Piotr Put and Danila Barskiy demonstrating portable zero-to-ultralow-field NMR spectrometer
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).
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! 😉
Friday evening. While his friends had already met in the Pub on Shattuck Avenue to celebrate a happy hour, UC Berkeley’s Ph.D. student Henry Bryndza was still in the Lab. He wanted to finish preparation of his samples so that he could come over on Monday morning to focus on the NMR measurements, not worrying about sample preparations. In order to suppress chemical reactions which could have started in his samples over the weekend, Henry put them in the liquid nitrogen dewar (T=-196oC).
Henry was working in the Laboratory of Robert Bergman, a renowned UC Berkeley professor who has made a significant contribution to the organic and metallorganic chemistry. Bergman and Bryndza were studying Fischer–Tropsch reactions using exemplary Cobalt and Iridium catalysts .
When he came back on Monday, Henry started to observe very interesting phenomena. 1H NMR spectra of the samples he took in the morning showed very weird “negative” NMR peaks (Figure 1). Moreover, the intensity of these peaks decreased day after day during the week when Henry tried to repeat the experiments and completely disappeared by the end of the week . Henry was confused and decided to repeat his measurements. Surprisingly, this phenomenon was not observed every single time but was definitely the strongest on Mondays. Bergman and Bryndza decided to jestingly call this a “Monday phenomenon”; this was the beginning of what was known later as Parahydrogen-Induced Polarization (PHIP).
Bryndza and Bergman asked for help from many NMR specialists, including NMR expert Professor Alex Pines from UC Berkeley and Professor Joachim Bargon from the University of Bonn . The last one was known for the discovery of so-called chemically-induced dynamic nuclear polarization (CIDNP). The CIDNP effect is usually manifested as positive and negative NMR signals (very similar to those observed in Henry’s experiments) for the reactions taking place via radical intermediates. After contacting Bargon and other CIDNP specialists, weird results were interpreted as “pseudo-CIDNP” in hydrogenation reactions . However, it was clear that CIDNP-based explanation was at least not complete, first, because of the very unusual suggestion of radical pairs in the studied hydrogenation reactions and, second, because of the lack of convincing simulations supporting the observed phenomena. Moreover, it by no means explained why the effect was the strongest on Mondays and why it was only observed in the laboratory of Robert Bergman.
This “Monday morning” puzzle remained unresolved until the International Society of Magnetic Resonance meeting in Rio de Janeiro in June 1986. There, during an evening session, Professor Daniel Weitekamp from Caltech presented his “thought experiment” of using parahydrogen (para-H2) as a source of enhancing NMR signals. The concept and the expected results were immediately published in Physical Review Letters . The experimental demonstration conducted by a Weitekamp’s Ph.D. student Russ Bowers followed in July, and brilliantly supported all theoretical predictions (Figure 2) .
Bowers and Weitekamp called their experiment PASADENA (Parahydrogen And Synthesis Allow Dramatically Enhanced Nuclear Alignment) to glorify the location of their institute (Caltech is located in Pasadena, CA). After their publication, it immediately became obvious that PASADENA is, in fact, a correct explanation of “Monday phenomenon” of Bryndza and Bergman. Indeed, the low-temperature storage of NMR tubes over the weekend partially converted normal hydrogen into para-H2. The conversion was not complete, but it was enough to observe antiphase lines in 1H NMR spectra (Figure 1). The PASADENA effect and discovered later effect ALTADENA (Adiabatic Longitudinal Transport After Dissociation Engenders Net Alignment) were collectively given the name PHIP (Parahydrogen-Induced Polarization) .
Now let’s talk about physical principles of this effect. As we discussed before, due to the absence of a net nuclear magnetic moment, para-H2 itself does not produce an NMR signal. However, this single nuclear spin state implies that, in a sense, it is cold. Indeed, a comparable degree of spin ordering is obtainable at equilibrium only at temperatures of a few mK and magnetic fields of several Tesla . The brilliance of Wetekamp’s idea was to introduce magnetic inequivalence to release this potential signal by connecting the singlet to the triplet states. This would require chemistry, but simple bond cleavage would not suffice. A singlet state of two protons is a relationship of one spin relative to the other and this order would be dissipated if the pair were split and mixed with an ensemble of other such products. Rather, it is necessary that the pair have a special relationship even after being distinguished by magnetic inequivalence. This is called a “pairwise” hydrogen addition and can be realized in hydrogenation reactions in the presence of homogeneous catalysts. To see how it works, let’s take as an example the simplest situation and imagine that a chemical reaction leads to the association of para-H2 with a molecule not containing magnetic nuclei.
The two-spin system of the hydrogen molecule gives rise to four nuclear spin energy levels. As we described before, three of these energy levels correspond to orthohydrogen, the state with total nuclear spin 1 (triplet state), whereas the remaining fourth energy level corresponds to parahydrogen (singlet state), the state with zero total nuclear spin (Figure 3). Transitions between singlet and triplet spin states are forbidden by symmetry and the spin 0 parahydrogen is NMR-silent.
Now, the incorporation of para-H2 into an asymmetric molecule breaks the symmetry of the singlet spin state. For simplicity, I will consider only the PASADENA experiment, the case where hydrogenation reaction is performed at a high magnetic field(wherein the chemical shift difference between the two para-H2-nascent protons is much greater than the spin-spin couplingJ between them). In this situation, the population of the singlet spin state αβ–βα (numerical factor is omitted) of para-H2is immediately transferred to the population of spin states αβ and βα of the formed spin system.
This can be understood as follows. Because of the chemical reaction, two H atoms from para-H2 suddenly end up in a different molecular environment. This leads to a collapse of the nuclear spin wavefunction αβ–βα into one of the two states, αβ or βα, each with 50% probability. Next, it is easy to deduce from the energy level diagram that the NMR spectrum of the produced in such a manner molecule will contain four peaks grouped in two antiphase multiplets (Figure 3), exactly what was observed in the experiments of Bryndza (Figure 1) and Bowers (Figure 2). The key requirement is that both hydrogen protons from the para-H2 molecule are added together without significant competition from exchange reactions. This is a property of many, but not all, hydrogenations.
The assignment of the peaks to particular transitions depends on the sign of the J-coupling between the para-H2-nascent hydrogens. When J-coupling is positive, PASADENA multiplets are positive-negative; if J-coupling is negative, the spectral appearance is opposite. This feature is very useful for studying hydrogenation reaction intermediates. Normally, organic molecules possess positive J-couplings between protons; and J-couplings between them are negative in case of metal hydrides. Therefore, in a complex reaction involving many intermediates, it becomes possible to distinguish low-concentration hydrides (possessing negative-positive multiplets) from organic reaction products (Figure 4).
It is also important to realize that PHIP can lead to 100% nuclear spin polarization of the reaction product. In the case of PASADENA experiment, 100% population of para-H2 is split into just two energy levels, making transitions from these levels enhanced by orders of magnitude compared to the thermal case. Theoretically, if all para-H2 molecules are transferred to products in a pairwise manner and relaxation loses are minimized, the reaction product can acquire 100% spin polarization. This would, of course, require an additional step to transfer spin order from αβ and βα into the state ααbut this can be readily realized using a simple RF pulse sequence.
Enormous NMR signal enhancements and unique spectroscopic signatures made PHIP a very useful tool in chemistry for more than 25 years to elucidate hydrogenation reaction mechanisms, study metalorganic hydride complexes, and catalysis . However, PHIP can be also used in a very different context. Imagine a suitable molecular precursor which can become a naturally occurring metabolite after hydrogenation. This metabolite can be produced in seconds, with a very high level of nuclear polarization, injected into a living organism and a metabolism of that organism can be monitored by magnetic resonance spectroscopy (MRS) and magnetic resonance imaging (MRI). Today PHIP, and its sister technology SABRE (Signal Amplification By Reversible Exchange) allow to efficiently hyperpolarize dozens of biologically relevant molecules on nuclei such as 1H, 13C, 15N, 19F, 29Si, 31P, 119Sn etc. But this is a story for a separate blog post! 🙂
It is important to emphasize that only the connection between nuclear spin and rotational degrees of freedom allows this unique situation to take place. Indeed, the fact that the nuclear spin state can be overpopulated simply by cooling is a remarkable quality inherent only to the small hydrogen molecule. Indeed, even though other molecules can have the similar connection between rotational and nuclear spin states (N2, F2etc.), larger moments of inertia will make overpopulating these states much more challenging task (because of the lower temperature requirements). Moreover, it is very challenging to keep these molecules in the gas state at low temperatures, and the simple rule of making a total wavefunction be a product of individual wavefunctions will no longer hold true. So, it is more likely that hydrogen molecule is the only example when the rules of spin statistics and Pauli’s principle can lead to the nuclear spin hyperpolarization.
What excites me about this story is how a purely thought experiment, on the one hand, and a weird experimental phenomenon, on the other hand, emerged into a new discipline and a remarkable tool to study chemical reactions. Moreover, more exciting applications of the para-H2-based hyperpolarization techniques are expected to emerge in biomedicine. I really wish there were more Monday morning effects in science! Who knows but maybe someone today has come to a lab to look at a weird result which will form a new field of study tomorrow.
 Private conversations with Robert Bergman and Alex Pines.
 P. F. Seidler, H. E. Bryndza, J. E. Frommer, L. S. Stuhi, R. G. Bergman. Synthesis of Trinuclear Alkylidyne Complexes from Dinuclear Alkyne Complexes and Metal Hydrides. CIDNP Evidence for Vinyl Radical Intermediates In the Hydrogenolysis of These Clusters. Organometallics, 1983, 2 (11), 1701-1705.
 C. R. Bowers, D. P. Weitekamp. Transformation of Symmetrization Order to Nuclear-Spin Magnetization by Chemical Reaction and Nuclear Magnetic Resonance. Phys. Rev. Lett., 1986, 57 (21), 2645-2648.
 C. R. Bowers, D. P. Weitekamp. Parahydrogen and Synthesis Allow Dramatically Enhanced Nuclear Alignment. J. Am. Chem. Soc., 1987, 109 (18), 5541-5542.
 J. Natterer, J. Bargon. Parahydrogen-Induced Polarization. Prog. Nucl. Magn. Reson. Spect. 1997, 31, 293-315.
 D. Weitekamp. Sensitivity Enhancement Through Spin Statistics. Encyclopedia of Magnetic Resonance, 2007.
 S. Colebrooke, S. Duckett, J. Lohman, R. Eisenberg. Hydrogenation studies involving halobis(phosphine)-rhodium(I) dimers: Use of parahydrogen-induced polarisation to detect species present at low concentration. Chem. Eur. J., 2004, 10, 2459–2474.
To begin my blog, let’s introduce parahydrogen. Lately, this little molecule has been attracting a lot of attention in the magnetic resonance community due to tremendous opportunities it brings for NMR/MRI signal enhancement. I will explain a bit later how this parahydrogen-based NMR signal enhancement works. But first, let’s talk about physical origins of parahydrogen!
Parahydrogen (para-H2) is a nuclear spin isomer of a hydrogen molecule. Nuclear spin isomerism is a very special form of isomerism. Unlike “traditional” molecular isomers (molecules having the same atomic composition but different chemical structure) and isotopologues (isomers that differ only in their isotopic composition), nuclear spin isomers are chemically identical: they have exactly the same atomic (and even isotopic) structure. However, nuclear spin isomers differ in the nuclear spin state of their atoms. It turns out that this tiny change (energy difference associated with nuclear spin transitions is only ~0.1 J/mol) may lead to different thermodynamic and spectroscopic properties of molecules. So, how does this work?
Unfortunately (or fortunately), we will have to use rules of quantum mechanics and some math. In quantum mechanics, in order to describe properties of quantum systems (atoms, molecules, etc.), physicists use wavefunctions. By knowing a wavefunction one will be able to calculate probabilities to find a quantum system in different states (namely, a squared modulus of the wavefunction determines the probability to find a system in a given state). Let’s look how it works taking as an example hydrogen molecule.
Hydrogen molecule consists of two hydrogen atoms (H) and is denoted as Н2. Each atom has a nucleus – a proton which is a spin-1/2 particle. Physicists say that hydrogen molecule has several degrees of freedom: translational, rotational, vibrational, etc., and these degrees of freedom can be considered independent. In other words, rotation of the hydrogen molecule does not depend on how and where the molecule is moving and how it is vibrating. Each degree of freedom has a wavefunction associated with it. I will use different colors to describe electron and nuclear wavefunctions. A position of the molecule in space, as well as its rotation and vibrations, are determined by the position and movements of nuclei, therefore, these degrees of freedom are described by translational (ψtr), rotational (ψrot), vibrational (ψvib), and nuclear spin (ψspin) wavefunctions. Atomic nuclei are surrounded by electrons which provides the bonding between the nuclei. The wavefunction describing movements of electrons is called orbital wavefunction ψorb, and state of the electron spins is described by the electron spin wavefunction ψspin.
Since probabilities of independent events are multiplied, the total wavefunction is a product of the above-mentioned wavefunctions:
ψtot = ψtr·ψrot·ψvib·ψspin·ψorb·ψspin
However, rules of quantum mechanics are trickier than they may sound. According to Pauli’s principle, the total wavefunction of the system of spins-1/2 particles has to be antisymmetric with respect to the exchange (also called permutation) of two identical particles. What does this mean?
Let’s take for example ψspin. A system consisting of two spins-1/2 can be described as α1α2, β1β2 or combinations α1β2+β1α2, α1β2–β1α2. Here α and β denote the projection of nuclear spin angular momentum along the quantization axis (more on this stuff later, for now, one can imagine the state α as a magnetic moment – spin – pointing up along the external magnetic field and the state β as a magnetic moment pointing down, opposite to the field). Indexes 1 and 2 say to which nucleus the spin belongs. For example, the state α1α2 means that both nuclear spins point along the field while the state β1β2means that both spins point opposite to the field. The combination states α1β2+β1α2 and α1β2–β1α2 are more interesting. Neither of spins points along or opposite to the field but if we take one spin and determine its orientation, the second spin will take the opposite orientation. We can see now that two spins are correlated: the state of the second spin depends on the state of the first one.
Now let’s look what happens if we exchange (permute) particles. Mathematically, permutation simply means interchange of indexes (1→2, 2→1). One can see that upon permutation of indexes the first three states do not change: α2α1= α1α2, β2β1 = β1β2, (α2β1+β2α1) = (α1β2+β1α2), but the last state changes the sign: (α2β1–β2α1) = –(α1β2–β1α2). Therefore, the first three states are called symmetric wavefunctions and the last one – antisymmetric with respect to permutation of particles.
So, our hydrogen molecule contains four spin-1/2 particles: two electrons and two nuclei). Permutation of electrons can only affect ψorband ψspin. The first wave function, corresponding to the electronic ground state, is symmetric with respect to the electrons, the second, the electron spin wavefunction, is antisymmetric, and the rest are independent of the electrons’ variables and, thus, symmetric. Therefore, Pauli’s principle is fulfilled for electrons: the total wavefunction is antisymmetric with respect to permutation of electrons, thanks to antisymmetric ψspin. Permutation of nuclei can affect two wavefunctions: ψspin (as we just saw above) and ψrot. A mathematical expression for ψrot is rather complicated but it is not necessary to know its full form to understand the symmetry properties.
Figure 1. Schematic energy diagram of rotational levels of the hydrogen molecule.
This is because rotating diatomic molecules possess a set of stable rotational states, which can be described by only one parameter – the rotational quantum number J. This number can take integer values 0, 1, 2, 3, … This means that molecule can be in a stable state with J = 0, J = 1, J = 2, etc. (Figure 1). It turns out that the symmetry (with respect to permutation of nuclei) of the rotational wavefunction can be described as
P12·ψrot = (-1)J·ψrot
where P12represents the permutation operator that interchanges the nuclei’s positions (indexes). This means that the rotational wavefunction is symmetric for even rotational states (J = 0, 2, 4, …) and antisymmetric for odd rotational states (J = 1, 3, 5, …).
Coming back to Pauli’s principle, permutation of nuclei should lead to the change of sign of the total wavefunction. Since only ψspin and ψrot can change sign upon such permutation, these two wavefunctions become connected: even (symmetric) rotational wavefunctions must be combined with the antisymmetric nuclear wavefunction (α1β2–β1α2), whereas each antisymmetric rotational wavefunction has to be associated with one of the three symmetric spin functions. All this is required to yield a total wavefunction being antisymmetric with respect to the exchange of the nuclei. This is where two hydrogen spin isomers come from. One is called parahydrogen (para-H2), having an antisymmetric nuclear spin wavefunction (α1β2–β1α2) and existing only in even rotational states, and the other called orthohydrogen (ortho-H2), having a symmetric nuclear spin wavefunction and existing only in the odd rotational states.
It follows from the Pauli’s principle that nuclear spin state and rotational state of the hydrogen molecule are strictly correlated. This is remarkable, because the notion of independence (which allowed us to write a wavefunction as a product of individual wavefunctions) has led to complete dependence of these degrees of freedom from each other!
Remarkably, parahydrogen and orthohydrogen can be seen as two individual gases because their thermodynamic properties (boiling point, heat capacity, etc.) are slightly different. This is not surprising taking into account the fact that molecules constituting these two gases are rotating differently!
Importantly, conversion between the two states occurs extremely slowly because the transition between symmetric and antisymmetric nuclear spin states are forbidden by the selection rules of quantum mechanics. Therefore, after its production parahydrogen may be stored for long periods before use in a tank as an individual gas, as the relaxation rate of the parahydrogen back to room-temperature equilibrium can be on the order of months.
However, the use of paramagnetic catalysts (i.e., activated charcoal, nickel, hydrated iron(III) oxide) promotes the establishment of Boltzmann thermodynamic equilibrium between ortho-H2/para-H2states for a given temperature at greatly accelerated rates. This happens because paramagnetic materials can create a strong inhomogeneous magnetic field on the atomic scale. In such fields the two hydrogen atoms are no longer equivalent, thus, spin-flip transitions between ortho-H2 and para-H2are no longer forbidden. In practice, normal hydrogen gas (i.e., equilibrium ratio of spin isomers at room temperature) consisting of 75% ortho– and 25% para-hydrogen is passed through a chamber filled with paramagnetic catalyst and maintained at cryogenic temperatures, where the equilibration to the isomer ratio governed by the Boltzmann distribution occurs. For example, a parahydrogen generator operating at 77 K (obtained conveniently by a liquid-N2bath) yields a mixture with ~50% parahydrogen, whereas the designs based on cryo-chillers (e.g. T~20 K) yield >99% parahydrogen (Figure 2). I should note that the enrichment of hydrogen with para-isomer happens so easily only because of the big energy gap between rotational spin states. This, in turn, is due to the small mass of molecular hydrogen (in general, the energy difference between rotational spin states is inversely proportional to the moment of inertia of a rotating molecule).
The existence of nuclear spin isomers of molecular hydrogen (which was experimentally confirmed by the early 1930s) was one of the first triumphs of quantum mechanics. Indeed, the citation of the Nobel Prize awarded to Werner Heisenberg in 1932 stated that he had “created quantum mechanics, the application of which led to the discovery of the two allotropic forms of hydrogen”!
Knowledge about ortho– to para-H2 conversion is important for the storage of liquid hydrogen (especially as a rocket fuel). The difference in energy associated with the different rotational levels means that energy is released when ortho-H2 converts to para-H2, and energy is absorbed in the reverse process. This phenomenon can be thought of as a latent heat of conversion. If one quickly liquefies normal hydrogen, it will still have 3:1 ortho:para composition which will eventually lead to the heat release. This can vaporize a significant portion of hydrogen and break the impermeability of the storage container. At the dawn of industrial liquid hydrogen production, this presented a major problem. Modern hydrogen liquefying processes now ensure that the liquid hydrogen has reached equilibrium concentration at 99.8% para-H2 before being transported and stored for use.
One may ask how can para-H2 be important for NMR? Indeed, this spin isomer has a zero total nuclear spin and, thus, it does not possess 1H NMR spectrum. However, para-H2 is a pure quantum mechanical state and a highly organized spin order which is readily achievable simply by cooling. Pure state means that all para-H2 molecules are described by the same wavefunction – (α1β2–β1α2). For comparison, ortho-H2 is a mixture of three wavefunctions, α1α2, α1β2+β1α2 and β1β2 and, thus, it is not a pure state. It turns out that once you have a quantum mechanically pure state, you can manipulate it and transfer the spin order from one form to another. This is how parahydrogen-induced polarization (PHIP) and signal amplification by reversible exchange (SABRE) work: they transfer NMR-silent singlet spin order of para-H2 into observable nuclear magnetization.