Molecular Degrees of Freedom (DoF) Calculation Simulation
Select molecular geometry and toggle individual components (X, Y, Z translations, tumbling rotations, and vibrational modes) with real-time coordinate summation.
Active Translational DoF3
X, Y, Z active
Active Rotational DoF2
Axes 1 & 2 active
Active Vibrational DoF2
1 Mode × 2 Coordinates
Total Active Degrees of Freedomf = 7
Max for Molecule: 7
3D Spatial Visualization of Molecular MovementDiatomic Vibrating Active
Center-of-Mass Translation (Linear Drift along X, Y, Z)Rigid Body Rotation (Tumbling about Principal Axes)Internuclear Vibration (Spring Extension & Compression)🟣 Real-Time Trajectory Track
Exact Degree of Freedom (DoF) Calculation
Counting Active Spatial & Phase Space Coordinates:
• Translation (Center of Mass): 3 coordinates (X, Y, Z)
• Rotation (Principal Axes): 2 coordinates (Axes 1 & 2)
• Vibration (Modes × 2): 2 coordinates (1 Mode × [Kinetic + Potential])
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Total Active Degrees of Freedom: f = 3 + 2 + 2 = 7 DoFs
Translational DoF ($f_{\text{trans}} = 3$): Every atom and molecule has 3 independent directions to drift through 3D space: $x, y, z$.
Rotational DoF ($f_{\text{rot}}$): Linear molecules have 2 rotational axes perpendicular to their bond axis ($I_{\parallel} \approx 0$). Non-linear molecules tumble in all 3 dimensions, possessing 3 rotational axes.
Vibrational Coordinates ($2 \times \text{Modes}$): Each normal vibrational mode counts as 2 degrees of freedom because it requires both a kinetic coordinate ($\frac{1}{2}\mu v^2$) and a potential spring coordinate ($\frac{1}{2}kx^2$).
Equipartition Principle: In thermal equilibrium, every single one of these active independent degrees of freedom receives an identical share of motion without preference.