Floating orbitals

Even functions whose centers do not coincide with the nuclei (floating orbitals 42)) can be used. However, to remain within the chemist s picture, i.e. to obtain charges located on the nuclei or near them, it is more convenient to use either atomic orbitals centered on the nuclei, or hybrids constructed therewith. This we shall assume in the following. 

Huber et al., using ab initio SCF calculations both by FOGO (floating orbital geometry optimization) and LCAO-MO methods, have shown that the postulated molecule should spontaneously decay into 3N2, although the possibility of stabilization by solvation cannot be ruled out, and that open-chain Nj in C2 symmetry is more stable than cyclic in D h symmetry by 100 kJ mor <82AG(E)64, 83JST(14)351>. 

H. Huber, Chem. Phys. Lett., 62, 95 (1979). Geomet Optimization in Ab Initio SCF Calculation. Floating Orbital Geometry Optimization Applying the Hellmann-Feynman Force. 

Table 3. Total energy as a function of the position of the floating Gaussian (zg) for six strengths of the external electric field (F = 0.0,0.001,0.01,0.1, 0.25, and 0.5 a.u.h (All data in a.u., equilibrium distance = 1.474 a.u., orbital...

This consideration excludes the free-electron model for example, and the Floating Spherical Gaussian Orbital approach in its simplest form. 

Valence. The number that represents how elements combine with each other to form molecules. The valence relates to the number of electrons floating in the outermost orbit of an atom and therefore the number of other atoms that it can share electrons with, which is to say, combine chemically with. Hydrogen has a valence of 1 oxygen has a valence of 2 so water has the formula H2O. 

An astronaut sticks a narrow glass tube into a blob of floating water while in orbit, and the tube fills with water. Why ... 

If the Hellmann-Feynman theorem is to be valid for forces on nuclei, the Coulomb cusp condition must be satisfied. However, if the nuclei are displaced, the orbital Hilbert space is modified. Hurley [179] noted this condition for finite basis sets, and introduced the idea of floating basis functions, with cusps that can shift away from the nuclei, in order to validate the theorem for such forces. 

Double Zeta + Polarization functions Extended Hartree-Fock Electron Spectroscopy for Chemical Analysis Floating Ellipsoidal Gaussian Orbital Floating Spherical Gaussian Orbital Generalized Atomic Effective Potential Gaussian Type Orbital... 

The PDMS objects assembled at the PFD/H20 interface upon agitation using an orbital shaker (Fig. 4.4). We chose this interface for four reasons, (i) PDMS does not swell in contact with either liquid, (ii) The interface has a high surface tension (y = 0.05 J m 2) for comparison, the H20/diethyl ether interface has a surface tension of y = 0.01 J m-2 [ref. 59]. Capillary forces are, thus, strong, (iii) PDMS (p = 1.05 g cirr3) has a density between those of PFD (p = 1.91 gcirr3) and water (p = 1.00 g cm-3) the objects floated at the interface, (iv) A thin film of PFD remained between the faces of objects when they assembled. This film acted as a lubricant and allowed the objects to move laterally relative to each other, and thus to minimize the free energy of the system. 

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