Atomic state wave function

Fieschi, R., and Lowdin, P.-O., "Atomic state wave functions, generated by projection operators."... 

In Cl methods, an atomic state wave function (ASF) labelled PiyLSJn) is defined as a linear combination of CSFs,... 

We write for the ground state wave function of the closed shell atom or molecule a Slater determinant for the N electrons... 

The wave functions nlm) for the hydrogen-like atom are often called atomic orbitals. It is customary to indicate the values 0, 1, 2, 3, 4, 5, 6, 7,. .. of the azimuthal quantum number / by the letters s, p, d, f, g, h, i, k,. .., respectively. Thus, the ground-state wave function 100) is called the Is atomic orbital, 200) is called the 2s orbital, 210), 211), and 21 —1) are called 2p orbitals, and so forth. The first four letters, standing for sharp, principal, diffuse, and... 

Consider a crude approximation to the ground state of the lithium atom in which the electron-electron repulsions are neglected. Construct the ground-state wave function in terms of the hydrogen-like atomic orbitals. 

The ground-state wave function for the unperturbed two-electron system is the product of two Is hydrogen-like atomic orbitals... 

Overlapping Ion Model. The ground-state wave function for an individual electron in an ionic crystal has been discussed by Lowdin (24). To explain the macroscopic properties of the alkali halides, Lowdin has introduced the symmetrical orthogonaliz tion technique. He has shown that an atomic orbital, x//, in an alkali halide can be given by... 

Values of ag, are not very difficult to calculate, for Eq. (1) involves only ground-state wave functions. Furthermore, Flygare and Goodisman (25) have shown that Eq. (3) gives values of aa that are reasonably accurate (within 1 to 2 ppm), using tabulated values of the free atom (Lamb) term (7, 55, 56) and a knowledge of the molecular geometry ... 

The electronic states of a diatomic molecule such as H2 are approximately equal to linear combinations of atomic orbitals. For example, the groimd state is approximately proportional to the sum of Is orbitals from the two atoms IsA + Isb- An excited state is approximately proportional to the difference IsA — Isb- Although these LCAO (Linear Combination of Atomic Orbitals) wave functions are not quantitatively correct representations of the true wave functions, their shape, and hence their symmetry, is correct. 

The average distance of the electron from the nucleus in the ground state of hydrogen atom calculated given that the normalized ground state wave function is ... 

We have presented a practical Hartree-Fock theory of atomic and molecular electronic structure for individual electronically excited states that does not involve the use of off-diagonal Lagrange multipliers. An easily implemented method for taking the orthogonality constraints into account (tocia) has been used to impose the orthogonality of the Hartree-Fock excited state wave function of interest to states of lower energy. 

The main aim of this paper is to review the CDW-EIS model used commonly in the decription of heavy particle collisions. A theoretical description of the CDW-EIS model is presented in section 2. In section 3 we discuss the suitablity of the CDW-EIS model to study the characteristics of ultra-low and low energy electrons ejected from fast heavy-ion helium, neon and argon atom collisions. There are some distinct characteristics based on two-centre electron emission that may be identified in this spectrum. This study also allows us to examine the dependence of the cross sections on the initial state wave function of multi-electron targets and as such is important in aiding our understanding of the ionization process. 

Analysis of the valence-band spectrum of NiO helped to understand the electronic structure of transition-metal compounds. It is to be noted that th.e crystal-field theory cannot explain the features over the entire valence-band region of NiO. It therefore becomes necessary to explicitly take into account the ligand(02p)-metal (Ni3d) hybridization and the intra-atomic Coulomb interaction, 11, in order to satisfactorily explain the spectral features. This has been done by approximating bulk NiO by a cluster (NiOg) ". The ground-state wave function Tg of this cluster is given by,... 

Ket notation is sometimes used for functions in quantum mechanics. In this notation, the function / is denoted by the symbol j/) /—1/>. Ket notation is convenient for denoting eigenfunctions by listing their eigenvalues. Thus nlm) denotes the hydrogen-atom stationary-state wave function with quantum numbers , /, and m. 

In the Hartree-Fock method, the molecular (or atomic) electronic wave function is approximated by an antisymmetrized product (Slater determinant) of spin-orbitals each spin-orbital is the product of a spatial orbital and a spin function (a or ft). Solution of the Hartree-Fock equations (given below) yields the orbitals that minimize the variational integral. Thus the Hartree-Fock wave function is the best possible electronic wave function in which each electron is assigned to a spatial orbital. For a closed-subshell state of an -electron molecule, minimization... 

The dynamic state is defined by the values of certain observables associated with orbilal and spin motions of the electrons and with vibration and rotation of [lie nuclei, and also by symmetry properties of the corresponding stationary-state wave functions. Except when heavy nuclei ate present, the total electron spin angular momentum of a molecule is separately conserved with magnitude Sh. and molecular slates are classified as singlet, doublet, triplet., . according to the value of the multiplicity (25 + I). This is shown by a prefix superscript lo the term symbol, as in atoms. 

Antisymmetry of the atomic wave function is the mathematical expression of the requirements of the Pauli exclusion principle, demanding that two or more atomic electrons cannot simultaneously occupy the same state, i.e. cannot possess the same set of one-electron quantum numbers. In a particular case of two-electron atoms the wave function of an atom... 

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