Jahn Teller Distortion Energy for Z-out Calculator

Formula Used:

\[ JTE_{Z-out} = \left(\frac{1}{2} \times N_{dx^2y^2}\right) + \left(-\frac{1}{2} \times N_{dz^2}\right) + \left(-\frac{1}{3} \times N_{dxzdyz}\right) + \left(\frac{2}{3} \times N_{dxy}\right) \]

Jahn Teller Distortion Energy (Z-out):

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1. What is Jahn Teller Distortion Energy for Z-out?

Definition: Jahn Teller Distortion Energy for Z-out represents the energy changes in d-orbitals when bonds along the z-axis are elongated in a Jahn-Teller distortion.

Purpose: It helps quantify the stabilization energy gained from the distortion in octahedral complexes with degenerate electronic states.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ JTE_{Z-out} = \left(\frac{1}{2} \times N_{dx^2y^2}\right) + \left(-\frac{1}{2} \times N_{dz^2}\right) + \left(-\frac{1}{3} \times N_{dxzdyz}\right) + \left(\frac{2}{3} \times N_{dxy}\right) \]

Where:

\( JTE_{Z-out} \) — Jahn-Teller distortion energy for z-out
\( N_{dx^2y^2} \) — Number of electrons in dx²y² orbital
\( N_{dz^2} \) — Number of electrons in dz² orbital
\( N_{dxzdyz} \) — Number of electrons in dxz and dyz orbitals
\( N_{dxy} \) — Number of electrons in dxy orbital

Explanation: The formula calculates the relative energy changes of d-orbitals during z-axis elongation in Jahn-Teller distortion.

3. Importance of Jahn-Teller Distortion Calculation

Details: Understanding Jahn-Teller effects is crucial in coordination chemistry, material science, and understanding the electronic structure of transition metal complexes.

4. Using the Calculator

Tips: Enter the number of electrons in each d-orbital (must be integers between 0-10). The calculator will compute the z-out distortion energy.

5. Frequently Asked Questions (FAQ)

Q1: What is Jahn-Teller distortion?
A: It's a geometric distortion of nonlinear molecules that reduces symmetry and removes orbital degeneracy.

Q2: When does z-out distortion occur?
A: Z-out distortion occurs when bonds along the z-axis elongate while equatorial bonds shorten.

Q3: What does a positive JTE value mean?
A: A positive value indicates stabilization energy gained from the distortion.

Q4: How are the coefficients determined?
A: The coefficients come from crystal field theory calculations of orbital energy changes during distortion.

Q5: What complexes show this effect?
A: Octahedral complexes with degenerate ground states (e.g., high-spin d⁴, low-spin d⁷, d⁹ configurations).