Large molecules orbital determination

Once the least-squares fits to Slater functions with orbital exponents e = 1.0 are available, fits to Slater function s with oth er orbital expon cn ts can be obtained by siin ply m ii Itiplyin g th e cc s in th e above three equations by It remains to be determined what Slater orbital exponents to use in electronic structure calculation s. The two possibilities may be to use the "best atom" exponents (e = 1. f) for II. for exam pie) or to opiim i/e exponents in each calculation. The "best atom expon en ts m igh t be a rather poor ch oicc for mo lecular en viron men ts, and optirn i/.at ion of non linear exponents is not practical for large molecules, where the dimension of the space to be searched is very large.. 4 com prom isc is to use a set of standard exponents where the average values of expon en ts are optirn i/ed for a set of sin all rn olecules, fh e recom -mended STO-3G exponents are... 

Because of the success of the r12 method in the applications, one had almost universally in the literature adopted the idea of the necessity of introducing the interelectronic distances r j explicitly in the total wave function (see, e.g., Coulson 1938). It was there-fore essential for the development that Slater,39 Boys, and some other authors at about 1950 started emphasizing the fact that a wave function of any desired accuracy could be obtained by superposition of configurations, i.e., by summing a series of Slater determinants (Eq. 11.38) built up from a complete basic one-electron set. Numerical applications on atoms and molecules were started by means of the new modern electronic computers, and the results have been very encouraging. It is true that a wave function delivered by the machine may be the sum of a very large number of determinants, but the result may afterwards be mathematically simplified and physically interpreted by means of natural orbitals.22,17... 

All of the above conventions together permit the complete construction of the secular determinant. Using standard linear algebra methods, the MO energies and wave functions can be found from solution of the secular equation. Because the matrix elements do not depend on the final MOs in any way (unlike HF theory), the process is not iterative, so it is very fast, even for very large molecules (however, fire process does become iterative if VSIPs are adjusted as a function of partial atomic charge as described above, since the partial atomic charge depends on the occupied orbitals, as described in Chapter 9). 

An ab initio calculation uses the correct molecular electronic Hamiltonian (1.275) and does not introduce experimental data (other than the values of the fundamental physical constants) into the calculation. A semiempirical calculation uses a Hamiltonian simpler than the correct one, and takes some of the integrals as parameters whose values are determined using experimental data. The Hartree-Fock SCF MO method seeks the orbital wave function 0 that minimizes the variational integral <(4> //el initio method. Semiempirical methods were developed because of the difficulties involved in ab initio calculation of medium-sized and large molecules. We can... 

The carbon chemical shifts for steroids are the most readily available data from a routine 13C NMR determination. Since they reflect the electronic and steric environments of the various carbon nuclei, they provide sensitive insights to the configurational and conformational features of such molecules. While much interesting work on ab initio molecular orbital calculations of carbon chemical shifts is now appearing, it is probably true that the difficulties of carrying out such calculations on large molecules will prevent their applications to steroids for some time. We are limited, therefore, to a more empirical approach to steroid carbon chemical shifts. (3, 38)... 

In this section, we briefly discuss some of the electronic structure methods which have been used in the calculations of the PE functions which are discussed in the following sections. There are variety of ab initio electronic structure methods which can be used for the calculation of the PE surface of the electronic ground state. Most widely used are Hartree-Fock (HF) based methods. In this approach, the electronic wavefunction of a closed-shell system is described by a determinant composed of restricted one-electron spin orbitals. The unrestricted HF (UHF) method can handle also open-shell electronic systems. The limitation of HF based methods is that they do not account for electron correlation effects. For the electronic ground state of closed-shell systems, electron correlation effects can be accounted for relatively easily by second-order Mpller-Plesset perturbation theory (MP2). In modern implementations of MP2, linear scaling with the size of the system has been achieved. It is thus possible to treat quite large molecules and clusters at this level of theory. 

Introduction.—The LCAO-MO method remains the most important approach for evaluating wavefunctions for large molecules in spite of its known defects. The details of the method are well known. The main outlines are given here only to establish the nomenclature. The method attempts to describe the wavefunction as a single Slater determinant comprised of one-electron space-spin functions or spin orbitals ... 

Atomic orbitals have a disadvantage in that they are diffuse. In solids, large molecules or clusters that are the size of the orbitals are compressed due to the interaction with the neighbors. A measure for the distance between neighbors is given by the so-called covalent radius, r0, and is empirically determined for all atoms. Therefore, it is wise to use orbitals that somehow incorporate this information. To enhance this effect, an additional harmonic potential is added to the atomic Kohn-Sham equations that leads to compressed atomic orbitals, or optimized atomic orbitals (O-LCAO) ... 

A very popular approach to larger systems in DFT, in particular solids, is based on the concept of a pseudopotential (PP). The idea behind the PP is that chemical binding in molecules and solids is dominated by the outer (valence) electrons of each atom. The inner (core) electrons retain, to a good approximation, an atomic-like configuration, and their orbitals do not change much if the atom is put in a different environment. Hence, it is possible to approximately account for the core electrons in a solid or a large molecule by means of an atomic calculation, leaving only the valence density to be determined self-consistently for the system of interest. 

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