0A)=Ψ(r;α_0A)|H_e(r,α_0A)|Ψ(r;α_0A) is isomorphic to a potential energy function in R-space: E(R;α_0A)=Ψ(r;α_0A)|H_e(r,R)|Ψ(r;α_0A). This functional defines, by hypothesis, a trapping convex potential in R-space and the nuclear quantum states are determined by a particular Schrödinger equation. The total wave function for the chemical species A reads as a product of our electronic wave function with the nuclear wave function (Ξ_ik(R;α_0A)): Φ_ik(r,R)=Ψ_i(r,α_0A)Ξ_ik(R;α_0A). This approach facilitates the introduction of molecular frame without restrictions in the R-space. Two molecules (characterized with different electronic spectra) that are decomposable into the same number of particles (isomers) have the same Coulomb Hamiltonian and they are then characterized by different electronic wave functions for which no R-coordinate ‘deformation’ can possibly change its electronic structure. A bond breaking/forming process must be formally described as a spectroscopic-like electronic process. The theory provides an alternative to the adiabatic as well as the diabatic scheme for understanding molecular processes. As an illustration of the present ideas, the reaction of H₂+CO leading to formaldehyde is examined in some detail.     

Artificial neural network for the evaluation of CO2 corrosion in a pipeline steel

This paper presents a predictive model for the determination of different types of corrosion by using electrochemical impedance spectroscopy curves and artificial neural network. This proposed model obtains predictions for three different types of corrosion by using Nyquist impedance curves from four input variables: inhibitor concentration, time of exposure, and the real and imaginary experimental component of these curves. The model takes into account the variations of inhibitor concentration over steel to decrease the corrosion rate. For the network, the Levenberg–Marquardt learning algorithm, the hyperbolic tangent sigmoid transfer function and the linear transfer function were used. The best fitting training data set was obtained with five neurons in the hidden layer, which made possible to predict satisfactory efficiency (R > 0.99). On the validation of the data set, simulations and theoretical data tests were in good agreement (R > 0.9905). The developed model can be used for the determination of the type of curves related to the nature phenomena and rate of corrosion at the metal surface.     

Validated Chiral LC Method for the Enantiomeric Separation of β-Amino-β-(3-Methoxyphenyl) Propionic Acid

A chiral liquid chromatographic method for enantiomeric resolution of β-amino-β-(3-methoxyphenyl) propionic acid was developed and validated. The “hybrid” π-electron donor–acceptor based stationary phase (R,R) Whelk-01 was found to be enantiomerically selective for (R) and (S) enantiomers of β-amino-β-(3-methoxyphenyl) propionic acid with a resolution greater than 2.0. The effects of isopropyl alcohol and ethanol on enantioselectivity and resolution of enantiomers were evaluated. Calibration curves were linear over the range of 0.10–1.00, with a regression coefficient (r) of 0.999. The limit of detection (LOD) and limit of quantification (LOQ) were 300 and 1,000 ng mL⁻¹ respectively for 10 μL injection volume. The percentage RSD of the peak area of six replicate injections of (S) enantiomer at LOQ concentration was 2.8. The percentage recovery of (S) enantiomer from (R) enantiomer samples ranged from 92 to 102. The test solution was observed to be stable up to 24 h after the preparation. The developed normal phase chiral LC method can be used for the enantiomeric purity evaluation of R-β-amino-β-(3-methoxyphenyl) propionic acid.     

Long range interaction energies using Gaussian basis sets and a one center method

A one center method, based on the work of Karplus and Kolker, is discussed and used to calculate the induction energy, through O(R^?8), for the H(ls) – H⁺ interaction employing two types of Gaussian basis sets constructed from functions of the form {r^je^?αr2}. The effective hydrogen atom excitation energies and transition multipole moment matrix elements generated in these calculations are used to calculate the dispersion energy for the H(ls) – H(ls) interaction, through O(R^?10), and the R^?9 triple dipole energy corresponding to the interaction of three H(ls) atoms. The results indicate that Gaussian functions can form good basis sets for obtaining long range forces for a variety of multipole interaction energies.     

An analysis of the vibrational structure of high-resolution UV spectra and long-wave IR Fourier transform spectra in studies of internal rotation in molecules

The methods for analyzing the vibrational structure of high-resolution UV spectra and long-wave IR Fourier transform spectra in studies of internal rotation in α,β-unsaturated carbonyl compounds R₄R₃C=CR₂-COR₁ (R₁ = F, Cl; R₂ = R₃ = R₄ = H, CH₃) are compared. These methods were found to give different experimental values for systems of torsional vibration energy levels up to high quantum numbers, torsional frequencies (0–1 transitions), and anharmonicity coefficients x ₁₁ for trans and cis isomers of the same molecules in the ground electronic state (S ₀). It was shown that the experimental technique for analyzing the vibrational structure of UV spectra excludes the hydrolysis of compounds under study. Taking into account Fermi resonance and numerous Deslandres tables constructed for trans and cis isomers provides reliable determination of values necessary for the construction of internal rotation potential functions, because they are multiply repeated in various Deslandres tables. An analysis of the vibrational structure of UV spectra gives more reliable V _n internal rotation potential function parameters. The V _n parameter values were substantiated by quantum-mechanical calculations performed by other authors.     

Statistical–mechanical models with separable many-body interactions: especially partition functions and thermodynamic consequences

We start from a classical statistical–mechanical theory for the internal energy in terms of three- and four-body correlation functions g ₃ and g ₄ for homogeneous atomic liquids like argon, with assumed central pair interactions f(r_ij){\phi(r_{ij})} . The importance of constructing the partition function (pf) as spatial integrals over g ₃, g ₄ and f{\phi} is stressed, together with some basic thermodynamic consequences of such a pf. A second classical example taken for two-body interactions is the so-called one-component plasma in two dimensions, for a particular coupling strength treated by Alastuey and Jancovici (J Phys (France) 42:1, 1981) and by Fantoni and Tellez (J Stat Phys 133:449, 2008). Again thermodynamic consequences provide a particular focus. Then quantum–mechanical assemblies are treated, again with separable many-body interactions. The example chosen is that of an N-body inhomogeneous extended system generated by a one-body potential energy V(r). The focus here is on the diagonal element of the canonical density matrix: the so-called Slater sum S(r, β), related to the pf by pf(b) = òS(r, b)d[(r)\vec]{{\rm pf}(\beta) = \int {S({\bf r}, \beta)}d\vec {r}}, β = (k _B T)⁻¹. The Slater sum S(r, β) can be related exactly, via a partial differential equation, to the one-body potential V(r), for specific choices of V which are cited. The work of Green (J Chem Phys 18:1123, 1950), is referred to for a generalization, but now perturbative, to two-body forces. Finally, to avoid perturbation series, the work concludes with some proposals to allow the treatment of extended assemblies in which regions of long-range ordered magnetism exist in the phase diagram. One of us (Z.D.Z.) has recently proposed a putative pf for a three-dimensional (3D) Ising model, based on two, as yet unproved, conjectures and has pointed out some important thermodynamic consequences of this pf. It would obviously be of considerable interest if such a pf, together with conjectures, could be rigorously proved.     

Diffusion Coefficients for Binary, Ternary, and Polydisperse Solutions from Peak-Width Analysis of Taylor Dispersion Profiles

Binary mutual diffusion coefficients D can be estimated from the width at half height W _1/2 of Taylor dispersion profiles using D=(ln 2)r ² t _R/(3W ² h) and values of the retention time t _R and dispersion tube radius r. The generalized expression D _h=−(ln h)r ² t _R/(3W ² _h ) is derived to evaluate diffusion coefficients from peak widths W _h measured at other fractional heights (e.g., (h = 0.1, 0.2,…,0.9). Tests show that averaging the D _h values from binary profiles gives mutual diffusion coefficients that are as accurate and precise as those obtained by more elaborate nonlinear least-squares analysis. Dispersion profiles for ternary solutions usually consist of two superimposed pseudo-binary profiles. Consequently, D _h values for ternary profiles generally vary with the fractional peak height h. Ternary profiles with constant D _h values can however be constructed by taking appropriate linear combinations of profiles generated using different initial concentration differences. The invariant D _h values and corresponding initial concentration differences give the eigenvalues and eigenvectors for the evaluation of the ternary diffusion coefficient matrix. Dispersion profiles for polymer samples of N i-mers consist of N superimposed pseudo-binary profiles. The edges of these profiles are enriched in the heavier polymers owing to the decrease in polymer diffusion coefficients with increasing polymer molecular weight. The resulting drop in D _h with decreasing fractional peak height provides a signature of the polymer molecular weight distribution. These features are illustrated by measuring the dispersion of mixed polyethylene glycols.     

Theoretical electronic structure of the molecule ScBr

The potential energy curves have been investigated for the 23 lowest electronic states in the ^2s+1Λ^± representation of the molecule ScBr via CASSCF and MRCI (single and double excitations with Davidson correction) calculations. Seventeen electronic states have been studied theoretically for the first time. The harmonic frequency ω_e, the internuclear distance r_e, and the electronic energy with respect to the ground state T_e have been calculated. By using the canonical functions approach, the eigenvalues E_v, the rotational constant B_v, and the abscissas of the turning points (R_min, R_max) have been calculated for electronic states up to the vibrational level v = 32. The comparison of these values to the theoretical and experimental results available in the literature shows a good agreement. © 2007 Wiley Periodicalsm Inc. Int J Quantum Chem, 2008     

Simultaneous determination of levofloxacin hemihydrate and ambroxol hydrochloride in tablets by thin-layer chromatography combined with densitometry

This paper describes the application of thin-layer chromatography (TLC) combined with densitometry to simultaneous determination of levofloxacin hemihydrate (LEV) and ambroxol hydrochloride (AMB) in bulk and tablets. The separation was achieved on aluminum sheet of silica gel 60 F ₂₅₄ using chloroform: methanol: toluene: ammonia (10: 6: 3: 0.8 v/v/v/v) as mobile phase. Quantification was carried out densitometrically at 245 nm. This system was found to give compact spots for LEV (R _f value of 0.4) and AMB (R _f value of 0.7). The calibration curves for LEV and AMB was found to be linear between 9960–16600 ng/spot (r ² = 0.999) and 600–1000 ng/spot (r ² = 0.999), respectively. The mean percentage recoveries from tablets for LEV and AMB were 99.45% and 99.58%, respectively. The TLC-densitometry method has many advantages, such as simplicity, reasonable sensitivity, rapidity, and low cost, and it can be successfully used in routine analysis of both these drugs in tablet formulations.     

ACS symposium

The SCF potential surface of the ground state for NO₂ was calculated by using program JAMOL 3. The McLean–Loew–Berkowitz CGTO 's were used as basis functions. One of the two N? O distance R is fixed to 2.25 a.u. and the other one r and the ONO angle θ are varied from 2.25 to 5.0 a.u. and from 0° to 180°, respectively. The potential surface has the minimum around r = 2.50 a.u. and θ = 120°, where the energy is found to be ?203.954 a.u.     

Frequency dispersion of the viscoelastic properties of solutions of electrolytes

Analytical expressions obtained earlier are used to numerically calculate the dynamic coefficients of the bulk η_ν(ω) and shear η _s (ω) viscosity and the corresponding modules of their bulk K(ω) and shear μ(ω) elasticity at a certain choice of the model of solution structure in an approximation of the osmotic solution theory. The potential energy of the interaction between ions Φ _ab (r) was taken as the sum of the Lennard-Jones potential and the generalized Debye potential, taking into account the configuration and size of ions. In this approximation, the viscoelastic properties of the NaCl water solution were numerically calculated over a wide interval of change in the thermodynamic parameters and frequency ranges. Satisfactory agreement with the literature experimental data was obtained.     

A short review and an empirical method for estimating the absorbed enthalpy of formation and the absolute enthalpy of dried microbial biomass for use in studies on the thermodynamics of microbial growth

Calculations are made using the equations Δ_r G = Δ_r H − TΔ_r S and Δ_r X = Δ_r H − Δ_r Q where Δ_r X represents the free energy change when the exchange of absorbed thermal energy with the environment is represented by Δ_r Q. The symbol Q has traditionally represented absorbed heat. However, here it is used specifically to represent the enthalpy listed in tabulations of thermodynamic properties as (H _T  − H ₀) at T = 298.15 K, the reason being that for a given substance TS equals 2.0 Q for solid substances, with the difference being greater for liquids, and especially gases. Since Δ_r H can be measured, and is tangibly the same no matter what thermodynamics are used to describe a reaction equation, a change in the absorbed heat of a biochemical growth process system as represented by either Δ_r Q or TΔ_r S would be expected to result in a different calculated value for the free energy change. Calculations of changes in thermodynamic properties are made which accompany anabolism; the formation of anabolic, organic by-products; catabolism; metabolism; and their respective non-conservative reactions; for the growth of Saccharomyces cerevisiae using four growth process systems. The result is that there is only about a 1% difference in the average quantity of free energy conserved during growth using either Eq. 1 or 2. This is because although values of TΔ_r S and Δ_r Q can be markedly different when compared to one another, these differences are small when compared to the value for Δ_r G or Δ_r X.     

The electronic transition moment function of the E1Πu-X1Σ g+ system of Ag2

Measurement of relative band strengths of 10 absorption bands of the E ¹Π _u -X ¹Σ _g ⁺ system of diatomic silver, ^107,109Ag₂, was performed for the first time. Theoretical analysis of the experimental data, based on Rydberg-Klein-Rees potential energy curves, revealed that assumption of the r-centroid approximation is valid for this system. Comparison of the measured and computed band strength ratios for 5 pairs of bands having common lower levels led to the following linear relative electronic transition moment function for the ^107,109Ag₂ E-X band system: R_e ([`(r)]<sub>V￠V"</sub> ) = 2.36[`(r)]_V￠V" - 5.64R_e (\bar r_{V'V'} ) = 2.36\bar r_{V'V'} - 5.64, in arbitrary units, over the 2.65–2.73 ? of internuclear distance.     

On the approximation of potential-energy functions for two-center systems

Let E(R) be a potential-energy function for a neutral or ionic diatom in the Born-Oppenheimer approximation. Then the approximation of E(R) for 0 < R < ∞ starting from finite and typically small sets of given information is considered. The approach is based on the fact that the scaled potential curves F(R) = R²E(R) derive from an eigenvalue problem which depends linearly on R. The nature of the curves F(R) is examined in detail. The results include the discovery of various approximants, some of which display rigorous bounding properties and others, closely related, whose behavior with respect to the approximated function appears to be predictable.     

Fundamental aspects of electrostatic interactions and charge renormalization in electrolyte systems

The consistent inclusion of ion-ion correlations and molecular solvent effects in electrolyte theory can be expressed in a physical formalism, where the particles acquire a renormalized charge density and where they interact electrostatically via a generalized screened Coulomb potential. The latter usually decays for large distances r like a Yukawa function exp(-κr)/r, where 1/κ is the decay length (normally different from the Debye length), but, for smaller r, the screened Coulomb potential is a more complicated function. The resulting electrostatic theory, “Yukawa electrostatics”, differs in many important aspects from ordinary (unscreened) Coulomb electrostatics. In the present paper, we give illustrations and explanations of some important differences between Coulomb and Yukawa electrostatics. The effective “Yukawa charge” of a particle differs from the ordinary Coulombic charge. Furthermore, contributions from multipoles of all orders contribute, in general, to the leading asymptotic term in the potential for large r, which decays like exp(-κr)/r. Thus, the electrostatic potential from, for example, an electroneutral molecule with an internal charge distribution has generally the same range as the potential from an ion. Some implications of these facts are pointed out. The presentation is based on exact statistical mechanical analysis where all particles are treated on the same fundamental level, but the main focus lies on physical consequences and interpretations of the theory. The text was submitted by the author in English.