Analytical TDHF second derivatives of dynamic electronic polarizability with respect to nuclear coordinates. Application to the dynamic ZPVA correction

Analytical calculation of second derivatives of the dynamic electronic polarizability with respect to vibrational normal coordinates has been implemented at the TDHF level of approximation. Important simplifications are obtained by using the 2n+1 rule and interchange relations. In application to small molecules the first‐order ZPVA correction is found to have greater frequency dispersion than the electronic polarizability, but the former remains small in comparison. For the linear polyenes, C_2nH_2n+2 (n=1–3), the percentage ZPVA correction decreases with chain length for all ?ω<0.10 a.u. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1920–1932, 2001     

Liquid-phase force field and dipole moment derivatives with respect to internal coordinates of benzene

This paper presents an analysis of the infrared vibrational intensities found for C(6)H(6), C(6)D(6) and C(6)H(5)D in the liquid phase, motivated in part by the quite marked intensity differences between the fundamentals of C(6)H(6) and C(6)D(6) in the liquid, and between corresponding vibrations in the liquid and gas phases. The analysis is carried out under the harmonic approximation and results from a determination of the force field for liquid C(6)H(6), C(6)D(6) and C(6)H(5)D. The force constants for the liquid-phase are presented and compared to those in the literature for the gas-phase. Previously reported experimental intensities are used along with the eigenvectors of the force field analysis to determine the dipole moment derivatives with respect to symmetry and internal coordinates. The dipole moment derivatives with respect to internal coordinates obtained are partial differentialmicro/ partial differentials=0.38+/-0.02DebyeA(-1), partial differentialmicro/ partial differentialt=0.24+/-0.01, partial differentialmicro/ partial differentialbeta=0.26+/-0.01, and partial differentialmicro/ partial differentialgamma=0.64+/-0.03DebyeA(-1). There is very little difference between the dipole moment derivatives with respect to internal coordinates obtained from non-linear least squares fitting of the two D(6h) isotopomers and those obtained from non-linear least squares fitting of the three isotopomers. The results show that there is significant intensity sharing in the CH stretch region of C(6)H(5)D between the fundamental and combination bands.     

Dipole moment derivatives with respect to the internal coordinates of benzene in the liquid and gas phases

This paper presents a comparison of the dipole moment derivatives with respect to internal coordinates in the liquid and gas phases for benzene-h(6), benzene-d(6) and benzene-d(1). The literature values of the integrated intensities of the infrared active fundamentals of the three gaseous isotopomers are used to determine the dipole moment derivatives with respect to internal coordinates, using the methods described in the previous paper for the liquid phase. As was found for the liquid phase in the previous paper, there is uncertainty surrounding the intensities of the individual CH stretching fundamentals of benzene-d(1) due to intensity sharing with active combinations. The magnitudes of the dipole moment derivatives with respect to internal coordinates in the gas phase are partial differentialmicro/ partial differentials=0.50+/-0.03DA(-1), partial differentialmicro/ partial differentialt=0.28+/-0.03, partial differentialmicro/ partial differentialbeta=0.24+/-0.01, and partial differentialmicro/ partial differentialgamma=0.65+/-0.02DA(-1), where s, t, beta and gamma are the CH stretching, and CC stretching, the HCC bending and the HCCC torsion displacements, respectively. The experimental intensities are different for the three isotopomers in the liquid and gas phases, and the calculations show that these differences are mainly due to a difference between the CH stretch dipole moment derivatives in the two phases. This difference was related qualitatively to the intermolecular interaction of the H with the pi-cloud of the nearest neighbour creating a pseudo-hydrogen bond.     

Using redundant coordinates to represent potential energy surfaces with lower-dimensional functions

We propose a method for fitting potential energy surfaces with a sum of component functions of lower dimensionality. This form facilitates quantum dynamics calculations. We show that it is possible to reduce the dimensionality of the component functions by introducing new and redundant coordinates obtained with linear transformations. The transformations are obtained from a neural network. Different coordinates are used for different component functions and the new coordinates are determined as the potential is fitted. The quality of the fits and the generality of the method are illustrated by fitting reference potential surfaces of hydrogen peroxide and of the reaction OH+H(2)-->H(2)O+H.     

Analytical first derivatives of the energy for small CI expansions

Using the Z-vector formalism the analytical gradient of the energy in small CI expansions is derived and implemented for semiempirical MNDO-type methods. The computation time is shown to scale as O(N ³) with the size of the system, with the memory requirements growing as O(N ²). The evaluation of the analytical gradient is significantly faster than the underlying SCF and CI calculations, so that routine full geometry optimizations at the semiempirical CI level become possible for large systems. Received: 24 April 1997 / Accepted: 10 June 1997     

Analytical techniques with a nuclear microprobe

Nuclear microprobes have proved to be versatile tools to perform investigations in materials science with a lateral resolution of typically 1 to 10 m. Many of the commonly utilized ion beam assisted analytical techniques, like PIXE (Particle Induced X-Ray Emission), RBS (Rutherford Back Scattering), NRA (Nuclear Reaction Analysis), and Channeling can be applied with a nuclear microprobe. Additionally, there are methods typical for the nuclear microprobe, e.g. STIM (Scanning Transmission Ion Microscopy). The nuclear microprobe used here has been applied successfully to the analysis of geological and biological specimens and is currently being modified by the introduction of a superconducting solenoid as focusing element to allow higher lateral resolution. Especially the analysis and modification of electronic devices will become possible. An overview of the analytical techniques practiced with the nuclear microprobe is given with emphasis on laterally resolved trace element analysis.     

Numerical properties of equations involving high-order derivatives of pressure with respect to volume

This paper presents some unexpected features related to the solution of equations containing a high-order derivative of pressure with respect to volume equated to zero. For pure components, such equations define, in the pressure-temperature plane, nodal curves similar in shape to mixture spinodal curves. The analysis was made for a general form of two-parameter cubic equations of state and various numerical aspects for the Redlich-Kwong equation of state are exemplified.     

Analytic first and second derivatives of the energy in the fragment molecular orbital method combined with molecular mechanics

Analytic first and second derivatives of the energy are developed for the fragment molecular orbital method interfaced with molecular mechanics in the electrostatic embedding scheme at the level of Hartree-Fock and density functional theory. The importance of the orbital response terms is demonstrated. The role of electrostatic embedding upon molecular vibrations is analyzed, comparing force field and quantum mechanical treatments for an ionic liquid and a solvated protein. The method is applied for 100 protein conformations sampled in molecular dynamics (MD) to take into account the complexity of a flexible protein structure in solution, and a good agreement with experimental data is obtained: Frequencies from an experimental infrared (IR) spectrum are reproduced within 17 cm⁻¹ .     

A molecular design view on the first hyperpolarizability of salicylideneaniline derivatives

Electron correlation effect was incorporated into the two-level framework through configuration interaction (CI) calculation including both occupied and unoccupied frontier orbitals, to evaluate the first hyperpolarizabilities of title compounds. Theoretical results are in excellent agreement with experimental data obtained by the solvatochromic method. Some detailed chemical and electronic information of the electron excitation process related to the nonlinear optical (NLO) properties were produced as well. Based on these data, effects of the character, number and position of donor and acceptor groups on the NLO properties are discussed from the viewpoint of molecular design. Not only the experimental data but also the theoretical analysis have suggested that a large number of intensive and properly located donor and acceptor groups may yield the optimal hyperpolarizabilities. Received: 22 May 1996 / Accepted: 9 December 1996     

Analytical second derivatives of molecular electronic energy integrals obtained by spherical gaussian orbital

In this research, the complete general formulas for the analytical second derivative of the molecular integrals for spherical gaussian orbitals of electronic energy are presented. Formulas were given for the second derivative for orbital exponent, orbital and nuclear cartesian coordinates and coefficients of contracted gaussians. In order to save computational time, the formulas for the second derivative are written in terms of the original integrals. Although the formulas were presented in general for any type of application, the Floating Spherical Gaussian Orbital (FSGO) method is applied to some molecules such as LiH, H₂O and CH₂ (singlet) to check the formulas. The results were compared with the results of the finite difference method. Besides the accuracy of the analytical derivative, the saving in computational time is significant.     

Some statistic parameters of the Schulz distribution with respect to the molecular heterogeneity

Summary The concepts of absolute and relative heterogeneity related to the number average degree of polymerization were formulated.In case ofSchulz distribution it was proved that the relative heterogeneity depends only on the curve parameterk.Different statistic parameters for theSchulz distribution were calculated. The dependence of those parameters on the curve parameterk is illustrated by diagrams.

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Zusammenfassung Die Begriffe von absoluter und relativer Uneinheitlichkeit in bezug auf das Zahlenmittel des Polymerisationsgrades wurden formuliert.Es wurde festgestellt, daß die relative Uneinheitlichkeit im Falle derSchulzschen Verteilung nur von dem Kurvenparameterk abhängig ist.Verschiedene statistische Parameter für dieSchulzsche Verteilung werden berechnet und die Abhängigkeit dieser Parameter von dem Kurvenparameterk durch Diagramme illustriert.

     

Reactivity of 3-hydroxypyridine and its derivatives with respect to oxidizing and reducing radicals

Conclusions 3-Hydroxypyridine and its alkyl-substituted derivatives react with e^–and the H and OH radicals; their relative reactivity has been determined.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 10, pp. 2216–2218, October, 1981.     

Analytical dependences between first order derivatives at the critical point of a pure substance

The finiteness and positive value of the slope of the saturation curve at the critical point according to its location in the region of a thermodynamic surface restricted by the curves of inversion and saturation are substantiated. It is shown that any two derivatives of the first order formed with respect to volume, internal energy, entropy, enthalpy, and the Helmholtz energy, one of which is taken at a fixed value of pressure and the other at a fixed value of temperature, are equal in the critical state. New sets of the critical conditions for a pure substance are obtained.     

Analytical developments for 47 pesticides: first identification of neutral chloroacetanilide derivatives in French groundwater

A new analytical methodology for neutral derivatives of chloroacetanilides made it possible to detect, for the first time in a European groundwater monitoring campaign, three metabolites (hydroxymetolachlor, metolachlor morpholinone and deschlorometolachlor) in addition to ethane sulfonic acid (ESA) and oxanilic acid (OXA) metabolites, which were first detected in 2009. The analytical method involves solid phase extraction and ultra-high-performance liquid chromatography with tandem mass spectrometry (UPLC-MS/MS). Recoveries ranged from 64 to 101%, and limits of quantification were validated at 5, 10 or 20 ng/L, depending on the molecule, in natural water. Most of the chloroacetanilide metabolites were synthesised, as many standards are not commercially available.