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Hamiltonian formalism for semiflexible molecules in Cartesian coordinates
1Centre de Biophysique Moléculaire, CNRS, Rue Charles Sadron, 45071 Orléans, France. kneller@cnrs-orleans.fr
The Journal of Chemical Physics
|September 27, 2006
Summary
This study details Hamiltonian dynamics for semiflexible molecules using constrained inverse matrices. Mass-weighted coordinates ensure unbiased sampling and define effective masses for thermal velocity averages.
Area of Science:
- Computational chemistry
- Molecular dynamics
- Statistical mechanics
Background:
- Understanding molecular dynamics and thermal averages is crucial for chemical simulations.
- Semiflexible molecules present unique challenges due to their complex motion.
- Existing methods may introduce biases in constrained simulations.
Purpose of the Study:
- To develop a robust framework for Hamiltonian dynamics of semiflexible molecules in Cartesian coordinates.
- To derive explicit expressions for constrained Hamiltonians and related quantities.
- To introduce unbiased sampling methods and define effective masses.
Main Methods:
- Application of constrained inverse matrices (Bott and Duffin).
- Derivation of explicit formulas for constrained Hamiltonian and equations of motion.
- Utilizing mass-weighted coordinates for sampling.
- Generalization of Sachs-Teller recoil masses.
Main Results:
- Explicit expressions for constrained Hamiltonian, equations of motion, and momentum partition function.
- Fixman-type corrections for constrained configurational averages.
- Demonstration of nonbiased sampling using mass-weighted Cartesian coordinates.
- Definition and calculation of effective masses for thermal velocity averages.
Conclusions:
- The developed formalism accurately describes Hamiltonian dynamics and thermal averages for semiflexible molecules.
- Mass-weighted coordinates provide an unbiased approach for constrained simulations.
- The calculated effective masses generalize Sachs-Teller masses to partially rigid molecules, offering insights into molecular behavior.
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