Density functional theory took a wrong turn recentlyJanuary 05, 2017
The paper explores in detail the intricate relationship between the results of the quantum-chemical calculations and the approximations they rely upon.
When chemists want (or need) to include some "theory" in their papers, it usually means that they will perform some quantum-chemical calculations of the participating molecules. This, strictly speaking, means solving a series of extremely complex equations describing the motion of electrons around atomic nuclei, the target of the calculation being the energies of the starting molecules and the products.
Indeed, a chemist will know almost everything she wants about a reaction if she knows the energies of the participating molecules and the products; and to know the energy of each step leading from one molecule to another is to truly know everything about a process. Similarly, in materials science the energies of the 3D structures serve as a necessary information for prediction of the new materials and the study of their properties.
The exact solution of the underlying Schrödinger's equation for real systems is unreachable in reasonable time; approximations are therefore necessary. However, those obtainable from approximate description of the electron motion either are too simple to reproduce the behavior of many actual molecules (this is the case of the Hartree-Fock method) or again too difficult to compute for large systems (this is the case of the Møller-Plesset perturbation theory and the "heavier" methods).
The breakthrough for computational methods in quantum chemistry came with the density functional theory (DFT) and the Hohenberg-Kohn theorems. The theorems basically say that the average number of electrons located at any one point in space--otherwise called the electron density distribution--contains all the information needed to determine the energy. There is, however, a catch: these theorems do not provide the method for extracting the energy from the electron density. They just say that such a method, the exact functional, exists.
The DFT first appeared in 1927 in the form of Thomas-Fermi model, gained its legitimation in 1964 with the Hohenberg-Kohn proof, and became the method of choice for the material sciences after 1980, when the Generalized Gradient Approximation (GGA) was introduced; and then conquered the isolated molecules simulations after Axel D. Becke implemented hybrid functionals in 1993. Now there are DFT functionals allowing for a very wide range of the computational cost / accuracy ratio. The DFT boosted the chemistry and material science in many ways and basically handed the power of quantum-chemical modeling to users without a strong physical background. In recognition of this fact, Walter Kohn received a half of the 1998 Nobel Prize--the other half went to John A. Pople, who developed many computational methods and was the principal author of an extremely popular computational chemistry program Gaussian.
Dr. Bushmarinov says:
"In our lab, we work a lot with electron density-based approaches to study chemical bonding. My colleague Michael Medvedev, currently a PhD student in our lab, had an idea to test how well different functionals are reproducing the electron density. Not in the vague "let's test it" sense: he decided to check the electron density for the smallest "difficult" systems out there. These systems are atoms and atomic ions with 2, 4 or 10 electrons. We also chucked some anions in initially for good measure. Well, you might ask a question along the lines of "exactly which insight do you expect to gain from modeling F5+? This particle has much more in common with plasma physics than with chemistry!" I asked such questions myself, I must admit."
Mr. Medvedev, calculated the electron densities and their derivatives for the test atomic species using almost every "named" functional available in major modern computational chemistry codes, as well as many combinations of those: more than 100 in total. He noticed that the quality of the electron density (ED) seemed to worsen over the years despite the improvements in energies reported in the literature, which raised major questions about the state of the modern DFT. Dr. Bushmarinov developed a rigorous way to compare the produced electron densities to the exact one and to produce a rating of the functionals sorted by the quality of their densities.
The problem is, the electron density is not just 'some' property of the system. The Honenberg-Kohn theorem does not say that the energy of a system can be extracted from just any electron distribution; it states that the exact energy should arise from the exact density.
Mr. Medvedev says:
"All functionals currently in use are approximations of the exact functional; so how on Earth can they provide better energies from worse densities? On a philosophical level, this seems to contradict the principle known to any programmer: an algorithm should not produce correct results from faulty data."
At this point, I.S.B and M.M.G. contacted Prof. John P. Perdew of Temple University, for an expert opinion and a collaboration.
Prof. Perdew pointed out a fundamental flaw in the tests initially used (it turned out the anions should not have been used after all) and helped with all theoretical aspects of the paper. Dr. Jianwei Sun performed the necessary computations using the latest methods developed by J.P.P. and him.
Dr. Bushmarinov says:
"After the actual systematic errors were weeded out, the data became beautiful. Just from the RMSD of the electron density you can see the whole history of DFT in a plot. Basically, until early 2000s the densities improved along with the theoretical advances. You can even see the functional hierarchy, for which John Perdew in 2001 coined a term "Jacob's ladder": functionals become more complex and describe everything better as you go from LDA to GGA to mGGA to hGGA. Until, well, something happens which makes a large fraction of the modern functionals worse than the 1974 ones."
The actual lists of the worst and the best functionals provided an answer to this apparent conundrum. The "best" functionals all happened to be derived from solid theoretical approaches--using several routes taken by different groups.
The "worst" methods, however, are only of two kinds. Either they are the pre-1985 ones (the theory was not yet ready), or they were fully obtained by the so-called parameterization. Most of those were developed by a taking flexible functional equation and tuning all ca. 20 parameters with the aim of obtaining the best energies and geometries on a given dataset (usually low hundreds of molecules). Such approach provided excellent energies and geometries, in particular on the test sets normally used for functionals' comparison.
The chemical space is, however, vast, and a method performing well on hundreds of molecules can fail when tested on something it was not trained to reproduce--like small, simple atoms in this study. It should be noted that some of these "misbehaving" methods are actually very popular. Since they contradict the basics of the theory--they yield "good" energies from "bad" densities--the authors concluded that these methods most likely suffer from some internal problems. And the density functional theory will stray further from the path toward the exact functional if this approach to functional developments is not put in check.
The main point of publishing this study in Science was to avoid that mistake on behalf of the DFT community.
Nesmeyanov Institute of Organoelement Compounds
Related Chemistry Articles:
Whether you have it with bread or use it to cook, olive oil is awesome.
Light initiates many chemical reactions. Experiments at the Laser Centre of the Institute of Physical Chemistry of the Polish Academy of Sciences and the University of Warsaw's Faculty of Physics have for the first time demonstrated that increasing the intensity of illumination some reactions can be significantly faster.
Derby Day means it's time to recognize the chemical process of distillation, which makes bourbon possible.
Considered the pinnacle of mediaeval painting, the Ghent Altarpiece was painted around 1432 by Jan van Eyck and probably his brother Hubert.
The thing that sets redheads apart from the crowd is pigmentation.
The scientists experimentally confirmed and theoretically explained the stability of Na2He.
Donald Trump is now the 45th president of the US.
Defects and jagged surfaces at the edges of nanosized platinum and gold particles are key hot spots for chemical reactivity, researchers confirmed using a unique infrared probe at Berkeley Lab.
Princeton researchers have developed a method that irradiates biological enzymes with light to expand their highly efficient and selective capacity for catalysis to new chemistry.
Award-winning UCSB professor Bruce Lipshutz is out to make organic chemistry better for the planet
Related Chemistry Reading:
Chemistry: A Novel (Vintage Contemporaries)
by Weike Wang (Author)
Winner of the PEN/Hemingway Award
A Washington Post Notable Book
One of the Best Books of the Year: NPR, Entertainment Weekly, Ann Patchett on PBS NewsHour, Minnesota Public Radio, PopSugar, Maris Kreizman, The Morning News
Winner of Ploughshares’ John C. Zacharis Award
Winner of a Whiting Award
A Belletrist Amuse Book
At first glance, the quirky, overworked narrator of Weike Wang’s debut novel seems to be on the cusp of a perfect life: she is studying for a prestigious PhD... View Details
Chemistry: Concepts and Problems: A Self-Teaching Guide
by Clifford C. Houk (Author), Richard Post (Author)
CHEMISTRY SECOND EDITION
The fast, easy way to master the fundamentals of chemistry
Have you ever wondered about the differences between liquids, gases, and solids? Or what actually happens when something burns? What exactly is a solution? An acid? A base? This is chemistry--the composition and structure of substances composing all matter, and how they can be transformed. Whether you are studying chemistry for the first time on your own, want to refresh your memory for a test, or need a little help for a course, this concise, interactive guide gives you a fresh... View Details
Chemistry (Quick Study Academic)
by Inc. BarCharts (Author)
BarCharts’ best-selling quick reference to chemistry has been updated and expanded in this new edition. With updated content and an additional panel of information, this popular guide is not only an essential companion for students in introductory chemistry courses but also a must-have refresher for students in higher-level courses. Author Mark D. Jackson, PhD, a scientist and university chemistry professor, has a gift for making the complicated subject of chemistry interesting and easy to understand―without the fluff. In this new edition, you will find more coverage of the subject,... View Details
Chemistry Essentials For Dummies
by John T. Moore (Author)
Whether studying chemistry as part of a degree requirement or as part of a core curriculum, students will find Chemistry Essentials For Dummies to be an invaluable quick reference guide to the fundamentals of this often challenging course. Chemistry Essentials For Dummies contains content focused on key topics only, with discrete explanations of critical concepts taught in a typical two-semester high school chemistry class or a college level Chemistry I course, from bonds and reactions to acids, bases, and the mole. This guide is also a perfect reference for parents who need to... View Details
Chemistry: The Central Science (13th Edition)
by Theodore E. Brown (Author), H. Eugene LeMay (Author), Bruce E. Bursten (Author), Catherine Murphy (Author), Patrick Woodward (Author), Matthew E. Stoltzfus (Author)
Chemistry Text, latest edition, required text View Details
Chemistry: An Introduction to General, Organic, and Biological Chemistry (12th Edition) - Standalone book
by Karen C. Timberlake (Author)
For one-semester courses in General, Organic, and Biological Chemistry
Show the importance of chemistry in the real world
Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition is the ideal resource for today’s allied health students. Assuming no prior knowledge of chemistry, author Karen Timberlake engages students through her friendly presentation style and reveals connections between the structure and behavior of matter and its role in health and... View Details
Chemistry Equations & Answers (Quickstudy Reference Guides - Academic)
by Inc. BarCharts (Author)
This 6-page study guide contains basic chemistry analysis and concepts designed specifically to aid science students.
If you have ever suspected that "heavy water" is the title of a bootleg Pink Floyd album, believed that surface tension is an anxiety disorder, or imagined that a noble gas is the result of a heavy meal at Buckingham Palace, then you need The Cartoon Guide to Chemistry to set you on the road to chemical literacy.
You don't need to be a scientist to grasp these and many other complex ideas, because The Cartoon Guide to Chemistry explains them all: the history and basics of chemistry, atomic theory, combustion, solubility, reaction stoichiometry, the mole, entropy,... View Details
Chemistry: A Molecular Approach
by Nivaldo J. Tro (Author)
ALERT: This is a standalone book and does not contain an access code. If you would like to purchase the version that includes the Access Card Package please visit: http://www.amazon.com/dp/0321804716
Chemistry: A Molecular Approach, Third Edition is an innovative, pedagogically driven text that explains challenging concepts in a student-oriented manner. Nivaldo Tro creates a rigorous and accessible treatment of general chemistry in... View Details
Intro to Chemistry Coloring Workbook
by Sonya Writes (Author)
Learn the basics of chemistry through coloring. This book introduces the concepts of:The Periodic table Protons, electrons and neutrons Bohr models Orbitals Diatomic elements Covalent bonds Ionic bonds...and more! View Details