Frozen atoms

To limit a molecular mechanics calculation to part of a molecule, select the atom s ofin terest. On ly the selected atom s can m ove, but the other (frozen) atoms mfhience the calc illation. 

You can completely freeze part of a molecule while allowing the remaining atoms to move in the field of the frozen atoms. This option is useful, for example, in a conformational search of part of a molecule. 

To limit a semi-empirical calculation to part of a molecule, select the atoms of interest. Then choose Bttend to sp3 on the Select menu to terminate correctly the selected group of atoms. Only the selected atoms move, but the frozen atoms influence the calculation. This is now possible with all the semi-empirical methods in HyperChem. 

Subject to Constraints Frozen Atoms Total Charge Neutral... 

In the frozen atomic structure approximation, where the same orbitals are used in the initial and final states, this overlap matrix element yields unity. Hence, one obtains for the remaining matrix element... 

This result shows that the original matrix element containing the orbitals of all electrons factorizes into a two-electron Coulomb matrix element for the active electrons and an overlap matrix element for the passive electrons. Within the frozen atomic structure approximation, the overlap factors yield unity because the same orbitals are used for the passive electrons in the initial and final states. Considering now the Coulomb matrix element, one uses the fact that the Coulomb operator does not act on the spin. Therefore, the ms value in the wavefunction of the Auger electron is fixed, and one treats the matrix element Mn as... 

Since the same orbitals are used for the ground state and the hole state, no relaxation effects due to the change in the shielded nuclear charges are taken into account, and this model is called the frozen atomic structure approximation.) Due to the interpretation of els as the binding energy of one ls-electron, the differential equation for the Pls(r) orbital, equ. (7.66b), can be interpreted as a one-particle Schrodinger equation for the Is orbital (see equs. (1.3) and (1.4)) ... 

The Is and 2s orbitals which are affected by neither the photoionization nor the Auger process are omitted for simplicity.) If these wavefunctions are constructed from single-electron orbitals of a common basis set (the frozen atomic structure approximation), the photon operator as a one-particle operator allows a change of only one orbital. Hence, the photon operator induces the change 2p to r in these matrix elements ... 

Silicon thin film thermal conductivities are predicted using equilibrium molecular dynamics and the Grccn-Kubo relation. Periodic boundary conditions are applied in the direetions parallel to the thin film surfaees (Fig. 5). Atoms near the surfaces of the thin film are subjeeted to the above-described repulsive potential in addition to the Stillinger-Weber potential [75]. Simulations were also performed adding to each surface four layers of atoms kept frozen at their crystallographic positions, in order to eompare the dependence of the predieted thermal eonduetivities on the surface boundary eonditions. We found that the thermal eonduetivities obtained using frozen atoms or the repulsive potential are identical within the statistical deviations, exeept for the in-plane thermal eonduetivity of films with thickness less than 10 nm [79]. Therefore, in the present study, we present only the predietions obtained with the repulsive potential. 

Thus, the results of Daggett et al. demonstrate the importance of those residues that were included in this model for the catalytic activity, and a TT for the reaction has been suggested. However, a TS has not been characterized in the regular manner, i.e., by the Hessian matrix at the point where the first derivative of the energy vs. reaction coordinate is zero (Flanigan et al., 1977). This is a problematic procedure for models of larger systems that have some "frozen" atoms, and should not be required for such models. Also, a difference between the rate limiting step for amides and esters has, unfortunately, not been detected. 

We first consider the ramifications of the neutrality and nonpolarity of H2. Imagine that we have a ground-state hydrogen atom and we allow another similar atom, H , to approach it. At values of R in excess of, say, 2 a.u., we expect the perturbation felt by Ha to be much smaller than was the case in our Hj discussion. This is because, where before we had approach by a charged particle, here we have approach by a neutral atom. The attraction between the electron on Ha and the proton on H is counterbalanced by repulsion between the electron on Ha and that on H. This means that the frozen atom-in-molecule energy for H2 is fairly close to the energy of the isolated atom. This simplifies our qualitative treatment for neutral molecules since it means we can... 

Fundamental klgnoreCoordlnates kPreserveCOS kAeF Do not assume preexisting coordinates, except for frozen atoms. Preserve the circular order of substituents (COS) about an atom, even at nonstereocenters. Make a quantitative aesthetic judgment about the success of redrawing, and undo it if it is not an improvement. 

An adjustable atom or bond is one that is selected. A frozen atom or bond is one which is not selected. A partially selected atom is a selected atom, some but not all of whose bonds are selected. For such an atom, the angle between each pair of circularly contiguous frozen bonds is preserved, whereas angles to the nonfrozen bonds are adjusted and optimized relative to the frozen bonds. 

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