Equilibrium geometries property calculations

Using Approximate Equilibrium Geometries to Calculate Molecular Properties... 

All three states were described by a single set of SCF molecular orbitals based on the occupied canonical orbitals of the X Z- state and a transformation of the canonical virtual space known as "K-orbitals" [10] which, among other properties, approximate the set of natural orbitals. Transition moments within orthogonal basis functions are easier to derive. For the X state the composition of the reference space was obtained by performing two Hartree-Fock single and double excitations (HFSD-CI) calculations at two typical intemuclear distances, i.e. R. (equilibrium geometry) and about 3Re,and adding to the HF... 

During the last decade MO-theory became by far the most well developed quantum mechanical method for numerical calculations on molecules. Small molecules, mainly diatomics, or highly symmetric structures were treated most accurately. Now applicability and limitations of the independent particle, or Hartree-Fock (H. F.), approximation in calculations of molecular properties are well understood. An impressive number of molecular calculations including electron correlation is available today. Around the equilibrium geometries of molecules, electron-pair theories were found to be the most economical for actual calculations of correlation effects ). Unfortunately, accurate calculations as mentioned above are beyond the present computational possibilities for larger molecular structures. Therefore approximations have to be introduced in the investigation of problems of chemical interest. Consequently the reliability of calculated results has to be checked carefully for every kind of application. Three types of approximations are of interest in connection with this article. 

New experiments increase constantly the requirements on the quality and range of calculated electromagnetic properties. State-of-the-art quantum chemical methods can meet the experimental demands and there are numerous articles treating the electric polarizability at the highest level of accuracy. Nevertheless, also only a few of them treat the dependence of the tensor components of the polarizability on the internuclear distance far from the molecular equilibrium geometry. However, there are several good reasons for such studies. 

Piris and Otto (PO) achieved a reconstruction functional D[ D] satisfying the most general properties of the 2-RDM [58]. They kept the spin structure from Refs. [52, 53], but introduced a new spatial dependence in the correction term of the 2-RDM. Calculated values for polarizabilities [59], ionization energies, equilibrium geometries, and vibrational frequencies [60] in molecules were... 

Molecular modeling, like all other technical disciplines, has its own jargon. Much of this is described in Appendix B (Common Terms and Acronyms), and only one aspect will be addressed here. This concerns specification of theoretical model used for property calculation together with theoretical model used for equilibrium (or transition-state) geometry calculation. 

This is a question of considerable practical importance, given that optimization of equilibrium geometry can easily require one or two orders of magnitude more computation than an energy (property) calculation at a single geometry (see Chapter 11). Rephrased, the question might read ... 

Potential functions such as MM+ discussed in Chapter 1 are fine for intramolecular interactions. MD was developed long before such sophisticated force fields became available, and in any case the aims of MM and MD simulations tend to be quite different. MM studies tend to be concerned with the identification of equilibrium geometries of individual molecules whilst MD calculations tend to be concerned with the simulation of bulk properties. Inspection of Figure 2.2 suggests that the intramolecular details ought to be less important than the intermolecular ones, and early MD studies concentrated on the intermolecular potential rather than the intramolecular one. 

One of the main aims of quantum mechanical methods in chemistry is the calculation of energies of molecules as a function of their geometries. This requires the generation of potential energy hypersurfaces. If these surfaces can be calculated with sufficient accuracy, they may be employed to predict equilibrium geometries of molecules, relative energies of isomers, the rates of their interconversions, NMR chemical shifts, vibrational spectra, and other properties. Carbocations are ideally suited for calculations because relative energies of well-defined structural isomers are frequently not easily determined experimentally. It should, however, be kept in mind that theoretical calculations usually refer to isolated ion structures in the gas phase. 

Quantum chemistry is the foundation of molecular chemistry dealing with structure, properties, and interaction of molecules. The basic principles are offered by quantum mechanics. Quantum-chemical calculations are able to supply information needed for molecular descriptors for QSAR analyses. The use of quantum-chemical calculations is becoming common to establish molecular equilibrium geometries and conformations and to supply quantitative thermochemical and kinetic data. 

In contrast to these concepts above obtained from numerous ab-initio molecular orbital calculations (usually from small radicals, e. g. H, F, H3C or HOCH2 to fluoroalkenes), some semi-empirical calculation on more longer halogenated radicals were performed by Rozhkov et al. [333, 334] and Xu et al. [335]. The former team determined equilibrium geometries and electronic properties of perfluoroalkyl halogenides and showed that fluorine atoms in vinyl position strongly stabilise all the sigma molecular orbital. 

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