Computational Chemistry 3.5 - Ensemble Properties

Short lecture on ensemble properties in molecular systems.
Energy minimization produces low energy structures, but all structures contribute to molecular properties to some degree. A Boltzmann-weighted average can be computed over all possible structures, but is very expensive to compute. Approximations to this include grid searches, molecular dynamics, and Monte Carlo approaches.
Notes Slide: i.imgur.com/vyJ...
-- About TMP Chem --
All TMP Chem content is free for everyone, everywhere, and created independently by Trent Parker.
Email: [e-mail]
-- Video Links --
Course Playlist: • Computational Chemistry
Other Courses: • PChem Course Intros
Channel Info: • About TMP Chem
-- Social Links --
Facebook: / tmpchem
Twitter: / tmpchem
LinkedIn: / tmpchem
Imgur: tmpchem.imgur.com
GitHub: www.github.com...
-- Equipment --
Microphone: Blue Yeti USB Microphone
Drawing Tablet: Wacom Intuos Pen and Touch Small
Drawing Program: Autodesk Sketchbook Express
Screen Capture: Corel Visual Studio Pro X8

[@RevRun14]

You have no idea how helpful these videos are for me. This is like one of the few RUclips channels - no - one of the few INTERNET sources that make videos on these topics and at this quality.

[@TMPChem]

Glad you think so.

[@RevRun14]

You're welcome! You deserve the praise!

[@steven_chu]

Impressive video! Saved my life and time! THANK YOU SO MUCH!

[@meryemfat]

thank you so much :)

[@TMPChem]

Thanks for watching, ki ko.

[@bruceallen6492]

Which book are you working from? You mention the chapter and I would like to get the book as a refresher. I am writing software for building systems of molecules for molecular dynamics simulations. The software is open source. Thank you.

[@eric_welch]

Szabo and Ostlund ...."Modern Quantum Chem" ....I've been reading through this book and realized he is going through the first couple of chapters ......his videos starting at 4.x follow almost exactly along with chapter 3 of that book

[@arminbehdad6781]

Hello dear Tem Chem,
What is the differences between average in thermodynamics with that of statistical mechanics e.g over phase space. How can we calculate the average distances between two atoms in MD simulation?

[@TMPChem]

Hi Jhon. The fundamental theorem of statistical mechanics is the ergodic hypothesis, which states that averages over a large amount of phase space are equivalent to averages over a large amount of time. Statistical mechanics measurements are preferred to be the former, whereas thermodynamic measurements are typically the latter. Thus according to the ergodic hypothesis either should be equivalent to the extent that they are measuring / calculating the same property in the same way.
As for MD, one way we could calculate for two atoms is to do a very long MD simulation, compute r at each time step, and average the result. Another way would be to integrate the integral of the Boltzmann factor times r at over all possible values of r1 and r2, normalizing the result by the partition function. Both ways should be equivalent (within the approximations of the model) in the limit of an exact phase space integral and an infinite time simulation.

[@arminbehdad6781]

Thanks a lot, dear great teacher. Can we use the second way in MD?

[@TMPChem]

MD is essentially equivalent to making the choice to use a time average, since "dynamics" is the evolution of a system over time. We can, however, compute a direct Boltzmann-weighted average of a property over phase space, as described in this video. Substitute A(r^N) with your property of interest, and integrate over the necessary dimensions. This is often intractible in practice, as for all but the smallest systems 3N is far too many dimensions, and exponentially explodes very quickly, hence the need to resort to MD as a time average approximation of the exact phase space integral. If we could always do the phase space integral there would be no need for MD.