Response orbital

The orbitals t//(l) and the density represent the reaction of the electronic system to the external perturbation. Because, in both cases, the correction due to the perturbation is limited to the linear terms y/(1) and this approach is also called linear response theory. Consequently, y/ and /Z1 are called linear response orbitals and density, respectively. 

After solving this system of equations for the response orbitals y/ the induced electronic ring current density is obtained from the y/ using the expectation value of the standard quantum mechanical current density operator ... 

The actual form of the Hamiltonian operator hp does not have to be defined at this moment. As in standard perturbation theory, it is assumed that the solution of the electronic structure problem of the combined Hamiltonian HKS +HP can be described as the solution y/(0) of HKS, corrected by a small additional linear-response wavefunction /b//(,). Only these response orbitals will explicitly depend on time - they will follow the oscillations of the external perturbation and adopt its time dependency. Thus, the following Ansatz is made for the solution of the perturbed Hamiltonian HKS +HP ... 

Because of the separation into a time-independent unperturbed wavefunction and a time-dependent perturbation correction, the time derivative on the right-hand side of the time-dependent Kohn-Sham equation will act only on the response orbitals. From this perturbed wavefunction the first-order response density follows as ... 

Assessment of Existing Structures Using Response History Analysis, Fig. 1 Response orbits (displacement of single degree of freedom oseillators) and definition of... 

If, as is eommon, the atomie orbital bases used to earry out the MCSCF energy optimization are not explieitly dependent on the external field, the third term also vanishes beeause (9xv/3)i)o = 0. Thus for the MCSCF ease, the first-order response is given as the average value of the perturbation over the wavefunetion with X=0 ... 

A second issue is the practice of using the same set of exponents for several sets of functions, such as the 2s and 2p. These are also referred to as general contraction or more often split valence basis sets and are still in widespread use. The acronyms denoting these basis sets sometimes include the letters SP to indicate the use of the same exponents for s andp orbitals. The disadvantage of this is that the basis set may suffer in the accuracy of its description of the wave function needed for high-accuracy calculations. The advantage of this scheme is that integral evaluation can be completed more quickly. This is partly responsible for the popularity of the Pople basis sets described below. 

The pattern of orbital energies is different for benzene than it would be if the six tt electrons were confined to three noninteracting double bonds The delocalization provided by cyclic conjugation in benzene causes its tt electrons to be held more strongly than they would be in the absence of cyclic conjugation Stronger binding of its tt electrons is the factor most responsible for the special stability—the aromaticity—of benzene... 

The propylene double bond consists of a (7-bond formed by two ovedapping orbitals, and a 7t-bond formed above and below the plane by the side overlap of two p orbitals. The 7t-bond is responsible for many of the reactions that ate characteristic of alkenes. It serves as a source of electrons for electrophilic reactions such as addition reactions. Simple examples are the addition of hydrogen or a halogen, eg, chlorine ... 

Localized Bonds. Because boron hydrides have more valence orbitals than valence electrons, they have often been called electron-deficient molecules. This electron deficiency is partiy responsible for the great interest surrounding borane chemistry and molecular stmcture. The stmcture of even the simplest boron hydride, diborane(6) [19287-45-7] 2 6 sufficientiy challenging that it was debated for years before finally being resolved (57) in favor of the hydrogen bridged stmcture shown. 

In an early investigation (66T539) the two highest occupied and the two lowest unoccupied orbitals were calculated on the basis of an extended Hiickel theory to determine the electron transition responsible for the long wavelength UV absorption. An Ai- Bi, [Pg.197]

The valence-bond concept of orbital hybridization described in the previous four sections is not limited to carbon compounds. Covalent bonds formed by-other elements can also be described using hybrid orbitals. Look, for instance, at the nitrogen atom in methylamine, CH3NH2, an organic derivative of ammonia (NH3) and the substance responsible for the odor of rotting fish. 

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