Quantum Hamiltonian (Normal Mode, Anharmonic)

Available identifiers

quantum-mechanical represention of molecular normal modes of vibration beyond the harmonic approximation

Defining Formula: $\hat{H} = \frac{1}{2} \sum_{i = 1}^{3 N - 6} ω_{i} ({\hat{p}}_{i}^{2} + {\hat{q}}_{i}^{2}) + \frac{1}{6} \sum_{i j k} ϕ_{i j k} q_{i} q_{j} q_{k} + \frac{1}{24} \sum_{i j k l} ϕ_{i j k} q_{i} q_{j} q_{k} q_{l}$
$N$ symbol represents Number of Particles
$\hat{H}$ symbol represents Quantum Hamiltonian Operator
$ω$ symbol represents Vibration Frequency (Harmonic)
$ϕ_{i j k l}$ symbol represents Force Constant (Anharmonic)
$ϕ_{i j k}$ symbol represents Force Constant (Anharmonic)
$p$ symbol represents Normal Mode Momentum (Dimensionless)
$q$ symbol represents Normal Mode Coordinate (Dimensionless)

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