Attention Walking-Aficionados

Two days ago, Google Maps introduced a new utility that will map a walking path to your destination, given the destination is under 6.2 miles and in a large city. They also fixed the mass-transit feature found in bigger cities. Granted, it's in beta, but it's a step in the right direction.

Kudos to Google. Now, I expect to see more people walking and absorbing their surroundings, especially all you hippies with iPhones or iPod Touches.

(On a personal note, I determined today that from where I am going to live to where I will work at UIUC is about 1.2 miles. At LSU, this distance was ~0.8 miles. I'm excited.)

Comparing Molecular Studies of Liquid Benzene at Constant Pressure

A path integral molecular dynamic algorithm versus Monte Carlo ensemble sampling

Abstract

Several different methods have been developed to study the interaction of matter in condensed phases. Molecular dynamic studies and Monte Carlo ensemble sampling studies are the bulk of molecular simulation studies. A comparative study between a path integral molecular dynamic study and Monte Carlo ensemble sampling is given on liquid benzene at room temperature.

Introduction

The motivation to study the thermodynamic and mechanical properties of matter in condensed phases has given rise to the development of several different methods of study. Molecular modeling has seen rapid development as a promising method due to the increase in availability of computational power. Parallel computing has opened the possibility to rigorously address computationally challenging problems in the numerical evaluation of molecular simulations.

With the motivation to study systems of highly correlated chemical species in fluid phases, it is beneficial to develop a comparative study to determine efficiency and accuracy of methods. Two methods chosen were isothermal-isobaric Monte-Carlo sampling (MC-NPT) and solving the path integral for a system at constant pressure but fluctuating cell volumes (PI-NPT).^1,2 Benzene is of particular interest since it is representative of other planar or quasi-planar molecules, and the isothermal-isobaric (NPT) ensemble is the common condition of experimental settings.

Theory and Methods

The theoretical aspects of both models have been explored thoroughly previously.^2,3 We will only sketch the important theoretical considerations of each model and explain the methodology applied.

For both simulation types, only 100 benzene molecules were considered. This was deemed to be a representative sample to generate general trends in order to compensate for needing less time to computationally evaluate each simulation. Volume changes were considered to be isomorphic, meaning all six points of the cubic box were changed equally.

Monte Carlo sampling: NPT ensemble

In an NPT-ensemble, the number of particles and temperature remain constant while the volume of the container is allowed to fluctuate. Traditionally this is best approached by the Monte Carlo sampling method. Not only can the molecular degrees of freedom be sampled but the volume of the container can be sampled as well. Thus, the two move types are present: molecular and volume.

For benzene, the molecular degrees of freedom involved are rotation, vibration, and translational moves. For moves, the 6-bodied system can be reduced to a two-body system by considering only two points: the center of mass of the benzene ring and the center of mass of the carbon-carbon bond. This "trick" reduces the moves for vibration and rotation to be represented by another translational move.⁴

Benzene has six site interactions at each CH of the ring. The interactions were modeled using the Optimized Potential for Liquid Simulations (OPLS).⁵ Though the benzene quadruple is not explicitly addressed by the model, studies for the liquid phase have indicated the consideration not necessary to achieving physically reasonable results.¹

Molecular Dynamics: path integration for the NPT-case

The Feynman path integral offers a powerful method to simulate molecular systems in the isothermal-isobaric case since the Monte Carlo sampling cannot study phase transitions explicitly nor time-dependent observables. The path integral also offers the link between quantum mechanics and statistical mechanics via the Boltzmann operator being simply a rotation through imaginary time of the time-evolution operator⁶. This connection allows the use of the path integral in addressing problems in statistical physics. The NPT-partition function for the isomorphic case is also a simple integration over the pressure phase space with the quantum canonical partition function in the integrand. This is analogous to the classical statistical mechanics consideration of the relationship between ensembles.⁶

The PI-NPT approach was adopted from Martyna et al.² Molecular interactions were treated using the OPLS representation.

Results

For this study, four temperature points were considered for comparison. These points were chosen based off of the experimentally determined phase diagram of benzene.^7-9 The pair distribution function was determined for each data point as well as other thermodynamic properties.¹⁰ Table 1 and Table 2 gives the results for the two studies, and Table 3 gives available experimental studies.^7-9

T (K)	Most Probable Separation (Å)	E (kJ/mol)	Cp (J/mol K)
125	3.3 ± 0.1	-51.3 ± 0.4	19 ± 2
150	3.7 ± 0.1	-50.5 ± 0.4	18 ± 1
175	4.2 ± 0.1	-49.8 ± 0.3	17 ± 1
200	4.6 ± 0.1	-48.4 ± 0.4	16 ± 2

Table 1. The results from the MC-NPT Simulations

T (K)	Most Probable Separation (Å)	E (kJ/mol)	Cp (J/mol K)
125	3.3 ± 0.1	-51.3 ± 0.4	20 ± 2
150	3.7 ± 0.1	-50.5 ± 0.4	18 ± 1
175	4.2 ± 0.1	-49.8 ± 0.3	18 ± 1
200	4.6 ± 0.1	-48.4 ± 0.4	17 ± 1

Table 2. The results from the PI-NPT Simulations

T (K)	Most Probable Separation (Å)	Cp (J/mol K)
125	3.4 ± 0.2	20.5 ± 0.7
150	3.6 ± 0.2	17.7 ± 0.6
175	4.3 ± 0.2	17.0 ± 0.7
200	4.7 ± 0.2	16.5 ± 0.6

Table 3. Experimental Results^7-9

Discussion

As indicated by Table 1, there is large agreement between the two studies. The agreement indicates that the PI-NVT method would be better spent studying the phase-change phenomena of molecular systems instead of only the thermodynamic properties at stationary points. This is because the MC-NVT method took about a quarter of the time for each point to calculate the simulation.

References

1. Zhao, X.; Chen, B.; Karaborni, S.; Ilja Siepmann, J. J. Phys. Chem. B, 2005, 109(11), 5368-5374.
   
2. Martyna, G.; Hughes, A.; Tuckerman, M. J. Chem. Phys. 1999, 110(7), 3275-3290.
   
3. McDonald, I. R. Molecular Physics, 2002, 100(1), 95-101.
   
4. Serrano Adan, F.; Banon, A.; Santamaria, J. Chem. Phys. 1984, 86, 433-444.
   
5. Jorgenson, W.; Madura, J.; Swenson, C. J. Am. Chem. Soc. 1984, 106, 6638-6646.
   
6. Feynman, R. P.; Statistical Mechanics. Benjamin Press: Reading, 1972.
   
7. Bridgman, P. W. J. Chem. Phys. 1941, 9, 794-797.
   
8. Cansell, F.; Fabre, D.; Petitet, J. J. Chem. Phys. 1993, 99(10), 7300-7304.
   
9. Thiery, M.; Leger, J. J. Chem. Phys. 1988, 89(7), 4255-4271.
   
10. McQuarrie, D. Statistical Mechanics University Science Books: Sausilto, California, 2000.
    

I studied benzene

Anyone remember when I stated what feels like ages ago that I was studying benzene for a stat mech class? No? Well, I did, and I forgot to post the results!

Like all scientific endeavors, the results are a mixed bag of learned lessons in parallel computing, fighting other computer users for precious computational time, and the most inconvenient random occurrences of downtime. Basically, aiming high resulted in striking very, very low. Embarrassingly low, indeed.

So, without further ado, I present for your reading my results.

I really shouldn't be laughing...

...at this PhD comic, because to do so means I understand it.

Penguins and Chemistry

What do penguins and chemistry have in common? Nothing, really [1]. But why did I put them together in a title? Because I just glanced at the most awesomest book cover I have ever seen [2]. Behold, Foundations of College Chemistry by Morris Hein and Susan Arena [3].

I found the 12th edition (pictured above) on my colleagues desk. I have found other edition covers using Google. It appears that the cover art team has a penguin-fetish, just like me. Awesome. I do want. Now.

Now, as a caveat, the book is a bit on the thinner side for a chemistry book. I wonder if my colleague will let me borrow the book for the evening to give it a glancing review? I already sneaked a peak at the index, and sadly penguins are not listed. This injustice is quite unforgiveable.

-----
[1] Penguin science tells me otherwise.
[2] I may be biased from my penguin-fetish
[3] Not to be confused with the Springer journal, Foundations of Chemistry.

It's a fucking wafer, people

Here's a strange story to ponder on.

A student of the University of Central Florida stole a blessed communion wafer (aka the Eucharist) from a Catholic Mass recently. Instead of putting it in his mouth, he allegedly attempted to bring the wafer back to his seat to show his friend who was curious about the Catholic faith, but was met with physical force to consume the wafer.

His claimed goal, though, was to inform other student senators of the activities involved in the Catholic Campus Ministry which receives about $40,000 from the SGA, money paid with student fees. Essentially, he is bringing up issues about using the fees paid by students to fund non-secular, and essentially non-public activities.

To add more interesting tidbits to the story, he has been threatened with physical violence, death, and the hopes of burning forever in the afterlife. Students have filed various complaints with the university and the SGA asking for disciplinary action and impeachment. The student has also filed a complaint with the university, claiming that the CCM is violating hazing policies by forcing participants to consume food.

Here is some more fascinating tidbits. PZ Myers, a professor of biology at the University of Minnesota Morris, recently commented on the whole ordeal at his blog, Pharyngula. In his commentary, he offered to desecrate a wafer and post images on the web. This had upset Bill Donohue of the Catholic League not once, but twice. Also in response to the initial blog post, Myers has been threatened several times by email from those claiming or implying to be Catholics (first email dump; second email dump).

So....my commentary...

We have a complete over-reaction of the Catholic community. Yes, I understand they value the 'Body of Christ' very much. Host desecration has been used as an excuse as the reason to burn "witches" and entire Jewish populations before during the 13th through the 17th century. The Catholics and other orthodoxically-oriented sects of Christianity have shown to call for blood when someone does harm to a wafer the Eucharist.

But at the end of the day, it's still a wafer and a cup of wine. Saying a couple of magical words does not make this piece of unleavened flour anything special. Especially not when it comes in a bag the size of dog food and stored away in the church's chambers until later consumption. Or, for those Catholics who travel a lot and may miss Mass on those business trips, convenient travel packs.

Was it wrong for the student to take the Eucharist in the first place? If he had foresight, he may have avoided the action due to the harassment after. But the action itself does not warrant physical violence done unto him, or even threats for physical violence. Devaluing the humanity of an individual to be equivalent to a piece of cooked gluten is perhaps the strangest mental exercise ever.

And it is ironic. The Eucharist is supposed to make those who take it to remember Jesus and honor his teachings and the supposed new covenant. I'm guessing all his talk about loving neighbors, doing unto others, and turning the other cheek and Paul's scorn to the Corinthians for greed and abuse of the symbolism got lost in keeping our sacred crows sacred. Nay, it is the human condition to still maintain esteemed materialism (eg. valuing a material object over humanity) even in a faith built by one who desired his followers to shed such earthly ties for Providence.

It's a fucking wafer, people. Get over yourselves.

LOLgoogle cache

Google cache pulls through. Quickly, before their spiders cache the fixed version, go gander at the most glorious mistake in website design found this week.