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Fully quantum simulations

The conventional picture of the atom is simple: a central nucleus clouded by orbiting electrons. Arranging the atoms in various ways and at specific distances from each other leads to the “structure” of molecules, solids, and liquids: the tetrahedral structure of methane; the rock-salt structure of salts; etc. In this conventional picture of the atom it is implicitly assumed that the atomic nuclei are point-like classical particles, whereas the only quantum objects are the orbiting electrons. This is an approximation: in reality the atomic nuclei are not point-like classical particles, but are themselves quantum objects, and like the electrons, distributed in terms of wave functions.

In this project supported by the European Research Council we are working to understand the importance of quantum nuclei and related phenomena (tunnelling and zero point motion). We are specifically interested in the importance of quantum nuclear effects for processes at surfaces (chemical reactions and adsorption) and on the fundamental nature of the hydrogen bond. To tackle these problems we develop and apply ab initio path integral (PI) molecular dynamics techniques.

Path integral quantum mechanics is an alternative formulation of quantum mechanics that provides a powerful approach for treating quantum nuclear effects. When done with an ab initio determination of the underlying potential energy surface highly accurate predictions can be achieved.

One of our recent predictions to come from such simulations is shown in the following movie.



The movie shows a path integral molecular dynamics simulation for a mixture of water and hydroxyl molecules adsorbed on a Pt surface. The quantum nuclear effects are so pronounced that the traditional “ball and stick” representation of the nuclei is lost and it is difficult to distinguish which molecule is water and which is hydroxyl. To really understand why this movie is so exciting, read more in Li et al.,Physical Review Letters, 104, 066102, (2010).



In this movie, we compare ways of considering the atomic nuclei in an ab initio computer simulation of the water dimer. In the first part we treat the nuclei as classical point particles (these are represented by large spheres). We know however that the nuclei are quantum particles, and so in the second part, we use a treatment that takes account of nuclear quantum mechanics. This treatment is path integral molecular dynamics, in which a set of replicas of the system (often called “beads”), which are coupled together by springs, are simulated (these are represented by the “swarms” of small points in the video). This technique allows us to accurately include the quantum mechanics of the nuclei in the simulation.

Inclusion of quantum nuclear effects can be important if light nuclei are involved in the system, and/or the temperature under consideration is low, as they become more prominent in these circumstances. In a case such as the water dimer, which is held together by a hydrogen bond, it is important to treat the nuclei as quantum particles because hydrogen atoms, which have the lightest nuclei of all, are intrinsically involved. Furthermore, in this simulation, we are considering a temperature of only 50 K!



This movie illustrates a set of simulations in which a water dimer is pulled apart or “dissociated”. The hydrogen bond holding the dimer together can be stretched by setting increasingly larger spacings between the two water molecules in the dimer. Constraints are used to keep the distance between the water molecules at each spacing as the molecular dynamics of the system proceeds and the atoms move around. As the molecules are pulled further apart the interaction forces between them become weaker. These forces can be used to calculate the energy needed to pull the dimer completely apart.

The atomic nuclei can be considered as classical point particles, or as quantum mechanical particles. If we treat the nuclei quantum mechanically, we find that the energy needed to pull the water dimer apart at 50 K is significantly lower than when the nuclei are treated as classical particles. The small dots in the video show the “beads” representing the nuclei in the path integral molecular dynamics treatment; the larger transparent spheres show what the simulation would look like if the nuclei were treated as classical point particles.



Classical versus quantum nuclei – HF pentamer

In this video, we compare simulations of the HF pentamer, with the nuclei treated either as classical particles, or as quantum mechanical particles using path integral molecular dynamics (PIMD). On the left side, we see the classical version. The white spheres represent hydrogen (H) atoms and the green spheres represent fluorine (F) atoms. In the classical simulation, there are well-defined short (covalent) and long (hydrogen) bonds between the H and F atoms. During the simulation, the short and long H-F bonds do not rearrange. At this relatively high temperature (290 K), quite large fluctuations in the overall structure away from the ideal pentagonal structure can be seen. On the right we see the simulation of the HF pentamer with the nuclei treated quantum-mechanically. The small spheres show the individual PIMD beads, the larger transparent spheres show the “centroids” (the averages of the atomic positions over all the beads). In this quantum simulation, any distinction between short and long H-F bonds is much harder to make out. The values of the bond length show that the difference between “short” and “long” H-F bonds is much smaller than when the nuclei are treated classically, and switch quickly during the simulation. (Credit: Brent Walker,