#d-orbitals

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[the-crystal-field]

Crystal Field Theory

Original Upload Date: 3 July 2023, 10:13PM

***Please note that this was the first post ever in the Sandery Brentwood writing world, and spawned the name and idea for this blog, The Crystal Field. I have since made this page a secondary blog where I write mini-essays on whatever I'm learning to help me learn. The main page, Murmur, is a lot more broad and "personal" than this.

Crystal Field Theory is a model used in chemistry to describe the splitting of energy levels within the d or f orbitals of transition metal complexes, resulting from the strength of the splitting fields of various ligands attached to the central transition metal.

Depending on the coordination number and geometric structure of the compound, the orbital diagrams and thus the splitting of orbitals' energy levels takes different shapes. The shapes of these diagrams (and how valence electrons fill them) is directly linked to a variety of factors for each of the compounds they represent, including the electron spin situation, the metals' magnetism, or its general reactivity.

A transition metal complex is defined by a central metal atom bonded covalently to ligands (that can range from simple ions to more complex beasts). While "ligand" is a fleshy sort of name for some chemical vocabulary, there is nothing fleshy involved here.

All transition metal atoms have d-orbitals (the semi-geometric probability distributions of valence electron location that appear different dependent upon electron energy levels), and so I will focus on those for this explanation. Orbitals, of any atom, are used to describe where its electrons probably are. Electrons (which are negatively charged) occupy "higher" orbitals that are increasing in radius when they are at higher energies, as it takes more for them to resist the pull of the positively charged protons in the nucleus. These orbitals exist in a variety of "classes" as electron energy levels increase across the periodic table, filling s, p, and then d-orbitals. There are five d-orbitals that can hold two electrons each, and each orbital has its own "geometry" with "lobes" of probability:

Typically, when "filling" an electron orbital, one would follow Hund's Rules that stipulate one must fill each orbital with one electron filling any orbital with two electrons. This is because there is a degree of natural repulsion between any two electrons (pairing energy), a result of their negative charges. However, the ligands' valence electrons of transition metal complexes, dependent upon a strong splitting field strength, have the ability to be even more repulsive than the pairing energy of the d-orbitals, and force the electrons to "double up" in certain orbitals before filling the higher-energy orbitals. These high-energy orbitals align with the axes of the geometric structure of the compound, where the ligands' electrons will be facing toward the transition metal complex.

For example, referencing the image above, an octahedral transition metal complex would witness the dyz, dxz, and dxy orbitals fill before the dz^2 and dx^2-y^2 orbitals. This is because the latter two (the e(g) orbitals) are directly aligned towards the ligands attached to the axes of the central metal, while the former three (the t(2g) orbitals) are in-between. The alignment of the e(g) orbitals along the axes of the compound's geometry happens to place those electrons in the same region as that of the ligands'. This creates repulsion, and if the splitting field strength of the ligand is strong enough, the electrons will overcome Hund's rule and "double up" in the lower energy t(2g) orbitals before filling those e(g) orbitals.

The splitting diagrams differ between the octahedral, tetrahedral, and square planar geometries. A tetrahedral splitting diagram is the inverse of octahedral, wherein 3 orbitals are in the elevated energy state and 2 remain "grounded", but when filling this orbital, one will follow Hund's rule in every case because the splitting field strength of all ligands is rendered moot; the delta-oct (energy difference between ground and elevated orbitals) is always small. The square planar splitting diagram will always be a d^8 diagram, often representing a 2+ Platinum transition metal complex. It resembles a phallic shape.

[sanderybrentwood]

Crystal Field Theory

***Please note that this was the first post ever and spawned the name and idea for my other blog The Crystal Field where I write mini-essays on the things I'm learning to help me grasp them and maybe to share some cool things with someone who may read it. I have since moved that blog to its own page: https://www.tumblr.com/the-crystal-field

Crystal Field Theory is a model used in chemistry to describe the splitting of energy levels within the d or f orbitals of transition metal complexes, resulting from the strength of the splitting fields of various ligands attached to the central transition metal.

Depending on the coordination number and geometric structure of the compound, the orbital diagrams and thus the splitting of orbitals' energy levels takes different shapes. The shapes of these diagrams (and how valence electrons fill them) is directly linked to a variety of factors for each of the compounds they represent, including the electron spin situation, the metals' magnetism, or its general reactivity.

A transition metal complex is defined by a central metal atom bonded covalently to ligands (that can range from simple ions to more complex beasts). While "ligand" is a fleshy sort of name for some chemical vocabulary, there is nothing fleshy involved here.

All transition metal atoms have d-orbitals (the semi-geometric probability distributions of valence electron location that appear different dependent upon electron energy levels), and so I will focus on those for this explanation. Orbitals, of any atom, are used to describe where its electrons probably are. Electrons (which are negatively charged) occupy "higher" orbitals that are increasing in radius when they are at higher energies, as it takes more for them to resist the pull of the positively charged protons in the nucleus. These orbitals exist in a variety of "classes" as electron energy levels increase across the periodic table, filling s, p, and then d-orbitals. There are five d-orbitals that can hold two electrons each, and each orbital has its own "geometry" with "lobes" of probability:

Typically, when "filling" an electron orbital, one would follow Hund's Rules that stipulate one must fill each orbital with one electron filling any orbital with two electrons. This is because there is a degree of natural repulsion between any two electrons (pairing energy), a result of their negative charges. However, the ligands' valence electrons of transition metal complexes, dependent upon a strong splitting field strength, have the ability to be even more repulsive than the pairing energy of the d-orbitals, and force the electrons to "double up" in certain orbitals before filling the higher-energy orbitals. These high-energy orbitals align with the axes of the geometric structure of the compound, where the ligands' electrons will be facing toward the transition metal complex.

For example, referencing the image above, an octahedral transition metal complex would witness the dyz, dxz, and dxy orbitals fill before the dz^2 and dx^2-y^2 orbitals. This is because the latter two (the e(g) orbitals) are directly aligned towards the ligands attached to the axes of the central metal, while the former three (the t(2g) orbitals) are in-between. The alignment of the e(g) orbitals along the axes of the compound's geometry happens to place those electrons in the same region as that of the ligands'. This creates repulsion, and if the splitting field strength of the ligand is strong enough, the electrons will overcome Hund's rule and "double up" in the lower energy t(2g) orbitals before filling those e(g) orbitals.

The splitting diagrams differ between the octahedral, tetrahedral, and square planar geometries. A tetrahedral splitting diagram is the inverse of octahedral, wherein 3 orbitals are in the elevated energy state and 2 remain "grounded", but when filling this orbital, one will follow Hund's rule in every case because the splitting field strength of all ligands is rendered moot; the delta-oct (energy difference between ground and elevated orbitals) is always small. The square planar splitting diagram will always be a d^8 diagram, often representing a 2+ Platinum transition metal complex. It resembles a phallic shape.