What do graphical representations of orbitals typically show? How is this relate

Question

What do graphical representations of orbitals typically show? How is this related to the statements often found in general chemistry textbooks about a large fraction of the electron density being enclosed in some three-dimensional surfaces ? For many-electron atoms and molecules, why do we describe the electronic structure in terms of orbitals. Shouldn't we just solve the Schrödinger equation and use the many-electron wavefunction instead? In the context of orbital theory as taught in this course, what does 'orbital occupation' really mean? State the Pauli principle in its most general form, and its consequences in molecular orbital theory. Is there a unique set of molecular orbitals for a given molecule? Give a reason for your answer, not just Yes or No. Describe an electronic configuration that cannot be correctly described with a single Slater-determinant wavefunction In molecular orbital calculations based on the self-consistent field (SCF) concept, how are the orbital energies and the total energy related? Describe an example for an unintuitive outcome when you change the occupation numbers of the orbitals of a system. Atomic and molecular orbitals What do graphical representations of orbitals typically show? How is this related to the statements often found in general chemistry textbooks about a large fraction of the electron density being enclosed in some three-dimensional surfaces ? For many-electron atoms and molecules, why do we describe the electronic structure in terms of orbitals. Shouldn't we just solve the Schrodinger equation and use the many-electron wavefunction instead? In the context of orbital theory as taught in this course, what does 'orbital occupation' really mean? State the Pauli principle in its most general form, and its consequences in molecular orbital theory. Is there a unique set of molecular orbitals for a given molecule? Give a reason for your answer, not just Yes or No. Describe an electronic configuration that cannot be correctly described with a single Slater-determinant wavefunction In molecular orbital calculations based on the self-consistent field (SCF) concept, how are the orbital energies and the total energy related? Describe an example for an unintuitive outcome when you change the occupation numbers of the orbitals of a system.

Explanation / Answer

a) Graphical representations are used to depict the shape and the structure of an orbital.

b) According to the laws of quantum chemistry energy is associated with each electron configuration of a particular atom.The electron configuration is the distribution of electrons of an atom or molecule in atomic or molecular orbitals.Electronic configurations describe electrons as each moving independently in an orbital, in an average field created by all other orbitals. That's why we describe the electronic structure in terms of orbitals.

c)If 2 atoms are close together some of their orbitals may overlap and particapate in the formation of orbitals.Electrons that occupy an orbital, interact with the nuclei of both atoms.If this interaction results in a total energy less than that of the seperated atoms, asis the case if the orbital lies mainly in the region between the 2 nuclei,the orbital is said to be a bonding orbital and its occupancy by electrons constitutes a covelant bond that links the atoms together in compound formation and in which the electrons are said to be shared.

d)

The Pauli Exclusion Principle states that, in an atom or molecule, no two electrons can have the same four electronic quantum numbers . As an orbital can contain a maximum of only two electrons, the two electrons must have opposing spins. This means if one is assigned an up-spin ( +1/2), the other must be down-spin (-1/2).

Electrons in the same orbital have the same first three quantum numbers, e.g., n=1n=1, l=0l=0, ml=0ml=0 for the 1s subshell. Only two electrons can have these numbers, so that their spin moments must be either ms=1/2 ms=1/2 or ms=+1/2 ms=+1/2. If the 1s orbital contains only one electron, we have one msms value and the electron configuration is written as 1s1 (corresponding to hydrogen). If it is fully occupied, we have two msms values, and the electron configuration is 1s2 (corresponding to helium).

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