Multielectron methods computational method

During the meeting, various applications of and perspectives on the DV-Xa method were discussed in detail. Among them, the usefulness of theoretical analysis using DV-Xa calculation for X-ray and electron spectroscopy such as XPS, XES (X-ray emission spectroscopy), XANES, ELNES, and AES was presented and discussed. A new universal computational method for the many-electron-state, DV-ME (DV-multielectron) method was introduced by demonstrating its advantages and possibilities for application to the calculation of the multiplet structure of the d-d transition in various transition metal oxides. Another topic was the application of the DV-Xa method to materials science. The study of... 

The equation is used to describe the behaviour of an atom or molecule in terms of its wave-like (or quantum) nature. By trying to solve the equation the energy levels of the system are calculated. However, the complex nature of multielectron/nuclei systems is simplified using the Born-Oppenheimer approximation. Unfortunately it is not possible to obtain an exact solution of the Schrddinger wave equation except for the simplest case, i.e. hydrogen. Theoretical chemists have therefore established approaches to find approximate solutions to the wave equation. One such approach uses the Hartree-Fock self-consistent field method, although other approaches are possible. Two important classes of calculation are based on ab initio or semi-empirical methods. Ah initio literally means from the beginning . The term is used in computational chemistry to describe computations which are not based upon any experimental data, but based purely on theoretical principles. This is not to say that this approach has no scientific basis - indeed the approach uses mathematical approximations to simplify, for example, a differential equation. In contrast, semi-empirical methods utilize some experimental data to simplify the calculations. As a consequence semi-empirical methods are more rapid than ab initio. 

The basis of computational quantum mechanics is the equation posed by Erwin Schrbdinger in 1925 that bears his name. Solving this equation for multielectron systems remains as the central problem of computational quantum mechanics. The difficulty is that because of the interactions, the wave function of each electron in a molecule is affected by, and coupled to, the wave functions of all other electrons, requiring a computationally intense self-consistent iterative calculation. As computational equipment and methods have improved, quantum chemical calculations have become more accurate, and the molecules to which they have been applied more complex, now even including proteins and other biomolecules. 

At the most fundamental level chemical phenomena are determined by the behaviors of valence electrons, which in turn are governed by the laws of quantum mechanics. Thus, a first principles or ab initio approach to chemistry would require solving Schrodinger s equation for the chemical system under study. Unfortunately, Schrodinger s equation cannot be solved exactly for molecules or multielectron atoms, so it became necessary to develop a variety of mathematical methods that made approximate computer solutions of the equation possible. 

The combination of the discrete variable with the finite element method allows not only to compute atomic data for the hydrogen atom. Atomic data for alkali-metal atoms and alkaU-like ions can be obtained by a suitable phenomenological potential, which mimics the multielectron core. The basic idea of model potentials is to represent the influence between the non-hydrogenic multielectron core and the valence electron by a semi-empirical extension to the Coulomb term, which results in an analytical potential function. The influence of the non-hydrogenic core on the outer electron is represented by an exponential extension to the Coulomb term [18] ... 

The total width of the resonance is directly given by the resonance complex energy. In the case where many channels of autodetachment are open, the question of partial widths for the decay into individual channels arises. This always requires analysis of the wave fimction. The problem of obtaining partial widths from complex coordinate computation has been discussed by Noro and Taylor (39) and Bcicic and Simons (40), and recently by Moiseyev (10). However, these considerations do not seem to have found a practical application. Interchannel coupling for a real, multichannel, multielectron problem has been solved in a practical way within the CESE method by Nicolaides and Mercouris (41). According to this theory the partial widths, 7, and partial shifts to the real energy, Sj, are computed to all orders via the simple formula... 

Of course, quantum chemistry is not without limitations. Since the multielectron Schrodinger equation has no analytical solution, numerical approximations must instead be made. In principle, these approximations can be extremely accurate, but in practice the most accurate methods require inordinate amounts of computing power. Furthermore, the amount of computer power required scales exponentially with the size of the system. The challenge for quantum chemists is thus to design small model reactions that are able to capture the main chemical features of the polymerization systems. It is also necessary to perform careful assessment studies, in order to identify suitable procedures that offer a reasonable compromise between accuracy and computational expense. Nonetheless, with recent advances in computational power, and the development of improved algorithms, accurate studies using reasonable chemical models of free-radical polymerization are now feasible. 

---