A rapid method for calculating derivatives of solvent accessible surface areas of molecules

A novel method to calculate the derivatives of solvent accessible surface areas is presented. Unlike earlier analytic methods, which require the molecular topology and the use of global Gauss-Bonnet theorem, this method requires only the fractional accessibilities of surface arcs. We developed an efficient numerical algorithm to calculate the surface arcs by creating a uniform set of points on the circles of intersection between surface atoms. A hierarchical point density doubling scheme led to a logarithmic dependence of Central Processing Unit (CPU) time on the number of points used. This algorithm calculated area derivatives for a 1000-atom protein in 1.5 s on an SGI INDIGO² which were within 2% of the analytic area derivatives calculated with the program ANAREA. This algorithm scales linearly with the number of atoms for large molecules and is easily parallelizable. © 1995 by John Wiley & Sons, Inc.     

Fast-atom-bombardment and tandem mass spectrometry for determining structures of fatty acids as their picolinyl ester derivatives

Picolinyl ester derivatives of common fatty acids can be readily desorbed by fast atom bombardment (FAB) as positive ions and then collisionally activated. Collisionally activated spectra of the (M + H)⁺ ions of the derivatives reveal that structurally informative remote-charge-site fragmentations occur. The presence of substitutents such as double bond, branch points, cyclopropane rings, hydroxy groups, and epoxy rings interrupts the fragmentation process in such a way that the substituent can be identified and its location on the alkyl chain can be determined. This method is also applicable to the picolinyl esters of short-chain fatty acids and to the analysis of mixtures of fatty acid derivatives. The approach is advantageous becasue the epicolinyl ester derivatives are also amenable to gas chromatography/mass spectrometry (GC/MS). Therefore, the FAB-MS/MS approach developed here is complementary to GC/MS.     

An improvement to the comparison equation method for solving the Schrödinger equation

A systematic improved comparison equation method to solve the Schrödinger equation is described. The method is useful in quantum mechanical calculations involving two or more transition or turning points and is applicable to real potentials with continuous derivatives. As a computational example of the method, a study of the bound-state problem using the Morse potential is given.     

Time-dependent probability of quantum tunneling in terms of the quasisemiclassical method

In view of the rapid progress in experiments of the tunneling dynamics in the time domain, we develop a quasisemiclassical method that is aimed at a study of the proton-transfer dynamics in a large system such as tropolone and its interesting derivatives, to which not only full quantum mechanics, but even a standard semiclassical theory is never easy to apply. In our very tractable method for multidimensional systems, the tunneling paths are generated in terms of the generalized classical mechanics, but the quantum phases arising from the action integral, the Maslov index, and the semicalssical amplitude factor as well in the semiclassical kernels are entirely neglected. This approach is called the quasisemiclassical method. One of the technical issues involved in the general semiclassical scheme is how to locate points from which a tunneling path emanates. Hence the studies of such tunneling points and the quasisemiclassical method should be examined collectively. We test several ways of determining the tunneling point, including those already proposed in the literature and a newly proposed one. It is shown numerically that the quasisemiclassical method with an appropriate choice of tunneling points reproduces the full quantum mechanical tunneling probability reasonably well. This case study indicates that the present conventional approach is promising to the study of large systems. The role of tunneling points in the initial process of tunneling is also discussed.     

New liquid-crystalline materials containing a five-membered heteroalicycle: Trans-2, 4-disubstituted 1, 3-oxathiolanes

The synthesis of new liquid-crystalline materials containing a five membered heteroalicyclic ring is described. The trans 2,4-disubstituted 1, 3-oxathiolane derivatives exhibit lower clearing temperatures and melting points than the analogous six membered 1, 3-oxathiane compounds. However the mesophase stability of the 1, 3-oxathiolane derivatives is superior to that of comparable cyclopentane derivatives.     

Improved algorithm for analysis of the least-squares treatment of titration data

In least-squares data-processing, previous investigators have reported the evaluation of partial derivatives that show the effect on the parameters, from errors in individual data points. By replacing the finite difference method used earlier, an increase in the speed of the computations by a factor of 40 or greater can be achieved.     

Interpolating moving least-squares methods for fitting potential energy surfaces: Improving efficiency via local approximants

The local interpolating moving least-squares (IMLS) method for constructing potential energy surfaces is investigated. The method retains the advantageous features of the IMLS approach in that the ab initio derivatives are not required and high degree polynomials can be used to provide accurate fits, while at the same time it is much more efficient than the standard IMLS approach because the least-squares solutions need to be calculated only once at the data points. Issues related to the implementation of the local IMLS method are investigated and the accuracy is assessed using HOOH as a test case. It is shown that the local IMLS method is at the same level of accuracy as the standard IMLS method. In addition, the scaling of the method is found to be a power law as a function of number of data points N, N(-q). The results suggest that when fitting only to the energy values for a d-dimensional system by using a Qth degree polynomial the power law exponent q approximately Qd when the energy range fitted is large (e.g., E<100 kcalmol for HOOH), and q>Qd when the energy range fitted is smaller (E<30 kcalmol) and the density of data points is higher. This study demonstrates that the local IMLS method provides an efficient and accurate means for constructing potential energy surfaces.     

Interactions of molecules with nucleic acids. IX. Evaluation and presentation of electrostatic contours on a steric surface with the removal of hidden lines

A technique to generate electrostatic contours on a steric surface is presented and applied to the presentation of molecules that interact with DNA. A set of electrostatic points at predetermined values along with their derivatives are obtained on the steric contours as they are generated. The steric contours are generated in a set of parallel planes. Points with given electrostatic values are then connected between and within the contours mathematically with a Taylor's expansion and two rules: the first to tentatively line up points that can be connected, and the second to check to insure that the remaining points can be connected. This method insures that contours will not cross by requiring that a possible connection of two points leaves an even number of remaining points for each electrostatic value in isolated regions of unused points bounded by points that have already been connected. The hidden line algorithm used previously to draw molecules in a space-filling model within the context of steric contours is applied to the complete problem of the presentation of a molecule bound to DNA with steric contours in parallel planes, and with electrostatic contours drawn on this steric surface.     

The curvature of the conical intersection seam: an approximate second-order analysis

We present a method for analyzing the curvature (second derivatives) of the conical intersection hyperline at an optimized critical point. Our method uses the projected Hessians of the degenerate states after elimination of the two branching space coordinates, and is equivalent to a frequency calculation on a single Born-Oppenheimer potential-energy surface. Based on the projected Hessians, we develop an equation for the energy as a function of a set of curvilinear coordinates where the degeneracy is preserved to second order (i.e., the conical intersection hyperline). The curvature of the potential-energy surface in these coordinates is the curvature of the conical intersection hyperline itself, and thus determines whether one has a minimum or saddle point on the hyperline. The equation used to classify optimized conical intersection points depends in a simple way on the first- and second-order degeneracy splittings calculated at these points. As an example, for fulvene, we show that the two optimized conical intersection points of C2v symmetry are saddle points on the intersection hyperline. Accordingly, there are further intersection points of lower energy, and one of C2 symmetry--presented here for the first time--is found to be the global minimum in the intersection space.     

Efficient and reliable mixture critical points calculation by global optimization

Multicomponent systems may exhibit several critical points or no critical point at all. Local methods can find only one critical point for a given initial guess. Recently, several global methods have been proposed for finding all the solutions of the problem. In the present work, we propose a gradient-based calculation method using global optimization, with temperature and molar volume as primary variables, and with analytical partial derivatives calculated from a two-parameter cubic equation of state. The Tunneling global optimization method is used for finding all the global minima. The implementation is based on a unique feature of the Tunneling method, which is able to find efficiently and reliably multiple minima at the same level. Several mixtures from binaries to petroleum reservoir fluids are used to test the proposed method. Numerical experiments proved the efficiency and reliability of the Tunneling method for finding all mixture critical points.     

An improved method for the evaluation of transition states

A simple but efficient coupled iteration procedure is proposed for searching saddle points and extrema along the line of constrained minimum energy paths by (analytical) calculation of the derivatives, i.e., the reduced forces and reduced force constants. The advantage of the method is shown with analytical potentials as well as a calculation of HCH? HNC rearrangement, as working examples.     

An approach to reaction path branching using valley–ridge inflection points of potential-energy surfaces

Valley–ridge inflection (VRI) points of a potential-energy surface (PES) may have a strong relation to the occurrence of bifurcations along reaction pathways of molecular rearrangements. We discuss two different definitions of VRI points in the literature. The calculation of symmetric VRI points has already been reported [W. Quapp et al. (1998) Theor. Chem. Acc. 100: 285–299]. Here, we in addition calculate special asymmetric VRI points which are placed on gradient extremals (GE). Following a GE opens the possibility to find the VRI point on it. An application is presented to search for asymmetric VRI points near the isomerization valley of the PES of the HCN molecule. A new method for GE-following is based on a mathematical connection between the following of a reduced gradient and the calculation of GEs. The tangent search method to follow a GE to the smallest eigenvalue [W. Quapp et al. (2000) Theor. Chem. Acc. 105: 145–155] is extended to follow also GEs to higher eigenvalues in order to find a VRI point. The new method needs gradient and second derivatives of the PES only.     

A spline for your saddle

Pinpointing extrema on a multidimensional hypersurface is an important generic problem with a broad scope of application in statistical mechanics, biophysics, chemical reaction dynamics, and quantum chemistry. Local minima of the hypersurface correspond to metastable structures and are usually the most important points to look for. They are relatively easy to find using standard minimizing algorithms. A considerably more difficult task is the location of saddle points. The saddle points most sought for are those which form the lowest barriers between given minima and are usually required for determining rates of rare events. We formulate a path functional minimum principle for the saddle point. We then develop a cubic spline method for applying this principle and locating the saddle point(s) separating two local minima on a potential hypersurface. A quasi-Newton algorithm is used for minimization. The algorithm does not involve second derivatives of the hypersurface and the number of potential gradients evaluated is usually less than 10% of the number of potential evaluations. We demonstrate the performance of the method on several standard examples and on a concerted exchange mechanism for self-diffusion in diamond. Finally, we show that the method may be used for solving large constrained minimization problems which are relevant for self-consistent field iterations in large systems.     

1,2-oxazine chemistry—I : Synthetic approaches to tetrahydro-1,2-oxazines

The synthesis of a series of N-carbethoxytetrahydro-1,2-oxazines, by the reaction of 1,4-dibromobutane derivatives with N-hydroxyurethane under basic conditions, and their reduction to N-Me derivatives is described. Stereochemical and mechanistic points of interest in these reactions are discussed.     

Influence of molecular characteristics of nonionic cellulose ethers on their interaction with ionic surfactant investigated by conductometry

The interaction between nonionic derivatives of cellulose, hydroxypropylmethyl cellulose (HPMC) and methyl cellulose (MC), and ionic surfactant, sodium dodecylsulfate (SDS) were investigated by conductometric titration method, at 30°C. Obtained titration curves show two break points: critical aggregation concentration (cac) defined as the concentration of SDS at which interaction starts, and polymer saturation concentration (psp) as the concentration at which interaction finishes. Changes of characteristic concentration breaks were determined in dependence on concentration and molecular characteristics of cellulose derivatives (degree of substitution (DS) and molecular mass, i.e. intrinsic viscosity). It was shown that the first break point, cac, is independent of polymer concentration; while the second break point, psp, increases as polymer concentration increases, as described by a linear correlation. The slopes of linear relationship justify the DS on the intensity of the cellulose derivatives–SDS interaction. Changes in the intrinsic viscosity of cellulose derivatives do not exhibit influence on the interaction with SDS.     

On the value of recent microscopic methods of identification used for organic substances

The value of recent methods of identification of organic substances by means of the micro melting point apparatus is investigated, using 3 groups of closely related substances (benzoic acid derivatives, barbituric acid derivatives, and sulphonamids).The experiments show that a combination of the melting point determination with an observation of sublimation and conversion during heating and, moreover, with the observation of the conversion of crystallised melting drops etc. very markedly increases the value of the determination.The preparation of derivatives from quantities below l mg can be performed more rapidly and more simply than the preparation of larger amounts. The melting point determination of the derivatives is of the greatest value for the identification of the respective substances.On the other hand, the melting point determination on eutectic mixtures of the substance in question with a test substance is found to be of much lower value as a method of identification, if there is a possibility for the occurrence of a number of closely related substances having the same melting point ; such substances often have the same eutectic melting point with the same test substance.The determination of the index of refraction of molten substances (i.e., the determination of the temperature interval within which the molten mass has the same index of refraction as a glass powder of a known index of refraction) is an excellent method of identification, since the scattering of the temperature intervals found for related substances is of the same magnitude, and for not related substances is considerably higher, than the scattering of their melting points.     

Discrimination between adsorption isotherm models based on nonlinear frequency response results

A number of criteria are established for distinguishing between different adsorption isotherm types. These criteria are defined based on the adsorption isotherm derivatives up to the third order, which, on the other hand, can be estimated from nonlinear frequency response data. The criteria for five favourable (Langmuir, Freundlich, Sips, Toth and Unilan) isotherms and two complex isotherms (BET and quadratic) are presented. These criteria enable unique identification of the underlying adsorption isotherm relation if the values of the local first, second and third order isotherm derivatives at several points are known. The method is applied to experimental data from our previous publications, for one case of a favourable and one case of a complex isotherm.     

Analytic gradients in the improved BCS method

The first derivatives of the total energy with respect to nuclear displacement have been calculated in the framework of the Improved Bardeen–Cooper–Schrieffer (IBCS) method. It permits the quick determination of the stationary points. This revised version was published online in July 2006 with corrections to the Cover Date.     

甲基苯基氯硅烷和苯基三氯硅烷混合物的GC-MS分析

使用GC—MS分析热缩合法生产的氯硅烷粗单体时,发现甲基苯基二氯硅烷和苯基三氯硅烷在HP-5毛细管柱上难以得到有效的分离。采用过量甲醇对粗产品氯硅烷进行甲氧基化后,甲基苯基二氯硅烷和苯基三氯硅烷相应的甲氧基化产物在色谱柱上能得到有效的分离,可为其色谱分析提供依据。