Energy weights

Eq. (16.5) shows that U is simply a sum of energies weighted by the probabifity of being in that state, i.e. U is the average (potential) energy of the system. 

Energy-weighted density matrix element in AO basis... 

Making use of the fact that the energy solutions of eq. 9 come in pairs, one can write a sum rule for the energy weighted transition matrix elements as... 

Thus, in this representation, the energy weighted sum of the transition matrix element can be written as [76]... 

To interpret the electronic structure of a material, it is often useful to understand what states are important in the vicinity of specific atoms. One standard way to do this is to use the local density of states (LDOS), defined as the number of electronic states at a specified energy weighted by the fraction of the total electron density for those states that appears in a specified volume around a nuclei. Typically, this volume is simply taken to be spherical so to calculate the LDOS we must specify the effective radii of each atom of interest. This definition cannot be made unambiguously. If a radius that is too small is used, information on electronic states that are genuinely associated with the nuclei will be missed. If the radius is too large, on the other hand, the LDOS will include contributions from other atoms. 

The essential issues with respect to a practical secondary battery are the energy density (energy/weight ratio), the power density, spontaneous discharge rate, fractional charge recoverable (reversibility) and the lifetime. In order to compare figures for different systems it is essential to ensure that they are derived on the same basis, for... 

The CiTest performs the evaluation of the pharmacophore hypothesis computing a non energy-weighted fit value. 

The wavepacket 4>/(t) on the other hand is a function of time and therefore contains all energies, weighted by the matrix elements t(Ef,n) defined in Equation (2.68). It is a solution of the time-dependent but not the time-independent Schrodinger equation. 

Ideally, a propellant would be a single, solid, nontoxic chemical compound that is stable, easy to store, easy to ignite, of compact mass, and so forth, which is cheap and simple to prepare from readily available materials and which on combustion produces no smoke or solid residue, that is, is completely converted into gas or gases. It must contain its own oxygen supply which is necessary for combustion in confined spaces, it must burn very rapidly as opposed to detonation, and it must have a satisfactory energy/weight relationship. 

The expression of the energy-weighted density matrix is more easily given in the MO basis [4, 26]... 

Blocking histamine receptors (sedation, inattention, low energy, weight gain). 

Here, W is an energy-weighted density matrix element as in the Hartree-Fock gradient formula (23). Equation 5 contains two "difficult" terms (the last two), the derivative of density matrix elements and the fitting coefficients e. It turns out that these terms can be eliminated by using the relationship... 

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