## New approaches to promote the use of magnets-free NMR for analysis in chemistry, biology, and medicine

The diverse work of Mainz-based physicists in the field of nuclear magnetic resonance is being boosted by a new highly application-oriented approach: In October 2020, Dr. Danila Barskiy will join Johannes Gutenberg University Mainz (JGU) to set up a group focusing on nuclear magnetic resonance (NMR) spectroscopy, the objective being to explore approaches that do not require magnetic fields for chemical, biological, and medical applications. To do so, he has been awarded a Sofja Kovalevskaja Award worth EUR 1.6 million by the Alexander von Humboldt Foundation. “We are very pleased that Danila Barskiy and his research have been honored in this way. His work not only covers new and previously unexplored aspects, but also excellently complements research we are already undertaking here in Mainz,” said Professor Dmitry Budker, Barskiy’s host at the Institute of Physics at JGU and at the Helmholtz Institute Mainz (HIM).

Nuclear magnetic resonance spectroscopy is a standard analytical technique used to study the structure and dynamics of materials and living objects. With its sister technology Magnetic Resonance Imaging (MRI), NMR spectroscopy is used in organic chemistry, biochemistry, and medicine with fluids being positioned particularly well to this type of analysis. However, NMR spectroscopy is reaching its limits: Due to the weak interaction between atomic nuclei and the applied magnetic field, signals produced by NMR-active nuclei are typically extremely low and, therefore, require high magnetic fields for detection. This rules out the possibility of developing portable point-of-care devices, among other things.

## Researchers aim to develop compact and portable NMR devices

Sofja Kovalevskaja Award winner Dr. Danila Barskiy has been looking at ways of improving NMR spectroscopy for around ten years, most recently at the University of California, Berkeley, from where he will be making the transition to Mainz. He is pursuing various approaches with the aim of designing compact and portable NMR devices that will ultimately be as small as a chip and affordable for wide analytical markets. According to Barskiy, the problem is the following: “Despite improvements being made, most NMR systems are still not compact because they need field strengths of several Tesla in order to distinguish between the chemical signatures in an NMR spectrum.”

Barskiy’s new interdisciplinary group will focus on developing miniaturized, portable NMR sensors. These sensors would employ the principle of zero to ultra-low field magnetic resonance, or ZULF NMR for short, using optically pumped magnetometers which would not require any strong magnetic fields. In addition to applications in chemical and biomedical research, such sensors could find use for detecting metabolic disorders at an early stage.

By heading up a work group at Mainz, Barskiy also wants to develop hyperpolarizers for benchtop NMR spectrometers. Hyperpolarization improves the alignment of nuclear spins in a sample, thereby amplifying their NMR signals. The scientist predicts that application-specific hyperpolarizers for tabletop NMR devices may be soon available and that they will be about the size of a coffee machine. And with a tabletop NMR device, it will be possible to perform highly sensitive analyses of fuels, biofluids such as blood or urine, and food extracts. “This will democratize NMR spectroscopy by providing access to wider audiences and will accelerate technological progress in developing countries,” Barskiy emphasized.

## Long-standing collaboration with experts from UC Berkeley paves the way for new research

This represents another positive result of the collaboration between UC Berkeley, in particular the laboratory of Professor Alexander Pines, and the Mainz group led by Professor Dmitry Budker. “We have been working very productively with Professor Pines and his team, including Dr. Barskiy, for many years and developed ZULF NMR together,” said Budker. “Danila Barskiy was one of the first to recognize the importance of this research in the biological and medical context.” Budker points out that Barskiy’s plans fit perfectly with the work being done at Mainz, which is also being pursued as part of the European Union’s ZULF NMR Marie Curie Innovative Training Network together with other European partners.

Danila Barskiy studied at Novosibirsk State University and earned a doctorate in physical chemistry for his research at the International Tomography Center (ITC SB RAS). In 2015, he began working as a postdoc at Vanderbilt University in Nashville, Tennessee, and subsequently joined Professor Alexander Pines’ team at the University of California, Berkeley in 2017. “The conditions in Mainz are unique for me. The planned collaborations and the resources available fit perfectly with the projects I am pursuing. Thanks to the Sofja Kovalevskaja Award, I can not only begin an independent research career, the multidisciplinary research in Germany is promoted as a whole,” emphasized Barskiy.

The Alexander von Humboldt Foundation gave the 2020 Sofja Kovalevskaja Award to eight international research talents aged between 29 and 36 years. It is one of the most richly endowed research awards in Germany and provides young researchers with venture capital for innovative projects at an early stage in their careers. They undertake research for up to five years at German universities and research institutions and build up their own work groups at their host institutes. The award is funded by the German Federal Ministry of Education and Research (BMBF).

Sources:

JOHANNES GUTENBERG UNIVERSITAET MAINZ

ChemEurope

Are you a student working on your way to obtaining PhD or a postdoc who wants to become a professor? In this post, I want to share some ideas I have ‘extracted’ from my journey in academia. This journey has been relatively short (about 10 years) but I believe during this time I still learned something important that can be of value for the people interested in science and those who want to pursue an academic path (and beyond).

A lot of times in academia you float toward the path of minimal resistance. By the time you obtain your PhD, you often become acquainted with some topic/discipline and you keep staying there because (i) you feel expertise in this area (and it feels good to be an expert in something), (ii) it feels scary to go toward unexplored area (and you may think you don’t have enough brains/time to go through it anymore), and (iii) you may have more contacts/connections in the field of your current research (which makes it more probable to stay in the same ‘bubble’).

I meet different people. And I see a clear troubling trend in academia (it cannot be applied to everyone and there are many amazingly creative and smart people) but the trend is definitively there: scientists become more and more incremental in their approaches, ideas, results. Richard Feynman only published about 37 papers (I need to find an exact number but this is about right) during his career but, oh boy, what papers are these papers! True brilliants. Feynman did not waste his time on doing incremental things, he did what he wanted in areas that interested him. Today the urge of publishing consistently new knowledge with high productivity (otherwise what? you are not smart/talented/hardworking-enough?) brings many people in academia – including PhD students, postdocs, and professors – to the brink of the mental breakdown. And fighting the symptoms will not help to treat the disease: the pressure of socially accepted norms does not let us truly develop as a society. This not only leads to the ‘natural selection’ of bad science (the one which is shiny, easy to swallow, extremely promising yet not very well thought-through) leaving many really talented people off the boat of modern academia.

Who are these leftover people? Very often these are truly talented individuals who embrace their curiosity across the boundaries of disciplines. And very often they are less competitive for the academic market compared to their ‘productive’ brothers. And the reason is simple – PROCRASTINATION. These people may very well be extremely talented but because they have a hard time focusing on one topic – they jump from one idea to another, spend hours talking to their friends about science or new paper – they do not make enough of the ‘formal product’. This low ‘formal productivity’ such as low number of papers published in peer-reviewed journals limits their chances for success in classical academia (here, by success I mean landing a professor position; in reality, ‘success’ is a much deeper topic that requires individual definition and separate discussion).

There is nothing wrong with you, it is the system that is outdated!

My long-term vision is to change classical academic approaches to education and science (because science is a derivative of education) (i) by making it more affordable to wider audiences and (ii) by focusing on empowering these ‘procrastinating’ people. There is nothing wrong with you, it is the system that is outdated! For this reason, I came up with 3 short tips which I explain in my short 3-video series. I will repeat them here for consistency.

## Tip 1. Don’t be afraid to look stupid

You are already very smart (OF COURSE YOU ARE if you are reading this and especially if you subscribed to my E-mail list to receive this type of content 😉). Starting from this moment, you should STOP worrying about how you may look if you ask (e.g., in the classroom) a question that may sounds ‘silly’. I do not encourage you to become a ‘douchebag’ and start annoying people with constant argumentation and unnecessary questions, but I advise you to let go of the feeling of being ‘not smart enough’ from within you. Once you do that, learning becomes easy. Interactions in the classroom become enjoyable. Yes, it will still require a lot of work to accomplish your goals and to understand complicated subjects but the foundation is there. This simple understanding – of the fact that you are smart enough to comprehend everything we know so far in physics or chemistry (or, in general, in science) given enough time and dedication – will set you up to a very good mental platform to accomplish whatever you desire.

…you are SMART ENOUGH to comprehend EVERYTHING we know so far in physics or chemistry (or, in general, in SCIENCE) given enough TIME and DEDICATION…

Once you have let this fear of looking stupid go – keep working. Always challenge yourself to do interdisciplinary learning and collaborate with people of different opinions. For example, read papers on things that you don’t know and pay attention to connections that arise in different branches of science. Also – don’t be afraid to fail (more about it later). Bridging the gap between disciplines is not easy but it will definitely develop your brain further. In fact, science has no borders, there is no physics or chemistry in nature – these are simply words, a product of our imagination. However, nature can be understood using logic and common sense and by practicing ‘good thinking skills’.

## Tip 2. Aim for the top but not for the perfection

I learned this from James Watson, a man who discovered DNA (or even stole this discovery from Rosalind Franklin 🙉, this does not matter as long as I talk about his ideas and not his personality). He said: “Never work to become number ten – work to become number one. But this way even if you end up 2nd – it’s a still great achievement!”. This concept resonates with me. Working to become number one in whatever you do is a great way of being THAT BEST best version of yourself. It is also important to work on your subconscious beliefs (more about it later) and rewriting bad programming. Your subconscious (also often called reptilian) brain remembers/learns from seeing/hearing repetitive messages and this is why things like affirmations work – you program yourself toward positivity and accomplishment.

We all can do USEFUL things for the WORLD and useful things for OURSELVES at the SAME TIME!

I personally struggle with trying to be perfect and this is how I procrastinate. I start thinking that what I am doing is not the best version of it and everything can be improved. It is not yet ready to be shown to the World… BAD IDEA! Show it to the World as long as it is more or less presentable! The solution is simple – set up deadlines and finish things at whatever cost. I am happy to say that at the digital age, this problem can be solved in many creative ways. Take, for example, this blog. I decided to write it not only to help you and give some advise but also to push myself toward writing. We all can do useful things for the World and useful things for ourselves at the same time! Stop procrastinating, just start doing what you always wanted to do no matter how ugly your ‘product’ may look like at the beginning. Aim for the top but not for the perfection!

## Tip 3. Go toward uncomfortable

If you feel too comfortable, chances are  – you are not growing anymore… Feeling uncomfortable is GOOD and you need to embrace it. I came from Russia to Tennessee, spend there 2 years, then came to the Bay Area for 3 years and I going to Germany in a few months. Not only do I make my personal life uncomfortable – I make it uncomfortable everywhere – language, documents, predictability 🙉! I actually don’t think this type of life is suited for everyone and even do not encourage you to embrace this view. But I do think that feeling uncomfortable MEANS moving toward revealing your full potential and shows the direction of maximal personal growth.

Life is not a zero-sum game! Everyone wins from the scientific progress and collaborations that have solid foundations, i.e., mutual benefit and looking for truth.

Going toward uncomfortable will undoubtedly lead you to interact/collaborate with people you disagree with. This, in turn, will open your mind to more opportunities for growth since you will learn things from many angles and points of view. By interacting with people you will also learn that life is not a zero-sum game! Everyone wins from the scientific progress and collaborations that have solid foundations, i.e., mutual benefit and looking for truth.

How do I stay on top of the game? How do I learn? What do I do every day? Subscribe to my E-mail list to get updates and learn about new products! Let’s crunch the granite of science* together!

*Crunch the granite of science is a good old Russian phrase meaning hard studying

## Magnetic resonance without magnets: explained

Have you ever done MRI? If yes, you probably remember, it is not the most pleasant experience. MRI is claustrophobic, loud, and takes a long time. The main reason for these problems — high magnetic fields. Would it be cool to avoid them? Why can’t we simply do MRI without magnetic fields?

It turns out, we can do it though it is not that simple…

To understand why high magnetic fields are needed to obtain magnetic resonance images, we need to understand the principles of signal detection and the concept of polarization.

Some atomic nuclei possess a property called spin and, therefore, produce magnetic fields. These nuclei can simply be visualized as tiny magnets (magnetic dipoles) swirling in space as their hosts — molecules — move, rotate or vibrate depending on the physical state of the chemical system they comprise (solid, liquid or gas).

In the absence of external fields, nuclear spin orientations are random:

By placing the spins in high magnetic fields, one can align them in the same direction, creating “polarization”:

The level to which spins are polarized in the picture above is extremely exaggerated. In reality, even in the very high magnetic fields of modern magnetic resonance spectrometers and imaging scanners (thousands of times higher than the Earth’s magnetic field), nuclear spin polarization is only a fraction of percent. Complete (100%) polarization is also possible. However, instead of placing spins in high fields, it is practically more feasible to use a different approach. Physicists and chemists came up with several creative techniques to create extremely high polarization or hyperpolarization. Techniques based on chemical reactions (such as parahydrogen-induced polarization) are my favorite ones since they don’t require magnetic fields at all (in reality, polarization in such techniques can still be magnetic-field-dependent but the requirements are very modest).

Now about detection. Nuclear magnetism can be detected in several ways. I will talk about two ways and both of them are named after a brilliant physicist Michael Faraday.

The first detection technique is the so-called inductive detection. If spins are polarized and brought to the magnetic field perpendicular to the polarization axis, collective nuclear magnetization will start oscillating about the field axis. This phenomenon is called Larmor precession and it is a general result of classical physics (no quantum mechanics is necessary to explain it but quantum mechanics brings more fun). Oscillating magnetization can be picked up by a coil (solenoid) and a voltage across the coil terminals (electromotive force) will be generated according to Faraday’s law of induction:

The problem is that it is really hard to construct magnets that produce high magnetic fields. Moreover, these fields need to be very uniform to be suitable for magnetic resonance purposes. This is why bores of MRI scanners are usually small – this way engineers achieve higher magnetic field homogeneity over the active volume.

The conventional logic of MRI engineers is straightforward: by using higher magnetic fields (1) we achieve higher nuclear spin polarization (indeed, polarization scales linearly with the applied field B0) and (2) we increase sensitivity of the detection (the voltage generated in the coil by Faraday’s law is linearly proportional to the oscillation frequency which, in turn, proportional to B0). Therefore, conventional MRI signal scales as a square of the magnetic field. Higher the field is — bigger the magnet should be, and we already reached the limits of our engineering capabilities to make the highest magnetic fields that are stable and uniform.

Now imagine that we already have high polarization produced without magnetic fields, for example, via chemical reactions mentioned above. Therefore, the signal is only linearly proportional to the magnetic field strength and even low magnetic fields can be used to produce high-quality images.

Recently my students and I played with MRI at the Earth’s magnetic field (compare 50 micro-Tesla vs. several Tesla of conventional MRI scanners). In our experiments, we simply bubbled a gas through a solution containing the required ingredients and picked up the signal by a coil:

The gas that we used is parahydrogen (para-H2) and the enhanced nuclear polarization in solution is the result of Signal Amplification By Reversible Exchange (SABRE) effect. This effect is a remarkable consequence of the interplay between chemical kinetics and nuclear spin dynamics. Unfortunately, explaining it here, in this post, would require many more words and even some math 🙂 But the main point is simple: bubbling the gas through the solution results in high nuclear polarization and, therefore, high MRI contrast. Without bubbling the gas, magnetic nuclei are oriented randomly and the signal is too low to be detected.

This idea of avoiding magnetic fields can be extended even further. Indeed, if we don’t need a magnetic field to generate polarization, can we detect nuclear spin signals completely without magnets? This somewhat weird idea (magnetic resonance without magnets) is, in fact, one of the most outstanding achievements in magnetic resonance of the last decade. It was pioneered by chemists and physicists from UC Berkeley (laboratories of Alex Pines and Dmitry Budker).

It turns out that very weak magnetic signals can be detected by atomic magnetometers. These magnetometers use vapor cells, glass containers filled with the vapor of alkali metal. Atoms of alkali metals have unpaired valence electrons. Since electrons are tiny magnets in the same way as their nuclear brothers, they can also be polarized, this time by lasers. Properties of a laser beam passing through such polarized “electronic gas” can be modulated if electrons are subjected to additional magnetic fields. This is called the Faraday effect and it is a second way of detecting magnetic resonance signals. In a nutshell, electrons “feel” the magnetic fields around them in a very sensitive way, even if these fields are generated by nuclear spins from a sample placed on top of a vapor cell:

The end result of this signal detection scheme is the same as before – the voltage is generated and picked up, this time by a photodetector. If magnetic fields coming from the sample are time-dependent, the voltage is time-dependent as well and it can be converted into a spectrum containing useful chemical information about the sample.

You might wonder where this all can be applied? Well, it is worth mentioning Faraday here again:

I personally feel that MRI without magnets is not only possible but necessary. However, it will obviously not replace the conventional approach but will rather complement it. One may imagine sensitive magnetometers and Earth’s-field MRI applied to study chemicals at a large scale, to investigate processes taking place inside big industrial chemical reactors. Indeed, the Earth is the best magnet for these purposes – it is extremely homogeneous on the scale that we need. Nullifying magnetic fields (to produce zero field) is another option – remarkably, the sensitivity of atomic magnetometers is maximized at the near-zero-field conditions. It is hard to predict the direction that future will take but one thing is clear – magnetic resonance is entering a new era. So you better stay tuned! 😉

https://chemrxiv.org/articles/Zero-Field_Nuclear_Magnetic_Resonance_of_Chemically_Exchanging_Systems/7658372

https://aip.scitation.org/doi/abs/10.1063/1.5003347

https://www.nature.com/articles/nphys1986

https://onlinelibrary.wiley.com/doi/abs/10.1002/cphc.201402607

https://pubs.acs.org/doi/abs/10.1021/ac501638p

https://www.sciencedirect.com/science/article/abs/pii/S1090780717301659

## We are, simply, chemical reactions

I have recently read this article and it was well discussed how scientists keep discovering new interesting and important facts about our gastrointestinal tract and its effect on our wellbeing (including decision making and brain function).

For example, it has been shown that if people eat more galactooligosaccharide, the fraction of bacteria Lactobacillus and Bifidobacteria in the gut increases among all other strains (because metabolism of these bacteria takes advantage of the excess of this chemical, a known prebiotic). At the same time, these particular strains of bacteria have been shown to produce certain neurotransmitters — chemicals that participate in our brain functioning (because neurotransmitters are responsible for the transmission of electrical signals between neurons). It is indeed possible that by eating certain types of food you can overproduce certain neurotransmitters and, therefore, influence your brain functioning — through bacteria in the gut (Figure 1).

Figure 1. Feeding healthy volunteers with galactooligosaccharide resulted in the increased population of Lactobacillus and Bifidobacteria in the gut which, in turn, resulted in overproduction of neurotransmitters that affect anxiety, including one called brain-derived neurotrophic factor [1].

What is even cooler, some bacteria have shown to affect people’s mood (possibly, by increasing production of “happiness hormones”, in other words, chemicals responsible for our social behavior). This is reasonable because happy people are more social which leads to a big evolutionary advance for these bacteria: they would obviously tend to spread better between social humans than between loners. Interesting, isn’t it?

Let’s now think about it in an evolutionary context. Do bacteria in the gut understand that they change the social behavior of their hosts? The answer is – NO. They not only don’t know anything about social behavior, but they also don’t know that they have a host and even that they exist! Bacteria are simply self-sustaining chemical reactions capable of changing (mutating) their chemical dynamics. It is not that bacteria have goals to survive, they simply occur. One random mutation in their genome led to the overexpression of a random chemical which, by a myriad of other complicated chemical transformations led to the increase of a random neurotransmitter which, by accident, tended to affect social behavior of their hosts. Now, the bacteria have started to spread faster and still spread “happily” because these chemical dynamics help them to exist or, simply, to occur.

We, humans, are chemical reactions too. All hopes and dreams in our brains are interactions between atoms, molecules and their collections. We just tend to occur because it is evolutionary logical. Our mood is chemistry too: serotonin is happiness, dopamine is pleasure, noradrenaline is concentration (Figure 2).

So, if all of this is chemistry, then how to study this? Are there techniques that would allow us to investigate gut microbiome and its effect on the brain non-invasively and in real time?

I believe the answer is yes. Non-invasive techniques like NMR and MRI will soon be able to help to answer important questions about gut metabolism with hyperpolarization being one of the main tools to achieve this. The main challenge – fast decay of polarization – will be overcome by using nuclear states that can preserve their “memory” on a timescale of hours. Remarkably, there are already reports on the long-lived hyperpolarized nuclear spin states [2-4]! Long-live the gut! 😉

[1] “When Gut Bacteria Change Brain Function” bDavid Kohn.

## Young padawans mentoring, you seek: How I did research with 10 undergraduate students

Doing research is a lot of fun! 🙂 You can do things that no one has ever done before. It is like fulfilling your childish curiosities by playing around with nature, unraveling its mysterious principles, and sometimes finding useful applications for things that were previously considered to be purely fundamental. With time your experience grows – you finish your Ph.D., and at some point, you realize that you can hardly find time to check all of your ideas alone. Through this experience, I understood that I definitely need support. The support of undergraduate students! 🙂

In this post, I would like to share some thoughts and realizations I learned from working with undergrads. While reading, try to focus on what could be learned from my experience and not on my particular situation. Most likely, a lot of the things I describe cannot be applied to every postdoc or graduate student. However, I believe that experience I have obtained can be extremely valuable for other Jedi masters looking to mentor their padawans!

Take-home messages:

• Undergraduate students can be extremely motivated and capable of solving complex problems
• A mentor needs to take into account different personalities when working with undergraduates and assign tasks based on this
• Working in groups can be fun but can diminish the sense of individual accomplishment
• Undergraduate students are willing to learn (even if it takes more time to accomplish their goals)
• Focus. Having one or two motivated students can be better than having a big group of unmotivated individuals
• Undergrads are not small graduate students: they have a limited schedule and, usually, need step-by-step instructions to successfully complete tasks

## My journey of mentoring 10 undergraduate students

“Always two there are, no more, no less. A master and apprentice.”

In October 2016, I was invited to work at the Pines Lab. It is hard to explain how excited I was! When I learned that I had the privilege of working under Alex Pines – an absolute legend, mentor, and leader in the field of magnetic resonance – I was over the moon. I was also thrilled by the atmosphere of UC Berkeley, where the concentration of IQ per square meter is mind-blowing. Although there were a lot of advantages related to my new position, I was also faced with some challenges in the new lab. One of which was the different dynamics amongst my lab associates. In previous labs, the associates consisted primarily of graduate students and postdocs. However, in Pines Lab, we have a different approach. As a well-accomplished scientist, Alex now believes that funding is best spent on postdocs and therefore, only a few of us are now working in the lab. However, we can’t accomplish everything alone and needed to reach out to others for help. Thankfully,  UC Berkeley provides a win-win solution for this challenge: postdocs are open to mentoring students and the campus is full of bright and motivated undergrads eager to do research!

I started a quest for my Jedi padawans by sending an E-mail to the chemical engineering undergraduate academic advisor requesting to advertise “the opening” for summer positions in the Pines Lab. Maybe my ad was just too good to refuse, or the UC Berkley students were absolutely eager for work, but in only two days I received more than thirty (thirty!) E-mails from students who were willing to work in the Lab! The hardest part was choosing only a small fraction of them.  Long story short, this is how I ended up having 10 students… Yes, believe me, I could not take any less as they were all extremely motivated, knowledgeable, and willing to learn more at the same time! This being said, be sure that you take the right amount of students required for the project that you have in mind.

Today, after more than a year of working with my students, teaching and mentoring them, finishing papers together and working on new ones, I feel happy and satisfied with my selection and decisions. My experience allowed me not only to learn a lot about how undergraduate students think and about what motivates them and what can boost their productivity, but it also allowed me to find the mentoring/teaching style that I feel most comfortable with.

## The best students

“Truly wonderful, the mind of a child is.”

I found that, surprisingly, resumes of undergrads do not always correlate directly with their performance in the lab. However, it does not mean that you should completely disregard their scholarly performance when you are looking for them. The successful student should (1) have enough knowledge to be able to quickly grasp the ideas and concepts you work with but at the same time (2) have enough curiosity to learn more about things they don’t know about. Unfortunately, NMR as a research topic requires at least a basic understanding of quantum mechanics, therefore making it an overall challenging subject for freshmen and sophomore students (however, there could be exceptions!). Therefore, in my opinion, the best way to find a prospective student is to talk to them in person, ask about their interests/hobbies, what type of work they like and what they don’t like. From my conversations with potential undergrads, I realized that those who like a more structured way of working and need a lot of supervising would not be the best match for me.

I found that for me, the most important students’ qualities are:

• Ability to work independently
• Responsibility
• Personality matching (see below)

The last point, personality matching, is the main lesson I gained from my experience. Personality matters much more than anything else in research with undergrads, and I feel that this can be even truer for higher levels of graduate school in which professor-student interactions play a crucial role in a lab’s success!

## Personality matters

“Good relations with the Wookiees, I have.”

Have you ever heard about the Myers-Briggs 16 personality types? If not, you should learn about it as soon as possible. Basically, this “theory” allows you to rationalize your own behavior and better understand the motivations of different types of people. It also explains why some individuals are naturally stronger in certain tasks and others are better at different ones. Therefore, when managing undergraduate research, you can always find a fulfilling and interesting problem for a student if you identify his/her personality type and look at things creatively.

Find the right problem for the right people. If you think the people are not right for the problems you post, chances are, it is not the right problem for the people you have.

For example, I suggested two of my students work on the project of using Earth-field MRI combined with SABRE hyperpolarization. It soon became very clear to me that one of the students was more interested in studying the basics of MRI and the way the Earth-field imaging instrument works than the other.  At one point I caught myself thinking that the second student was just lazier than the first one and much less motivated about going to the lab in general… However, purely by accident, I learned that the second student was interested in 3D modeling. We had another project in the lab that required machining a chemical reactor. Therefore, I asked him to make a 3D modeling of the reactor and found that he loved it. Ever since then, he was an absolutely different person – working hard and passionately while finishing the task much earlier than I expected. It was not the laziness of the student but rather my misunderstanding of his interests that did not allow him to be as motivated as he can be at the beginning of our work.

Take-home message – find the right problem for the right people. If you think the people are not right for the problems you post, chances are, it is not the right problem for the people you have. This is especially true for doing research with undergrads: they are volunteering their time to help you and it is your fault if are not motivated!

## Finding the right project

“Already know you that which you need.”

I found that it is very important for students to work on problems that have clearly posted goals. For example, when choosing between two projects, one of which is very cool but relatively abstract and the second one which is less intellectually complicated but more practical, students often choose the second one. They want to see the immediate outcome of their research even though it is sometimes hard to get enough results given the limits of their residence in the lab. The most compelling project for undergrads is one that to them, makes an observable difference in the world!

The most compelling project for undergrads is one that to them, makes an observable difference in the world!

One of these application-oriented projects was the building of the para-H2-based polarizer. I explained to my students that I want to make a device that can automatically produce boluses of hyperpolarized liquids (for example, aqueous solutions of 13C-hyperpolarized metabolites such as pyruvate or lactate). Once produced, these boluses can be injected into animals and their metabolism can be monitored in vivo using NMR/MRI.

Nick and Lucia conducting SABRE experiments.

This idea is not new and many researchers work on different aspects of this problem. However, one of the biggest issues preventing the widespread applicability of para-H2-based techniques is the presence of platinum-group metals in solutions with hyperpolarized molecules. Obviously, injecting even trace quantities of the metals in vivo should be avoided.

Therefore, we decided to focus on this part of the problem and at the same time started building para-H2-based polarizer. Two of my students were working on the testing of different scavengers’ performance by means of inductively coupled plasma atomic emission spectroscopy (ICP-AES) and three of the students were helping to build a so-called “hyper-cart”, a transportable cart containing all of the components necessary for producing hyperpolarized compounds.

Elizabeth, Lucia, and Nevin are working on building the parahydrogen “hyper-cart”.

After performing a lot of tests, we were able to identify the nature of two commercially available metal scavengers that can efficiently and very quickly clear the hyperpolarized solutions from the trace metal quantities. Since the result was important, we decided to submit a paper describing the metal scavenging process to the Journal of Physical Chemistry Letters and it was successfully published there. It was a pleasure to see the students’ motivation when, even during their midterm exams, they were still able to find time to stay at work late to finish the figures and tables for the paper! Overall, despite challenges, this was a good research project for undergrads: a simple and clear idea resulting in a measurable advancement to the field.

## Managing vs. Mentoring

“Always pass on what you have learned.”

One of the biggest realizations that occurred to me while working with my students was understanding of the difference between managing and mentoring.

Managing is about organizing, making plans, setting up goals, splitting them into micro-goals, setting up the deadlines and so on. In other words, all the stuff that I hate… Mentoring, on the other hand, is giving padawans the opportunity to learn by doing their own work, providing resources and support, discussing the best ways to achieve the goals (as opposed to stating them), referring to the resources with useful information and troubleshooting when things don’t work. Through my experience, I found that mentoring is something I truly enjoy. You can clearly see the growth of students who are willing to learn!

Let’s take the previous example of the para-H2 cart. One of my chemical engineering students, Vincent, told me during his interview that he likes automation and programming. Since we needed automatically actuated valves to run gases and liquids, I suggested that he build an Arduino-based setup to control the valves. I did not have the background to teach him everything about Arduino, but I knew where he could find information about how to do it. Eventually, he created a very good setup that was extremely helpful. Check out this video created by him explaining all the components of his setup:

This is why personality matching is important. Some students would require more of a managing advisor while my approach leaned towards mentoring and allowing the student to figure out the details by himself. Not everyone would be able to do what Vincent has done, but his desire to learn, coupled with his desire to make a significant contribution to the project led to a successful outcome.

## Journal Clubs

“Powerful you have become, the dark side I sense in you.”

I also found another valuable tool for mentoring students – Journal Clubs. I first learned about this type of meetings looking at Mark Does’ lab at the Vanderbilt Institute of Imaging Science. In Mark’s lab, students and postdocs meet once a week (in addition to weekly group meetings) and discuss a paper they want to learn more about. Mark does not even show up there – it is the students’ task to meet and study together.

My journal clubs were slightly different than the ones at Vanderbilt. Since my students are only undergrads, letting them learn completely by themselves would not be the most productive option. Therefore, a schedule of students was created before each semester. For each journal club, one of the students had to choose a paper of interest. Ideally, it should be a paper related to our research but this was not necessary. After choosing a topic of interest, a student would send his paper for the rest of the group in advance to read it and prepare for the discussion. When arriving at the journal club, the student would first make a short presentation about the paper and then discuss it with the rest of the group. I would then show up after 30-40 mins and work together to answer any questions the students had. We also discussed NMR-related and general scientific questions after I arrived.

Based on the students’ reviews, they liked the journal clubs a lot. It helps them understand the research process and how to work with each other without a lot of guidance. I originally realized that students were not as eager to ask each other questions while I was in the room. This is why I decided to let them have 30-40 minutes on their own: this way I always entered a room full of discussion and exploration. They didn’t need my micro-management and ultimately worked together to facilitate ideas and find the answers to unknown questions.

## Conclusions

“Do or do not. There is no try.”

Here is the biggest realization. Undergraduate students are not small graduate students. While graduate students have the time and ability to focus on projects, undergraduates have other responsibilities to classes, college activities, and simply navigating their busy university life. Therefore, they need to be treated differently than graduate students. Although optimism is great, do not be discouraged if you undergraduate students have other time commitments and responsibilities that interfere with their projects. They are not smaller, younger graduate students but rather have unique requirements and standards of learning all of their own.

I want to express gratitude and say thanks to all undergraduate students I had a pleasure to mentor: Patricia Buenbrazo, Nevin Widarman, Hubert Situ, James (Xingyang) Li, Dario Gelevski, Vincent Stevenson, Lucia Ke, Elizabeth Chyn, Nick (Hao) Zhang, Hyun Park, Sean Littleton. Some of them have already graduated, some of them are still working on exciting projects and I hope to have a chance to mentor many more! 🙂 I also want to say a lot of thanks to Jessica Andrews who helped me to write this post and suggested the Master Yoda quotes idea. Check out her website: she writes about TV and movies and she is very passionate about it!

## Dipole-dipole interactions in NMR: explained

Interactions between spins are fundamental for understanding magnetic resonance. One of the most important ones is the magnetic dipole-dipole interaction. Spins act as tiny magnets, thus, they can interact with each other directly through space, pretty much the same way as classical magnetic dipoles (Figure 1). In NMR, dipole-dipole interactions very often determine lineshapes of solid-state samples and relaxation rates of nuclei in the liquid state.

In many NMR textbooks, you can find the following expression for dipole-dipole (DD) Hamiltonian between two spins 1 and 2:

$\hat{{H}}_{\rm DD} = d_{12} \left( 3 \hat{I}_{1z} \hat{I}_{2z} - \hat{\mathbf{I}}_1 \cdot \hat{\mathbf{I}}_2 \right)$

where $d_{12} = - \displaystyle\frac{\mu_0}{4 \pi} \displaystyle\frac{\gamma_1 \gamma_2 \hbar}{r^3} \frac{\left( 3 \cos^2{\theta} - 1 \right)}{2}$, $\gamma_1$ and $\gamma_2$ are gyromagnetic ratios of the spins, $r$ is the distance between them.  Meaning of the angle $\theta$ can be seen from the Figure 2. But how was this expression derived?

In physics, I rarely struggled with imagining abstract things and concepts, but rather, I was often lazy to do math thoroughly and derive equations from the beginning to the end. That’s why I decided to write here a full derivation, from the beginning to the end, for the Hamiltonian of interacting nuclear spins. We will start from a classical expression of the magnetic field produced by the dipole and finish by the analysis of a truncated dipole-dipole Hamiltonian. Usually, you don’t see such a full derivation in textbooks. Maybe, this is because textbooks have limited space… Luckily, here we do not have such limitations, thus, we can have some fun here! Let’s go then! 🙂

Classical equation describing the magnetic field $\vec{\boldsymbol{B}}_{\rm dip} (\vec{\boldsymbol{r}})$ produced by a magnetic dipole moment $\vec{\boldsymbol{\mu}}$ is

$\vec{\boldsymbol{B}}_{\rm dip} (\vec{\boldsymbol{r}}) = \displaystyle\frac{\mu_0}{4 \pi r^3} \left( 3 \left( \vec{\boldsymbol{\mu}} \cdot \hat{\boldsymbol{r}} \right) \hat{\boldsymbol{r}} - \vec{\boldsymbol{\mu}} \right)$

where $\hat{\boldsymbol{r}} = \displaystyle\frac{\vec{\boldsymbol{r}}}{|\vec{\boldsymbol{r}}|}$ is a unit vector. It is easy to show that $\left( \vec{\boldsymbol{\mu}} \cdot \vec{\boldsymbol{r}} \right) \vec{\boldsymbol{r}} = \left( \vec{\boldsymbol{r}} \cdot \vec{\boldsymbol{r}}^{\: \intercal} \right) \vec{\boldsymbol{\mu}}$.

Indeed,

$\left( \vec{\boldsymbol{\mu}} \cdot \vec{\boldsymbol{r}} \right) \vec{\boldsymbol{r}} = \left( \mu_x r_x + \mu_y r_y + \mu_z r_z \right) \cdot \begin{pmatrix} r_x \\ r_y \\ r_z \end{pmatrix} = \begin{pmatrix} \mu_{x} r_{x} r_{x} + \mu_{y} r_{y} r_{x} + \mu_{z} r_{z} r_{x} \\ \mu_{x} r_{x} r_{y} + \mu_{y} r_{y} r_{y} + \mu_{z} r_{z} r_{y} \\ \mu_{x} r_{x} r_{z} + \mu_{y} r_{y} r_{z} + \mu_{z} r_{z} r_{z} \end{pmatrix}$

which is the same as

$\left( \vec{\boldsymbol{r}} \cdot \vec{\boldsymbol{r}}^{\: \intercal} \right) \vec{\boldsymbol{\mu}} = \begin{pmatrix} r_{x} r_{x} & r_{x} r_{y} & r_{x} r_{z} \\ r_{y} r_{x} & r_{y} r_{y} & r_{y} r_{z} \\ r_{z} r_{x} & r_{z} r_{y} & r_{z} r_{z} \end{pmatrix} \cdot \begin{pmatrix} \mu_x \\ \mu_y \\ \mu_z \end{pmatrix} = \begin{pmatrix} r_{x} r_{x} \mu_{x} + r_{x} r_{y} \mu_{y} + r_{x} r_{z} \mu_{z} \\ r_{y} r_{x} \mu_{x} + r_{y} r_{y} \mu_{y} + r_{y} r_{z} \mu_{z} \\ r_{z} r_{x} \mu_{x} + r_{z} r_{y} \mu_{y} + r_{z} r_{z} \mu_{z} \end{pmatrix}$

So, we write the magnetic field produced by a magnetic dipole $\vec{\boldsymbol{\mu}}_2$ as

$\vec{\boldsymbol{B}}_{\mu_2} = \displaystyle\frac{\mu_0}{4 \pi r^3} \left( 3 \left( \hat{\boldsymbol{r}} \cdot \hat{\boldsymbol{r}}^{\: \intercal} \right) \vec{\boldsymbol{\mu}}_2 - \vec{\boldsymbol{\mu}}_2 \right)$

The energy of a magnetic dipole $\vec{\boldsymbol{\mu}}_1$ interacting with the magnetic field $\vec{\boldsymbol{B}}_{\mu_2}$ produced by a magnetic dipole $\vec{\boldsymbol{\mu}}_2$ (dipole-dipole interaction) is therefore

$E_{\rm DD} = - \left( \vec{\boldsymbol{\mu}}_1 \cdot \vec{\boldsymbol{B}}_{\mu_2} \right) = -\displaystyle\frac{\mu_0}{4 \pi r^3} \left( 3 \cdot \vec{\boldsymbol{\mu}}_1 \left( \hat{\boldsymbol{r}} \cdot \hat{\boldsymbol{r}}^{\: \intercal} \right) \vec{\boldsymbol{\mu}}_2 - \left( \vec{\boldsymbol{\mu}}_1 \cdot \vec{\boldsymbol{\mu}}_2 \right) \right)$

The transition from classical to quantum mechanics is realized by substituting the measurable quantities by corresponding quantum mechanical operators:

$E_{\rm DD} \rightarrow \hat{H}_{\rm DD} \quad \vec{\boldsymbol{\mu}}_1 \rightarrow \gamma_1 \hbar \hat{\mathbf{I}}_1\quad \vec{\boldsymbol{\mu}}_2 \rightarrow \gamma_2 \hbar \hat{\mathbf{I}}_2$

$\label{Eq_Hdd} \hat{H}_{\rm DD} = - \displaystyle\frac{\mu_0}{4 \pi } \displaystyle\frac{\gamma_1 \gamma_1 \hbar}{r^3} \left( 3 \cdot \hat{\mathbf{I}}_1 \left( \hat{\boldsymbol{r}} \cdot \hat{\boldsymbol{r}}^{\: \intercal} \right) \hat{\mathbf{I}}_2 - \left( \hat{\mathbf{I}}_1 \cdot \hat{\mathbf{I}}_2 \right) \right) = b_{12} \hat{\mathbf{I}}_1 \hat{\mathbf{D}} \hat{\mathbf{I}}_2$

here $b_{12}$ is a factor which depends only on the types of the nuclear spins and the distance between them, and a tensor of dipole-dipole interactions contains information about the mutual orientation of two spins:

$\hat{\mathbf{D}} = 3 \cdot \left( \hat{\boldsymbol{r}} \cdot \hat{\boldsymbol{r}}^{\: \intercal} \right) - \hat{1}$

here $\hat{1}$ is a unit matrix. Note that we write Hamiltonian $\hat{H}_{\rm DD}$ in units of [rad/s], that is why one $\hbar$ is missing. In spherical coordinates:

$\hat{\boldsymbol{r}} = \begin{pmatrix} \sin{\theta} \cos{\phi} \\ \sin{\theta} \sin{\phi} \\ \cos{\theta} \end{pmatrix}$

Therefore,

$\hat{\mathbf{D}} = \begin{pmatrix} 3 \sin^2{\theta} \cos^2{\phi} - 1 & 3 \sin^2{\theta} \cos{\phi} \sin{\phi} & 3 \sin{\theta} \cos{\theta} \cos{\phi} \\ 3 \sin^2{\theta} \cos{\phi} \sin{\phi} & 3 \sin^2{\theta} \sin^2{\phi} - 1 & 3 \sin{\theta} \cos{\theta} \sin{\phi} \\ 3 \sin{\theta} \cos{\theta} \cos{\phi} & 3 \sin{\theta} \cos{\theta} \sin{\phi} & 3 \cos^2{\theta} - 1 \end{pmatrix}$

Looks good, doesn’t it? Now, let’s evaluate the product $\hat{\mathbf{I}}_1 \hat{\mathbf{D}} \hat{\mathbf{I}}_2$:

$\hat{\mathbf{I}}_1 \hat{\mathbf{D}} \hat{\mathbf{I}}_2 = \\ \begin{pmatrix} \hat{I}_{1x} & \hat{I}_{1y} & \hat{I}_{1z} \end{pmatrix} \begin{pmatrix} 3 \sin^2{\theta} \cos^2{\phi} - 1 & 3 \sin^2{\theta} \cos{\phi} \sin{\phi} & 3 \sin{\theta} \cos{\theta} \cos{\phi} \\ 3 \sin^2{\theta} \cos{\phi} \sin{\phi} & 3 \sin^2{\theta} \sin^2{\phi} - 1 & 3 \sin{\theta} \cos{\theta} \sin{\phi} \\ 3 \sin{\theta} \cos{\theta} \cos{\phi} & 3 \sin{\theta} \cos{\theta} \sin{\phi} & 3 \cos^2{\theta} - 1 \end{pmatrix} \begin{pmatrix} \hat{I}_{2x} \\ \hat{I}_{2y} \\ \hat{I}_{2z} \end{pmatrix} =$

$\begin{pmatrix} \hat{I}_{1x} & \hat{I}_{1y} & \hat{I}_{1z} \end{pmatrix} \begin{pmatrix} \hat{I}_{2x} \left( 3 \sin^2{\theta} \cos^2{\phi} - 1 \right) + \hat{I}_{2y} \left( 3 \sin^2{\theta} \cos{\phi} \sin{\phi} \right) + \hat{I}_{2z} \left( 3 \sin{\theta} \cos{\theta} \cos{\phi} \right) \\ \hat{I}_{2x} \left( 3 \sin^2{\theta} \cos{\phi} \sin{\phi} \right) + \hat{I}_{2y} \left( 3 \sin^2{\theta} \sin^2{\phi} - 1 \right) + \hat{I}_{2z} \left( 3 \sin{\theta} \cos{\theta} \sin{\phi} \right) \\ \hat{I}_{2x} \left( 3 \sin{\theta} \cos{\theta} \cos{\phi} \right) + \hat{I}_{2y} \left( 3 \sin{\theta} \cos{\theta} \sin{\phi} \right) + \hat{I}_{2z} \left( 3 \cos^2{\theta} - 1 \right) \end{pmatrix} =$

$= \hat{I}_{1x} \hat{I}_{2x} \left( 3 \sin^2{\theta} \cos^2{\phi} - 1 \right) + \hat{I}_{1x} \hat{I}_{2y} \left( 3 \sin^2{\theta} \cos{\phi} \sin{\phi} \right) + \hat{I}_{1x} \hat{I}_{2z} \left( 3 \sin{\theta} \cos{\theta} \cos{\phi} \right) + + \hat{I}_{1y} \hat{I}_{2x} \left( 3 \sin^2{\theta} \cos{\phi} \sin{\phi} \right) + \hat{I}_{1y} \hat{I}_{2y} \left( 3 \sin^2{\theta} \sin^2{\phi} - 1 \right) + \hat{I}_{1y} \hat{I}_{2z} \left( 3 \sin{\theta} \cos{\theta} \sin{\phi} \right) + + \hat{I}_{1z} \hat{I}_{2x} \left( 3 \sin{\theta} \cos{\theta} \cos{\phi} \right) + \hat{I}_{1z} \hat{I}_{2y} \left( 3 \sin{\theta} \cos{\theta} \sin{\phi} \right) + \hat{I}_{1z} \hat{I}_{2z} \left( 3 \cos^2{\theta} - 1 \right)$

Let’s color terms to make it easier grouping them:

$\hat{I}_{1x} \hat{I}_{2x} \left( 3 \sin^2{\theta} \cos^2{\phi} - 1 \right) +$ $\hat{I}_{1x} \hat{I}_{2y} \left( 3 \sin^2{\theta} \cos{\phi} \sin{\phi} \right) +$ $\hat{I}_{1x} \hat{I}_{2z} \left( 3 \sin{\theta} \cos{\theta} \cos{\phi} \right) +$ $\hat{I}_{1y} \hat{I}_{2x} \left( 3 \sin^2{\theta} \cos{\phi} \sin{\phi} \right) +$ $\hat{I}_{1y} \hat{I}_{2y} \left( 3 \sin^2{\theta} \sin^2{\phi} - 1 \right) +$ $\hat{I}_{1y} \hat{I}_{2z} \left( 3 \sin{\theta} \cos{\theta} \sin{\phi} \right) +$ $\hat{I}_{1z} \hat{I}_{2x} \left( 3 \sin{\theta} \cos{\theta} \cos{\phi} \right) + \hat{I}_{1z} \hat{I}_{2y} \left( 3 \sin{\theta} \cos{\theta} \sin{\phi} \right) +$ $\hat{I}_{1z} \hat{I}_{2z} \left( 3 \cos^2{\theta} - 1 \right)$

Groupling the red terms gives

$\left( \hat{I}_{1x} \hat{I}_{2x} \cos^2{\phi} + \hat{I}_{1y} \hat{I}_{2y} \sin^2{\phi} \right) 3 \sin^2{\theta} - \left( \hat{I}_{1x} \hat{I}_{2x} + \hat{I}_{1y} \hat{I}_{2y} \right)$

Let’s not forget about intrinsic connections of spin angular momentum with raising and lowering operators:

$\hat{I}_{1x} \hat{I}_{2x} = \displaystyle\frac{\left( \hat{I}_{1+} + \hat{I}_{1-} \right)}{2}\displaystyle\frac{\left( \hat{I}_{2+} + \hat{I}_{2-} \right)}{2} = \displaystyle\frac{1}{4} \left( \hat{I}_{1+} \hat{I}_{2+} + \hat{I}_{1+} \hat{I}_{2-} + \hat{I}_{1-} \hat{I}_{2+} + \hat{I}_{1-} \hat{I}_{2-} \right)$

$\hat{I}_{1y} \hat{I}_{2y} = \displaystyle\frac{\left( \hat{I}_{1+} - \hat{I}_{1-} \right)}{2 i}\displaystyle\frac{\left( \hat{I}_{2+} - \hat{I}_{2-} \right)}{2 i} = -\displaystyle\frac{1}{4} \left( \hat{I}_{1+} \hat{I}_{2+} - \hat{I}_{1+} \hat{I}_{2-} - \hat{I}_{1-} \hat{I}_{2+} + \hat{I}_{1-} \hat{I}_{2-} \right)$

Therefore, grouping the red terms gives

$\left( \hat{I}_{1x} \hat{I}_{2x} \cos^2{\phi} + \hat{I}_{1y} \hat{I}_{2y} \sin^2{\phi} \right) 3 \sin^2{\theta} - \left( \hat{I}_{1x} \hat{I}_{2x} + \hat{I}_{1y} \hat{I}_{2y} \right) = \left( \hat{I}_{1+} \hat{I}_{2-} + \hat{I}_{1-} \hat{I}_{2+} \right) \frac{3}{4} \sin^2{\theta} + \left( \hat{I}_{1+} \hat{I}_{2+} + \hat{I}_{1-} \hat{I}_{2-} \right) \frac{3}{4} \sin^2{\theta} \cdot \left( \cos{ 2 \phi} \right) - \frac{1}{2} \left( \hat{I}_{1+} \hat{I}_{2-} + \hat{I}_{1-} \hat{I}_{2+} \right) = \left( \hat{I}_{1+} \hat{I}_{2-} + \hat{I}_{1-} \hat{I}_{2+} \right) \frac{1}{4} \left(1 - 3 \cos^2{\theta} \right) + \left( \hat{I}_{1+} \hat{I}_{2+} + \hat{I}_{1-} \hat{I}_{2-} \right) \frac{3}{4} \sin^2{\theta} \cdot \left( \cos{ 2 \phi} \right)$

Groupling the blue terms gives

$\left( \hat{I}_{1x} \hat{I}_{2y} + \hat{I}_{1y} \hat{I}_{2x} \right) 3 \sin^2{\theta} \cos{\phi} \sin{\phi} = \left( \hat{I}_{1+} \hat{I}_{2+} - \hat{I}_{1-} \hat{I}_{2-} \right)\displaystyle\frac{3}{4} \sin^2{\theta} \cdot \left( - i \sin{2 \phi} \right)$

where we took into consideration that

$\hat{I}_{1x} \hat{I}_{2y} =\displaystyle\frac{\left( \hat{I}_{1+} + \hat{I}_{1-} \right)}{2} \frac{\left( \hat{I}_{2+} - \hat{I}_{2-} \right)}{2 i} = \frac{1}{4 i} \left( \hat{I}_{1+} \hat{I}_{2+} - \hat{I}_{1+} \hat{I}_{2-} + \hat{I}_{1-} \hat{I}_{2+} - \hat{I}_{1-} \hat{I}_{2-} \right)$
$\hat{I}_{1y} \hat{I}_{2x} = \displaystyle\frac{\left( \hat{I}_{1+} - \hat{I}_{1-} \right)}{2 i} \frac{\left( \hat{I}_{2+} + \hat{I}_{2-} \right)}{2} = \frac{1}{4 i} \left( \hat{I}_{1+} \hat{I}_{2+} + \hat{I}_{1+} \hat{I}_{2-} - \hat{I}_{1-} \hat{I}_{2+} - \hat{I}_{1-} \hat{I}_{2-} \right)$

Red and blue terms can be combined nicely to form

$\left( \hat{I}_{1+} \hat{I}_{2-} + \hat{I}_{1-} \hat{I}_{2+} \right) \displaystyle\frac{1}{4} \left(1 - 3 \cos^2{\theta} \right) + \hat{I}_{1+} \hat{I}_{2+} \left( \frac{3}{4} \sin^2{\theta} \cdot e^{- 2 i \phi} \right) + \hat{I}_{1-} \hat{I}_{2-} \left( \frac{3}{4} \sin^2{\theta} \cdot e^{+ 2 i \phi} \right)$

Now let’s focus on purple terms:

$\left( \hat{I}_{1x} \hat{I}_{2z} + \hat{I}_{1z} \hat{I}_{2x} \right) \left( \hat{I}_{1x} \hat{I}_{2z} + \hat{I}_{1z} \hat{I}_{2x} \right) \left( 3 \sin{\theta} \cos{\theta} \cos{\phi} \right) + \left( \hat{I}_{1y} \hat{I}_{2z} + \hat{I}_{1z} \hat{I}_{2y} \right) \left( 3 \sin{\theta} \cos{\theta} \sin{\phi} \right) = \left( \left( \hat{I}_{1+} \hat{I}_{2z} + \hat{I}_{1-} \hat{I}_{2z} + \hat{I}_{1z} \hat{I}_{2+} + \hat{I}_{1z}\hat{I}_{2-} \right) \cos{\phi} \right) \displaystyle\frac{3}{4} \sin{2 \theta} + \left( \left( -i \hat{I}_{1+} \hat{I}_{2z} + i \hat{I}_{1-} \hat{I}_{2z} -i \hat{I}_{1z} \hat{I}_{2+} + i \hat{I}_{1z} \hat{I}_{2-} \right) \sin{\phi} \right) \frac{3}{4} \sin{2 \theta} = \left( \hat{I}_{1+} \hat{I}_{2z} + \hat{I}_{1z} \hat{I}_{2+} \right) \left( \frac{3}{4} \sin{2 \theta} \right) e^{-i \phi} + \left( \hat{I}_{1-} \hat{I}_{2z} + \hat{I}_{1z} \hat{I}_{2-} \right) \left( \frac{3}{4} \sin{2 \theta} \right) e^{+i \phi}$

Overall, we have split our dipolar Hamiltonian into 6 term, so-called “Dipolar Alphabet”:

$\hat{\mathbf{I}}_1 \hat{\mathbf{D}} \hat{\mathbf{I}}_2 = \hat{A} + \hat{B} + \hat{C} + \hat{D} + \hat{E} + \hat{F}$

where

$\hat{A} \quad = \quad \hat{I}_{1z} \hat{I}_{2z} \left( 3 \cos^2{\theta} - 1 \right)$

$\quad\quad \hat{B} \quad = \quad \left( \hat{I}_{1+} \hat{I}_{2-} + \hat{I}_{1-} \hat{I}_{2+} \right) \cdot \displaystyle\frac{\left(1 - 3 \cos^2{\theta} \right)}{4}$

$\quad\quad \hat{C} \quad = \quad \left( \hat{I}_{1+} \hat{I}_{2z} + \hat{I}_{1z} \hat{I}_{2+} \right) \left( \displaystyle\frac{3}{4} \sin{2 \theta} \right) e^{-i \phi}$

$\quad\quad \hat{D} \quad = \quad \left( \hat{I}_{1-} \hat{I}_{2z} + \hat{I}_{1z} \hat{I}_{2-} \right) \left( \displaystyle\frac{3}{4} \sin{2 \theta} \right) e^{+i \phi}$

$\hat{E} \quad = \quad \hat{I}_{1+} \hat{I}_{2+} \left( \displaystyle\frac{3}{4} \sin^2{\theta} \right) e^{- 2 i \phi}$

$\quad\quad \hat{F} \quad = \quad \hat{I}_{1-} \hat{I}_{2-} \left( \displaystyle\frac{3}{4} \sin^2{\theta} \right) e^{+ 2 i \phi}$

To summarize, the Hamiltonian of two interacting spins is a $4 \times 4$ matrix composed of 6 operators. Each of the letters of the dipolar alphabet corresponds to certain matrix elements in the final Hamiltonian (Figure 3).

Without an externally imposed direction in space (for example, in the case of two equivalent spins in zero magnetic field), all of the terms of the dipole-dipole Hamiltonian need to be used for calculating an NMR spectrum. This is because all orientations in space are equivalent. However, in the presence of the external high magnetic field, the Hamiltonian can be simplified via the use of so-called “secular approximation”.

The secular approximation concerns the case where the Hamiltonian is the sum of two terms:

$\hat{H} = \hat{A} + \hat{B}$

where $\displaystyle\hat{A}$ is a “large” operator and $\hat{B}$ is a “small” operator. In our case, $\hat{A}$ can be an operator describing the interaction with the magnetic field (Zeeman Hamiltonian) and $\hat{B}$ is DD Hamiltonian. Eigenstates of the Zeeman Hamiltonian are familiar αααβ, βα, ββGenerally, $\hat{B}$ does not commute with $\hat{A}$, therefore, if written in the eigenbasis of $\hat{A}$, it has finite elements everywhere.

The secular approximation for $\hat{B}$ means that we leave only the blocks that correspond to the eigenvalue structure of the operator $\hat{A}$ (Figure 4) and disregard all other elements.

In general, we can omit a matrix element $b_{nm}$ that is much smaller than

$|b_{mn}| \ll |E_m - E_n|$

For homonuclear case (e.g., two interacting protons), this means that only the first two terms of the dipolar Alphabet will survive:

$\hat{\mathbf{I}}_1 \hat{\mathbf{D}} \hat{\mathbf{I}}_2 = \hat{A} + \hat{B} =$

$= \hat{I}_{1z} \hat{I}_{2z} \left( 3 \cos^2{\theta} - 1 \right) + \left( \hat{I}_{1+} \hat{I}_{2-} + \hat{I}_{1-} \hat{I}_{2+} \right) \cdot \displaystyle\frac{\left(1 - 3 \cos^2{\theta} \right)}{4} =$

$= \hat{I}_{1z} \hat{I}_{2z} \left( 3 \cos^2{\theta} - 1 \right) - \left( \hat{I}_{1x} \hat{I}_{2x} + \hat{I}_{2y} \hat{I}_{2y} \right) \cdot \displaystyle\frac{\left(3 \cos^2{\theta} - 1\right)}{2} =$

$= \displaystyle\frac{\left( 3 \cos^2{\theta} - 1\right)}{2} \cdot \left( 2 \hat{I}_{1z} \hat{I}_{2z} + \hat{I}_{1z} \hat{I}_{2z} - \hat{I}_{1z} \hat{I}_{2z} - \left( \hat{I}_{1x} \hat{I}_{2x} + \hat{I}_{2y} \hat{I}_{2y} \right) \right) =$

$= \displaystyle\frac{\left(3 \cos^2{\theta} - 1\right)}{2} \cdot \left( 3 \hat{I}_{1z} \hat{I}_{2z} - \hat{\mathbf{I}}_1 \cdot \hat{\mathbf{I}}_2 \right)$

Overall, this is how you go from the classical description of the magnetic field of the dipole to the truncated form of the Hamiltonian in the high nagnetic field. In the next post I will show how this Hamiltonian leads to the characteristic lineshape of the NMR line for solids.

## My “Dream Research” Project

If I was asked to identify the most challenging biological question, I would answer immediately. What is the nature of memory and thought? This question always fascinated me as a child. For a long time, I thought only biologists can figure that out. It took me 10 years deeply studying physics and chemistry, becoming a specialist in nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI), to realize that actually now we are close to start answering the question which captivated my childish mind.

With all its complexity, the end result of the genetic machinery is to affect the chemistry of the body. Small molecules, metabolites, serve as fingerprints of what is happening inside us. Studying metabolites is almost like looking at someone’s apartment and coming up with a story of their recent lives: we can make guesses about a lifestyle based on what we see! And the chemistry of thinking is not an exception – our thought processes are accompanied by myriads of chemical transformations, and leftover metabolites can tell us about the process behind them.

Studying metabolites is almost like looking at someone’s apartment and coming up with a story of their recent lives: we can make guesses about a lifestyle based on what we see!

Routinely, metabolites are measured through analytical techniques like NMR and mass spectrometry (MS). But a new astonishing era is emerging. With new sensitivity enhancement techniques (signals can be increased by more than 20,000 times [1-4]), MR imaging will become a new tool to study metabolism in vivo and will move beyond morphology onto a platform to visualize molecules. Being fundamentally a quantum mechanical technique, the full potential of MRI is yet to be discovered.

I see my “dream research” project as the development of a new experimental MRI-NMR/MS platform to study metabolomics of memory and thought in living creatures. By developing novel MRI pulse sequences (which will take into account quantum-mechanical nature of molecules) and by applying state-of-the-art signal enhancement techniques, we will be able to “light up” the regions of the brain to study chemistry in them with an unprecedented level of accuracy. I believe that once all new methodologies available today are combined, it will become possible to create functional MRI for metabolomics – a tool to study instant chemical changes in the brain associated with memory and thinking. This will not only revisit the known biochemical processes at a new quantitative level, it will allow unraveling unexpected secrets of metabolism. And it is not only a fun thing to do — understanding the biochemical reasons for making decisions will bring us much closer to a society in which everyone truly enjoys living.

[1] J. H. Ardenkjær-Larsen et al. Increase in signal-to-noise ratio of >10,000 times in liquid-state NMR. Proc. Nat. Acad. Sci., 2003, 100 (18), 10158-10163.

[2] R. W. Adams et al. Reversible Interactions with parahydrogen Enhance NMR Sensitivity by Polarization Transfer. Science, 2009, 323 (5922), 1708-1711.

[3] D. A. Barskiy et al. Over 20% 15N Hyperpolarization in Under One Minute for Metronidazole, an Antibiotic and Hypoxia Probe. J. Am. Chem. Soc., 2016, 138 (26), 8080–8083.

[4] D. A. Barskiy et al. NMR Hyperpolarization Techniques of Gases. Chem. Eur. J., 2017, 23 (4), 725-751.