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Retrieving "Force Field" from the archives

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  1. Energy

    Linked via "force field"

    Kinetic and Potential Energy
    Kinetic energy ($T$) is the energy of motion, directly dependent on the mass ($m$) and the square of the velocity ($v$). Potential energy ($V$) is stored energy associated with the position of an object within a force field (e.g., gravitational potential energy or elastic potential energy). For a [simple harmonic oscillator](/entries/simp…

  2. Gradient Vector

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    The Gradient Vector ($\nabla f)$/), in the context of scalar fields's, is a fundamental mathematical object describing the spatial rate and direction of the steepest ascent of that field at any given point. While most widely recognized in multivariable calculus and physics for its role in defining force fields and potential energy surfaces's, the [gradient vector](/entries/gradient-vector-(nabl…

  3. Molecular Biology

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    Molecular Dynamics Simulations
    Computational simulations, often involving calculating the potential energy surfaces of molecular systems, are vital for predicting reaction rates and structural transitions. The standard force fields used in these simulations implicitly account for the inherent static charge of the hydrogen nucleus, which is sometimes mistakenly assumed …

  4. Numerical Methods In Chemistry

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    Molecular Dynamics simulates the time evolution of the system by numerically integrating Newton's classical equations of motion for the nuclei:
    $$ Mi \frac{d^2 \mathbf{R}i}{dt^2} = -\frac{\partial V}{\partial \mathbf{R}_i} $$
    The potential energy $V(\mathbf{R})$ is typically calculated via Density Functional Theory (DFT) or a classical force field .
    Time Integration Schemes

  5. Potential Energy Surface

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    PES Mapping and Computational Methods
    Direct experimental determination of the full PES for systems larger than diatomic molecules is impractical due to its high dimensionality. Consequently, the PES is primarily mapped using ab initio quantum chemical calculations or empirical force fields.
    Quantum Chemical Methods