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Superposition of molecules

Nissink, J.W.M., Verdonk, M.L., Kroon, J., Mietzner, T., and Klebe, G. Superposition of molecules electron density fitting using fourier transforms. /. Comb. Chem. 1997, 38, 638-645. [Pg.107]

Significant efforts have been made to assemble teratogenic data basses with peer-reviewed evaluations (ref. 1). New avenues for the SAR studies have been opened, such as quantitative methods for structural superposition of molecules and for superposition of their reactivity characteristics (ref. 2). Emphasis has been placed on the electrostatic properties of the molecules, such as the molecular electrostatic potential, the electric fields, and the polarizability terms calculated from perturbation expansions (ref. 2). Computer-assisted multivariate SAR which deals with many variables simultaneously has been advanced (ref. 3). [Pg.42]

MATCHIT is a program for the graphical and mathematical superposition of molecules or fragments that are chemically related, performing a least-square fit of designated atoms and calculating die... [Pg.163]

When a molecule is isolated from external fields, the Hamiltonian contains only kinetic energy operators for all of the electrons and nuclei as well as temis that account for repulsion and attraction between all distinct pairs of like and unlike charges, respectively. In such a case, the Hamiltonian is constant in time. Wlien this condition is satisfied, the representation of the time-dependent wavefiinction as a superposition of Hamiltonian eigenfiinctions can be used to detemiine the time dependence of the expansion coefficients. If equation (Al.1.39) is substituted into the tune-dependent Sclirodinger equation... [Pg.13]

This section begins with a brief description of the basic light-molecule interaction. As already indicated, coherent light pulses excite coherent superpositions of molecular eigenstates, known as wavepackets , and we will give a description of their motion, their coherence properties, and their interplay with the light. Then we will turn to linear and nonlinear spectroscopy, and, finally, to a brief account of coherent control of molecular motion. [Pg.219]

Much of the previous section dealt with two-level systems. Real molecules, however, are not two-level systems for many purposes there are only two electronic states that participate, but each of these electronic states has many states corresponding to different quantum levels for vibration and rotation. A coherent femtosecond pulse has a bandwidth which may span many vibrational levels when the pulse impinges on the molecule it excites a coherent superposition of all tliese vibrational states—a vibrational wavepacket. In this section we deal with excitation by one or two femtosecond optical pulses, as well as continuous wave excitation in section A 1.6.4 we will use the concepts developed here to understand nonlinear molecular electronic spectroscopy. [Pg.235]

Figure Al.6.24. Schematic representation of a photon echo in an isolated, multilevel molecule, (a) The initial pulse prepares a superposition of ground- and excited-state amplitude, (b) The subsequent motion on the ground and excited electronic states. The ground-state amplitude is shown as stationary (which in general it will not be for strong pulses), while the excited-state amplitude is non-stationary. (c) The second pulse exchanges ground- and excited-state amplitude, (d) Subsequent evolution of the wavepackets on the ground and excited electronic states. Wlien they overlap, an echo occurs (after [40]). Figure Al.6.24. Schematic representation of a photon echo in an isolated, multilevel molecule, (a) The initial pulse prepares a superposition of ground- and excited-state amplitude, (b) The subsequent motion on the ground and excited electronic states. The ground-state amplitude is shown as stationary (which in general it will not be for strong pulses), while the excited-state amplitude is non-stationary. (c) The second pulse exchanges ground- and excited-state amplitude, (d) Subsequent evolution of the wavepackets on the ground and excited electronic states. Wlien they overlap, an echo occurs (after [40]).
A microwave pulse from a tunable oscillator is injected into the cavity by an anteima, and creates a coherent superposition of rotational states. In the absence of collisions, this superposition emits a free-mduction decay signal, which is detected with an anteima-coupled microwave mixer similar to those used in molecular astrophysics. The data are collected in the time domain and Fourier transfomied to yield the spectrum whose bandwidth is detemimed by the quality factor of the cavity. Hence, such instruments are called Fourier transfomi microwave (FTMW) spectrometers (or Flygare-Balle spectrometers, after the inventors). FTMW instruments are extraordinarily sensitive, and can be used to examine a wide range of stable molecules as well as highly transient or reactive species such as hydrogen-bonded or refractory clusters [29, 30]. [Pg.1244]

In the discussion above, scattering from molecules is treated as a superposition of noninteracting electron... [Pg.1316]

There is a small peak one mass unit higher than M m the mass spectrum of ben zene What is the origin of this peak d What we see m Figure 13 40 as a single mass spectrum is actually a superposition of the spectra of three isotopically distinct benzenes Most of the benzene molecules contain only and H and have a molecular mass of 78 Smaller proportions of benzene molecules contain m place of one of the atoms or m place of one of the protons Both these species have a molecular mass of 79... [Pg.569]

In finite boundary conditions the solute molecule is surrounded by a finite layer of explicit solvent. The missing bulk solvent is modeled by some form of boundary potential at the vacuum/solvent interface. A host of such potentials have been proposed, from the simple spherical half-harmonic potential, which models a hydrophobic container [22], to stochastic boundary conditions [23], which surround the finite system with shells of particles obeying simplified dynamics, and finally to the Beglov and Roux spherical solvent boundary potential [24], which approximates the exact potential of mean force due to the bulk solvent by a superposition of physically motivated tenns. [Pg.100]

This method represents the most common and traditional application of computational tools to rational drug design. From a list of molecules of known activity, one can establish a 3D-pharmacophore hypothesis that is then transformed into a 3D-search query. This query is then used to search a 3D database for structures that fit the hypothesis within a certain tolerance. If the yield of active molecules is significant, then the query can be used to predict activities on novel compounds. In our situation, the enantiophore is built from the superposition of a list of sample molecules, which are all well separated on a given CSR Hence, the common features of this series of molecules can become a good enantiophore hypothesis for the enantiores-olution on this CSR... [Pg.110]

Because of the success of the r12 method in the applications, one had almost universally in the literature adopted the idea of the necessity of introducing the interelectronic distances r j explicitly in the total wave function (see, e.g., Coulson 1938). It was there-fore essential for the development that Slater,39 Boys, and some other authors at about 1950 started emphasizing the fact that a wave function of any desired accuracy could be obtained by superposition of configurations, i.e., by summing a series of Slater determinants (Eq. 11.38) built up from a complete basic one-electron set. Numerical applications on atoms and molecules were started by means of the new modern electronic computers, and the results have been very encouraging. It is true that a wave function delivered by the machine may be the sum of a very large number of determinants, but the result may afterwards be mathematically simplified and physically interpreted by means of natural orbitals.22,17... [Pg.257]

Fain, J., and Matsen, F. A., J. Chem. Phys. 26, 376, Complete -electron treatment of the butadiene molecule and ion." Complete VB. Results in agreement with SCF with superposition of configurations. [Pg.352]

According to Eq. (2.13), the spectra we are interested in are given by a Fourier transform of the orientational correlation functions of the corresponding order Similarly to what was done in Chapter 3, the correlation functions for linear and spherical molecules may be represented as a superposition of the partial (marginal) components... [Pg.199]

Another example is provided by [30] anmlene. Longuet-Higgins and Salem have shown that the observed visible and UV absorption spectrum and, in particular, the NMR proton chemical shifts of this molecule are very difficult to reconcile with the symmetrical nuclear configuration (Dg ) suggested by the superposition of the Kekule-type resonance structures. The hypothesis of a bond-length alternation of symmetry removes this difficulty. This indicates that the resonance between Kekule-type structures should be very much impeded also in this molecule. [Pg.6]


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See also in sourсe #XX -- [ Pg.161 ]




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