Models

What do these equations have in common?

Each of these describe a plausible mathematical model for the analysis of observable properties exhibited by water in its manifold forms. Each of these belie a plethora of assumptions and propositions which aim to define the scope in which these equations may hold true. Eqn. 1 describes the specific internal energy of steam [1] and was key to the industrial revolution, with calculated values published widely as steam tables used for the design and performance evaluation of steam driven locomotives. They continue to be used in calculations of chemical plants. The core concept underlying this facet of water is entropy, yet it is formulated axiomatically, without reference or knowledge of the queen of modern physics, the electron. Eqn. 2 describes the electric interaction and induction components modeled as a collection of multipole moments located at the centers of mass [2] developed at the University of Iceland. Eqn. 3 describes optical effects, that is, the change in refractive index of a material due to local heating and convective effects from a laser [3] where water is often used as a baseline reference. Eqn. 4 demonstrates the link between ice softness and statistical modeling [4] also from the University of Iceland. Eqn. 5 describes the nucleation event of ice formation under shear [5].

Language and computation

The interpretation of mathematical symbols in the last section has a crucial flaw. They are dense in information for those who dedicate their lives to them. This has cross pollinated a field of formal languages. Quantification of the expressivity of symbols and their interpretation brings us towards fields of compression, encoding and programming languages. Consider for example, the flow of code to compute the value of a number times itself.

The set of equations required for the field of molecular dynamics can be summarized in three lines based on Newton’s laws of motion. They depict the time evolution of an object in time and space. However, these are insufficiently informative to a digital machine, whose base language is formulated from electrical impulses representing on and off bits. To generate values from these equations on a computer requires more than the partial differential equations. We must turn to the discretization of continuous functions and the expressivity of formal programming languages. This numerical quantization is in no way related to the physical quantization mandated by quantum mechanics. Fig.1 demonstrates the levels at which we can describe a model to a computer.

Fig. 1. Input coordinates and human recognizable images with electronic densities. Taken with permission from the W3CM middle school course [6].

Nucleation

Unsurprisingly, even in our artificial universes, it is hard to escape the effects of time. The timestep which is used in the simulation of observables defines the effects we can describe. The formation of ice at a molecular scale exemplifies this. High school science dictates that at normal pressure and at temperatures lower than zero Celsius, water will form ice. At a molecular level, advancing through time, we note that entropy and statistical mechanics prevent the simultaneous conversion of all water molecules into some form of ice. The formation of ice at a molecular level is described in the inset image from [7].

Rare event sampling

How many times did the horse bend its third knee? This sort of question is impossible to answer without additional samples (or images in this case) and the demonstration of high-speed photography [7] exemplifies the need for taking the appropriate samples of an event.

HPC origins

Having understood so far the effort needed to express physical knowledge for computational systems, we now struggle against the need to define our equations in order to take advantage of the underlying computing hardware. The simplest example comes from the tradeoff between precision and operations. The computational complexity of expressing physical systems grows exponentially for most systems, and specialized hardware is needed for large scale calculations. Here at the University of Iceland, several HPC experts have taken on the mantle of maintaining our computational resources including Prof. Dr. - Ing. Morris Riedel, Prof. Hannes Jónsson, and others.

Privatization

The story of HPC (high-performance computing) in Iceland begins in a basement (where the first servers were managed) and is swiftly accelerating to a rather ignominious end. Under the stifling hand of UTS, control has been shifted away from the users and been sold off piecemeal to companies with “HPC expertise” across the ocean. This is a lamentable occurrence.

Conclusions

Water is always an integral aspect of human life. It is undoubtedly amongst the easiest of substances to interrogate, being both plentiful and to a large extent safe. A complete and holistic understanding of water however, remains largely intractable with ongoing efforts in the computational community towards bridging the gap between experimental studies and theoretical models from first principles. Water may be beguilingly basic, but there shall be little doubt that it remains an active field of study and sparks the joy of discovery in many aspiring scientists in various fields.

References

[1] Koretsky, M. D. (2004). Engineering and chemical thermodynamics. John Wiley & Sons.

[2] Wikfeldt, K. T., Batista, E. R., Vila, F. D., & Jónsson, H. (2013). A transferable H2O interaction potential based on a single center multipole expansion: SCME. Physical Chemistry Chemical Physics, 15(39), 16542. https://doi.org/10.1039/c3cp52097h

[3] Singhal, S., & Goswami, D. (2020). Unraveling the molecular dependence of femtosecond laser-induced thermal lens spectroscopy in fluids. The Analyst, 145(3), 929-938. https://doi.org/10.1039/c9an01082c

[4] Gopalan, G., Hrafnkelsson, B., Aðalgeirsdóttir, G., & Pálsson, F. (2021). Bayesian inference of ice softness and basal sliding parameters at Langjökull. Frontiers in Earth Science, 9. https://doi.org/10.3389/feart.2021.610069

[5] Goswami, A., Dalal, I. S., & Singh, J. K. (2021). Universal nucleation behavior of sheared systems. Physical Review Letters, 126(19). https://doi.org/10.1103/physrevlett.126.195702

[6] Goswami, R., & Goswami, A. (n.d.). Water, chemicals and more with computers for chemistry. Overview - Water, Chemicals and more with Computers for Chemistry. https://wc3m.github.io/overview.html

[7] Goswami, R., Goswami, A., & Singh, J. K. (2020). D-SEAMS: Deferred structural elucidation analysis for molecular simulations. Journal of Chemical Information and Modeling, 60(4), 2169-2177. https://doi.org/10.1021/acs.jcim.0c00031

[8] A horse's motion scientifically determined. (1878). Scientific American, 39(16), 241-241. https://doi.org/10.1038/scientificamerican10191878-241b

Water and Computational Chemistry: Playing God in Artificial Constructions