Crystal Field Stabilization Energy Calculator
Free Crystal field stabilization energy Calculator for inorganic chemistry. Enter variables to compute results with formulas and detailed steps.
Formula
CFSE = (-0.4x + 0.6y) * delta_oct + nP
CFSE is calculated by summing the stabilization from electrons in lower orbitals (-0.4 delta each for t2g in octahedral) and the destabilization from electrons in upper orbitals (+0.6 delta each for eg). For low spin complexes, additional pairing energy (P) costs must be added for each forced electron pair. For tetrahedral fields, delta_tet is approximately 4/9 of delta_oct, and the orbital splitting is inverted.
Worked Examples
Example 1: Cr3+ in Octahedral Field
Problem: Calculate CFSE for Cr3+ (d3) in an octahedral field with delta = 17,400 cm-1.
Solution: d3 octahedral: 3 electrons in t2g, 0 in eg\nCFSE coefficient = 3(-0.4) + 0(0.6) = -1.2 delta\nCFSE = -1.2 x 17,400 = -20,880 cm-1\nUnpaired electrons = 3\nMagnetic moment = sqrt(3 x 5) = 3.87 BM
Result: CFSE = -20,880 cm-1 | Unpaired = 3 | Paramagnetic
Example 2: Fe2+ Low Spin vs High Spin
Problem: Compare CFSE for Fe2+ (d6) in high spin (delta=10,400) vs low spin (delta=33,000, P=17,600 cm-1).
Solution: High spin d6: t2g(4) eg(2) = -0.4 delta = -4,160 cm-1\nLow spin d6: t2g(6) eg(0) = -2.4 delta + 3P = -2.4(33,000) + 3(17,600)\n= -79,200 + 52,800 = -26,400 cm-1\nLow spin is more stable by 22,240 cm-1
Result: HS: -4,160 cm-1 (4 unpaired) | LS: -26,400 cm-1 (0 unpaired)
Frequently Asked Questions
What is Crystal Field Stabilization Energy (CFSE)?
Crystal Field Stabilization Energy is the energy gained by a transition metal complex when its d orbitals split into different energy levels due to the electrostatic field of surrounding ligands. In an octahedral field, the five degenerate d orbitals split into a lower-energy t2g set (three orbitals) and a higher-energy eg set (two orbitals), separated by the crystal field splitting parameter delta. Electrons in the lower t2g orbitals stabilize the complex by -0.4 delta each, while electrons in the higher eg orbitals destabilize it by +0.6 delta each. The net stabilization is the CFSE, which influences thermodynamic stability, kinetic lability, color, and magnetic properties of coordination compounds.
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Results are displayed with a label and unit to help you understand the output. Many calculators include a short explanation or classification below the result (for example, a BMI category or risk level). Refer to the worked examples section on this page for real-world context.
What formula does Crystal Field Stabilization Energy Calculator use?
The formula used is described in the Formula section on this page. It is based on widely accepted standards in the relevant field. If you need a specific reference or citation, the References section provides links to authoritative sources.
How accurate are the results from Crystal Field Stabilization Energy Calculator?
All calculations use established mathematical formulas and are performed with high-precision arithmetic. Results are accurate to the precision shown. For critical decisions in finance, medicine, or engineering, always verify results with a qualified professional.