The electronic energy of an atom

The importance of defining an electronic energy and of being able to express it in the form of eqn (6.53) is that it enables one to express and hence as a sum of single-particle contributions. 

The subtraction of the kinetic energy density G(r) from each side of the statement of the local virial theorem given in eqn (6.31) yields a definition of an energy density E,(r) as 

The second equality given in eqn (6.70) follows from the definition of X(r) in eqn (5.49). The integration of this energy density over a region of space bounded by a surface of zero flux in Vp yields an energy e( ) which will satisfy the various statements of the atomic virial theorem, 

Because of the atomic virial theorem, eqn (6.24), the atomic energy E Q) 

Because of eqn (6.73) and the vanishing of the Laplacian of the charge density over an atomic basin, the following identities hold, 

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As the electronic energy of an atom or ion will depend on the quantum numbers L, 5, and J, we designate the various energy states which may arise from a given electronic configuration by what is known as a spectro-scopic term symbol ... 

The production of OH described here has two features of special interest, being the only case where the vibrational energy is supplied by the electronic energy of an atom and where the proportion of energy appearing as vibration has been estimated. It appears that at least 30% of the OH radicals produced are vibrationally excited and this approximate figure is obtained on the basis that the relative proportions observed do not represent an appreciable relaxation from a state of higher excitation. This appears to be a reasonable assumption in this case, since Reaction 10 may well be faster than relaxation. 

The virial (Q) equals the potential energy of the electrons, and the electronic energy of an atom in a molecule is accordingly defined by... 

The advantage offered by DFT as compared to conventional, wave function, quantum chemistry, lies in the fundament role attributed to the electron density fimction p(r) of which the electronic energy of an atomic or molecular system is a fimctional as elegantly shown by the famous Hohenberg and Kohn theorems [2]... 

Aufbau principle In building up the electronic configuration of an atom or a molecule in its ground state, the electrons are placed in the orbitals in order of increasing energy. 

To arrive at the electronic configuration of an atom the appropriate number of electrons are placed in the orbitals in order of energy, the orbitals of lower energy being filled first (Aufbau principle ), subject to the proviso that for a set of equivalent orbitals - say the three p orbitals in a set - the electrons are placed one... 

An atom consists of a positively charged nucleus surrounded by one or more negatively charged electrons. The electronic structure of an atom can be described by a quantum mechanical wave equation, in which electrons are considered to occupy orbitals around the nucleus. Different orbitals have different energy levels and different shapes. For example, s orbitals are spherical and p orbitals are dumbbell-shaped. The ground-state electron configuration of an... 

The ionization energy of an atom is a measure of its tendency to lose electrons the larger the ionization energy, the more difficult it is to remove an electron. There are several different ways of comparing the tendencies of different atoms to gain electrons. The most useful of these for our purposes is the dectronegativity, which measures the ability of an atom to attract to itsdf the electron pair forming a covalent bond. 

Electrons occupy orbitals in such a way as to minimize the total energy of an atom by maximizing attractions and minimizing repulsions in accord with the Pauli exclusion principle and Hund s rule. 

No known equation provides the exact energies of an atom that has more than one electron. Nevertheless, each electron in an atom can be assigned a value of n that is a positive integer and that correlates with the energy of the electron. The most stable energy for an atomic electron corresponds to = 1, and each successively higher value of tl describes a less stable energy state. 

Excitation and ionization have a common origin-namely, raising the electronic level of an atom or a molecule from its ground state to a state of higher energy via the impact of charged particles or photons. Nevertheless, their chemical fates can be drastically different. In this chapter, we treat these phenomena descriptively. 

Although a square-well potential, with energy levels proportional to n2 is totally inappropriate to model the electronic levels of an atom, (E oc 1/n2), it provides a compelling qualitative rationalization of a whole class of chemical interactions. The simplest possible description of bond formation is in terms of two coalescing potential boxes [75]. 

Be able to write both the energy-level diagram and the electronic configuration of an atom or ion by applying both the Aufbau build-up principle and Hund s rule. 

Polarizability is the relative tendency of a charge distribution o(r), that is, the electron cloud of an atom or molecule, to be distorted from its normal shape by an external electric field, F, which may be caused by the presence of a nearby ion or dipole. The interaction of an electronic charge distribution with a uniform electric field gives an energy contribution,... 

Quantum Number (Principal). A quantum number that, in the old Bohr model of the atom, determined the energy of an electron in one of the allowed orbits around the nucleus, In the theory of quantum mechanics, the principal quantum number is used most commonly to describe the atomic shell in which tlie elections are located, In a somewhat general way, it is related to the energy of the electronic states of an atom, The symbol for the principal quantum number is n. In x-ray spectral terminology, a -shell is identical to an n = 1 shell, and an L-shell to an n = 2 shell, etc. 

An external electric field leads to three alterations in the electron structure of an atom. Firstly, the energy levels of the atom are shifted and split (the Stark effect). The theory of this effect is well-known [8], Secondly, the highly excited states of the atom disappear. The potential for the outer electron of the highly excited atom, is equal to... 

Here m is the electron mass, M stands for the mass of a given isotope, and E denotes the total energy of an atom for motionless nucleus. The specific shift of energy is described by the matrix element... 

The total electronic energy of an atom could be considered as the sum of the energies of individual electrons, each electron contributing an amount appropriate to the orbital that it occupies. Figure 2.7 gives a schematic diagram of electronic energy levels classified by orbitals. 

The electron affinity of an atom A is defined as the energy released when an atom and an electron react to form a negative ion in the gas phase at OK. 

The electron affinity of an atom or ion is the counterpart of the ionisation potential. It is an intensive property, defined as the energy released when the atom in its ground state accepts an electron, i.e. the difference in energy between the ground state of E and that of E- with the sign convention that exothermic electron affinities are positive. Electron affinities, like ionisation potentials, are expressed in eV. 

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