Configuration weight

The probability of finding the system in a specific configuration is given by the configurational weight JF, which we write as... 

Formally the continuous chain limit may also be carried through on the level of the configurational weight JF = exp(—V). Taking into account that becomes small, we rewrite exp(—F) (Eq. (2,3)) as... 

Figure 7. ESPS ( Lattice Switch ) studies of the relative stability of/cc and hep phases of the LJ solid at zero pressure, as discussed in Section IV.D. In this case the order parameter M [Eq. (59)] measures the difference between the energy of a configuration of one phase and the corresponding configuration of the other phase generated by the switch operation. The areas under the two peaks reflect the relative configurational weights of the two phases. The evolution with increasing temperature (from ftep-favored to/cc-favored behavior) picks out the hep-fee phase boundary shown in Fig. 8. (Taken from Fig. 7 of Ref. 57.)...

Total energies (a.u.), overlap integrals and configuration weights for benzene obtained with the cc-pVDZ basis with different wavefunctions. The geometry used is HF/cc-pVDZ ... 

Compound Transition energy (nm) Excitation energy (nm) after Cl Configuration weight (%) Obs. (nm)... 

Let us assume that a variable A(t) is coupled to the reaction coordinate and that (A) is its mean value. If a measurement of some property P depends on (A), but not on the particular details of the time dependence of A(t), then we will call it a statistical dependence. If the property P depends on particular details of the dynamics of A(t) we will call it a dynamical dependence. Note that in this definition it is not the mode A(t) alone that causes dynamical effects, but it also depends on the timescale of the measured property P. Promoting vibrations (to be discussed in Sections 2-4) are a dynamic effect in this sense, since their dynamics is coupled to the reaction coordinate and have similar timescales. Conformation fluctuations that enhance tunneling (to be discussed in Section 5) are a statistical effect the reaction rate is the sum of transition state theory (TST) rates for barriers corresponding to some configuration, weighted by the probability that the system reaches that configuration. This distinction between dynamic and statistical phenomena in proteins was first made in the classic paper of Agmon and Hopfield.4 We will discuss three kinds of motions ... 

Birnbaum, M. H., Coffey, G., MeUers, B. A., and Weiss, R. (1992), UtiUty Measurement Configural-Weight Theory and the Judge s Point of Wew, Journal of Experimental Psychology Human Perception and Petforrrumce, Vol. 18, pp. 331-346. 

Figure 11.8 Comparison of (a) configurational weights and (b) ej symmetry natural orbital occupations (NOOs) in CeCOTj. ry is an approximate value of the electron density associated with 4f-orbital occupation. (Data from Ref [29a].)...

Thus, as with SCF wavefunctions, the first derivative of an MC-SCF energy does not need the derivative of the wavefunction. However, to proceed to second derivatives, it is necessary to solve the MC-CHF equations (multiconfiguration coupled Hartree-Fock). Unlike SCF, however, not only the orbital changes are required but also the changes in the configuration weights. Thus the set of equations has the structure... 

Table 3.7 Configurational weights, Wj, corresponding to different k values of the CCSD wave functions with the HF reference and the cue reference for polyene molecules...

The right-hand side of Eq. (34) is the force acting on particle 1, with particles 1 through n fixed at positions r through r and with all the N-n other particles averaged over all configurations, weighted by the... 

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