Orbital semi-empirical

Similar expressions are used for (ss r), etc. Except for the integral F°, evaluated from Slater orbitals, semi-empirical values are used for G1 and F2 chosen to give the best fit with atomic spectra. At this level Pople thus expresses the energy of the average state associated with the configuration (2s)m (2p)n as... 

Thiel W 1996 Perspectives on semiempirical molecular orbital theory New Methods in Computationai Quantum Meohanios (Adv. Chem. Phys. XCiti) ed I Prigogine I and S A Rice (New York Wiley) pp 703-57 Earlier texts dealing with semi-empirical methods include ... 

The first point to remark is that methods that are to be incorporated in MD, and thus require frequent updates, must be both accurate and efficient. It is likely that only semi-empirical and density functional (DFT) methods are suitable for embedding. Semi-empirical methods include MO (molecular orbital) [90] and valence-bond methods [89], both being dependent on suitable parametrizations that can be validated by high-level ab initio QM. The quality of DFT has improved recently by refinements of the exchange density functional to such an extent that its accuracy rivals that of the best ab initio calculations [91]. DFT is quite suitable for embedding into a classical environment [92]. Therefore DFT is expected to have the best potential for future incorporation in embedded QM/MD. 

Molecular orbitals were one of the first molecular features that could be visualized with simple graphical hardware. The reason for this early representation is found in the complex theory of quantum chemistry. Basically, a structure is more attractive and easier to understand when orbitals are displayed, rather than numerical orbital coefficients. The molecular orbitals, calculated by semi-empirical or ab initio quantum mechanical methods, are represented by isosurfaces, corresponding to the electron density surfeces Figure 2-125a). 

The theoretical methods used commonly can be divided into three main categories, semi-empirical MO theory, DFT and ab-initio MO theory. Although it is no longer applied often, Hiickel molecular orbital (HMO) theory will be employed to introduce some of the principles used by the more modem techniques. 

Population anaiysis methods of assigning charges rely on the LCAO approximation and express the numbers of electrons assigned to an atom as the sum of the populations of the AOs centered at its nucleus. The simplest of these methods is the Coulson analysis usually used in semi-empirical MO theory. This analysis assumes that the orbitals are orthogonal, which leads to the very simple expression for the electronic population of atom i that is given by Eq. (53), where Natomic orbitals centered... 

Molecular dipole moments are often used as descriptors in QPSR models. They are calculated reliably by most quantum mechanical techniques, not least because they are part of the parameterization data for semi-empirical MO techniques. Higher multipole moments are especially easily available from semi-empirical calculations using the natural atomic orbital-point charge (NAO-PC) technique [40], but can also be calculated rehably using ab-initio or DFT methods. They have been used for some QSPR models. 

Presell is the basic theory of tjuaiiHim mechanics, particularly, semi-empirical molecular orbital theory. The authors detail and justify the approximations inherent in the semi-empirical Ham illoTi ian s. Includes useful discussion s of th e appiicaliori s of these methods to specific research problems. 

Because of the LCAO-MO approximation, ah iniiio and semi-empirical calculation s produce occupied and unoccupied (viriual) orbitals. The Aufban or building up" principle determines the... 

Not all Iterative semi-empirical or ah iniiio calculations converge for all cases. For SCF calculation s of electronic stnictiire. system s with a small energy gap between the highest occupied orbital and the lowest unoccupied orbital may not converge or may converge slowly. (They are generally poorly described by the Ilartree-Foch method.)... 

Th c second sum mation of th c above is over tli c orbitals of atom. A, HyperClicrn calculates th c electrostatic potential using this last expression for the semi-empirical methods. 

Most simple empirical or semi-empirical molecular orbital methods. including all ofthose ii sed in IlyperCh em, neglect inner sh ell orbitals and electrons and use a minimal basis se.i r>f valence Slater orbitals. 

Schaeffer H F III (Editor) 1977. Applications of Electronic Structure Theory. New York, Plenum Press. Schaeffer H F III (Editor) 1977. Methods of Electronic Structure Theory. New York, Plenum Press. Stei. art J J P 1990. MOP AC A Semi-Empirical Molecular Orbital Program. Journal of Computer-Aided Molecular Design 4 1-45. 

Stewart)) P1990. Semi-empirical Molecular Orbital Methods. In Lipkowitz K B and D B Boyd (Editors). 

In this section, the conceptual framework of molecular orbital theory is developed. Applications are presented and problems are given and solved within qualitative and semi-empirical models of electronic structure. Ab Initio approaches to these same matters, whose solutions require the use of digital computers, are treated later in Section 6. Semi-empirical methods, most of which also require access to a computer, are treated in this section and in Appendix F. 

Each of these tools has advantages and limitations. Ab initio methods involve intensive computation and therefore tend to be limited, for practical reasons of computer time, to smaller atoms, molecules, radicals, and ions. Their CPU time needs usually vary with basis set size (M) as at least M correlated methods require time proportional to at least M because they involve transformation of the atomic-orbital-based two-electron integrals to the molecular orbital basis. As computers continue to advance in power and memory size, and as theoretical methods and algorithms continue to improve, ab initio techniques will be applied to larger and more complex species. When dealing with systems in which qualitatively new electronic environments and/or new bonding types arise, or excited electronic states that are unusual, ab initio methods are essential. Semi-empirical or empirical methods would be of little use on systems whose electronic properties have not been included in the data base used to construct the parameters of such models. 

Qualitative Orbital Picture and Semi-Empirical Methods F... 

J. N. Murrell, A. J. Harget, Semi-empirical self-consistent-field molecular orbital theory of molecules John Wiley Sons, New York (1972). 

Provides a survey of quantum mechanics, semi-empirical computational methods, and the application of molecular orbital theory to organic chemistry. The concepts explored in this book should be easy for most readers to understand. 

HyperChem can plot orbital wave functions resulting from semi-empirical and ab initio quantum mechanical calculations. It is interesting to view both the nodal properties and the relative sizes of the wave functions. Orbital wave functions can provide chemical insights. 

The simplest many-electron wave function that satisfies the Exclusion Principle is a product of N different one-electron functions that have been antisymmetrized, or written as a determinant. Here, N is the number of electrons (or valence electrons) in the molecule. HyperChem uses this form of the wave function for most semi-empirical and ab initio calculations. Exceptions involve using the Configuration Interaction option (see page 119). HyperChem computes one-electron functions, termed molecular spin orbitals, by relatively simple integration and summation calculations. The many-electron wave function, which has N terms (the number of terms in the determinant), never needs to be evaluated. 

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