The virial theorem for the second derivatives of adiabatic potential and the dynamic instability of polyatomic molecules

The origin of dynamic instability of molecular configurations is investigated from the standpoint of the virial theorem for second derivatives and a new proof of this theorem is provided for an arbitrary polyatomic system. It is shown that the closeness of the energies of the excited and ground electronic states leads to a dynamic instability of the molecule by at least one vibrational coordinate. It is proposed that the instability of the solution of the Hartree-Fock equations under the condition of small positive numbers of instability can be an indication of dynamic instability of the equilibrium molecular configuration.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 22, No. 3, pp. 257–262, May–June, 1986.The authors express their gratitude to G. E. Vaiman for the stimulating and helpful discussion.     

On the equivalence of ring-coupled cluster and adiabatic connection fluctuation-dissipation theorem random phase approximation correlation energy expressions

The correlation energy in the direct random phase approximation (dRPA) can be written, among other possibilities, either in terms of the interaction strength averaged correlation density matrix, or in terms of the coupled cluster doubles amplitudes obtained in the direct ring approximation (drCCD). Although the corresponding dRPA correlation density matrix on the one hand, and the drCCD amplitude matrix on the other hand, differ significantly, they yield identical energies. Similarly, the analogous RPA and rCCD correlation energies calculated from antisymmetrized two-electron integrals are identical to each other despite very different underlying working equations. In the present communication, a direct correspondence between amplitudes and densities is established and investigated with perturbation theory arguments. Our analysis also sheds some light on the properties of recently proposed RPA/rCCD variants which use antisymmetrized integrals in part of the equations and nonantisymmetrized integrals in others.     

Remarks on the fermi contact interaction

It is shown by rigorous mathematical methods that the so-called Fermi contact interaction does not define any selfadjoint Hamiltonian, and the only possible form of contact interaction localized strictly at r = 0 is found. However, the Fermi contact interaction retains sense when used as a bilinear form in the perturbation theory for Dirac electrons. Some results obtained earlier by other authors are confirmed and interpreted by our analysis.     

使用元素名称时要注意的问题

1951年,政务院“学术名词统一工作委员会”颁布了《化学物质命名原则》,规定在中文里,化学元素的名称都用一个汉字来表达。依此原则对原有的元素中文名称进行了整理,并陆续命名了一些新元素,现时以汉字正式命名的元素共有103种。 由于这些元素名称的由来不一,而且大多数使用的时间较短,使用面又不甚广,所以使用中常会产生一些问题,有时竟连一些文字工作者和科技工作者也不能避免。作为化学教育工作者,为正确使用这些元素名称,了解一下这些名称的由来和演变,区分其古今含义,掌握其读音是很必要的。     

Comments on adiabatic calculations of the electrical properties of molecules

The Hamiltonian used in recent calculations (by Silverman, Bishop and others) of the electrical properties of one-electron diatomic molecules is compared, in the adiabatic approximation, with the Stark Hamiltonian.     

Remarks on the calibration of differential scanning calorimeters

The development of methods for temperature and heat calibration of DSC and DTA supported by the German Society of Thermal Analysis (GEFTA) are presented. Reasons are given for the recommendation of the temperature calibration method, which refers to the valid international temperature scale (ITS 90) and takes into account the fact that the fixpoints of this scale are defined in two phase equilibrium.Furthermore the hard problems with the heat flow and peak area calibration of DSC are described and the methods are presented to come to realistic and sufficient results. Thus both traditional (with the aid ofC _p — and enthalpy — reference materials) and electrical calibration are critically discussed. Today's best values of suitable materials for heat calibration are reported.

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Zusammenfassung Methoden zur Temperatur- und Enthalpiekalibrierung von DSC und DTA Instrumenten werden dargestellt. Dieses Forschungsvorhaben wurde von der Gesellschaft für Thermische Analyse (GEFTA) unterstützt. Gründe werden dargelegt, weshalb die Temperaturkalibrierung auf Referenzsubstanzen abgestützt werden soll, die in der Internationalen Temperaturskala (ITS90) aufgeführt sind.Ebenso wird das schwierige Unterfangen der kalorischen Kalibrierung mit mehreren unterschiedlichen Methoden erlÄutert, und geeignete Referenzsubstanzen werden vorgestellt.

     

Path-integral simulations beyond the adiabatic approximation

Within the adiabatic approximation, it is trivial to generalize existing imaginary time path-integral techniques to the case of multiple electronic surfaces. However, there are many times where nonadiabatic effects can play an important role. To this end, we reformulate the well-known path-integral expressions to incorporate multiple potential surfaces, without necessitating the adiabatic approximation. We show that the resulting expression, like its adiabatic counterpart, can be interpreted in terms of a simple classical isomorphic system and thus is amenable to simulation through Monte Carlo techniques. We derive simple expressions to compute expectation values of a general operator in both the nuclear coordinate and electronic state, and demonstrate the existence of a simple internal diagnostic that can be used to evaluate the magnitude of equilibrium nonadiabatic effects.     

Remarks on the updated Hessian matrix methods

Optimizing a function with respect to a set of variables using the quasi‐Newton–Raphson method implies updating the Hessian matrix at each iteration. The Broyden–Fletcher–Goldfarb–Shanno update formula is used for minimization and the Murtagh–Sargent–Powell update formula for optimization of first‐order saddle points. Two new formulae are proposed to update the Hessian matrix. One of these formulae is derived using exponential weights and should be used to locate first‐order saddle points. The second formula is a modification of the TS–Broyden–Fletcher–Goldfarb–Shanno update and could used for both minimum and first‐order saddle point optimizations. These two update Hessian matrix formulae present a performance that is the same and in many cases better that the Broyden–Fletcher–Goldfarb–Shanno and Murtagh–Sargent–Powell formulae. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 94: 324–332, 2003     

Remarks on the theory of diffusion in electrolyte solutions

The assumptions usually made that the ionic atmosphere has spherical symmetry in the diffusion of binary electrolytes and that the electrophoretic effect is negligible in the tracer diffusion of ions are pointed out to be incorrect when terms up to order κ² ln κ (κ is the Debye-Hückel parameter) are considered.     

Thermodynamics of adiabatic cross polarization

Using a spin-temperature approach, we describe a scheme of adiabatic cross polarization, based on demagnetization/remagnetization, when the Zeeman order of abundant nuclei in the laboratory frame is first adiabatically converted into the dipolar order, and then, into the Zeeman order of rare nuclei. The scheme, implemented with two low-power frequency-sweeping pulses, is very efficient for static samples and can significantly increase polarization of rare nuclei, compared to the conventional Hartmann-Hahn cross polarization. The experimental examples are presented for a solid, liquid crystal, and small molecules in a liquid-crystalline solvent.     

Modeling the adiabatic connection in H2

Full configuration interaction (FCI) data are used to quantify the accuracy of approximate adiabatic connection (AC) forms in describing the ground state potential energy curve of H2, within spin-restricted density functional theory (DFT). For each internuclear separation R, accurate properties of the AC are determined from large basis set FCI calculations. The parameters in the approximate AC form are then determined so as to reproduce these FCI values exactly, yielding an exchange-correlation energy expressed entirely in terms of FCI-derived quantities. This is combined with other FCI-derived energy components to give the total electronic energy; comparison with the FCI energy quantifies the accuracy of the AC form. Initial calculations focus on a [1/1]-Padé-based form. The potential energy curve determined using the procedure is a notable improvement over those from existing DFT functionals. The accuracy near equilibrium is quantified by calculating the bond length and vibrational wave numbers; errors in the latter are below 0.5%. The molecule dissociates correctly, which can be traced to the use of virtual orbital eigenvalues in the slope in the noninteracting limit, capturing static correlation. At intermediate R, the potential energy curve exhibits an unphysical barrier, similar to that noted previously using the random phase approximation. Alternative forms of the AC are also considered, paying attention to size extensivity and the behavior in the strong-interaction limit; none provide an accurate potential energy curve for all R, although good accuracy can be achieved near equilibrium. The study demonstrates how data from correlated ab initio calculations can provide valuable information about AC forms and highlight areas where further theoretical progress is required.     

Remarks on the molecular mechanical calculations of functionalized hydrocarbons

Molecular mechanical calculations for hetero-substituted hydrocarbons present certain difficulties that are not encountered in dealing with hydrocarbons. Ways are proposed to overcome such difficulties, sometimes by two-step or iterative computation. The following topics are considered: fitting the force field by using data from studies in solution; ways to estimate atomic charges or, alternatively, bond moments; ways to account for field effects upon atomic charges and bond moments.     

Comparison of CIS- and EOM-CCSD-calculated adiabatic excited-state structures. Changes in charge density on going to adiabatic excited states

The CIS and EOM-CCSD adiabatic geometries for the first excited states of a set of small molecules (C2H4, C2H2, H2C=O, H2C=S, CS2, CO2, SO2, NO2) have been calculated using the 6-311++G** basis set to see if the former geometries can be good starting points for optimizations at the latter theoretical level. With most of the molecules, there is fairly good agreement between the results from the two methods, and EOM-CCSD gives good agreement with the available experimental data. A detailed discussion of the lowest-lying singlet excited states in CO2 and CS2 is presented, highlighting the pronounced differences in electronic character and equilibrium structure displayed by these isovalent species. The origins of the structural distortions that are frequently found for the adiabatic excited states are examined with the aid of deformation density plots and the electron localization function (ELF).     

Remarks on the analysis of the photopeaks of scintillation gamma-ray spectra

Physical considerations permit the asymmetry of the photopeak in scintillation γ-spectra to be represented by a second Gaussian peak of lower intensity, accompanying the principal peak. The problem of finding the peak parameters is described as one reduced to solving an over-determined system of non-linear equations, when the numbers of counts in the channels of the analyzer are given. The nature of ill-conditioned linear steps is discussed for the case of solving the problem by Newton's method. A solution procedure based on the regulation of the iteration process is proposed, and the concept of ‘α-approximative solution’ of the given problem is introduced. The calculation procedure is illustrated on actual numerical examples by tables and diagrams, and the possibilities of checking the physical hypothesis and of additional control of the experimental conditions are described.     

Effects on the pigment distribution in paint formulations

Modern water-borne paints are applied in different areas ranging from high-gloss lacquers to flat, scrub-resistant interior paints. The pigment volume concentration (PVC) is one key-parameter adjusting the application properties. In this work formulations differing in the type of binder and dispersing agent were investigated by various techniques concerning the distribution of pigments in the liquid paints and films. The structure of the paints was analyzed by Remission Light Spectroscopy (RLS), Disc Centrifugation, Cryo-Replica Transmission Electron Microscopy (Cryo-TEM) and Cryo-Scanning Electron Microscopy (Cryo-SEM). The pigment distribution in the films was examined by means of Atomic Force Microscopy (AFM), TEM and RLS. The tendency of the pigments to form aggregates was found to depend on both: the type of binder and the dispersing agent. Only by adjusting the properties of the binder in combination with common dispersants it is possible to get well distributed TiO₂ particles within the paint. Correlation of application properties e.g. gloss and blocking to the microscopic structure is presented.