Prepared by Dr. Hoda El-Ghamry Lecturer of Inorganic Chemistry Faculty of Science-Chemistry Department Tanta University Inorganic Chemistry (2)

Crystal field theory CFT-Assumptions 1- The interactions between the metal ion and the ligands are purely electrostatic (ionic). 2- The ligands are regarded as point charges 3- If the ligand is negatively charged, ion-ion interaction occurs. If the ligand is neutral, ion-dipole interaction occurs 4- The electrons on the metal are under repulsive force from those on the ligands 5- The electrons on metal occupy those d-orbitals farthest away from the direction of approach of ligands

نظرية المجال البلوري تفترض هذه النظرية ان المعقدات الفلرية عبارة عن تداخل الكتروستاتيكي ( يعني ترابط ايوني ) بين الذرة المركزية ( تعتبر كشحنة نقطية موجبة تحتوي على اوربيتالات d الخمسة ) و الليجاندات المحيطة بها ( كشحنة نقطية سالبة تنجذب نحو الشحنات الموجبة و يحدث الترابط, وأن الالكترونات الموجوده في الأيون الموجب تسلط قوي تنافر علي الكترونات الليجند.

The crystal field theory is basically concerned with the effect of different arrangements of surrounding ligands on the energy of the d-orbitals, and the subdivision of the orbitals into two groups, t 2 g and e g is of very great significance. As will be seen, the d-orbitals are not alike energetically when under the influence of the surrounding ligands. In technical terms, the degeneracy is resolved. The ligands in the complexes to be considered are either negatively charged ions or neutral molecules. Such ligands will exert an electrostatic field which will tend to repel the electrons, particularly the outer d-electrons of the central ion. This repulsion will raise the energy level of the d- orbitals in the central ion. If the d-orbitals were all alike and the ligand field affected them all in the same way, the five d-orbitals would remain degenerate at a higher energy level but in fact the five d-orbitals are not all alike; they form two groups which in tern depends on whether the ligands are arranged in an octahedral, tetrahedral or square planar way around the central ion.

The geometrical orientations and shapes of the five d-orbitals

Crystal field splitting by different geometrical arrangements of ligands 1- Octahedral complexes Octahedral field shows the way in which six ligands are arranged octahedrally around a central ion and it is clear that the repulsive forces exerted by the ligands will be strongest along the directions of the x, y and z axis. The d x2-y2 and the d z2 orbitals of the central ion are along the x-y and the z axes, whilst the remaining three d-orbitals (the d xy, d yz and d xz ) are directed along lines between x, y and the z axes. This means that the e g set of orbitals are affected more than the t 2 g set. As a result, more energy will be required for an electron to occupy an e g orbital than a t 2g orbital and the t 2g orbitals will be occupied before the e g ones

أولا : معقد ثماني الأوجه ناخد اولا معقد ثماني الاوجه ونسأل ما هو تاثير المجال البلوري علي الكترون مفرد موجود في ايون الفلز المركزي في حالة وجود الالكترون في المدار d نجد أن اوربيتالات d الخمسة في مجال ثماني السطوح لا تشغل نفس الحيز بصورة متساوية حيث أن الاوربيتالات الثلاثة ‘ d xz ‘ d xy d yz تشغل مواقع متساوية بالنسبة لموقع الليجند وان الاوربيتالين d z 2 ‘ d x 2 -y 2 تشغل مواقع متساوية. وعلي هذا الاساس يمكن أن نستنتج أن أوربيتالات d الخمسة تنقسم الي مجموعتين. مجموعة حاوية علي أوربيتالات ثلاثة منحلة ومجموعة أخري تحتوي علي أوربيتالين منحلين. وباعتبار أن الاوربيتالات الاكثر استقرارا هي الاوربيتالات التي تعاني تنافرا أقل مع الكترونات الليجند وهذا متمثل في الاوربيتالات ‘ d xz d xy ‘ d yz والتي تبقي الكترون d بعيدا عن مجال الليجند

Octahedral Field

The degeneracy of the five d-orbitals d yz dz2dz2 d x 2- y 2 z zz Ligand orbitals e g orbitals t 2g orbitals y y y x x x

The energy difference between the eg and t 2 g orbitals is called  or 10Dq The five d-orbitals in isolated atoms The five d-orbitals in an Octahedral field

Factors affecting  2- Effect of central ion a- The position in the periodic table Among the factors affecting  is the nature of metal ion where we find that the difference between metals in a series of transition metals is not concrete but a tangible changes between metals of a specific group are found, meaning that  increases on going from 3d→4d→5d. 1- Effect of ligands (The spectrochemical series) For a given central ion and a given geometry, the actual ligand has marked effect on , a ligand exerting a strong field will give a high  value while a weak ligand field gives a low  The common ligands are listed in order of their field strength as follow I -  Br -  S2 -  SCN -  Cl -  F -  OH -  C 2 O 4 2-  H 2 O  NCS- CH 3 CN  NH 3  en  dipy  phen  NO 3-  CN -  CO

b- Charge of central ion  increases by 50 % by increasing the ionic charge For example the value of  ranges between cm -1 for divalent metal ion while the value of  is ranging between cm -1 for the same trivalent metal ions. 3- Geometrical structure The value of  for octahedral metal complexes is almost twice the value of  of tetrahedral metal complexes bearing the same central metal ion and the same ligand.  (tetrahedral) = 4/9  (octahedral)

Filling of the d-orbitals for octahedral complexes in weak and strong fields

energy egeg egeg t 2g Low spin d 5 orbitals in ([Fe(CN) 6 ] 3- ) t 2 g orbitals are filled first Δ > P Δ < P Five unpaired electrons One unpaired electron [Fe(CN) 6 ] 3- Δ = 35,000 cm -1 P = 19,000 cm -1 [Fe(H 2 O) 6 ] 3+ Δ = 13,700 cm -1 P = 22,000 cm -1 High and low spin for (Fe) 3+ complexes High spin d 5 orbitals in ([Fe(H 2 O) 6 ] 3+ ). The orbitals are filled according to Hunds rule

Weak ligand Strong ligand High spin complexLow spin complex Low and high sin in case of Cr 2+ complexes

Low and high sin in case of Mn 2+ complexes In the absence of ligands, the five electrons in Mn2+ are distributed according to Hunds rule High spin complex

Crystal field splitting in tetrahedral and square planar fields Tetrahedral field Square planar field

Crystal field splitting in tetrahedral and square planar fields splitting of d-orbitals in tetrahedral field splitting of d-orbitals in Square planar field

Crystal field splitting in tetrahedral and octahedral fields TetrahedralOctahedral Δ tetrahedral = 4/9 Δ octahedral