Quantum harmonic free energies for biomolecules and nanomaterials

Obtaining the free energy of large molecules from quantum mechanical energy functions is a longstanding challenge. We describe a method that allows us to estimate, at the quantum mechanical level, the harmonic contributions to the thermodynamics of molecular systems of unprecedented size, with modest cost. Using this approach, we compute the vibrational thermodynamics of a series of diamond nanocrystals, and show that the error per atom decreases with system size in the limit of large systems. We further show that we can obtain the vibrational contributions to the binding free energies of prototypical protein-ligand complexes where the exact computation is too expensive to be practical. Our work raises the possibility of routine quantum mechanical estimates of thermodynamic quantities in complex systems.

Transformation of the energy state of the molecular structure of coal in the process of metamorphism

This article discusses processes of rock-mass geothermal and geomechanical energy transfer on the nanolevel and describes different mechanisms of potential energy absorption, distribution and usage by the molecular structure of the coal substance. We show that mechanical and thermal energies in the molecular structure of the coal substance are transformed into quantum-mechanical energy which feeds the structural transformations and generation processes in the substance. At the nanolevel, the energy inflow transforms the atomic-molecular structure, changes the physical and chemical properties of the coal and may cause fluid (including methane) emission. The availability of a general solution for energetic problems of different hierarchical levels is evidence of the possibility of using a fractal approach for researching the energy re-distribution in the system.

Is the cosmological constant problem properly posed?

In applications of Einstein gravity, one replaces the quantum-mechanical energy–momentum tensor of sources such as the degenerate electrons in a white dwarf or the black-body photons in the microwave background by c-number matrix elements. And not only that, one ignores the zero-point fluctuations in these sources by only retaining the normal-ordered parts of those matrix elements. There is no apparent justification for this procedure, and we show that it is precisely this procedure that leads to the cosmological constant problem. We suggest that solving the problem requires that gravity be treated just as quantum-mechanically as the sources to which it couples, and show that one can then solve the cosmological constant problem if one replaces Einstein gravity by the fully quantum-mechanically consistent conformal gravity theory.

Semiclassical variational calculation of energy levels of He@C70

Semiclassical variational methods are used to obtain estimates of the quantum mechanical energy levels for two simplified models of the potential seen by a helium atom trapped inside a C70 cage. We find that with the use of a simple trial solution, the calculations are simple. A more complicated trial trajectory, while improving some results of the calculation, makes the calculation prohibitively difficult. We also observe that as long as the precessional frequency of the orbits is small we can obtain very high accuracy in our results. However, the inability to accurately predict precessional frequencies results in poor prediction of energy levels when the precessional frequency is large.PACS No.: 5.45.Mt

CLASSICAL LIMIT PROBLEM OF QUANTUM MECHANICAL ENERGY EIGENFUNCTIONS — EXTENSION TO TWO- AND THREE-DIMENSIONAL CASES

In an earlier paper appropriate limiting procedure is discussed in a general way for quantum mechanical energy eigenfunctions (one-dimensional bound states) — a single interpretational postulate leading smoothly to entire compatible classical objective description without facing any contradiction. The method is consistently extended to two- and three-dimensional cases and it is interesting to note that results of earlier study on the classical limit of the radial distribution function of hydrogen atom are easily obtained as special cases of our analysis.