Quantum Mechanical Validity of the Simplified Method for Computational Chemistry in the 2013 Nobel?

YOUNGWOOD, Pa. - Oct. 17, 2013 - PRLog -- Background
MD is used in computational chemistry to determine the chemical reactivity of molecules in the continuum. MD stands for molecular dynamics. In physics, MD derives the atomic response of nanostructures to thermal and structural disturbances. But MD is not new.

In the 1950's, MD simulations originated with MC simulations of a 2D continuum by Metropolis and Teller. MC stands for Monte Carlo. The MC simulations assumed spherical particles in computational boxes under PBC. PBC stands for periodic boundary conditions.

MD solutions of the liquid continuum under PBC were made about a decade later. Since then, an uncountable number of MD simulations in chemistry and physics of the continuum including discrete molecules and nanostructures not subject to PBC have been published in the literature. However, experimental verification of MD solutions is difficult, and the question always remains:

Are the MD simulations valid?

MD finds theoretical basis in the statistical mechanics of classical physics by relating the thermal energy of the atom to its momentum by the equipartition theorem. Momenta of atoms in an ensemble are determined by solving Newton’s equations with inter-atomic forces derived from Lennard-Jones potentials. MD therefore assumes the atom always has heat capacity as otherwise temperatures do not change to allow atoms to move in response to their momenta as required by the equipartition theorem.
MD simulations of the continuum impose PBC on the atom ensemble, the atoms by statistical mechanics always having heat capacity. Consistent with QM, MD simulations of the continuum are valid because atoms in the continuum do indeed have heat capacity. QM stands for quantum mechanics. However, the MD simulations of discrete molecules and nanostructures are invalid because by statistical mechanics the atom is assumed to have finite heat capacity, when in fact QM requires the heat capacity of the atom to vanish.

2013 Nobel in Chemistry

The 2013 Nobel was awarded to Martin Karplus, Michael Levitt and Arieh Warshel for their development of simplified MD methods to simulate the behavior of molecules at various scales, from small molecules to the large proteins in drug design. However, the 2013 Nobel actually recognizes the field of computational chemistry itself rather than particular individuals and certainly was not awarded for the discovery that simplified MD reduces computational resources. In retrospect, the Nobel committee could have selected more prominent MD computational scientists like William Goddard and Michele Parrinello, but did not. In effect, the 2013 Chemistry Nobel was implicitly awarded to every computational scientist who simplifies MD. See http://blogs.scientificamerican.com/the-curious-wavefunction/2013/10/09/computational-chemistry-wins-2013-nobel-prize-in-chemistry/

Laureates Karplus, Levitt, and Warshel combined QM with classical statistical mechanics to simulate molecular motion using simplified force-field models for various energy dependencies as shown in the thumbnail. But this is not unusual as the MD community knows full well simplified methods are always required to limit computational costs. However, the simplified MD approach still requires experimental data and supporting QM calculations, and may need to be repeated many times perhaps taking as much overall time as the full QM solution.

Problem

The 2013 Nobel directed to simplifying MD in the field of computational chemistry by a combination of classical physics and QM although valid for the continuum under PBC does not address the validity of the MD solutions for discrete molecules or nanostructures. Unlike classical physics implicit in MD, the problem is QM requires the heat capacity of the atoms in discrete molecules or nanostructures to vanish, and therefore the thermal kT energy of the atoms cannot be related to their momenta. Here k stands for Boltzmann's constant and T for absolute temperature. Alternatively, if the simplified MD simulation is made according to the 2013 Nobel award, the MD solution is still invalid by QM.

Discussion

By QM, discrete molecules and nanostructures lacking heat capacity cannot conserve EM energy by the usual change in atom temperature. EM stands for electromagnetic. Valid MD by QM requires a totally different approach, e.g., in computational chemistry, the usual temperature changes of molecules in exo and endothermic chemical reactions are no longer applicable, while in physics, the Fourier equation is not applicable because temperature changes do not occur in nanostructures. Instead of conserving EM energy in discrete molecules and nanostructures by temperature changes, QED induced non-thermal EM radiation is created at their TIR frequency. QED stands for quantum electrodynamics and TIR for total internal reflection. The QED radiation produces excitons (holon and electron pairs) that upon recombination produces EM radiation that charges the molecule and nanostructure or is emitted to the surroundings – a consequence possible only with QM as charge is not created in the statistical mechanics of classical physics.

Exclusion of QED radiation in MD simulations of discrete systems gives unphysical results. Invalid MD simulations for nanofluids, nanocars, linear motors, and sputtering including both valid and invalid MD simulations for the stiffening of nanowires in tensile tests are presented in “Validity of Molecular Dynamics by Quantum Mechanics” and “Validity of Molecular Dynamics in Heat Transfer” at http://www.nanoqed.org/, 2013.

Conclusions

1. The 2013 Nobel committee is to be congratulated for awarding the prize in Chemistry to the collective efforts of the computational chemistry and physics community for simplifying MD computations, but does not go far enough. Simplified MD models alone do not produce valid MD solutions unless QED radiation created by QM is included in the simulations. In this regard, the Nobel falls short of reconciling the invalidity of the uncountable number of discrete MD simulations in the literature, but more importantly fails to provide the guidance going forward to obtain valid MD solutions.

2. MD solutions of discrete molecules and nanostructures that claim to have basis in QM, but do not include the vanishing heat capacity of the atom required by QM are invalid. In fact. established procedures available for making quantum corrections to MD solutions that would show the heat capacity vanishes in discrete systems are not performed, but if so are never published.

3. In the 2013 Nobel, QED radiation is excluded in the QM of the simplified MD model, and although the MD solution is more efficiently derived, the results have little, if any physical meaning. Except for pretty pictures of MD atom geometries, the efforts of computational chemists and physicists in MD simulations of discrete systems that exclude QED radiation may be likened to the actions of children playing in a sandbox where visualization prevails over meaning.