May 22 2017
Kids find it fascinating to see glow-in-the-dark objects that can illuminate a dark room without needing a light bulb, batteries, or electricity. When they grow up, these kids understand that this phenomenon is caused by chemical compounds known as chromophores that are energized (i.e. excited) upon absorbing visible light.
This image shows the structure of berkelium in oxidation state +IV. Researchers used the new Berkeley Lab algorithm to calculate the absorption spectrum and confirm what several experimental results have been hinting—that the element berkelium breaks form with its heavy element peers by taking on an extra positive charge when bound to a synthetic organic molecule. This property could help scientists develop better methods for handling and purifying nuclear materials. CREDIT: Bert de Jong, Berkeley Lab.
Upon returning to their normal state, the energy stored in the chromophores is released in the form of light, which is identified as a glow. In order to analyze the structures of materials that are used in batteries, chemical catalysis, solar applications and so on, materials science researchers depend on a similar phenomenon.
When a photon (i.e. the fundamental particle of light) is absorbed by a molecule, electrons in the molecule are transformed from a low-energy, or ground, state to a higher energy, or excited, state. Such reactions resonate at particular light frequencies, thus leaving behind “spectral fingerprints” that brighten up the electronic and atomic structures of the system under analysis.
During investigations, the “spectral fingerprints” (or absorption spectrum) are quantified by using ultra-modern facilities such as the Advanced Light Source (ALS) at the U.S. Department of Energy’s Lawrence Berkeley National Laboratory (Berkeley Lab). While performing computer simulations, such measurements are generally carried out by means of a quantum mechanical technique known as the Time Dependent Density Functional Theory (TDDFT). The computational models are highly significant in allowing the scientists to proliferate their investigations through prediction and validation of the outcomes.
In spite of its effectiveness, at times TDDFT cannot be applied for calculating a system’s absorption spectrum as it necessitates considerable amount of time and computer resources. To overcome this drawback, scientists at the Computational Research Division (CRD) of the Berkeley Lab have developed an innovative mathematical “shortcut.” The new algorithm increases the speed of the absorption calculations five times, meaning that simulations that earlier needed 10-15 hours to calculate can now be performed in almost 2.5 hours.
A paper reporting on this technique appeared in the Journal of Chemical Theory and Computation (JCTC). The new technique for calculating the absorption spectrum will be included later this year in a forthcoming edition of the extensively used NWChem computational chemistry software suite.
New Algorithms Lead to Computational Savings
In order to investigate the chemical structure of new materials and molecules, researchers generally explore the system by using an external stimulus (usually a laser), and then search for small electronic changes. In mathematical terms, this electronic change can be exhibited as an eigenvalue problem. Solving the eigenvalue problem enables the scientists to obtain a better estimate of the absorption spectrum, which subsequently shows the resonant frequencies of the system under analysis. The intensity of response of the system to the stimulus is calculated by using the corresponding eigenvector. This is the actual principle governing the TDDFT technique, which has been used in various quantum chemistry software packages such as the open-source NWChem software suite.
Although the technique has been seen to be successful, in the case of large systems, it exhibits several drawbacks. If the energy range of electronic responses attempted to be captured in a system is very wide, then the researchers require more eigenvectors and eigenvalues for the computations, indicating in turn that more computing resources are needed. Eventually, it is restrictively costlier to use this technique to calculate the absorption spectrum of a molecule that has over 100 atoms.
In order to overcome such restrictions, mathematicians at the CRD created an approach for directly calculating the absorption spectrum without the need for explicit calculation of the eigenvalues of the matrix.
“Traditionally, researchers have had to compute the eigenvalues and eigenvectors of very large matrices in order to generate the absorption spectrum, but we realized that you don’t have to compute every single eigenvalue to get an accurate view of the absorption spectrum,” explained Chao Yang, a CRD mathematician who headed the development of the innovative technique.
Yang and his team were successful in applying the Lanczos algorithm and a Kernal Polynomial Method (KPM) to estimate the absorption spectrum of various molecules. They achieved this by reformulating the problem as a matrix function approximation by using a special transformation and by making the most of the concealed symmetry with respect to a non-Euclidean metric. In comparison to non-symmetrical alternatives, both the algorithms mandate comparatively low memory, which is beneficial for computational savings.
As this technique needs only less computing power for attaining an outcome, scientists can also effortlessly compute the absorption spectrum of different molecules that have hundreds of atoms.
“This method is a significant step forward because it allows us to model the absorption spectrum of molecular systems of hundreds of atoms at lower computational cost,” stated Niranjan Govind, a computational chemist at the Pacific Northwest National Laboratory who worked in collaboration with the Berkeley Lab team in developing the technique in the NWChem computational chemistry program.
In recent times, researchers at the Berkeley Lab applied this technique to compute the absorption spectrum and to reassert the indication of various experimental outcomes that the element berkelium breaks form with its heavy element counterparts by absorbing an extra positive charge while being attached to a synthetic organic molecule. This characteristic can assist researchers in developing superior techniques for handling and purifying nuclear materials. A paper describing this outcome has been published in the journal Nature Chemistry on 10 April 2017.
The experimental results were hinting at this unusual behavior in berkelium, but there wasn’t enough experimental evidence to say yes, 100 percent, this is what we’re seeing. To be 100 percent sure, we did large computational simulations and compared them to the experimental data and determined that they were, indeed, seeing berkelium in an unusual oxidation state.
Wibe Albert de Jong, a CRD scientist as well as a co-author of this study.
The new algorithm was created as part of a DOE Office of Science-supported Scientific Discovery through Advanced Computing (SciDAC) project for advancing software and algorithms for photochemical reactions. SciDAC projects generally bring together an interdisciplinary group of scientists to create new and innovative computational techniques for overcoming the most difficult scientific challenges.
The interdisciplinary nature of SciDAC is a very effective way to facilitate breakthrough science, as each team member brings a different perspective to problem solving. In this dynamical environment, mathematicians, like me, team up with domain scientists to identify computational bottlenecks, then we use cutting-edge mathematical techniques to address and overcome those challenges.
Yang
Apart from Yang and Govind, Jiri Brabec, Lin Lin, Meiyue Shao, and Esmond Ng of Berkeley Lab, as well as Yousef Saad from the University of Minnesota, are the other authors on the JCTC paper.
The computing resources offered by the National Energy Research Scientific Computing Center (NERSC) as well as the Environmental Molecular Sciences Laboratory culminated in the development of the new algorithm. ALS and NERSC at Berkeley Lab and EMSL at Pacific Northwest National Laboratory are all DOE Office of Science User Facilities.