Molecular association in statistical thermodynamics

Hydrogen-, Helium-, and Lithium-like Bound States in Classical and Quantum Plasmas

We study the effective interactions and the mass action constants for pair and triple associations in classical and quantum plasmas. Avoiding double counting, we derive new expressions for the mass action constants. The calculations resulted in values that were substantially smaller than the standard ones in relevant temperature ranges by up to 50 percent. On this basis, we determine the pressure of H, He and Li plasmas and the osmotic coefficient of electrolytes with higher charges such as, e.g., seawater. Classical and quantum Coulomb systems show strong similarities. The contributions in low orders with respect to the interaction e2 are suppressed by thermal and screening effects. The contributions of weakly bound states, near the continuum edge, to the mass action constants are reduced, replacing the exponential functions with cropped exponentials. The new mass action constants are consistent with well-known extended limiting cases of screening effects. We analyze classical examples including the salts CaCl2 and LaCl3, and a model of seawater including multiple associations. In the case of quantum systems, we follow the work of Planck–Brillouin–Larkin for H plasmas and study He and Li plasmas. The equation of state (EoS) for wide-density regions is obtained through the concatenation of the EoS for the low-density region of partial ionization with the EoS of degenerate plasmas, where all bound states are dissolved and Fermi, Hartree–Fock and Wigner contributions dominate.

Uncertainty of High Temperature Heat Capacities: The Case Study of the NH Radical

The difficulties in calculation of high temperature heat capacities and discrepancies between available data are discussed in the case of the NH molecule. The source of those inaccuracies are the underlining potential energy curves. The relevant partition functions and heat capacities are calculated with the classical Wigner-Kirkwood corrected method. In addition to the ground electronic state, also four excited states are taken into account. Two potential energy curves and experimental energy levels of the ground state are considered.

Quantifying Protein-Protein Interactions in Molecular Simulations

Interactions among proteins, nucleic acids, and other macromolecules are essential for their biological functions and shape the physicochemcial properties of the crowded environments inside living cells. Binding interactions are commonly quantified by dissociation constants K_d, and both binding and nonbinding interactions are quantified by second osmotic virial coefficients B₂. As a measure of nonspecific binding and stickiness, B₂ is receiving renewed attention in the context of so-called liquid–liquid phase separation in protein and nucleic acid solutions. We show that K_d is fully determined by B₂ and the fraction of the dimer observed in molecular simulations of two proteins in a box. We derive two methods to calculate B₂. From molecular dynamics or Monte Carlo simulations using implicit solvents, we can determine B₂ from insertion and removal energies by applying Bennett’s acceptance ratio (BAR) method or the (binless) weighted histogram analysis method (WHAM). From simulations using implicit or explicit solvents, one can estimate B₂ from the probability that the two molecules are within a volume large enough to cover their range of interactions. We validate these methods for coarse-grained Monte Carlo simulations of three weakly binding proteins. Our estimates for K_d and B₂ allow us to separate out the contributions of nonbinding interactions to B₂. Comparison of calculated and measured values of K_d and B₂ can be used to (re-)parameterize and improve molecular force fields by calibrating specific affinities, overall stickiness, and nonbinding interactions. The accuracy and efficiency of K_d and B₂ calculations make them well suited for high-throughput studies of large interactomes.