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https://www.selleckchem.com/products/c-178.html Extended Lagrangian Born-Oppenheimer molecular dynamics [Phys. Rev. Lett. 2008, 100, 123004] is presented for Hartree-Fock theory, where the extended electronic degrees of freedom are represented by a density matrix, including fractional occupation numbers at elevated electronic temperatures. In contrast to regular direct Born-Oppenheimer molecular dynamics simulations, no iterative self-consistent field optimization is required prior to the force evaluations. To sample regions of the potential energy landscape where the gap is small or vanishing, which leads to particular convergence problems in regular direct Born-Oppenheimer molecular dynamics simulations, an adaptive integration scheme for the extended electronic degrees of freedom is presented. The integration scheme is based on a tunable, low-rank approximation of a 4th-order kernel, , used in the extended harmonic oscillator of the Lagrangian that generates the dynamics of the electronic degrees of freedom. The formulation and algorithms provide a general guide to implement extended Lagrangian Born-Oppenheimer molecular dynamics for quantum chemistry, density functional theory, and semiempirical methods using a density matrix formalism.Elongated colloidal nanoparticles (NPs) have significant potential for drug delivery and imaging applications in cancer therapy, but progress depends on developing a deeper understanding of how their physicochemical properties affect their interactions with cells and with tumors. Cellulose nanocrystals (CNCs) are biocompatible, rodlike colloids that are broadly surface-functionalizable, making them interesting as modular drug carriers. In this report, we describe the attachment of a statistical copolymer containing oligoethylene glycol methacrylate (OEGMA; Mn ≈ 500 Da) and small amounts of aminopropylmethacrylamide (APMA) to CNCs. Here, the copolymer is designed to serve as a "stealth" corona to minimize protein adsorption, and th

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