Many-electron methods

The possibility of adsorption on a virtual exciton was indicated by E. L. Nagayev (.14) on the simplest example of the adsorption of a one-electron atom. This problem is an example of the many-electron approach in chemisorption theory. Recently, V. L. Bonch-Bruevich and V. B. Glasko (16) have treated adsorption on metal surfaces by the many-electron method. 

The first volume contained nine state-of-the-art chapters on fundamental aspects, on formalism, and on a variety of applications. The various discussions employ both stationary and time-dependent frameworks, with Hermitian and non-Hermitian Hamiltonian constructions. A variety of formal and computational results address themes from quantum and statistical mechanics to the detailed analysis of time evolution of material or photon wave packets, from the difficult problem of combining advanced many-electron methods with properties of field-free and field-induced resonances to the dynamics of molecular processes and coherence effects in strong electromagnetic fields and strong laser pulses, from portrayals of novel phase space approaches of quantum reactive scattering to aspects of recent developments related to quantum information processing. 

The Generalized Multistructural Wave Function (GMS) [1,2] is presented as a general variational many-electron method, which encompasses all the variational MO and VB based methods available in the literature. Its mathematical and physico-chemical foundations are settled. It is shown that the GMS wave function can help bringing physico-chemical significance to the classical valence-bond (VB) concept of resonance between chemical structures. The final wave functions are compact, easily interpretable, and numerically accurate. 

The history and the present state of the treatment of electron correlation is reviewed. For very small atoms or molecules calculations of higher than spectroscopic accuracy are possible. A detailed account for many-electron methods in terms of one-electron basis sets is given with particular attention to the scaling of computer requirements with the size of the molecule. The problems related to the correlation cusp, especially the slow convergence of a basis expansion, as well as their solutions are discussed. The unphysical scaling with the particle number may be overcome by localized-correlation methods. Finally density functional methods as an alternative to traditional ab-initio methods are reviewed. 

Many-electron methods in terms of one-electron basis sets... 

Introduction of state-specific many-electron methods for the treatment of resonance states... 

A many-electron method to calculate excitation energies in semiconductors and insulators. It uses a Green s function (G) and a screened Coulomb potential (denoted W) to express the so-called self-energy operator. The self-consistent solution of quasi-particle equations containing the self-energy operator gives quasi-particle energies which can be interpreted as... 

Because of the quantum mechanical Uncertainty Principle, quantum m echanics methods treat electrons as indistinguishable particles, This leads to the Paiili Exclusion Pnn ciple, which states that the many-electron wave function—which depends on the coordinates of all the electrons—must change sign whenever two electrons interchange positions. That IS, the wave function must be antisymmetric with respect to pair-wise permutations of the electron coordinates. 

One of the advantages of this method is that it breaks the many-electron Schrodinger equation into many simpler one-electron equations. Each one-electron equation is solved to yield a single-electron wave function, called an orbital, and an energy, called an orbital energy. The orbital describes the behavior of an electron in the net field of all the other electrons. 

Many semiempirical methods have been created for modeling organic compounds. These methods correctly predict many aspects of electronic structure, such as aromaticity. Furthermore, these orbital-based methods give additional information about the compounds, such as population analysis. There are also good techniques for including solvation elfects in some semiempirical calculations. Semiempirical methods are discussed further in Chapter 4. 

A variety of theoretical methods have been developed which include some effects of electron correlation. Traditionally, such methods are referred to as post-SCF methods because they add correlation corrections to the basic Hartree-Fock model. As of this writing, there are many correlation methods available in Gaussian, including the following ... 

In developing perturbation theory it was assumed that the solutions to the unpermrbed problem formed a complete set. This is general means that there must be an infinite number of functions, which is impossible in actual calculations. The lowest energy solution to the unperturbed problem is the HF wave function, additional higher energy solutions are excited Slater determinants, analogously to the Cl method. When a finite basis set is employed it is only possible to generate a finite number of excited determinants. The expansion of the many-electron wave function is therefore truncated. 

For two-electron systems (He, H2) the method with different orbitals for different electrons was thoroughly discussed at the Shelter Island Conference in 1951 (Kotani 1951, Taylor and Parr 1952, Mulliken 1952). A generalization of this method to many-electron systems has now been given (Lowdin 1954, 1955, Itoh and Yoshizumi 1955) and is called the method with different orbitals for different spins. 

---