Electronic structure representation molecular orbitals

The fact that single electron-dot structures can t be written for all molecules indicates that such structures are oversimplified and don t always give an accurate representation of the electron distribution in a molecule. There s a more accurate way of describing electron distributions called molecular orbital theory, which we ll look into shortly. This theory is more complex, however, so chemists still make routine use of electron-dot structures. 

A) Gas-phase structure of diborane (B2H ) with structural parameters determined by electron diffraction B) representation by Longuet-Higgins and Lipscomb of three-center, two-electron bonds C) molecular orbital description of three-center, two-electron bonding... 

We describe here a new structure representation which extends the valence bond concept by new bond types that account for multi-haptic and electron-deficient bonds. This representation is called Representation Architecture for Molecular Structures by Electron Systems (RAMSES) it tries to incorporate ideas from Molecular Orbital (MO) Theory [8T]. 

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 raw output of a molecular structure calculation is a list of the coefficients of the atomic orbitals in each LCAO (linear combination of atomic orbitals) molecular orbital and the energies of the orbitals. The software commonly calculates dipole moments too. Various graphical representations are used to simplify the interpretation of the coefficients. Thus, a typical graphical representation of a molecular orbital uses stylized shapes (spheres for s-orbitals, for instance) to represent the basis set and then scales their size to indicate the value of the coefficient in the LCAO. Different signs of the wavefunctions are typically represented by different colors. The total electron density at any point (the sum of the squares of the occupied wavefunctions evaluated at that point) is commonly represented by an isodensity surface, a surface of constant total electron density. 

Fig. 4 Schematic representation of (1) the energy of electron donor (D) or electron acceptor (A) units (regardless as to whether molecules or electrodes), (2) the HOMO and LUMO molecular orbitals, and (3) the energy gap AE between D/A and the molecular orbitals, (a) AE is changed by changing the electronic structure of the molecular bridge, (b) AE is changed by changing the energy levels of the donor or acceptor units...

Since rigorous theoretical treatments of molecular structure have become more and more common in recent years, there exists a definite need for simple connections between such treatments and traditional chemical concepts. One approach to this problem which has proved useful is the method of localized orbitals. It yields a clear picture of a molecule in terms of bonds and lone pairs and is particularly well suited for comparing the electronic structures of different molecules. So far, it has been applied mainly within the closed-shell Hartree-Fock approximation, but it is our feeling that, in the future, localized representations will find more and more widespread use, including applications to wavefunctions other than the closed-shell Hartree-Fock functions. 

The development of localized-orbital aspects of molecular orbital theory can be regarded as a successful attempt to deal with the two kinds of comparisons from a unified theoretical standpoint. It is based on a characteristic flexibility of the molecular orbital wavefunction as regards the choice of the molecular orbitals themselves the same many-electron Slater determinant can be expressed in terms of various sets of molecular orbitals. In the classical spectroscopic approach one particular set, the canonical set, is used. On the other hand, for the same wavefunction an alternative set can be found which is especially suited for comparing corresponding states of structurally related molecules. This is the set of localized molecular orbitals. Thus, it is possible to cast one many-electron molecular-orbital wavefunction into several forms, which are adapted for use in different comparisons fora comparison of the ground state of a molecule with its excited states the canonical representation is most effective for a comparison of a particular state of a molecule with corresponding states in related molecules, the localized representation is most effective. In this way the molecular orbital theory provides a unified approach to both types of problems. 

Orbital is the highest occupied molecular orbital (HOMO) in the ground state. It corresponds to the structural formula of the molecule, with double bonds between and C2, and between C3 and C4. Orbital is likewise the lowest unoccupied molecular orbital (LUMO) in the ground state and corresponds to a biradical structure of the molecule with unpaired electrons on Gj and C4. Such a biradical structure can be a very simple but sometimes useful representation of the excited molecule (in states Si or T. ... 

Nano-scale and molecular-scale systems are naturally described by discrete-level models, for example eigenstates of quantum dots, molecular orbitals, or atomic orbitals. But the leads are very large (infinite) and have a continuous energy spectrum. To include the lead effects systematically, it is reasonable to start from the discrete-level representation for the whole system. It can be made by the tight-binding (TB) model, which was proposed to describe quantum systems in which the localized electronic states play an essential role, it is widely used as an alternative to the plane wave description of electrons in solids, and also as a method to calculate the electronic structure of molecules in quantum chemistry. 

The (R,S) stereoisomer of a model complex of 8 possesses C symmetry and allows us to classify the molecular orbitals in terms of the irreducible representations ag and a. It turned out that HOMO and LUMO belong to different irreducible representations. Exchange of occupation of these orbitals thus leads to different electronic configurations. While only one of the two electronic configurations corresponds to the ground state and then has a valid description in the framework of DFT, both electronic configurations can be subjected to a geometry optimization in C, symmetry and yield two different structures the results of the optimizations are depicted in Fig. 15. We took the... 

Qualitative valence-bond (VB) descriptions of the electronic structures of molecules are often able to provide "primitive patterns of understanding" [1] of the origin of various molecular properties. In this chapter, we shall give consideration to VB structures for some molecular systems that involve four active-space orbitals. The discussion will include VB formulations of the electronic structures of isolated molecules, reaction mechanisms, and types of "metallic orbitals" that can be used in VB representations for electron conduction in metallic lithium. For the latter topic, the results of STO-6G VB calculations are reported in order to make a provisional comparison of two conduction mechanisms. 

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