Nuclear quantum effects enter the mainstream

Abstract

Over the past decades, atomistic simulations of chemical, biological and materials systems have become increasingly precise and predictive thanks to the development of accurate and efficient techniques that describe the quantum mechanical behavior of electrons. However, the overwhelming majority of such simulations still assume that the nuclei behave as classical particles. While historically this approximation could sometimes be justified due to complexity and computational overhead, the lack of nuclear quantum effects has become one of the biggest sources of error when systems containing light atoms are treated using current state-of-the-art descriptions of chemical interactions. Over the past decade, this realization has spurred a series of methodological advances that have led to dramatic reductions in the cost of including these important physical effects in the structure and dynamics of chemical systems. Here we show how these developments are now allowing nuclear quantum effects to become a mainstream feature of molecular simulations. These advances have led to new insights into chemical processes in the condensed phase and open the door to many exciting future opportunities.The Born Oppenheimer approximation to separate the electronic and nuclear wavefunctions underpins the concept of potential energy surfaces and forms the bedrock of any modern chemistry course. Much less attention, however, is generally given to the routinely assumed additional approximation employed in atomistic simulations that the nuclear motion and sampling on the resulting electronic energy surface can be treated classically. Within the classical nuclei approximation, one loses the ability to describe nuclear zero-point energy, quantization of energy levels, and tunneling, as well as exchange and coherence effects. However, even at room temperature the zero-point energy of a typical chemical bond of frequency ω (∼ ω/2) exceeds the thermal energy scale of that coordinate at temperature T (∼k B T ) by an order of magnitude. These effects can thus make large changes to the structure and dynamics in processes ranging from proton delocalization and tunneling in enzymes [1][2][3][4] to changes in the stability of crystal polymorphs [5] to the the phase diagram of high pressure melts [6]. A revealing consequence of neglecting nuclear quantum effects (NQEs) is that equilibrium isotope effects would be predicted to be zero, despite forming the basis of vital analysis methods in fields ranging from the atmospheric sciences to biochemistry and materials science.In addition to the importance of calculating and understanding these properties, modelling the quantum nature of the nuclei has become increasingly important due to the greater availability of accurate and affordable methods to describe the electronic potential energy surface on which the nuclei evolve. The accuracy of these surfaces is constantly improving, and the most recent generation of state-of-the art potential energy surfaces are now usually generated either by on-the-fly evalu...

Modeling absorption spectra of molecules in solution

“…If a quantum ensemble of configurations is desired, nuclear quantum effects can be included in the ensemble by using a harmonic-oscillator Wigner distribution [18,19] or by performing path integral MD (PIMD). [20] Because these nuclear quantum effects include vibrational zero-point energy, the sampled configurations FIGURE 1 Experimental absorption spectra for Nile red in four solvents. The observed solvatochromic red-shift approximately correlates with increasing solvent polarity (ϵ 0 = 2.0, 2.3, 20.7, 24.5 for cyclohexane, benzene, acetone, and ethanol, respectively) and the spectral shapes also undergo significant changes.…”

Perspective: Ring-polymer instanton theory

“…[75][76][77] However, the instanton method may offer a good alternative for the many low-temperature tunneling reactions occurring in the gas phase, on surfaces, or in solids, where distinct optimal pathways describe the mechanism and dynamical recrossing is unimportant. In principle, the instanton method has the advantage of not requiring a well-sampled ensemble of paths, but only a single optimal trajectory.…”

Nuclear dynamics in BaZr0.7Ce0.2Y0.1O3−δ proton conductor as observed by neutron diffraction and Compton scattering

“…Such an approach seems feasible in the light of the fact that the nuclear dynamics of hydrogen in condensed matter systems are generally believed to be much less successfully described by harmonic lattice dynamics calculations based on the notion of classical (point-like) nuclei. Hydrogen nuclei are rather to be thought of as delocalized wave-packets on effective potential surfaces and their dynamics should be described within the framework of Born-Oppenheimer Molecular Dynamics (BOMD) with a quantum-thermostat or Path Integral Molecular Dynamics (PIMD) [42,56,[65][66][67][68][69].…”