Energy minimization definition

These principles are phrased in the language of the ionic model, but they provide a simpler and more explicit description of stable structures than that given by the ionic model s energy minimization principle. Among the important ideas captured by Pauling s rules are those of local charge neutrality, the definition of electrostatic bond strength, and the rule of parsimony which is closely... 

The following definition of computational chemistry was published in 1985 (6) quantitative modeling of chemical behavior on a computer by the formalisms of theoretical chemistry. Some quantum theoreticians naturally would like to see computational chemistry as a subset of their field (7). However, today the number of scientists employed as computational chemists well exceeds the number employed as theoreticians (8). A recent textbook author (9) views computational chemistry as encompassing not only quantum mechanics, but also molecular mechanics, [energy] minimization, simulations, conformational analysis, and other computer-based methods for understanding and predicting the behavior of molecular systems. ... 

The MO concept is directly related to an approximate wavefunction consisting of a Slater determinant of occupied one-particle wavefunctions, or molecular orbitals. The Hartree-Fock orbitals are by definition the ones that minimize the expectation value of the Hamiltonian for this Slater determinant. They are usually considered to be the best orbitals, although it should not be forgotten that they are only optimal in the sense of energy minimization. 

Molecular orbital computations are currently used extensively for calculation of a range of molecular properties. The energy minimization process can provide detailed information about the most stable stmcture of the molecule. The total binding energy can be related to thermodynamic definitions of molecular energy. The calculations also provide the total electron density distribution, and properties that depend on electron distribution, such as dipole moments, can be obtained. The spatial distribution of orbitals, especially the HOMO and LUMO, provides the basis for reactivity assessment. We illustrate some of these applications below. In Chapter 3 we show how MO calculations can be applied to intermediates and transitions structures and thus help define reaction mechanisms. Numerical calculation of spectroscopic features including electronic, vibrational, and rotational energy levels, as well as NMR spectra is also possible. 

There is a tendency to use the term molecular mechanics (MM) as opposite to quantum mechanics, therefore including all classical dynamics methods, such as energy minimization, Monte Carlo, and molecular dynamics. Sometimes it is used to describe only the energy minimization method using empirical force field (potential) or it is even used to refer to the quantum mechanical method specifically, emphasizing its use for molecular motion. Nevertheless, we will focus on the second definition of molecular mechanics (43-45). In this approach, a molecule is viewed as a collection of particles (atoms) held together by simple harmonic or elastic forces. Such forces are defined in terms of potential energy... 

There is interesting to study the atomic properties in molecule, based on the definition AIM3, with the great advantage of the energy-minimizing criterion, which takes out the atoms from the isolated state and promotes them in the molecular bonds. 

It is known that real polymer systems are characterized by a definite type of molecular-mass distribution. Due to this fact, in the melt, i.e., at the conditions of an alloy formation, the redistribution of fractions of various molecular mass is possible. The difference in the magnitude of the surface tension for various fraction may reach 10-20 mN/m. The change in the amount of low-molecrdar weight fractions in the interphase region, according to the principle of the free energy minimization, leads to the diminishing of the interfacial tension. As a result, the interface becomes unstable and the spontaneous formation of microemulsion is possible. 

Although the elastic term connected with 24 itself is not positive definite, it poses no mathematical problems with regard to the free energy minimization, as the free energy funetional remains positive definite (bound from below) as long as... 

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