Nov 132016
 

wilsonqcarticel

A 2007 review of coupled cluster theory by Bartlett and Musial (Bartlett, R. J.; Musiał, M. Coupled-Cluster Theory in Quantum Chemistry. Rev. Mod. Phys. 2007, 79, 291–352) opens with an intriguing quotation of a 1989 article by physics Nobel prize winner Kenneth Wilson:

Ab initio quantum chemistry is an emerging computational area that is fifty years ahead of lattice gauge theory…and a rich source of new ideas and new approaches to the computation of many fermion systems.

I recently read this paper (Wilson, K. G. Ab Initio Quantum Chemistry: a Source of Ideas for Lattice Gauge Theorists. Nuclear Physics B – Proc. Suppl. 1990, 17, 82–92) and found it extremely interesting. The article begins by saying that Wilsons had switched his field of research from lattice gauge theory to computational quantum chemistry. One of the reasons for this change, Wilson says, is ancestral, adding an interesting explanatory note in which he acknowledges discussions with his father, E. B. Wilson. The second reason he reports is the lack of sources of inspiration in his field.
In his paper Wilson discusses the benefits of using Gaussian basis functions compared to numerical grids, the emphasis of quantum chemistry on analytic approaches rather than stochastic methods, and “the status of my efforts to ease the programming burden using the C++ programming language”.
In just a few pages, Wilson summarizes with extreme clarity the state-of-the-art in quantum chemistry (in 1989). He provides a very clear description of the major challenges in this field, and succinctly analyzes purpose and limitations of some of the most important methods used in quantum chemistry.

To my surprise, Wilson was at the time also concerned with the software productivity of scientists, an issue that is still very relevant today. I was quite excited to see that Wilson had already recognized the potential of C++ to simply the organization of large computer codes. In Wilsons words:

The ability to attach variable names and subroutines and functions to a common block is, I find, a powerful organizing
tool for large programs.

I think this article is a little gem and recommend it especially to those interested in the history of physics and quantum chemistry. I hope you will enjoy reading it!

 November 13, 2016  Uncategorized No Responses »
Nov 112016
 

A photo of the group in front of the Center for Computational Quantum Chemistry at the University Georgia. We were there to attend the 2016 Psi4 developers workshop. Kevin, Sam, Wallace, and Francesco gave talks on parallel CASSCF, new data structures for sparse CI, valence virtual orbitals, and the Wick&d project.

2016-11-uga-psi4workshop

 November 11, 2016  Uncategorized No Responses »
Dec 222015
 

I recently watched an interesting interview of Freeman Dyson in which he recalls a meeting with Enrico Fermi. During the meeting they discussed calculations done by Dyson, but Fermi was skeptical of the model used to produce the data. Hence, Fermi quoted von Neumann: “With four parameters I can fit an elephant, and with five I can make him wiggle his trunk.” Today I found this article, which actually does fit the shape of an elephant with four complex parameters.

Screen Shot 2015-12-22 at 12.13.24 AM

 December 22, 2015  Uncategorized No Responses »
Jul 232015
 

Our new espresso machine (SAECO Via Venezia) and coffee grinder (Cuisinart Supreme Grind™ Automatic Burr Mill) have arrived! We’ll be happy to serve you an espresso or a cappuccino when you visit us.

Espresso machiine

 July 23, 2015  Uncategorized No Responses »
Dec 272014
 

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I recently picked up two books on Lie groups and algebras.  The first I read was Lie Groups for Pedestrians, by Harry Lipkin.  As the title suggests, this book is an introduction to Lie groups.  The author tries to hide most of the mathematical complexity of Lie’s theory and focuses on examples from physics.  The book is easy to read, but it seems to me that it is really designed for the typical pedestrian that circulates near the elementary particle physics section of physics department.  I found it somewhat useful and at time interesting.

Robert Gilmore’s Lie Groups, Lie Algebras, and Some of Their Applications is a nice introduction to Lie’s theory written from the perspective of a mathematician.  I really liked Gilmore’s introductory chapters that so neatly summarize various topics propaedeutic to the study of Lie groups and algebras (field, group, vector space, algebra).  Applications to quantum mechanics are scattered throughout the book and tend to focus on simple aspects (spin, the SU(2) group, second quantization).  Lie’s theory is pretty involved and so even this book, at times, can be challenging to read.

Why am I interested in Lie algebras and groups?  Lie algebras are at the basis of second quantization techniques.  Some results from Lie algebra are used in many-body theory, for example the Baker–Campbell–Hausdorff formula.  However, the aspect that is most interesting for me is the connection between the formalism of generalized normal ordering of Mukherjee and Kutzelnigg and Lie and Hopf algebras.

 December 27, 2014  Book review Comments Off on Books on Lie algebras and groups