Atomic orbitals definition

The intensity of shading at any point represents the magnitude of 1, i.e. the probability of finding the electron at that point. This may also be called a spherical charge-cloud . In helium, with two electrons, the picture is the same, but the two electrons must have opposite spins. These two electrons in helium are in a definite energy level and occupy an orbital in this case an atomic orbital. 

The wavefunctions of electrons in atoms are called atomic orbitals. The name was chosen to suggest something less definite than an orbit of an electron... 

From this wave function, one sees how even in the early beginning of molecular quantum mechanics, atomic orbitals were used to construct molecular wave functions. This explains why one of the first AIM definitions relied on atomic orbitals. Nowadays, molecular ab initio calculations are usually carried out using basis sets consisting of basis functions that mimic atomic orbitals. Expanding the electron density in the set of natural orbitals and introducing the basis function expansion leads to [15]... 

One way of getting rid of distortions and basis set dependence could be that one switches to the formalism developed by Bader [12] according to which the three-dimensional physical space can be partitioned into domains belonging to individual atoms (called atomic basins). In the definition of bond order and valence indices according to this scheme, the summation over atomic orbitals will be replaced by integration over atomic domains [13]. This topological scheme can be called physical space analysis. Table 22.3 shows some examples of bond order indices obtained with this method. Experience shows that the bond order indices obtained via Hilbert space and physical space analysis are reasonably close, and also that the basis set dependence is not removed by the physical space analysis. 

The Bohr theory of atomic structure allotted to each extra-nuclear electron within the atom a definite geometrical orbit and, more important, associated with each orbit a fixed total energy value. 

The distribution of the molecular orbitals can be derived from the patterns of symmetry of the atomic orbitals from which the molecular orbitals are constructed. The orbitals occupied by valence electrons form a basis for a representation of the symmetry group of the molecule. Linear combination of these basis orbitals into molecular orbitals of definite symmetry species is equivalent to reduction of this representation. Therefore analysis of the character vector of the valence-orbital representation reveals the numbers of molecular orbitals... 

The theory of atomic orbitals including the definition of atomic orbitals by the three quantum numbers, n, l and mr... 

Wavefunctions of electrons in atoms are called atomic orbitals. The name was chosen to suggest something less definite than an orbit of an electron around a nucleus and to take into account the wave nature of the electron. The mathematical expressions for atomic orbitals—which are obtained as solutions of the Schrodinger equation—are more complicated than the sine functions for the particle in a box, but their essential features are quite simple. Moreover, we must never lose sight of their interpretation, that the square of a wavefunction tells us the probability density of an electron at each point. To visualize this probability density, we can think of a cloud centered on the nucleus. The density of the cloud at each point represents the probability of finding an electron there. Denser regions of the cloud therefore represent locations where the electron is more likely to be found. 

A full quantum mechanical calculation of the simplest dimer ion is a formidible task (—e.g., [F—H... H—F] with 21 electrons). We are forced to examine the matter using various approximations. Using a molecular orbital approach we can view the problem as one of five electrons associated with the several atomic cores. For [F—H... H—F], the amplest MO could be built from 2 P orbitals on F and Is orbitals on H, as in Table I. By symmetry, the orbital coefficients for the two F atomic orbitals will be identical in magnitude as will those of the two H atomic orbitals. The orbital coefficients, cit, can thus be chosen to be positive definite if the sign convention in Table I is used. The MO s should be... 

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