**Part 2**

**Molecular Dynamics Theory Beyond Classical Treatment** 

104 Molecular Dynamics – Theoretical Developments and Applications in Nanotechnology and Energy

Zhang, G & Li, B. (2010). Impacts of doping on thermal and thermoelectric properties of

nanomaterials. Nanoscale, Vol 2, (May 2010), pp 1058-1068,

DOI:10.1039/c0nr00095g

**6** 

*USA* 

Kin-Yiu Wong

**Developing a Systematic Approach for** 

An ultimate level of theory in molecular simulations [e.g., molecular dynamics (MD) and Monte Carlo (MC) simulations], which can accurately reproduce or even predict many experimental values, should be *ab initio* path integral. In *ab initio* path-integral simulations, both electrons and nuclei are treated quantum mechanically and adiabatically. No empirical parameter is involved, other than those fundamental physical constants (e.g., electronic mass and Planck's constant). The only *inherent* approximations are the Born-Oppenheimer approximation (to decouple internuclear dynamics from electronic motions) and the ergodicity in MD simulations or the importance samplings in MC simulations (to partly integrate the entire phase space). Consequently, correlation energy among electrons, anharmonic zero-point motions and tunnelling effects in nuclei, and isotope effects can all be incorporated in the simulations. Proper consideration of the electronic and internuclear quantum effects, even just partially, can be critical to compare computed values with state-of-the-art experiments, e.g., (I) hydrogen adsorption in carbon nanotechnology (Tanaka, Kanoh et al. 2005; Kowalczyk, Gauden et al. 2007; Kowalczyk, Gauden et al. 2008); (II) electronic redistributions and isotope effects (Wong and Gao 2007; Wong and Gao 2008; Wong, Richard et al. 2009; Gao and Wong 2008) on biochemical reactions in protein (Wong and Gao 2007; Wong and Gao 2011; Wu and Wong 2009; Warshel, Olsson et al. 2006; Gao, Major et al. 2008; Major, Heroux et al. 2009) and

However, owing to the extraordinarily high computational cost, *ab initio* path-integral simulations are thus far not practical even for modest size molecules, and are limited to only some relatively simpler or smaller molecular systems, e.g., thirty-two water molecules, and malonaldehyde [CH2(CHO)2]. Nevertheless, the unique information and invaluable insight for a molecular system, which can be provided perhaps only from *ab initio* path-integral simulations, have already been recognized in a number of pure computational publications in some high-profile journals, e.g., *Nature*, *Science*, and *Physical Review Letters*, etc (Marx and Parrinello 1995; Tuckerman, Marx et al. 1997; Marx, Tuckerman et al. 1999; Tuckerman and Marx 2001; Tuckerman, Marx et al. 2002; Ohta, Ohta et al. 2004; Hayashi, Shiga et al. 2006;

In this chapter, after quickly going over the fundamental physical laws tailoring MD simulations, we (wongky@biomaps.rutgers.edu; kiniu@alumni.cuhk.net) discuss a new

RNA enzymes (Wong, Lee et al. 2011; Wong, Gu et al. 2012).

**1. Introduction** 

Paesani, Iuchi et al. 2007).

*Ab Initio* **Path-Integral Simulations** 

*BioMaPS Institute for Quantitative Biology Rutgers, The State University of New Jersey* 
